From a8b243f8b3723955d160d1838c22017166dd0e18 Mon Sep 17 00:00:00 2001 From: Thales Lima Oliveira Date: Tue, 28 Jul 2020 01:49:48 -0300 Subject: Documentation update --- docs/01a85c17.d61de859.js | 1 - docs/01a85c17.f9936b95.js | 1 + docs/08185850.26b2b5f8.js | 1 + docs/08185850.63b42924.js | 1 - docs/0b24b4d1.0b43c69d.js | 1 + docs/0b24b4d1.5746dd20.js | 1 - docs/0bf0c192.0c12431b.js | 1 + docs/0bf0c192.f4c281f5.js | 1 - docs/1.27fbcdaa.js | 1 - docs/1.837a9375.js | 1 + docs/1127cf6c.1ae775a4.js | 1 - docs/1127cf6c.59d7ebcf.js | 1 + docs/1533d792.447772de.js | 1 - docs/1533d792.adab0d77.js | 1 + docs/17896441.3edcb767.js | 1 - docs/17896441.e0b8f2d7.js | 1 + docs/2.19116c85.js | 2 ++ docs/2.19116c85.js.LICENSE.txt | 5 +++ docs/2.b95b4c2f.js | 2 -- docs/2.b95b4c2f.js.LICENSE.txt | 5 --- docs/2717ad88.2a9b1859.js | 1 + docs/27d78fdc.75b8e6d1.js | 1 - docs/27d78fdc.fe2c3481.js | 1 + docs/2e13228e.3bb0cb24.js | 1 + docs/2e13228e.51988f1d.js | 1 - docs/3.189ac30f.js | 1 + 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e=this.getRefinedDisjunctiveFacets();return this.disjunctiveFacets.filter((function(t){return-1===e.indexOf(t)}))},managedParameters:["index","facets","disjunctiveFacets","facetsRefinements","facetsExcludes","disjunctiveFacetsRefinements","numericRefinements","tagRefinements","hierarchicalFacets","hierarchicalFacetsRefinements"],getQueryParams:function(){var e=this.managedParameters,t={},i=this;return Object.keys(this).forEach((function(n){var r=i[n];-1===e.indexOf(n)&&void 0!==r&&(t[n]=r)})),t},setQueryParameter:function(e,t){if(this[e]===t)return this;var i={};return i[e]=t,this.setQueryParameters(i)},setQueryParameters:function(e){if(!e)return this;var t=l.validate(this,e);if(t)throw t;var i=this,n=l._parseNumbers(e),r=Object.keys(this).reduce((function(e,t){return e[t]=i[t],e}),{}),a=Object.keys(n).reduce((function(e,t){var i=void 0!==e[t],r=void 0!==n[t];return i&&!r?u(e,[t]):(r&&(e[t]=n[t]),e)}),r);return new this.constructor(a)},resetPage:function(){return void 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n=i(189),r=i(190),a=i(214),s=i(259),c=i(186),u=i(260),o=i(215),h=i(261);function f(e){var t={};return e.forEach((function(e,i){t[e]=i})),t}function l(e,t,i){t&&t[i]&&(e.stats=t[i])}function m(e,t){var i=t[0];this._rawResults=t,this.query=i.query,this.parsedQuery=i.parsedQuery,this.hits=i.hits,this.index=i.index,this.hitsPerPage=i.hitsPerPage,this.nbHits=i.nbHits,this.nbPages=i.nbPages,this.page=i.page,this.processingTimeMS=t.reduce((function(e,t){return void 0===t.processingTimeMS?e:e+t.processingTimeMS}),0),this.aroundLatLng=i.aroundLatLng,this.automaticRadius=i.automaticRadius,this.serverUsed=i.serverUsed,this.timeoutCounts=i.timeoutCounts,this.timeoutHits=i.timeoutHits,this.exhaustiveFacetsCount=i.exhaustiveFacetsCount,this.exhaustiveNbHits=i.exhaustiveNbHits,this.userData=i.userData,this.queryID=i.queryID,this.disjunctiveFacets=[],this.hierarchicalFacets=e.hierarchicalFacets.map((function(){return[]})),this.facets=[];var a=e.getRefinedDisjunctiveFacets(),o=f(e.facets),m=f(e.disjunctiveFacets),d=1,v=this,g=i.facets||{};Object.keys(g).forEach((function(t){var n,r,a=g[t],s=(n=e.hierarchicalFacets,r=t,c(n,(function(e){return(e.attributes||[]).indexOf(r)>-1})));if(s){var h=s.attributes.indexOf(t),f=u(e.hierarchicalFacets,(function(e){return e.name===s.name}));v.hierarchicalFacets[f][h]={attribute:t,data:a,exhaustive:i.exhaustiveFacetsCount}}else{var d,p=-1!==e.disjunctiveFacets.indexOf(t),y=-1!==e.facets.indexOf(t);p&&(d=m[t],v.disjunctiveFacets[d]={name:t,data:a,exhaustive:i.exhaustiveFacetsCount},l(v.disjunctiveFacets[d],i.facets_stats,t)),y&&(d=o[t],v.facets[d]={name:t,data:a,exhaustive:i.exhaustiveFacetsCount},l(v.facets[d],i.facets_stats,t))}})),this.hierarchicalFacets=s(this.hierarchicalFacets),a.forEach((function(a){var s=t[d],c=s&&s.facets?s.facets:{},o=e.getHierarchicalFacetByName(a);Object.keys(c).forEach((function(t){var a,h=c[t];if(o){a=u(e.hierarchicalFacets,(function(e){return e.name===o.name}));var f=u(v.hierarchicalFacets[a],(function(e){return e.attribute===t}));if(-1===f)return;v.hierarchicalFacets[a][f].data=n({},v.hierarchicalFacets[a][f].data,h)}else{a=m[t];var d=i.facets&&i.facets[t]||{};v.disjunctiveFacets[a]={name:t,data:r({},h,d),exhaustive:s.exhaustiveFacetsCount},l(v.disjunctiveFacets[a],s.facets_stats,t),e.disjunctiveFacetsRefinements[t]&&e.disjunctiveFacetsRefinements[t].forEach((function(i){!v.disjunctiveFacets[a].data[i]&&e.disjunctiveFacetsRefinements[t].indexOf(i)>-1&&(v.disjunctiveFacets[a].data[i]=0)}))}})),d++})),e.getRefinedHierarchicalFacets().forEach((function(i){var n=e.getHierarchicalFacetByName(i),a=e._getHierarchicalFacetSeparator(n),s=e.getHierarchicalRefinement(i);if(!(0===s.length||s[0].split(a).length<2)){var c=t[d],o=c&&c.facets?c.facets:{};Object.keys(o).forEach((function(t){var i=o[t],c=u(e.hierarchicalFacets,(function(e){return e.name===n.name})),h=u(v.hierarchicalFacets[c],(function(e){return e.attribute===t}));if(-1!==h){var f={};if(s.length>0){var l=s[0].split(a)[0];f[l]=v.hierarchicalFacets[c][h].data[l]}v.hierarchicalFacets[c][h].data=r(f,i,v.hierarchicalFacets[c][h].data)}})),d++}})),Object.keys(e.facetsExcludes).forEach((function(t){var n=e.facetsExcludes[t],r=o[t];v.facets[r]={name:t,data:i.facets[t],exhaustive:i.exhaustiveFacetsCount},n.forEach((function(e){v.facets[r]=v.facets[r]||{name:t},v.facets[r].data=v.facets[r].data||{},v.facets[r].data[e]=0}))})),this.hierarchicalFacets=this.hierarchicalFacets.map(h(e)),this.facets=s(this.facets),this.disjunctiveFacets=s(this.disjunctiveFacets),this._state=e}function d(e,t){if(!t.data||0===t.data.length)return t;var i=t.data.map((function(t){return d(e,t)})),r=e(i);return n({},t,{data:r})}function v(e,t){var i=c(e,(function(e){return e.name===t}));return i&&i.stats}function g(e,t,i,n,r){var a=c(r,(function(e){return e.name===i})),s=a&&a.data&&a.data[n]?a.data[n]:0,u=a&&a.exhaustive||!1;return{type:t,attributeName:i,name:n,count:s,exhaustive:u}}m.prototype.getFacetByName=function(e){function t(t){return t.name===e}return c(this.facets,t)||c(this.disjunctiveFacets,t)||c(this.hierarchicalFacets,t)},m.DEFAULT_SORT=["isRefined:desc","count:desc","name:asc"],m.prototype.getFacetValues=function(e,t){var i=function(e,t){function i(e){return e.name===t}if(e._state.isConjunctiveFacet(t)){var n=c(e.facets,i);return n?Object.keys(n.data).map((function(i){return{name:i,count:n.data[i],isRefined:e._state.isFacetRefined(t,i),isExcluded:e._state.isExcludeRefined(t,i)}})):[]}if(e._state.isDisjunctiveFacet(t)){var r=c(e.disjunctiveFacets,i);return r?Object.keys(r.data).map((function(i){return{name:i,count:r.data[i],isRefined:e._state.isDisjunctiveFacetRefined(t,i)}})):[]}if(e._state.isHierarchicalFacet(t))return c(e.hierarchicalFacets,i)}(this,e);if(i){var n=r({},t,{sortBy:m.DEFAULT_SORT});if(Array.isArray(n.sortBy)){var s=o(n.sortBy,m.DEFAULT_SORT);return Array.isArray(i)?a(i,s[0],s[1]):d((function(e){return a(e,s[0],s[1])}),i)}if("function"==typeof n.sortBy)return Array.isArray(i)?i.sort(n.sortBy):d((function(e){return function(e,t){return t.sort(e)}(n.sortBy,e)}),i);throw new Error("options.sortBy is optional but if defined it must be either an array of string (predicates) or a sorting function")}},m.prototype.getFacetStats=function(e){return this._state.isConjunctiveFacet(e)?v(this.facets,e):this._state.isDisjunctiveFacet(e)?v(this.disjunctiveFacets,e):void 0},m.prototype.getRefinements=function(){var e=this._state,t=this,i=[];return Object.keys(e.facetsRefinements).forEach((function(n){e.facetsRefinements[n].forEach((function(r){i.push(g(e,"facet",n,r,t.facets))}))})),Object.keys(e.facetsExcludes).forEach((function(n){e.facetsExcludes[n].forEach((function(r){i.push(g(e,"exclude",n,r,t.facets))}))})),Object.keys(e.disjunctiveFacetsRefinements).forEach((function(n){e.disjunctiveFacetsRefinements[n].forEach((function(r){i.push(g(e,"disjunctive",n,r,t.disjunctiveFacets))}))})),Object.keys(e.hierarchicalFacetsRefinements).forEach((function(n){e.hierarchicalFacetsRefinements[n].forEach((function(r){i.push(function(e,t,i,n){var r=e.getHierarchicalFacetByName(t),a=e._getHierarchicalFacetSeparator(r),s=i.split(a),u=c(n,(function(e){return e.name===t})),o=s.reduce((function(e,t){var i=e&&c(e.data,(function(e){return e.name===t}));return void 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client.initIndex(index).searchForFacetValues");var a=this.state.setQueryParameters(n||{}),c=a.isDisjunctiveFacet(e),u=s.getSearchForFacetQuery(e,t,i,a);this._currentNbQueries++;var o=this;return this.emit("searchForFacetValues",{state:a,facet:e,query:t}),(r?this.client.searchForFacetValues([{indexName:a.index,params:u}]):this.client.initIndex(a.index).searchForFacetValues(u)).then((function(t){return o._currentNbQueries--,0===o._currentNbQueries&&o.emit("searchQueueEmpty"),(t=Array.isArray(t)?t[0]:t).facetHits.forEach((function(t){t.isRefined=c?a.isDisjunctiveFacetRefined(e,t.value):a.isFacetRefined(e,t.value)})),t}),(function(e){throw o._currentNbQueries--,0===o._currentNbQueries&&o.emit("searchQueueEmpty"),e}))},f.prototype.setQuery=function(e){return this._change({state:this.state.resetPage().setQuery(e),isPageReset:!0}),this},f.prototype.clearRefinements=function(e){return 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i=t.getHierarchicalRefinement(e.name);i.length>0&&0!==i[0].indexOf(e.rootPath)&&(t=t.clearRefinements(e.name)),0===(i=t.getHierarchicalRefinement(e.name)).length&&(t=t.toggleHierarchicalFacetRefinement(e.name,e.rootPath))}})),t},l.validate=function(e,t){var i=t||{};return e.tagFilters&&i.tagRefinements&&i.tagRefinements.length>0?new Error("[Tags] Cannot switch from the managed tag API to the advanced API. It is probably an error, if it is really what you want, you should first clear the tags with clearTags method."):e.tagRefinements.length>0&&i.tagFilters?new Error("[Tags] Cannot switch from the advanced tag API to the managed API. It is probably an error, if it is not, you should first clear the tags with clearTags method."):e.numericFilters&&i.numericRefinements&&o(i.numericRefinements)?new Error("[Numeric filters] Can't switch from the advanced to the managed API. It is probably an error, if this is really what you want, you have to first clear the numeric filters."):o(e.numericRefinements)&&i.numericFilters?new Error("[Numeric filters] Can't switch from the managed API to the advanced. 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this.isConjunctiveFacet(e)?this:this.setQueryParameters({facets:this.facets.concat([e])})},addDisjunctiveFacet:function(e){return this.isDisjunctiveFacet(e)?this:this.setQueryParameters({disjunctiveFacets:this.disjunctiveFacets.concat([e])})},addHierarchicalFacet:function(e){if(this.isHierarchicalFacet(e.name))throw new Error("Cannot declare two hierarchical facets with the same name: `"+e.name+"`");return this.setQueryParameters({hierarchicalFacets:this.hierarchicalFacets.concat([e])})},addFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsRefinements,e,t)?this:this.setQueryParameters({facetsRefinements:h.addRefinement(this.facetsRefinements,e,t)})},addExcludeRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return 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t!==e}))}):this},removeHierarchicalFacet:function(e){return this.isHierarchicalFacet(e)?this.clearRefinements(e).setQueryParameters({hierarchicalFacets:this.hierarchicalFacets.filter((function(t){return t.name!==e}))}):this},removeFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsRefinements,e,t)?this.setQueryParameters({facetsRefinements:h.removeRefinement(this.facetsRefinements,e,t)}):this},removeExcludeRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return h.isRefined(this.facetsExcludes,e,t)?this.setQueryParameters({facetsExcludes:h.removeRefinement(this.facetsExcludes,e,t)}):this},removeDisjunctiveFacetRefinement:function(e,t){if(!this.isDisjunctiveFacet(e))throw new Error(e+" is not defined in the disjunctiveFacets attribute of the helper configuration");return h.isRefined(this.disjunctiveFacetsRefinements,e,t)?this.setQueryParameters({disjunctiveFacetsRefinements:h.removeRefinement(this.disjunctiveFacetsRefinements,e,t)}):this},removeTagRefinement:function(e){if(!this.isTagRefined(e))return this;var t={tagRefinements:this.tagRefinements.filter((function(t){return t!==e}))};return this.setQueryParameters(t)},toggleRefinement:function(e,t){return this.toggleFacetRefinement(e,t)},toggleFacetRefinement:function(e,t){if(this.isHierarchicalFacet(e))return this.toggleHierarchicalFacetRefinement(e,t);if(this.isConjunctiveFacet(e))return this.toggleConjunctiveFacetRefinement(e,t);if(this.isDisjunctiveFacet(e))return this.toggleDisjunctiveFacetRefinement(e,t);throw new Error("Cannot refine the undeclared facet "+e+"; it should be added to the helper options facets, disjunctiveFacets or hierarchicalFacets")},toggleConjunctiveFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return this.setQueryParameters({facetsRefinements:h.toggleRefinement(this.facetsRefinements,e,t)})},toggleExcludeFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return this.setQueryParameters({facetsExcludes:h.toggleRefinement(this.facetsExcludes,e,t)})},toggleDisjunctiveFacetRefinement:function(e,t){if(!this.isDisjunctiveFacet(e))throw new Error(e+" is not defined in the disjunctiveFacets attribute of the helper configuration");return this.setQueryParameters({disjunctiveFacetsRefinements:h.toggleRefinement(this.disjunctiveFacetsRefinements,e,t)})},toggleHierarchicalFacetRefinement:function(e,t){if(!this.isHierarchicalFacet(e))throw new Error(e+" is not defined in the hierarchicalFacets attribute of the helper configuration");var i=this._getHierarchicalFacetSeparator(this.getHierarchicalFacetByName(e)),n={};return void 0!==this.hierarchicalFacetsRefinements[e]&&this.hierarchicalFacetsRefinements[e].length>0&&(this.hierarchicalFacetsRefinements[e][0]===t||0===this.hierarchicalFacetsRefinements[e][0].indexOf(t+i))?-1===t.indexOf(i)?n[e]=[]:n[e]=[t.slice(0,t.lastIndexOf(i))]:n[e]=[t],this.setQueryParameters({hierarchicalFacetsRefinements:r({},n,this.hierarchicalFacetsRefinements)})},addHierarchicalFacetRefinement:function(e,t){if(this.isHierarchicalFacetRefined(e))throw new Error(e+" is already refined.");if(!this.isHierarchicalFacet(e))throw new Error(e+" is not defined in the hierarchicalFacets attribute of the helper configuration.");var i={};return i[e]=[t],this.setQueryParameters({hierarchicalFacetsRefinements:r({},i,this.hierarchicalFacetsRefinements)})},removeHierarchicalFacetRefinement:function(e){if(!this.isHierarchicalFacetRefined(e))return this;var t={};return 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Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o da linha durante o estudo de ',Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/lineSw.png"),alt:"Formul\xe1rio de chaveamento da linha",title:"Formul\xe1rio de chaveamento da linha"}))),Object(m.b)("hr",null),Object(m.b)("h3",{id:"geral"},"Geral"),Object(m.b)("h4",{id:"nome"},"Nome"),Object(m.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(m.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(m.b)("h4",{id:"tens\xe3o-nominal"},"Tens\xe3o nominal"),Object(m.b)("p",null,"Campo de informa\xe7\xe3o ",Object(m.b)("em",{parentName:"p"},"n\xe3o edit\xe1vel")," que apresenta a tens\xe3o nominal da linha. 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n={selectionMethod:"blur"};this.debug||(this.autoselectOnBlur&&t?this._select(t,n):this.autoselectOnBlur&&e?this._select(e,n):(this.isActivated=!1,this.dropdown.empty(),this.dropdown.close()))},_onEnterKeyed:function(t,e){var n,i;n=this.dropdown.getDatumForCursor(),i=this.dropdown.getDatumForTopSuggestion();var s={selectionMethod:"enterKey"};n?(this._select(n,s),e.preventDefault()):this.autoselect&&i&&(this._select(i,s),e.preventDefault())},_onTabKeyed:function(t,e){if(this.tabAutocomplete){var n;(n=this.dropdown.getDatumForCursor())?(this._select(n,{selectionMethod:"tabKey"}),e.preventDefault()):this._autocomplete(!0)}else this.dropdown.close()},_onEscKeyed:function(){this.dropdown.close(),this.input.resetInputValue()},_onUpKeyed:function(){var t=this.input.getQuery();this.dropdown.isEmpty&&t.length>=this.minLength?this.dropdown.update(t):this.dropdown.moveCursorUp(),this.dropdown.open()},_onDownKeyed:function(){var 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Retorna o \xe2ngulo em radianos.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"asinh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"asin()"),", mas para seno hiperb\xf3lico")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"atan(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Arco tangente de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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O valor retornado varia de ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mo",{parentName:"mrow"},"\u2212"),Object(b.b)("mi",{parentName:"mrow"},"\u03c0")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"-\\pi")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.66666em",verticalAlign:"-0.08333em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"\u2212"),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"\u03c0")))))," a ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mi",{parentName:"mrow"},"\u03c0")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"\\pi")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.43056em",verticalAlign:"0em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"\u03c0"))))),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"atanh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"atan()"),", mas para tangente hiperb\xf3lica.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"cbrt(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Raiz c\xfabica de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"conj(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Conjugado complexo de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"ceil(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Teto de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Arredonda para o pr\xf3ximo maior inteiro.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"cos(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cosseno de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o \xe2ngulo em radianos.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"cosh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"cos()"),", mas para cosseno hiperb\xf3lico")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"cot(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cotangente de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o \xe2ngulo em radianos.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"csc(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Cossecante de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o \xe2ngulo em radianos.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"exp(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Exponencial de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o valor de e elevado a pot\xeancia A.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"exp2(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Exponencial de ",Object(b.b)("inlineCode",{parentName:"td"},"A")," na base ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mn",{parentName:"mrow"},"2")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"2")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.64444em",verticalAlign:"0em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"2"))))),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"floor(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Piso de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Arredonda para o pr\xf3ximo menor inteiro.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"hypot(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Fun\xe7\xe3o de dist\xe2ncia Euclidiana.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"if(A,B,C)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"int(A)")," \xe9 diferente de ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math 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",Object(b.b)("inlineCode",{parentName:"td"},"C"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"imag(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Retorna a parte imagin\xe1ria do n\xfamero complexo ",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"int(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Arredonda ",Object(b.b)("inlineCode",{parentName:"td"},"A")," para o inteiro mais pr\xf3ximo.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"log(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Logaritmo natural (base ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math 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",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"log10(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Logaritmo na base ",Object(b.b)("span",Object(n.a)({parentName:"td"},{className:"math 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A.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"max(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"A>B"),", o resultado \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"A"),", sen\xe3o \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"B"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"min(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"A := ; \n")),Object(b.b)("p",null,"Por exemplo:"),Object(b.b)("pre",null,Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"comprimento := sqrt(x*x+y*y); 2*comprimento*sin(comprimento)\n")),Object(b.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"O caractere de espa\xe7o e de nova linha s\xe3o ignorados na interpreta\xe7\xe3o da express\xe3o, portanto para maior organiza\xe7\xe3o, o c\xf3digo anterior pode ser escrito da seguinte forma:"),Object(b.b)("pre",{parentName:"div"},Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"comprimento := sqrt(x*x+y*y);\n2*comprimento*sin(comprimento)\n")))),Object(b.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"Note que a express\xe3o que determina o valor de sa\xedda do bloco ",Object(b.b)("strong",{parentName:"p"},"n\xe3o possui")," o caractere ",Object(b.b)("inlineCode",{parentName:"p"},";")," em seu final."))),Object(b.b)("h2",{id:"formul\xe1rio-de-edi\xe7\xe3o-de-dados-do-bloco-de-express\xe3o-matem\xe1tica"},"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de Express\xe3o Matem\xe1tica"),Object(b.b)("p",null,"O formul\xe1rio de inser\xe7\xe3o e edi\xe7\xe3o das entradas do bloco e da express\xe3o matem\xe1tica gen\xe9rica, assim como ferramentas de aux\xedlio de sua constru\xe7\xe3o \xe9 apresentado na figura abaixo."),Object(b.b)("div",null,Object(b.b)("center",null,Object(b.b)("img",{src:Object(m.a)("images/mathExpressionForm.png"),alt:"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de express\xe3o matem\xe1tica no PSP-UFU",title:"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de express\xe3o matem\xe1tica no PSP-UFU"}))),Object(b.b)("p",null,"No campo de \u201cVari\xe1veis de entrada\u201d \xe9 inserida uma lista com os nomes das entradas separados por espa\xe7os. 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A sintaxe da express\xe3o inserida pelo usu\xe1rio possui realce (por meio de diferentes formas e cores da fonte) para n\xfameros, operadores, vari\xe1veis de entrada, fun\xe7\xf5es e constantes, facilitando a cria\xe7\xe3o, manipula\xe7\xe3o e identifica\xe7\xe3o de erros de digita\xe7\xe3o e l\xf3gica."),Object(b.b)("div",{className:"admonition admonition-info alert alert--info"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"Como ferramenta de aux\xedlio ao usu\xe1rio foi desenvolvida uma verifica\xe7\xe3o da express\xe3o inserida."))),Object(b.b)("p",null,"Tal ferramenta ir\xe1 encontrar erros e indicar\xe1 ao usu\xe1rio qual o tipo do erro, al\xe9m da sua localiza\xe7\xe3o, destacando-o. 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l.Input({input:o,hint:n}).onSync("focused",this._onFocused,this).onSync("blurred",this._onBlurred,this).onSync("enterKeyed",this._onEnterKeyed,this).onSync("tabKeyed",this._onTabKeyed,this).onSync("escKeyed",this._onEscKeyed,this).onSync("upKeyed",this._onUpKeyed,this).onSync("downKeyed",this._onDownKeyed,this).onSync("leftKeyed",this._onLeftKeyed,this).onSync("rightKeyed",this._onRightKeyed,this).onSync("queryChanged",this._onQueryChanged,this).onSync("whitespaceChanged",this._onWhitespaceChanged,this),this._bindKeyboardShortcuts(t),this._setLanguageDirection()}i.mixin(l.prototype,{_bindKeyboardShortcuts:function(t){if(t.keyboardShortcuts){var e=this.$input,n=[];i.each(t.keyboardShortcuts,(function(t){"string"==typeof t&&(t=t.toUpperCase().charCodeAt(0)),n.push(t)})),s.element(document).keydown((function(t){var i=t.target||t.srcElement,s=i.tagName;if(!i.isContentEditable&&"INPUT"!==s&&"SELECT"!==s&&"TEXTAREA"!==s){var r=t.which||t.keyCode;-1!==n.indexOf(r)&&(e.focus(),t.stopPropagation(),t.preventDefault())}}))}},_onSuggestionClicked:function(t,e){var n;(n=this.dropdown.getDatumForSuggestion(e))&&this._select(n,{selectionMethod:"click"})},_onCursorMoved:function(t,e){var n=this.dropdown.getDatumForCursor(),i=this.dropdown.getCurrentCursor().attr("id");this.input.setActiveDescendant(i),n&&(e&&this.input.setInputValue(n.value,!0),this.eventBus.trigger("cursorchanged",n.raw,n.datasetName))},_onCursorRemoved:function(){this.input.resetInputValue(),this._updateHint(),this.eventBus.trigger("cursorremoved")},_onDatasetRendered:function(){this._updateHint(),this.eventBus.trigger("updated")},_onOpened:function(){this._updateHint(),this.input.expand(),this.eventBus.trigger("opened")},_onEmpty:function(){this.eventBus.trigger("empty")},_onRedrawn:function(){this.$node.css("top","0px"),this.$node.css("left","0px");var t=this.$input[0].getBoundingClientRect();this.autoWidth&&this.$node.css("width",t.width+"px");var e=this.$node[0].getBoundingClientRect(),n=t.bottom-e.top;this.$node.css("top",n+"px");var i=t.left-e.left;this.$node.css("left",i+"px"),this.eventBus.trigger("redrawn")},_onShown:function(){this.eventBus.trigger("shown"),this.autoselect&&this.dropdown.cursorTopSuggestion()},_onClosed:function(){this.input.clearHint(),this.input.removeActiveDescendant(),this.input.collapse(),this.eventBus.trigger("closed")},_onFocused:function(){if(this.isActivated=!0,this.openOnFocus){var t=this.input.getQuery();t.length>=this.minLength?this.dropdown.update(t):this.dropdown.empty(),this.dropdown.open()}},_onBlurred:function(){var t,e;t=this.dropdown.getDatumForCursor(),e=this.dropdown.getDatumForTopSuggestion();var n={selectionMethod:"blur"};this.debug||(this.autoselectOnBlur&&t?this._select(t,n):this.autoselectOnBlur&&e?this._select(e,n):(this.isActivated=!1,this.dropdown.empty(),this.dropdown.close()))},_onEnterKeyed:function(t,e){var n,i;n=this.dropdown.getDatumForCursor(),i=this.dropdown.getDatumForTopSuggestion();var s={selectionMethod:"enterKey"};n?(this._select(n,s),e.preventDefault()):this.autoselect&&i&&(this._select(i,s),e.preventDefault())},_onTabKeyed:function(t,e){if(this.tabAutocomplete){var n;(n=this.dropdown.getDatumForCursor())?(this._select(n,{selectionMethod:"tabKey"}),e.preventDefault()):this._autocomplete(!0)}else this.dropdown.close()},_onEscKeyed:function(){this.dropdown.close(),this.input.resetInputValue()},_onUpKeyed:function(){var t=this.input.getQuery();this.dropdown.isEmpty&&t.length>=this.minLength?this.dropdown.update(t):this.dropdown.moveCursorUp(),this.dropdown.open()},_onDownKeyed:function(){var t=this.input.getQuery();this.dropdown.isEmpty&&t.length>=this.minLength?this.dropdown.update(t):this.dropdown.moveCursorDown(),this.dropdown.open()},_onLeftKeyed:function(){"rtl"===this.dir&&this._autocomplete()},_onRightKeyed:function(){"ltr"===this.dir&&this._autocomplete()},_onQueryChanged:function(t,e){this.input.clearHintIfInvalid(),e.length>=this.minLength?this.dropdown.update(e):this.dropdown.empty(),this.dropdown.open(),this._setLanguageDirection()},_onWhitespaceChanged:function(){this._updateHint(),this.dropdown.open()},_setLanguageDirection:function(){var t=this.input.getLanguageDirection();this.dir!==t&&(this.dir=t,this.$node.css("direction",t),this.dropdown.setLanguageDirection(t))},_updateHint:function(){var t,e,n,s,r;(t=this.dropdown.getDatumForTopSuggestion())&&this.dropdown.isVisible()&&!this.input.hasOverflow()?(e=this.input.getInputValue(),n=a.normalizeQuery(e),s=i.escapeRegExChars(n),(r=new RegExp("^(?:"+s+")(.+$)","i").exec(t.value))?this.input.setHint(e+r[1]):this.input.clearHint()):this.input.clearHint()},_autocomplete:function(t){var e,n,i,s;e=this.input.getHint(),n=this.input.getQuery(),i=t||this.input.isCursorAtEnd(),e&&n!==e&&i&&((s=this.dropdown.getDatumForTopSuggestion())&&this.input.setInputValue(s.value),this.eventBus.trigger("autocompleted",s.raw,s.datasetName))},_select:function(t,e){void 0!==t.value&&this.input.setQuery(t.value),this.clearOnSelected?this.setVal(""):this.input.setInputValue(t.value,!0),this._setLanguageDirection(),!1===this.eventBus.trigger("selected",t.raw,t.datasetName,e).isDefaultPrevented()&&(this.dropdown.close(),i.defer(i.bind(this.dropdown.empty,this.dropdown)))},open:function(){if(!this.isActivated){var t=this.input.getInputValue();t.length>=this.minLength?this.dropdown.update(t):this.dropdown.empty()}this.dropdown.open()},close:function(){this.dropdown.close()},setVal:function(t){t=i.toStr(t),this.isActivated?this.input.setInputValue(t):(this.input.setQuery(t),this.input.setInputValue(t,!0)),this._setLanguageDirection()},getVal:function(){return this.input.getQuery()},destroy:function(){this.input.destroy(),this.dropdown.destroy(),function(t,e){var n=t.find(i.className(e.prefix,e.input));i.each(n.data("aaAttrs"),(function(t,e){void 0===t?n.removeAttr(e):n.attr(e,t)})),n.detach().removeClass(i.className(e.prefix,e.input,!0)).insertAfter(t),n.removeData&&n.removeData("aaAttrs");t.remove()}(this.$node,this.cssClasses),this.$node=null},getWrapper:function(){return this.dropdown.$container[0]}}),l.Dropdown=o,l.Input=a,l.sources=n(284),t.exports=l},274:function(t,e,n){"use strict";var i;i={9:"tab",27:"esc",37:"left",39:"right",13:"enter",38:"up",40:"down"};var s=n(175),r=n(177),a=n(195);function o(t){var e,n,a,o,u,c=this;(t=t||{}).input||s.error("input is missing"),e=s.bind(this._onBlur,this),n=s.bind(this._onFocus,this),a=s.bind(this._onKeydown,this),o=s.bind(this._onInput,this),this.$hint=r.element(t.hint),this.$input=r.element(t.input).on("blur.aa",e).on("focus.aa",n).on("keydown.aa",a),0===this.$hint.length&&(this.setHint=this.getHint=this.clearHint=this.clearHintIfInvalid=s.noop),s.isMsie()?this.$input.on("keydown.aa keypress.aa cut.aa paste.aa",(function(t){i[t.which||t.keyCode]||s.defer(s.bind(c._onInput,c,t))})):this.$input.on("input.aa",o),this.query=this.$input.val(),this.$overflowHelper=(u=this.$input,r.element('').css({position:"absolute",visibility:"hidden",whiteSpace:"pre",fontFamily:u.css("font-family"),fontSize:u.css("font-size"),fontStyle:u.css("font-style"),fontVariant:u.css("font-variant"),fontWeight:u.css("font-weight"),wordSpacing:u.css("word-spacing"),letterSpacing:u.css("letter-spacing"),textIndent:u.css("text-indent"),textRendering:u.css("text-rendering"),textTransform:u.css("text-transform")}).insertAfter(u))}function u(t){return t.altKey||t.ctrlKey||t.metaKey||t.shiftKey}o.normalizeQuery=function(t){return(t||"").replace(/^\s*/g,"").replace(/\s{2,}/g," ")},s.mixin(o.prototype,a,{_onBlur:function(){this.resetInputValue(),this.$input.removeAttr("aria-activedescendant"),this.trigger("blurred")},_onFocus:function(){this.trigger("focused")},_onKeydown:function(t){var e=i[t.which||t.keyCode];this._managePreventDefault(e,t),e&&this._shouldTrigger(e,t)&&this.trigger(e+"Keyed",t)},_onInput:function(){this._checkInputValue()},_managePreventDefault:function(t,e){var n,i,s;switch(t){case"tab":i=this.getHint(),s=this.getInputValue(),n=i&&i!==s&&!u(e);break;case"up":case"down":n=!u(e);break;default:n=!1}n&&e.preventDefault()},_shouldTrigger:function(t,e){var n;switch(t){case"tab":n=!u(e);break;default:n=!0}return n},_checkInputValue:function(){var t,e,n,i,s;t=this.getInputValue(),i=t,s=this.query,n=!(!(e=o.normalizeQuery(i)===o.normalizeQuery(s))||!this.query)&&this.query.length!==t.length,this.query=t,e?n&&this.trigger("whitespaceChanged",this.query):this.trigger("queryChanged",this.query)},focus:function(){this.$input.focus()},blur:function(){this.$input.blur()},getQuery:function(){return this.query},setQuery:function(t){this.query=t},getInputValue:function(){return this.$input.val()},setInputValue:function(t,e){void 0===t&&(t=this.query),this.$input.val(t),e?this.clearHint():this._checkInputValue()},expand:function(){this.$input.attr("aria-expanded","true")},collapse:function(){this.$input.attr("aria-expanded","false")},setActiveDescendant:function(t){this.$input.attr("aria-activedescendant",t)},removeActiveDescendant:function(){this.$input.removeAttr("aria-activedescendant")},resetInputValue:function(){this.setInputValue(this.query,!0)},getHint:function(){return this.$hint.val()},setHint:function(t){this.$hint.val(t)},clearHint:function(){this.setHint("")},clearHintIfInvalid:function(){var t,e,n;n=(t=this.getInputValue())!==(e=this.getHint())&&0===e.indexOf(t),""!==t&&n&&!this.hasOverflow()||this.clearHint()},getLanguageDirection:function(){return(this.$input.css("direction")||"ltr").toLowerCase()},hasOverflow:function(){var t=this.$input.width()-2;return this.$overflowHelper.text(this.getInputValue()),this.$overflowHelper.width()>=t},isCursorAtEnd:function(){var t,e,n;return t=this.$input.val().length,e=this.$input[0].selectionStart,s.isNumber(e)?e===t:!document.selection||((n=document.selection.createRange()).moveStart("character",-t),t===n.text.length)},destroy:function(){this.$hint.off(".aa"),this.$input.off(".aa"),this.$hint=this.$input=this.$overflowHelper=null}}),t.exports=o},275:function(t,e,n){"use strict";var i,s,r,a=[n(276),n(277),n(278),n(279),n(280),n(281)],o=-1,u=[],c=!1;function l(){i&&s&&(i=!1,s.length?u=s.concat(u):o=-1,u.length&&h())}function h(){if(!i){c=!1,i=!0;for(var t=u.length,e=setTimeout(l);t;){for(s=u,u=[];s&&++o1)for(var n=1;n'),this.$menu.append(this.$empty),this.$empty.hide()),this.datasets=i.map(t.datasets,(function(e){return function(t,e,n){return new u.Dataset(i.mixin({$menu:t,cssClasses:n},e))}(a.$menu,e,t.cssClasses)})),i.each(this.datasets,(function(t){var e=t.getRoot();e&&0===e.parent().length&&a.$menu.append(e),t.onSync("rendered",a._onRendered,a)})),t.templates&&t.templates.footer&&(this.templates.footer=i.templatify(t.templates.footer),this.$menu.append(this.templates.footer()));var l=this;s.element(window).resize((function(){l._redraw()}))}i.mixin(u.prototype,r,{_onSuggestionClick:function(t){this.trigger("suggestionClicked",s.element(t.currentTarget))},_onSuggestionMouseEnter:function(t){var e=s.element(t.currentTarget);if(!e.hasClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0))){this._removeCursor();var n=this;setTimeout((function(){n._setCursor(e,!1)}),0)}},_onSuggestionMouseLeave:function(t){if(t.relatedTarget&&s.element(t.relatedTarget).closest("."+i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).length>0)return;this._removeCursor(),this.trigger("cursorRemoved")},_onRendered:function(t,e){if(this.isEmpty=i.every(this.datasets,(function(t){return t.isEmpty()})),this.isEmpty)if(e.length>=this.minLength&&this.trigger("empty"),this.$empty)if(e.length=this.minLength?this._show():this._hide());this.trigger("datasetRendered")},_hide:function(){this.$container.hide()},_show:function(){this.$container.css("display","block"),this._redraw(),this.trigger("shown")},_redraw:function(){this.isOpen&&this.appendTo&&this.trigger("redrawn")},_getSuggestions:function(){return this.$menu.find(i.className(this.cssClasses.prefix,this.cssClasses.suggestion))},_getCursor:function(){return this.$menu.find(i.className(this.cssClasses.prefix,this.cssClasses.cursor)).first()},_setCursor:function(t,e){t.first().addClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).attr("aria-selected","true"),this.trigger("cursorMoved",e)},_removeCursor:function(){this._getCursor().removeClass(i.className(this.cssClasses.prefix,this.cssClasses.cursor,!0)).removeAttr("aria-selected")},_moveCursor:function(t){var e,n,i,s;this.isOpen&&(n=this._getCursor(),e=this._getSuggestions(),this._removeCursor(),-1!==(i=((i=e.index(n)+t)+1)%(e.length+1)-1)?(i<-1&&(i=e.length-1),this._setCursor(s=e.eq(i),!0),this._ensureVisible(s)):this.trigger("cursorRemoved"))},_ensureVisible:function(t){var e,n,i,s;n=(e=t.position().top)+t.height()+parseInt(t.css("margin-top"),10)+parseInt(t.css("margin-bottom"),10),i=this.$menu.scrollTop(),s=this.$menu.height()+parseInt(this.$menu.css("padding-top"),10)+parseInt(this.$menu.css("padding-bottom"),10),e<0?this.$menu.scrollTop(i+e):s"+u(t)+"

"}}),this.css=i.mixin({},a,t.appendTo?a.appendTo:{}),this.cssClasses=t.cssClasses=i.mixin({},a.defaultClasses,t.cssClasses||{}),this.cssClasses.prefix=t.cssClasses.formattedPrefix||i.formatPrefix(this.cssClasses.prefix,this.cssClasses.noPrefix);var c=i.className(this.cssClasses.prefix,this.cssClasses.dataset);this.$el=t.$menu&&t.$menu.find(c+"-"+this.name).length>0?s.element(t.$menu.find(c+"-"+this.name)[0]):s.element(r.dataset.replace("%CLASS%",this.name).replace("%PREFIX%",this.cssClasses.prefix).replace("%DATASET%",this.cssClasses.dataset)),this.$menu=t.$menu,this.clearCachedSuggestions()}u.extractDatasetName=function(t){return s.element(t).data("aaDataset")},u.extractValue=function(t){return s.element(t).data("aaValue")},u.extractDatum=function(t){var e=s.element(t).data("aaDatum");return"string"==typeof e&&(e=JSON.parse(e)),e},i.mixin(u.prototype,o,{_render:function(t,e){if(this.$el){var n,a=this,o=[].slice.call(arguments,2);if(this.$el.empty(),n=e&&e.length,this._isEmpty=!n,!n&&this.templates.empty)this.$el.html(u.apply(this,o)).prepend(a.templates.header?l.apply(this,o):null).append(a.templates.footer?h.apply(this,o):null);else if(n)this.$el.html(c.apply(this,o)).prepend(a.templates.header?l.apply(this,o):null).append(a.templates.footer?h.apply(this,o):null);else if(e&&!Array.isArray(e))throw new TypeError("suggestions must be an array");this.$menu&&this.$menu.addClass(this.cssClasses.prefix+(n?"with":"without")+"-"+this.name).removeClass(this.cssClasses.prefix+(n?"without":"with")+"-"+this.name),this.trigger("rendered",t)}function u(){var e=[].slice.call(arguments,0);return e=[{query:t,isEmpty:!0}].concat(e),a.templates.empty.apply(this,e)}function c(){var t,n,o=[].slice.call(arguments,0),u=this,c=r.suggestions.replace("%PREFIX%",this.cssClasses.prefix).replace("%SUGGESTIONS%",this.cssClasses.suggestions);return t=s.element(c).css(this.css.suggestions),n=i.map(e,l),t.append.apply(t,n),t;function l(t){var e,n=r.suggestion.replace("%PREFIX%",u.cssClasses.prefix).replace("%SUGGESTION%",u.cssClasses.suggestion);return(e=s.element(n).attr({role:"option",id:["option",Math.floor(1e8*Math.random())].join("-")}).append(a.templates.suggestion.apply(this,[t].concat(o)))).data("aaDataset",a.name),e.data("aaValue",a.displayFn(t)||void 0),e.data("aaDatum",JSON.stringify(t)),e.children().each((function(){s.element(this).css(u.css.suggestionChild)})),e}}function l(){var e=[].slice.call(arguments,0);return e=[{query:t,isEmpty:!n}].concat(e),a.templates.header.apply(this,e)}function h(){var e=[].slice.call(arguments,0);return e=[{query:t,isEmpty:!n}].concat(e),a.templates.footer.apply(this,e)}},getRoot:function(){return this.$el},update:function(t){function e(e){if(!this.canceled&&t===this.query){var n=[].slice.call(arguments,1);this.cacheSuggestions(t,e,n),this._render.apply(this,[t,e].concat(n))}}if(this.query=t,this.canceled=!1,this.shouldFetchFromCache(t))e.apply(this,[this.cachedSuggestions].concat(this.cachedRenderExtraArgs));else{var n=this,i=function(){n.canceled||n.source(t,e.bind(n))};if(this.debounce){clearTimeout(this.debounceTimeout),this.debounceTimeout=setTimeout((function(){n.debounceTimeout=null,i()}),this.debounce)}else i()}},cacheSuggestions:function(t,e,n){this.cachedQuery=t,this.cachedSuggestions=e,this.cachedRenderExtraArgs=n},shouldFetchFromCache:function(t){return this.cache&&this.cachedQuery===t&&this.cachedSuggestions&&this.cachedSuggestions.length},clearCachedSuggestions:function(){delete this.cachedQuery,delete this.cachedSuggestions,delete this.cachedRenderExtraArgs},cancel:function(){this.canceled=!0},clear:function(){this.cancel(),this.$el.empty(),this.trigger("rendered","")},isEmpty:function(){return this._isEmpty},destroy:function(){this.clearCachedSuggestions(),this.$el=null}}),t.exports=u},284:function(t,e,n){"use strict";t.exports={hits:n(285),popularIn:n(286)}},285:function(t,e,n){"use strict";var i=n(175),s=n(222),r=n(223);t.exports=function(t,e){var n=r(t.as._ua);return n&&n[0]>=3&&n[1]>20&&((e=e||{}).additionalUA="autocomplete.js "+s),function(n,s){t.search(n,e,(function(t,e){t?i.error(t.message):s(e.hits,e)}))}}},286:function(t,e,n){"use strict";var i=n(175),s=n(222),r=n(223);t.exports=function(t,e,n,a){var o=r(t.as._ua);if(o&&o[0]>=3&&o[1]>20&&((e=e||{}).additionalUA="autocomplete.js "+s),!n.source)return i.error("Missing 'source' key");var u=i.isFunction(n.source)?n.source:function(t){return t[n.source]};if(!n.index)return i.error("Missing 'index' key");var c=n.index;return a=a||{},function(o,l){t.search(o,e,(function(t,o){if(t)i.error(t.message);else{if(o.hits.length>0){var h=o.hits[0],p=i.mixin({hitsPerPage:0},n);delete p.source,delete p.index;var f=r(c.as._ua);return f&&f[0]>=3&&f[1]>20&&(e.additionalUA="autocomplete.js "+s),void c.search(u(h),p,(function(t,e){if(t)i.error(t.message);else{var n=[];if(a.includeAll){var s=a.allTitle||"All departments";n.push(i.mixin({facet:{value:s,count:e.nbHits}},i.cloneDeep(h)))}i.each(e.facets,(function(t,e){i.each(t,(function(t,s){n.push(i.mixin({facet:{facet:e,value:s,count:t}},i.cloneDeep(h)))}))}));for(var r=1;r\n
\n {{{category}}}\n
\n
\n
\n {{{subcategory}}}\n
\n {{#isTextOrSubcategoryNonEmpty}}\n
\n
{{{subcategory}}}
\n
{{{title}}}
\n {{#text}}
{{{text}}}
{{/text}}\n
\n {{/isTextOrSubcategoryNonEmpty}}\n
\n \n ',suggestionSimple:'\n
\n
\n {{^isLvl0}}\n {{{category}}}\n {{^isLvl1}}\n {{^isLvl1EmptyOrDuplicate}}\n \n {{{subcategory}}}\n \n {{/isLvl1EmptyOrDuplicate}}\n {{/isLvl1}}\n {{/isLvl0}}\n
\n {{#isLvl2}}\n {{{title}}}\n {{/isLvl2}}\n {{#isLvl1}}\n {{{subcategory}}}\n {{/isLvl1}}\n {{#isLvl0}}\n {{{category}}}\n {{/isLvl0}}\n
\n
\n
\n {{#text}}\n
\n
{{{text}}}
\n
\n {{/text}}\n
\n
\n ',footer:'\n
\n Search by \n
\n ',empty:'\n
\n
\n
\n
\n
\n No results found for query "{{query}}"\n
\n
\n
\n
\n
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Essa op\xe7\xe3o \xe9 somente v\xe1lida caso esteja conectado um gerador s\xedncrono, caso contr\xe1rio uma mensagem de erro ser\xe1 exibida ao usu\xe1rio ao realizar algum dos c\xe1lculos do programa."),Object(m.b)("hr",null),Object(m.b)("h3",{id:"falta"},"Falta"),Object(m.b)("h4",{id:"inserir-falta"},"Inserir falta"),Object(m.b)("p",null,"Indica se existe um curto-circuito na barra nos estudos de ",Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"fault"}),"curto-circuito"),"."),Object(m.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(m.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(m.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(m.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Nota-se que essa op\xe7\xe3o ir\xe1 inserir uma falta no c\xe1lculo de ",Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"fault"}),"curto-circuito")," e ",Object(m.b)("strong",{parentName:"p"},"n\xe3o ser\xe1 considerado no estudo de estabilidade"),"."))),Object(m.b)("h4",{id:"tipo-de-falta"},"Tipo de falta"),Object(m.b)("p",null,"Seleciona o tipo de falha shunt da barra:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},"trif\xe1sico para a terra"),Object(m.b)("li",{parentName:"ul"},"fase-fase"),Object(m.b)("li",{parentName:"ul"},"fase-fase-terra"),Object(m.b)("li",{parentName:"ul"},"fase-terra")),Object(m.b)("h4",{id:"local-da-falta"},"Local da falta"),Object(m.b)("p",null,"Seleciona a fase em que se situa a falta (ou combina\xe7\xe3o delas no caso de falha entre duas fases), sendo essa op\xe7\xe3o desabilitada para o tipo de falta trif\xe1sica."),Object(m.b)("h4",{id:"resist\xeancia-e-reat\xe2ncia-de-falta"},"Resist\xeancia e reat\xe2ncia de falta"),Object(m.b)("p",null,"Representam a imped\xe2ncia da falta. 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Essa vari\xe1vel est\xe1 normalmente associada \xe0 refer\xeancia de tens\xe3o do AVR;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Velocidade inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR e RV"),"): Velocidade do sistema (2\u03c0f_ref), definida nas op\xe7\xf5es de simula\xe7\xe3o, em rad/s, fixa no tempo. 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\ No newline at end of file diff --git a/docs/77fbd900.1d4a0f5b.js b/docs/77fbd900.1d4a0f5b.js deleted file mode 100644 index c1bc693..0000000 --- a/docs/77fbd900.1d4a0f5b.js +++ /dev/null @@ -1 +0,0 @@ -(window.webpackJsonp=window.webpackJsonp||[]).push([[25],{126:function(e,a,t){"use strict";t.r(a),t.d(a,"frontMatter",(function(){return s})),t.d(a,"metadata",(function(){return c})),t.d(a,"rightToc",(function(){return b})),t.d(a,"default",(function(){return m}));var n=t(2),o=t(6),r=(t(0),t(161)),i=t(162),s={id:"installation",title:"Instala\xe7\xe3o",sidebar_label:"Instala\xe7\xe3o"},c={id:"installation",isDocsHomePage:!1,title:"Instala\xe7\xe3o",description:"Download",source:"@site/docs\\installation.md",permalink:"/PSP/docs/installation",editUrl:"https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/installation.md",sidebar_label:"Instala\xe7\xe3o",sidebar:"docs",previous:{title:"PSP-UFU",permalink:"/PSP/docs/"},next:{title:"Tela Principal",permalink:"/PSP/docs/mainScreen"}},b=[{value:"Download",id:"download",children:[]},{value:"Windows",id:"windows",children:[{value:"Problemas recorrentes no Windows",id:"problemas-recorrentes-no-windows",children:[]}]},{value:"Linux",id:"linux",children:[{value:"Problemas recorrentes no Linux",id:"problemas-recorrentes-no-linux",children:[]}]}],l={rightToc:b};function m(e){var a=e.components,t=Object(o.a)(e,["components"]);return Object(r.b)("wrapper",Object(n.a)({},l,t,{components:a,mdxType:"MDXLayout"}),Object(r.b)("h2",{id:"download"},"Download"),Object(r.b)("p",null,"O download do PSP-UFU pode ser realizado pelo ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"https://github.com/Thales1330/PSP/releases/latest"}),'"',Object(r.b)("em",{parentName:"a"},"last release"),'" do reposit\xf3rio do PSP-UFU no GitHub'),"."),Object(r.b)("p",null,"Ao acessar ao link, role a p\xe1gina at\xe9 encontrar os ",Object(r.b)("em",{parentName:"p"},"Assets"),":"),Object(r.b)("div",null,Object(r.b)("center",null,Object(r.b)("img",{src:Object(i.a)("images/download.png"),alt:"Assets download",title:"Informa\xe7\xf5es da Figura"}))),Object(r.b)("p",null,"Como o PSP-UFU \xe9 um ",Object(r.b)("em",{parentName:"p"},"software")," multiplataforma, voc\xea deve baixar o arquivo correto:"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"Para o sistema operacional ",Object(r.b)("a",Object(n.a)({parentName:"li"},{href:"installation#windows"}),"Windows")," baixe os arquivos ",Object(r.b)("em",{parentName:"li"},".exe")," (recomendado) ou ",Object(r.b)("em",{parentName:"li"},".zip"),"."),Object(r.b)("li",{parentName:"ul"},"Para os sistemas ",Object(r.b)("a",Object(n.a)({parentName:"li"},{href:"installation#linux"}),"Linux")," baseados no Debian (por exemplo, Ubuntu, Mint) ",Object(r.b)("em",{parentName:"li"},"64 bits")," baixe o pacote de instala\xe7\xe3o ",Object(r.b)("em",{parentName:"li"},".deb"),".")),Object(r.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Se voc\xea est\xe1 interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"https://github.com/Thales1330/PSP/issues"}),"GitHub")," ou ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"https://twitter.com/PspUfu"}),"Twitter"),"."))),Object(r.b)("p",null,"Na sequ\xeancia s\xe3o apresentados o passo-a-passo para instala\xe7\xe3o dos SOs ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"installation#windows"}),"Windows")," e ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"installation#linux"}),"Linux"),". 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O execut\xe1vel est\xe1 presente na pasta "',Object(r.b)("em",{parentName:"p"},"/PSP-UFU/bin/PSP-UFU.exe"),'".'),Object(r.b)("h3",{id:"problemas-recorrentes-no-windows"},"Problemas recorrentes no Windows"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"Ao baixar o navegador pode ",Object(r.b)("strong",{parentName:"li"},"falsamente"),' sinalizar que \xe9 um arquivo perigoso, basta clicar em "Manter arquivo";'),Object(r.b)("li",{parentName:"ul"},'Ao abrir o instalador, novamente o Windows sinaliza que o arquivo \xe9 perigoso, basta clicar em "Executar assim mesmo";'),Object(r.b)("li",{parentName:"ul"},"Ao abrir o programa e alterar o seu idioma, uma mensagem de erro \xe9 exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com bot\xe3o direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;"),Object(r.b)("li",{parentName:"ul"},'Ao criar um novo projeto a tela de trabalho n\xe3o \xe9 exibida ou \xe9 exibida uma tela preta. V\xe1 nas op\xe7\xf5es gerais e altere o renderizador para "Device Context". Caso apare\xe7a uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.')),Object(r.b)("h2",{id:"linux"},"Linux"),Object(r.b)("p",null,"A instala\xe7\xe3o no sistema Linux \xe9 facilmente realizado pelo pacote de instala\xe7\xe3o autom\xe1tico ",Object(r.b)("em",{parentName:"p"},".deb"),"."),Object(r.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 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",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"https://wiki.wxwidgets.org/Compiling_and_getting_started#Running_wxWidgets_projects"}),"diret\xf3rio das bibliotecas do wxWidgets")," nas vari\xe1veis de ambiente.\nPara isso, siga ",Object(r.b)("strong",{parentName:"p"},"UM")," dos m\xe9todos apresentados abaixo:"),Object(r.b)("h4",{id:"m\xe9todo-i-recomendado"},Object(r.b)("em",{parentName:"h4"},"M\xe9todo I (recomendado)")),Object(r.b)("p",null,"Insira o seguinte comando no arquivo ",Object(r.b)("strong",{parentName:"p"},"~/.bashrc"),":"),Object(r.b)("pre",null,Object(r.b)("code",Object(n.a)({parentName:"pre"},{className:"language-shell"}),'echo "export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib" >> ~/.bashrc\n')),Object(r.b)("h4",{id:"m\xe9todo-ii-n\xe3o-recomendado"},Object(r.b)("em",{parentName:"h4"},"M\xe9todo II (n\xe3o recomendado)")),Object(r.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Utilizando esse m\xe9todo os passos abaixo devem ser executados 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Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com bot\xe3o direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;"),Object(r.b)("li",{parentName:"ul"},'Ao criar um novo projeto a tela de trabalho n\xe3o \xe9 exibida ou \xe9 exibida uma tela preta. V\xe1 nas op\xe7\xf5es gerais e altere o renderizador para "Device Context". Caso apare\xe7a uma mensagem de erro, execute o programa como administrador e repita o processo. 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n=e.components,r=e.mdxType,a=e.originalType,c=e.parentName,u=i(e,["components","mdxType","originalType","parentName"]),d=l(n),m=r,f=d["".concat(c,".").concat(m)]||d[m]||p[m]||a;return n?o.a.createElement(f,s(s({ref:t},u),{},{components:n})):o.a.createElement(f,s({ref:t},u))}));function f(e,t){var n=arguments,r=t&&t.mdxType;if("string"==typeof e||r){var a=n.length,c=new Array(a);c[0]=m;var s={};for(var i in t)hasOwnProperty.call(t,i)&&(s[i]=t[i]);s.originalType=e,s.mdxType="string"==typeof e?e:r,c[1]=s;for(var u=2;u -2019w42a-beta | PSP-UFU - - - - - - - - +2019w42a-beta | PSP-UFU + + + + + + + +

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
- - - - - - - - + + + + + + + + \ No newline at end of file diff --git a/docs/blog/2019w44a-beta/index.html b/docs/blog/2019w44a-beta/index.html index 8cf4744..8c7c6dc 100644 --- a/docs/blog/2019w44a-beta/index.html +++ b/docs/blog/2019w44a-beta/index.html @@ -4,26 +4,26 @@ -22019w44a-beta | PSP-UFU - - - - - - - - +22019w44a-beta | PSP-UFU + + + + + + + +

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).
- - - - - - - - + + + + + + + + \ No newline at end of file diff --git a/docs/blog/2020w24a-beta/index.html b/docs/blog/2020w24a-beta/index.html index 7ec9268..4ef1247 100644 --- a/docs/blog/2020w24a-beta/index.html +++ b/docs/blog/2020w24a-beta/index.html @@ -4,26 +4,26 @@ -2020w24a-beta | PSP-UFU - - - - - - - - +2020w24a-beta | PSP-UFU + + + + + + + +

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.
- - - - - - - - + + + + + + + + \ No newline at end of file diff --git a/docs/blog/2020w28a-beta/index.html b/docs/blog/2020w28a-beta/index.html index 4b861d6..ab1c750 100644 --- a/docs/blog/2020w28a-beta/index.html +++ b/docs/blog/2020w28a-beta/index.html @@ -4,26 +4,26 @@ -2020w28a-beta | PSP-UFU - - - - - - - - +2020w28a-beta | PSP-UFU + + + + + + + +

2020w28a-beta

Thales

Thales

PhD
  • Voltage heatmap implemented (OpenGL enabled);
  • Several major and minor bugfixes.
- - - - - - - - + + + + + + + + \ No newline at end of file diff --git a/docs/blog/index.html b/docs/blog/index.html index 14b6a18..23839f0 100644 --- a/docs/blog/index.html +++ b/docs/blog/index.html @@ -4,34 +4,34 @@ -Blog | PSP-UFU - - - - - - - - - - - - +Blog | PSP-UFU + + + + + + + + + + + +

2020w28a-beta

Thales

Thales

PhD
  • Voltage heatmap implemented (OpenGL enabled);
  • Several major and minor bugfixes.

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
- - - - - - - - - - - - + + + + + + + + + + + + \ No newline at end of file diff --git a/docs/blog/tags/index.html b/docs/blog/tags/index.html index 797d06e..6518c49 100644 --- a/docs/blog/tags/index.html +++ b/docs/blog/tags/index.html @@ -4,24 +4,24 @@ -Tags | PSP-UFU - - - - - - - +Tags | PSP-UFU + + + + + + +

Tags

- - - - - - - + + + + + + + \ No newline at end of file diff --git a/docs/blog/tags/psp-ufu/index.html b/docs/blog/tags/psp-ufu/index.html index 420bf0a..6fc8888 100644 --- a/docs/blog/tags/psp-ufu/index.html +++ b/docs/blog/tags/psp-ufu/index.html @@ -4,34 +4,34 @@ -Posts tagged "psp-ufu" | PSP-UFU - - - - - - - - - - - - +Posts tagged "psp-ufu" | PSP-UFU + + + + + + + + + + + +

4 posts tagged with "psp-ufu"

View All Tags

2020w24a-beta

Thales

Thales

PhD
  • Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
  • Added Visual Studio solution to the GitHub project;
  • Several major and minor bugfixes.

22019w44a-beta

Thales

Thales

PhD
  • Minor changes to 32bit MSW version for compatibility;
  • Travis CI (Continuous Integration) implemented (Linux).

2019w42a-beta

Thales

Thales

PhD
  • Harmonic study implemented;
  • Autolayout from importation implemented;
  • Importation of Matpower files;
  • Several minor bugfixes.
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Nele \xe9 poss\xedvel tamb\xe9m acessar aos controles das m\xe1quinas s\xedncronas manipulados pelo ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"editor de controle"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/syncGeneratorStabForm.png"),alt:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU",title:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU"}))),Object(n.b)("p",null,'No formul\xe1rio de estabilidade pode ser observado o bot\xe3o "Chaveamento" na parte inferior esquerda do formul\xe1rio. Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o do gerador durante o estudo de ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/syncGeneratorSw.png"),alt:"Formul\xe1rio de chaveamento do gerador s\xedncrono",title:"Formul\xe1rio de chaveamento do gerador s\xedncrono"}))),Object(n.b)("hr",null),Object(n.b)("h3",{id:"geral"},"Geral"),Object(n.b)("h4",{id:"nome"},"Nome"),Object(n.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador."),Object(n.b)("p",null,"Caso a barra conectada seja PV o valor de pot\xeancia reativa ser\xe1 ignorado e caso seja de refer\xeancia ambos os valores inseridos ser\xe3o desprezados."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso mais de um gerador esteja conectado na mesma barra, os valores de pot\xeancia reativa (nas barras de refer\xeancia e PV) e ativa (nas barras de refer\xeancia) s\xe3o igualmente distribu\xeddas, respeitando os limites individuais de pot\xeancia reativa."))),Object(n.b)("h4",{id:"pot\xeancias-reativas-m\xe1xima-e-m\xednima"},"Pot\xeancias reativas m\xe1xima e m\xednima"),Object(n.b)("p",null,"Limites de pot\xeancia reativa m\xe1xima e m\xednima do gerador para controle de tens\xe3o em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade ser\xe1 limitado ao valor inserido e a barra conectada ser\xe1 transformada em PQ, n\xe3o controlando a tens\xe3o estabelecida."),Object(n.b)("h4",{id:"utilizar-pot\xeancia-nominal-como-base"},"Utilizar pot\xeancia nominal como base"),Object(n.b)("p",null,"Caso essa op\xe7\xe3o seja marcada, o programa ir\xe1 utilizar a pot\xeancia nominal do gerador como base para a convers\xe3o das unidades, inclusive aqueles no formul\xe1rio de estabilidade, caso contr\xe1rio ser\xe1 usada a ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"pot\xeancia base do sistema"),"."),Object(n.b)("hr",null),Object(n.b)("h3",{id:"falta"},"Falta"),Object(n.b)("h4",{id:"imped\xe2ncias-de-sequ\xeancia"},"Imped\xe2ncias de sequ\xeancia"),Object(n.b)("p",null,"Valores de resist\xeancia e reat\xe2ncia para c\xe1lculo das correntes de falta. S\xe3o inseridos dados de sequ\xeancia positiva, negativa e zero."),Object(n.b)("h4",{id:"imped\xe2ncia-de-aterramento"},"Imped\xe2ncia de aterramento"),Object(n.b)("p",null,"Valores utilizados para o c\xe1lculo das correntes de falta do tipo fase-terra e fase-fase-terra. Caso o neutro do gerador n\xe3o seja aterrado, o valor inserido nesse campo \xe9 ignorado."),Object(n.b)("h4",{id:"neutro-aterrado"},"Neutro aterrado"),Object(n.b)("p",null,"Indica se o neutro do gerador \xe9 aterrado."),Object(n.b)("hr",null),Object(n.b)("h3",{id:"bot\xe3o-estabilidade"},"Bot\xe3o Estabilidade"),Object(n.b)("h4",{id:"imprimir-dados-da-m\xe1quina-s\xedncrona"},"Imprimir dados da m\xe1quina s\xedncrona"),Object(n.b)("p",null,"Exibe os dados do gerador s\xedncrono nos gr\xe1ficos no tempo. Os seguintes dados s\xe3o exibidos:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},"tens\xe3o terminal"),Object(n.b)("li",{parentName:"ul"},"pot\xeancias ativa e reativas"),Object(n.b)("li",{parentName:"ul"},"pot\xeancia mec\xe2nica"),Object(n.b)("li",{parentName:"ul"},"frequ\xeancia"),Object(n.b)("li",{parentName:"ul"},"tens\xe3o de campo"),Object(n.b)("li",{parentName:"ul"},"\xe2ngulo ",Object(n.b)("span",Object(s.a)({parentName:"li"},{className:"math 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math-inline"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(n.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(n.b)("semantics",{parentName:"math"},Object(n.b)("mrow",{parentName:"semantics"},Object(n.b)("mi",{parentName:"mrow"},"p"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(n.b)("mi",{parentName:"mrow"},"u"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."))))),") de corrente de campo necess\xe1ria para atingir 1,2 p.u. de tens\xe3o terminal."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 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Os valores de eixo direto e em quadratura devem ser iguais ou muito pr\xf3ximos para representa\xe7\xe3o de uma m\xe1quina de polos lisos, enquanto para polos salientes esses valores s\xe3o distintos."),Object(n.b)("h4",{id:"reat\xe2ncias-e-constantes-de-tempo-transit\xf3rias"},"Reat\xe2ncias e constantes de tempo transit\xf3rias"),Object(n.b)("p",null,"Par\xe2metros transit\xf3rios da m\xe1quina s\xedncrona em ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(n.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(n.b)("semantics",{parentName:"math"},Object(n.b)("mrow",{parentName:"semantics"},Object(n.b)("mi",{parentName:"mrow"},"p"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(n.b)("mi",{parentName:"mrow"},"u"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),".")))))," ou segundos."),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O valor da reat\xe2ncia transit\xf3ria de eixo direto deve ser diferente de zero ou levar\xe1 o programa a erro."))),Object(n.b)("p",null,"De acordo com a quantidade de par\xe2metros inseridos \xe9 definido internamente pelo programa qual o modelo a ser utilizado."),Object(n.b)("h4",{id:"reat\xe2ncias-e-constantes-de-tempo-subtransit\xf3rias"},"Reat\xe2ncias e constantes de tempo subtransit\xf3rias"),Object(n.b)("p",null,"Par\xe2metros subtransit\xf3rios da m\xe1quina s\xedncrona em ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(n.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(n.b)("semantics",{parentName:"math"},Object(n.b)("mrow",{parentName:"semantics"},Object(n.b)("mi",{parentName:"mrow"},"p"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(n.b)("mi",{parentName:"mrow"},"u"),Object(n.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),".")))))," ou segundos, representando em detalhes a presen\xe7a de enrolamentos amortecedores. Assim como os dados transit\xf3rios, esses par\xe2metros definem o modelo da m\xe1quina."),Object(n.b)("hr",null),Object(n.b)("h3",{id:"bot\xe3o-chaveamento"},"Bot\xe3o Chaveamento"),Object(n.b)("p",null,'O bot\xe3o "Chaveamento" ir\xe1 abrir um formul\xe1rio, comum a v\xe1rios outros elementos, que permite a inser\xe7\xe3o e/ou remo\xe7\xe3o do gerador durante o estudo de ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(n.b)("p",null,'Nesse formul\xe1rio pode ser criada uma lista gen\xe9rica de inser\xe7\xf5es e remo\xe7\xf5es da linha no tempo, personalizada por um contexto de propriedades de chaveamento que s\xe3o editados o tipo de chaveamento (inser\xe7\xe3o ou remo\xe7\xe3o) e o instante (em segundos) do evento. Essas propriedades s\xe3o atribu\xeddas e retiradas da lista gen\xe9rica por meio dos bot\xf5es "Adicionar" e "Remover", respectivamente.'),Object(n.b)("h2",{id:"refer\xeancias"},"Refer\xeancias"),Object(n.b)("ol",null,Object(n.b)("li",{parentName:"ol"},"MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1007/978-3-642-13669-6"}),"https://doi.org/10.1007/978-3-642-13669-6")),Object(n.b)("li",{parentName:"ol"},"ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1002/9781118878286"}),"https://doi.org/10.1002/9781118878286")),Object(n.b)("li",{parentName:"ol"},"KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994."),Object(n.b)("li",{parentName:"ol"},"DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/TPAS.1972.293341"}),"https://doi.org/10.1109/TPAS.1972.293341")),Object(n.b)("li",{parentName:"ol"},"IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/IEEESTD.2003.94408"}),"https://doi.org/10.1109/IEEESTD.2003.94408")),Object(n.b)("li",{parentName:"ol"},"KIMBARK, E. W. Power System Stability: Volume III \u2013 Synchronous Machine. New York: Wiley-IEEE Press, 1995.")))}j.isMDXComponent=!0},160:function(a,e,t){"use strict";var s=t(0),m=t(35);e.a=function(){return Object(s.useContext)(m.a)}},161:function(a,e,t){"use strict";t.d(e,"a",(function(){return j})),t.d(e,"b",(function(){return i}));var s=t(0),m=t.n(s);function n(a,e,t){return e in a?Object.defineProperty(a,e,{value:t,enumerable:!0,configurable:!0,writable:!0}):a[e]=t,a}function b(a,e){var t=Object.keys(a);if(Object.getOwnPropertySymbols){var s=Object.getOwnPropertySymbols(a);e&&(s=s.filter((function(e){return Object.getOwnPropertyDescriptor(a,e).enumerable}))),t.push.apply(t,s)}return t}function p(a){for(var e=1;e=0||(m[t]=a[t]);return m}(a,e);if(Object.getOwnPropertySymbols){var n=Object.getOwnPropertySymbols(a);for(s=0;s=0||Object.prototype.propertyIsEnumerable.call(a,t)&&(m[t]=a[t])}return m}var r=m.a.createContext({}),O=function(a){var e=m.a.useContext(r),t=e;return a&&(t="function"==typeof a?a(e):p(p({},e),a)),t},j=function(a){var e=O(a.components);return m.a.createElement(r.Provider,{value:e},a.children)},N={inlineCode:"code",wrapper:function(a){var e=a.children;return m.a.createElement(m.a.Fragment,{},e)}},l=m.a.forwardRef((function(a,e){var t=a.components,s=a.mdxType,n=a.originalType,b=a.parentName,r=c(a,["components","mdxType","originalType","parentName"]),j=O(t),l=s,i=j["".concat(b,".").concat(l)]||j[l]||N[l]||n;return t?m.a.createElement(i,p(p({ref:e},r),{},{components:t})):m.a.createElement(i,p({ref:e},r))}));function i(a,e){var t=arguments,s=e&&e.mdxType;if("string"==typeof a||s){var n=t.length,b=new Array(n);b[0]=l;var p={};for(var c in e)hasOwnProperty.call(e,c)&&(p[c]=e[c]);p.originalType=a,p.mdxType="string"==typeof a?a:s,b[1]=p;for(var r=2;r -Barramento | PSP-UFU - - - - - - - - - - +Barramento | PSP-UFU + + + + + + + + + +
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Barramento

Condutor de baixa impedância ao qual vários circuitos elétricos podem ser conectados em pontos separados. -Nota - Em muitos casos, o barramento consiste em uma barra. tradução livre - IEC 60050.

Barramento no PSP-UFU

O elemento barramento, ou simplesmente barra, é um conector ou nó do diagrama unifilar do PSP-UFU. Essa barra pode representar um PAC (Ponto de Acoplamento Comum), um poste de distribuição, uma subestação, um barramento da subestação, entre inúmeros outros tipos pontos de análise e conexão entre elementos.

Formulário de edição dos barramentos

Atenção!

O barramento deve ser o primeiro elemento elétrico a ser inserido no diagrama de potência, uma vez que os demais componentes de potência são conectados nele.

A imagem abaixo apresenta o formulário de inserção/alteração de dados das barras:

Formulário dos barramentos no PSP-UFU

Esse formulário é subdividido em quatro contextos distintos:

  • Geral: no qual são inseridas informações gerais da barra e informações do fluxo de carga;
  • Falta: local onde o curto-circuito shunt deve ser inserido;
  • Estabilidade: contendo opções de visualização de dados da barra em gráficos no tempo e inserção de faltas trifásicas no cálculo de estabilidade transitória;
  • Qualidade de energia: contém a opção de de visualização da impedância harmônica vista pela barra.

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Utilizado para cálculo da impedância base de alguns elementos conectados, além do cálculo da relação de transformação dos transformadores conectados entre barras. Sua unidade pode ser selecionada, sendo expressa em V ou em kV.

A modificação desse parâmetro irá alterar toda a tensão do trecho conectado por linhas elétricas, sendo emitido um alerta ao usuário.

Tensão controlada

Caracteriza o barramento como barra de tensão controlada (Barra PV),

Atenção!

Essa opção é somente válida caso alguma máquina síncrona esteja conectado, caso contrário esse valor será ignorado. Caso o limite de potência reativa da máquina síncrona conectada seja ultrapassado esse valor também é ignorado.

O valor poderá ser inserido em p.u. ou em volts (ou kV caso a tensão nominal esteja nesta unidade).

Barra de referência

Caracteriza o barramento como barra de referência (Barra de oscilação). Essa opção é somente válida caso esteja conectado um gerador síncrono, caso contrário uma mensagem de erro será exibida ao usuário ao realizar algum dos cálculos do programa.

Falta

Inserir falta

Indica se existe um curto-circuito na barra nos estudos de curto-circuito.

Cuidado!

Nota-se que essa opção irá inserir uma falta no cálculo de curto-circuito e não será considerado no estudo de estabilidade.

Tipo de falta

Seleciona o tipo de falha shunt da barra:

  • trifásico para a terra
  • fase-fase
  • fase-fase-terra
  • fase-terra

Local da falta

Seleciona a fase em que se situa a falta (ou combinação delas no caso de falha entre duas fases), sendo essa opção desabilitada para o tipo de falta trifásica.

Resistência e reatância de falta

Representam a impedância da falta. Curtos-circuitos francos (sem impedância de falta) são representados inserindo valor zero em ambos os campos.

Estabilidade

Imprimir dados

Mostra os dados da barra editada no gráfico gerado pelo estudo de estabilidade transitória. Os seguintes dados são exibidos:

  • módulo da tensão do barramento
  • ângulo da tensão do barramento.

Inserir falta

Insere uma falta trifásica na barra no cálculo de estabilidade.

Cuidado!

Nota-se que essa opção irá inserir uma falta no cálculo de estabilidade e não será considerado no estudo de curto-circuito.

Tempo

Instante no tempo (tfaltat_{falta}) em que ocorre a falta durante os estudos de estabilidade. Esse campo e os próximos são somente acessados caso seja inserida uma falta no estudo de estabilidade.

Duração da falta

Duração da falta inserida (Δtfalta\Delta t_{falta}) no estudo de estabilidade. A falta irá iniciar no instante tfaltat_{falta} e será interrompida em tfalta+Δtfaltat_{falta}+\Delta t_{falta}.

Resistência e reatância de falta

Impedância de falta nos estudos de estabilidade. Uma falta franca é representada pela inserção de um valor de impedância shunt de valor muito baixo (j10−5p.u.j10^{-5} p.u.).

Qualidade de energia

Imprimir impedância harmônica da barra

Imprime a impedância harmônica vista por essa barra referente ao estudo de Resposta na Frequência.

Edit this page
- - - - - - - - - - +

Barramento

Condutor de baixa impedância ao qual vários circuitos elétricos podem ser conectados em pontos separados. +Nota - Em muitos casos, o barramento consiste em uma barra. tradução livre - IEC 60050.

Barramento no PSP-UFU

O elemento barramento, ou simplesmente barra, é um conector ou nó do diagrama unifilar do PSP-UFU. Essa barra pode representar um PAC (Ponto de Acoplamento Comum), um poste de distribuição, uma subestação, um barramento da subestação, entre inúmeros outros tipos pontos de análise e conexão entre elementos.

Formulário de edição dos barramentos

Atenção!

O barramento deve ser o primeiro elemento elétrico a ser inserido no diagrama de potência, uma vez que os demais componentes de potência são conectados nele.

A imagem abaixo apresenta o formulário de inserção/alteração de dados das barras:

Formulário dos barramentos no PSP-UFU

Esse formulário é subdividido em quatro contextos distintos:

  • Geral: no qual são inseridas informações gerais da barra e informações do fluxo de carga;
  • Falta: local onde o curto-circuito shunt deve ser inserido;
  • Estabilidade: contendo opções de visualização de dados da barra em gráficos no tempo e inserção de faltas trifásicas no cálculo de estabilidade transitória;
  • Qualidade de energia: contém a opção de de visualização da impedância harmônica vista pela barra.

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Utilizado para cálculo da impedância base de alguns elementos conectados, além do cálculo da relação de transformação dos transformadores conectados entre barras. Sua unidade pode ser selecionada, sendo expressa em V ou em kV.

A modificação desse parâmetro irá alterar toda a tensão do trecho conectado por linhas elétricas, sendo emitido um alerta ao usuário.

Tensão controlada

Caracteriza o barramento como barra de tensão controlada (Barra PV),

Atenção!

Essa opção é somente válida caso alguma máquina síncrona esteja conectado, caso contrário esse valor será ignorado. Caso o limite de potência reativa da máquina síncrona conectada seja ultrapassado esse valor também é ignorado.

O valor poderá ser inserido em p.u. ou em volts (ou kV caso a tensão nominal esteja nesta unidade).

Barra de referência

Caracteriza o barramento como barra de referência (Barra de oscilação). Essa opção é somente válida caso esteja conectado um gerador síncrono, caso contrário uma mensagem de erro será exibida ao usuário ao realizar algum dos cálculos do programa.

Edit this page
+ + + + + + + + + + \ No newline at end of file diff --git a/docs/docs/cadTools/index.html b/docs/docs/cadTools/index.html index c4db2b6..e4c443d 100644 --- a/docs/docs/cadTools/index.html +++ b/docs/docs/cadTools/index.html @@ -4,30 +4,30 @@ -Ferramentas CAD | PSP-UFU - - - - - - - - - - +Ferramentas CAD | PSP-UFU + + + + + + + + + +
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Ferramentas CAD

Desenho assistido por computador (DAC; em inglês: computer aided design - CAD) é o nome genérico de sistemas computacionais (software) utilizados pela engenharia, geologia, geografia, arquitetura e design para facilitar o projeto e desenho técnicos. No caso do design, este pode estar ligado especificamente a todas as suas vertentes (produtos como vestuário, eletroeletrônicos, automobilísticos, etc.), de modo que os jargões de cada especialidade são incorporados na interface de cada programa. Wikipedia

Ferramentas do menu

Todos os objetos criados contêm vários atributos gráficos, como: posição, orientação, cor, tamanho, etc. Para modificá-los foram inseridas algumas ferramentas intuitivas e de fácil utilização, as quais são: selecionar, mover, girar, arrastar, zoom, encaixar, copiar, colar e excluir.

Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo submenu Ferramentas.

Tais ferramentas permitem a personalização, navegação e auxiliam a criação de redes elétricas de potência, assim como diagramas de controle na plataforma.

Selecionar

A seleção de um único objeto é realizada clicando com o botão esquerdo do mouse sobre o elemento, que será identificado pelo contorno em azul do objeto.

Para a seleção de vários objetos simultaneamente é necessário clicar com o botão esquerdo do mouse em um local vazio da tela e arrastá-lo, criando assim um retângulo de seleção que irá acompanhar o ponteiro do mouse enquanto o botão esquerdo estiver pressionado. Ao soltá-lo todos os objetos que intercederem o retângulo serão selecionados.

Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções anteriores enquanto novos elementos são selecionados.

Para desmarcar todos os objetos basta clicar em uma área sem objetos.

Mover

Um elemento poderá ser movido para qualquer local por meio da ação drag-and-drop (clicando e arrastando) ou pela ferramenta mover.

Ao habilitar o “modo mover”, movendo todos os componentes selecionados à medida que a posição do mouse é alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado.

Girar

Alguns objetos poderão ser rotacionados através da ferramenta girar, acessado pela tecla de atalho “R”, girando o objeto no sentido horário, ou “Shift + R”, para o sentido anti-horário (essa opção irá afetar todos os objetos selecionados). O elemento também pode ser rotacionado pelo submenu Ferramentas ou ao acessar o menu de contexto clicando com o botão direito sobre o elemento.

Atenção!

O menu de contexto somente será exibido se o elemento estiver selecionado.

Ao utilizar essa ferramenta os objetos irão girar 45º a partir do seu ponto de origem. Para atingir a angulação pretendida basta repetir o processo de rotação.

Arrastar

Três ferramentas muito úteis na navegação do circuito, principalmente em grandes redes, são: arrastar, zoom e encaixar.

A ferramenta arrastar possibilita mover todo o circuito preservando as posições relativas entre os elementos. Esta ferramenta pode ser acessada pelo submenu “Ferramentas” ou mantendo pressionada o scroll do mouse, ativando assim o “modo arrastar”. Ao ativá-lo todo o circuito será movido clicando e arrastando na direção desejada.

Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.

Zoom

O zoom será aplicado ao utilizar o scroll do mouse para mais ou menos zoom. A ferramenta zoom irá aproximar ou distanciar o circuito a partir da posição do ponteiro do mouse na tela para encontrar objetos ou destaca-los.

Encaixar

A ferramenta encaixar irá mover o circuito e aplicar o zoom necessário para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada através do submenu “Ferramentas” ou pela combinação de teclas “Shift + F”.

Copiar e Colar

Duas ferramentas importantes durante o processo de criação da rede elétrica de potência no software são copiar e colar. Qualquer circuito criado no PSP-UFU poderá ser duplicado completamente ou parcialmente no mesmo projeto ou em múltiplos através dessas ferramentas.

Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu “Ferramentas” ou pressionando a combinação das teclas “Ctrl + C”, então os dados do circuito serão copiados para a área de transferência. Ao copiar um circuito ele poderá ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combinação das teclas “Ctrl + V”.

Excluir

Qualquer objeto poderá ser excluído do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o botão direito sobre o elemento selecionado.

Personalização gráfica os elementos

Alguns elementos permitem sua personalização gráfica, como as barras e linhas.

Barra

No caso dos barramentos, pode-se alterar o comprimento da barra clicando e arrastando no pickbox exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.

Linha

As linhas podem ser inseridas com "nós" (pontos de ancoragem), personalizando a disposição das linhas no diagrama unifilar. Esses nós são inseridos durante o processo de criação do elemento, anteriormente à seleção da segunda barra.

Após a sua inserção, novos nós podem ser anexados pelo menu de contexto acessado ao clicar com o botão direito sobre a linha selecionada. Sua remoção também é alcançada por uma opção do menu de contexto.

Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o pickbox exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.

Conexão e desconexão de elemetos na barra

Os elementos podem ser desconectados e reconectados às barras após sua inserção somente pela ferramenta drag-and-drop. Para isso, o elemento deve ser selecionado e o seu nó de conexão deve ser arrastado para o local requerido.

Cuidado!

O elemento a ser desconectado/reconectado deve ser previamente selecionado para efetuar a operação. Caso contrário a barra será movida ou nenhuma operação será realizada.

No caso de desconexão, o elemento será automaticamente removido da simulação, sendo indicado pela sua cor (o elemento passa a ter cor cinza).

Atenção!

Ao reconectar o elemento ao circuito, deve-se atentar para estado do seu "disjuntor", indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (vermelho), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.

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Ferramentas CAD

Desenho assistido por computador (DAC; em inglês: computer aided design - CAD) é o nome genérico de sistemas computacionais (software) utilizados pela engenharia, geologia, geografia, arquitetura e design para facilitar o projeto e desenho técnicos. No caso do design, este pode estar ligado especificamente a todas as suas vertentes (produtos como vestuário, eletroeletrônicos, automobilísticos, etc.), de modo que os jargões de cada especialidade são incorporados na interface de cada programa. Wikipedia

Ferramentas do menu

Todos os objetos criados contêm vários atributos gráficos, como: posição, orientação, cor, tamanho, etc. Para modificá-los foram inseridas algumas ferramentas intuitivas e de fácil utilização, as quais são: selecionar, mover, girar, arrastar, zoom, encaixar, copiar, colar e excluir.

Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo submenu Ferramentas.

Tais ferramentas permitem a personalização, navegação e auxiliam a criação de redes elétricas de potência, assim como diagramas de controle na plataforma.

Selecionar

A seleção de um único objeto é realizada clicando com o botão esquerdo do mouse sobre o elemento, que será identificado pelo contorno em azul do objeto.

Para a seleção de vários objetos simultaneamente é necessário clicar com o botão esquerdo do mouse em um local vazio da tela e arrastá-lo, criando assim um retângulo de seleção que irá acompanhar o ponteiro do mouse enquanto o botão esquerdo estiver pressionado. Ao soltá-lo todos os objetos que intercederem o retângulo serão selecionados.

Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções anteriores enquanto novos elementos são selecionados.

Para desmarcar todos os objetos basta clicar em uma área sem objetos.

Mover

Um elemento poderá ser movido para qualquer local por meio da ação drag-and-drop (clicando e arrastando) ou pela ferramenta mover.

Ao habilitar o “modo mover”, movendo todos os componentes selecionados à medida que a posição do mouse é alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado.

Girar

Alguns objetos poderão ser rotacionados através da ferramenta girar, acessado pela tecla de atalho “R”, girando o objeto no sentido horário, ou “Shift + R”, para o sentido anti-horário (essa opção irá afetar todos os objetos selecionados). O elemento também pode ser rotacionado pelo submenu Ferramentas ou ao acessar o menu de contexto clicando com o botão direito sobre o elemento.

Atenção!

O menu de contexto somente será exibido se o elemento estiver selecionado.

Ao utilizar essa ferramenta os objetos irão girar 45º a partir do seu ponto de origem. Para atingir a angulação pretendida basta repetir o processo de rotação.

Arrastar

Três ferramentas muito úteis na navegação do circuito, principalmente em grandes redes, são: arrastar, zoom e encaixar.

A ferramenta arrastar possibilita mover todo o circuito preservando as posições relativas entre os elementos. Esta ferramenta pode ser acessada pelo submenu “Ferramentas” ou mantendo pressionada o scroll do mouse, ativando assim o “modo arrastar”. Ao ativá-lo todo o circuito será movido clicando e arrastando na direção desejada.

Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.

Zoom

O zoom será aplicado ao utilizar o scroll do mouse para mais ou menos zoom. A ferramenta zoom irá aproximar ou distanciar o circuito a partir da posição do ponteiro do mouse na tela para encontrar objetos ou destaca-los.

Encaixar

A ferramenta encaixar irá mover o circuito e aplicar o zoom necessário para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada através do submenu “Ferramentas” ou pela combinação de teclas “Shift + F”.

Copiar e Colar

Duas ferramentas importantes durante o processo de criação da rede elétrica de potência no software são copiar e colar. Qualquer circuito criado no PSP-UFU poderá ser duplicado completamente ou parcialmente no mesmo projeto ou em múltiplos através dessas ferramentas.

Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu “Ferramentas” ou pressionando a combinação das teclas “Ctrl + C”, então os dados do circuito serão copiados para a área de transferência. Ao copiar um circuito ele poderá ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combinação das teclas “Ctrl + V”.

Excluir

Qualquer objeto poderá ser excluído do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o botão direito sobre o elemento selecionado.

Personalização gráfica os elementos

Alguns elementos permitem sua personalização gráfica, como as barras e linhas.

Barra

No caso dos barramentos, pode-se alterar o comprimento da barra clicando e arrastando no pickbox exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.

Linha

As linhas podem ser inseridas com "nós" (pontos de ancoragem), personalizando a disposição das linhas no diagrama unifilar. Esses nós são inseridos durante o processo de criação do elemento, anteriormente à seleção da segunda barra.

Após a sua inserção, novos nós podem ser anexados pelo menu de contexto acessado ao clicar com o botão direito sobre a linha selecionada. Sua remoção também é alcançada por uma opção do menu de contexto.

Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o pickbox exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.

Conexão e desconexão de elemetos na barra

Os elementos podem ser desconectados e reconectados às barras após sua inserção somente pela ferramenta drag-and-drop. Para isso, o elemento deve ser selecionado e o seu nó de conexão deve ser arrastado para o local requerido.

Cuidado!

O elemento a ser desconectado/reconectado deve ser previamente selecionado para efetuar a operação. Caso contrário a barra será movida ou nenhuma operação será realizada.

No caso de desconexão, o elemento será automaticamente removido da simulação, sendo indicado pela sua cor (o elemento passa a ter cor cinza).

Atenção!

Ao reconectar o elemento ao circuito, deve-se atentar para estado do seu "disjuntor", indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (vermelho), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.

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Capacitor

Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. tradução livre - IEC 60050.

Capacitor no PSP-UFU

O elemento capacitor representa, geralmente, um banco de capacitores shunt no circuito do PSP-UFU.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.

Formulário de edição dos capacitores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos capacitores:

Formulário dos capacitores no PSP-UFU

Além do único contexto geral, pode ser observado o botão "Estabilidade" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do capacitor durante o estudo de estabilidade.

Formulário de chaveamento do capacitor

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência reativa

Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou p.u.p.u. (na base de potência do sistema).

Botão Estabilidade

O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de estabilidade.

Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.

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Capacitor

Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. tradução livre - IEC 60050.

Capacitor no PSP-UFU

O elemento capacitor representa, geralmente, um banco de capacitores shunt no circuito do PSP-UFU.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.

Formulário de edição dos capacitores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos capacitores:

Formulário dos capacitores no PSP-UFU

Além do único contexto geral, pode ser observado o botão "Estabilidade" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do capacitor durante o estudo de estabilidade.

Formulário de chaveamento do capacitor

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência reativa

Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou p.u.p.u. (na base de potência do sistema).

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Constante

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Constante

As constantes são valores numéricos reais que permanecem inalteradas em todo o período de simulação. Esses elementos possuem somente um nó de saída, o qual poderá ser conectado a qualquer outro nó de entrada dos elementos de controle.

Informação

Esse elemento pode, por exemplo, ser utilizado para definir valores alvos ou deslocamentos de sinal.

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Editor de Controle

Os controles das máquinas síncronas são criados, modificados, importados e exportados em um editor distinto dos elementos de potência, apresentado na figura abaixo.

Editor de elementos de controle do PSP-UFU

O acesso ao editor é realizado por meio de dois botões presentes no formulário de edição dos dados de estabilidade dos geradores síncronos:

Elementos de Controle

O acesso aos elementos de controle é realizado em uma janela (removível e encaixável) por meio de ícones relacionados.

Uma vez que o usuário clicar no ícone desejado, o elemento de controle acompanhará o ponteiro do mouse até ser efetivamente inserido na posição desejada ao clicar novamente na área de trabalho. Os elementos são então conectados por “linhas de conexão” inseridas ao clicar nos nós dos componentes previamente adicionados, permitindo a construção da rede de controle genérica.

As ferramentas de manipulação e navegação, como arrastar, mover e excluir são herdadas do editor de elementos de potência, possuindo comportamento idêntico. A edição dos dados dos componentes inseridos também é realizada com duplo clique sobre o elemento inserido, exibindo um formulário de edição de dados.

Os seguintes blocos de controle estão presentes no PSP-UFU:

Inicialização do sistema de controle

Caso as entradas do sistema de controle apresentem valores diferentes de zero ou a primeira operação entre elas não resulte em uma saída nula, o sistema necessita de inicialização, de forma a adequar os valores de entradas e saída dos blocos elementares e dos vetores de estado das funções transferências presentes. Tal procedimento é realizado por meio da solução de toda rede de controle até que se obtenha sua convergência, ou seja, a diferença absoluta entre as mesmas saídas de uma solução anterior e uma atual deve ser nula ou muito próxima de zero.

info

O processo de inicialização é realizada automaticamente pelo PSP-UFU.

Uma vez que a inicialização é imposta pelas entradas do controle, erros de convergência podem ocorrer devido à má parametrização dos elementos dos sistemas de potência e controle.

Para otimizar e melhorar a estabilidade do processo de inicialização utilizou-se um passo de integração variável dentro de limites, de forma que o passo aumenta em condições de diferenças menores entre as soluções do sistema de controle e diminui caso essa diferença se torne elevada. A implementação dessa abordagem reduziu significativamente o encerramento do processo com erro causado pela instabilidade numérica, além de acelerar a inicialização.

O fluxograma abaixo evidencia o processo de inicialização implementado no PSP-UFU:

Estrutura da inicialização do sistema de controle

Teste do diagrama de controle

Na parte inferior esquerda do Editor de Controle está presente o botão "Testar Sistema...". O botão acessa o formulário de teste de controles, como é indicado na figura abaixo:

Formulário de teste de controles

Nesse formulário é possível inserir o comportamento de todas as entradas do diagrama:

  • Tipo de entrada: Define um dos tipos de entradas possíveis no PSP-UFU: "Passo (Step)", Rampa (Ramp) ou Quadrática (Quadratic);
  • Tempo de início (tit_i): Define o tempo de início na simulação da entrada definida. As entradas iniciais são sempre definidas como zero e assumem valores diferentes após o tempo de início;
  • Inclinação (α\alpha): Valor relacionado ao tipo de entrada:
    • Para entrada do tipo "Passo" - O valor da inclinação define o valor final do passo:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \end{cases}
    • Para entrada do tipo "Rampa" - define o coeficiente de inclinação da reta:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α×t\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t \end{cases}
    • Para entrada do tipo "Quadrática" - define o coeficiente de crescimento da curva:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α×t2\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t^2 \end{cases}
  • Passo de integração (hh): Passo do método de integração Trapezoidal Implícito;
  • Tempo de simulação (tft_f): Tempo total de simulação.
Atenção!

A mesma parametrização de entrada é aplicada em todos os blocos de entrada do sistema.

Dica

É possível aplicar várias entradas distintas (inclusive com condicionais!) utilizando o bloco de expressão matemática.

Utilizando o bloco de expressão matemática é possível inserir entradas complexas, como por exemplo testar o diagrama de blocos (AVR DC1C + PSS1A - IEEE Std. 421.5-2016) da figura abaixo:

Sistema de controle sob teste
Comparação do sistema de controle sob teste
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Editor de Controle

Os controles das máquinas síncronas são criados, modificados, importados e exportados em um editor distinto dos elementos de potência, apresentado na figura abaixo.

Editor de elementos de controle do PSP-UFU

O acesso ao editor é realizado por meio de dois botões presentes no formulário de edição dos dados de estabilidade dos geradores síncronos:

Atenção!

No PSP-UFU a opção de editar o AVR engloba mais que somente o controle de tensão da máquina. Nele deve ser inserida a malha de controle da máquina assim como a excitatriz da máquina síncrona. Outras estratégias de controle (opcionais), como PSS (Power System Stabilizer) e/ou controles de sobre e sub excitação, são também implementadas em conjunto (como apresentado na figura anterior).

Atenção!

Assim como no AVR, o Regulador de Velocidade engloba mais que a regulação primária da máquina. Nessa opção deve ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o modelo da turbina. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.

Elementos de Controle

O acesso aos elementos de controle é realizado em uma janela (removível e encaixável) por meio de ícones relacionados.

Uma vez que o usuário clicar no ícone desejado, o elemento de controle acompanhará o ponteiro do mouse até ser efetivamente inserido na posição desejada ao clicar novamente na área de trabalho. Os elementos são então conectados por “linhas de conexão” inseridas ao clicar nos nós dos componentes previamente adicionados, permitindo a construção da rede de controle genérica.

As ferramentas de manipulação e navegação, como arrastar, mover e excluir são herdadas do editor de elementos de potência, possuindo comportamento idêntico. A edição dos dados dos componentes inseridos também é realizada com duplo clique sobre o elemento inserido, exibindo um formulário de edição de dados.

Os seguintes blocos de controle estão presentes no PSP-UFU:

Inicialização do sistema de controle

Caso as entradas do sistema de controle apresentem valores diferentes de zero ou a primeira operação entre elas não resulte em uma saída nula, o sistema necessita de inicialização, de forma a adequar os valores de entradas e saída dos blocos elementares e dos vetores de estado das funções transferências presentes. Tal procedimento é realizado por meio da solução de toda rede de controle até que se obtenha sua convergência, ou seja, a diferença absoluta entre as mesmas saídas de uma solução anterior e uma atual deve ser nula ou muito próxima de zero.

info

O processo de inicialização é realizada automaticamente pelo PSP-UFU.

Uma vez que a inicialização é imposta pelas entradas do controle, erros de convergência podem ocorrer devido à má parametrização dos elementos dos sistemas de potência e controle.

Para otimizar e melhorar a estabilidade do processo de inicialização utilizou-se um passo de integração variável dentro de limites, de forma que o passo aumenta em condições de diferenças menores entre as soluções do sistema de controle e diminui caso essa diferença se torne elevada. A implementação dessa abordagem reduziu significativamente o encerramento do processo com erro causado pela instabilidade numérica, além de acelerar a inicialização.

O fluxograma abaixo evidencia o processo de inicialização implementado no PSP-UFU:

Estrutura da inicialização do sistema de controle

Teste do diagrama de controle

Na parte inferior esquerda do Editor de Controle está presente o botão "Testar Sistema...". O botão acessa o formulário de teste de controles, como é indicado na figura abaixo:

Formulário de teste de controles

Nesse formulário é possível inserir o comportamento de todas as entradas do diagrama:

  • Tipo de entrada: Define um dos tipos de entradas possíveis no PSP-UFU: "Passo (Step)", Rampa (Ramp) ou Quadrática (Quadratic);
  • Tempo de início (tit_i): Define o tempo de início na simulação da entrada definida. As entradas iniciais são sempre definidas como zero e assumem valores diferentes após o tempo de início;
  • Inclinação (α\alpha): Valor relacionado ao tipo de entrada:
    • Para entrada do tipo "Passo" - O valor da inclinação define o valor final do passo:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \end{cases}
    • Para entrada do tipo "Rampa" - define o coeficiente de inclinação da reta:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α×t\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t \end{cases}
    • Para entrada do tipo "Quadrática" - define o coeficiente de crescimento da curva:
      {Se t<ti→f(t)=0,0Se t≥ti→f(t)=α×t2\begin{cases} \text{Se~} t < t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t^2 \end{cases}
  • Passo de integração (hh): Passo do método de integração Trapezoidal Implícito;
  • Tempo de simulação (tft_f): Tempo total de simulação.

Após a simulação os resultados são exibidos no visualizador de gráficos.

Atenção!

A mesma parametrização de entrada é aplicada em todos os blocos de entrada do sistema.

Dica

É possível aplicar várias entradas distintas (inclusive com condicionais!) utilizando o bloco de expressão matemática.

Utilizando o bloco de expressão matemática é possível inserir entradas complexas, como por exemplo testar o diagrama de blocos (AVR DC1C + PSS1A - IEEE Std. 421.5-2016) da figura abaixo:

Sistema de controle sob teste
Comparação do sistema de controle sob teste
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Divisor

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Divisor

Esse elemento é bastante simples e cumpre com a função matemáticas de seu nome.

Possui duas entradas de valores reais e sua saída é computada na sequência do nó superior pelo inferior, ou seja, a saída será o valor presente no nó 1 dividido pelo nó 2.

Atenção!

Nós não conectados no divisor são considerados como valor nulo. Caso a divisão possua numerador zero, o valor da saída é definida como sendo 101510^{15}.

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Exponencial

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Exponencial

A função exponencial dos elementos de controle realiza essa operação com uma entrada real, obedecendo a expressão:

yn=AeBuny_n = \bold{A} e^{\bold{B} u_n}

Em que:

  • unu_n e yny_n é a entrada e a saída do bloco exponencial, respectivamente;
  • A\bold{A} e B\bold{B} são constantes definidas pelo usuário.

Formulário de edição de dados do bloco Exponencial

A figura abaixo apresenta o formulário de edição de dados do bloco exponencial.

Formulário de edição de dados do bloco exponencial no PSP-UFU

Esse bloco não linear é definido pelas constantes A e B, inseridas pelo usuário.

Informação

Tais blocos são úteis na representação de não linearidades, como, por exemplo, modelagem da saturação de máquinas de corrente contínuas presentes em alguns reguladores automáticos de tensão.

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Curto-Circuito

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Curto-Circuito

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Ganho

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Ganho

O bloco de ganho multiplica o valor de entrada por uma constante definida pelo usuário, possuindo comportamento idêntico à combinação de uma constante e um bloco multiplicador.

Esse valor de ganho permanece fixo durante todo o tempo de simulação e é identificado no elemento gráfico exibido no editor de elementos de controle.

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Visualizador de Gráficos

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Fonte de Corrente Harmônica

(Fonte de perturbação harmônica) Parte do sistema elétrico de potência ou das instalações a ele conectadas, que causa distorção harmônica da forma de onda da corrente e / ou tensão. tradução livre - IEC 60050.

Fonte de corrente harmônica no PSP-UFU

As fontes de corrente harmônica são responsáveis pela injeção de correntes harmônicas e são utilizadas pela ferramenta de cálculo de distorções harmônicas. Uma lista de correntes harmônicas pode ser inserida em um mesmo elemento, conforme é exibido na o formulário de edição de dados.

Atenção!

A presença da fonte de corrente harmônica não é considerada nos estudos de fluxo de carga, curto-circuito e estabilidade.

Formulário de edição das fontes de corrente harmônica

A imagem abaixo apresenta o formulário de inserção/alteração de dados da fonte de corrente harmônica:

Formulário dos indutores no PSP-UFU

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Ordem

Especifica a ordem harmônica a ser inserida na lista de correntes harmônicas do elemento. Caso a ordem harmônica já exista na lista, ela será substituída pelos novos parâmetros.

Corrente

Módulo da corrente harmônica.

Unidade

Unidade do módulo de corrente harmônica, em A ou p.u.p.u.

Ângulo

Ângulo da corrente harmônica, em graus.

Adicionar / Remover

Insere ou modifica a nova ordem harmônica ao clicar em “Adicionar”. Retira a ordem harmônica selecionada da lista ao clicar em “Remover”.

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Fonte de Corrente Harmônica

(Fonte de perturbação harmônica) Parte do sistema elétrico de potência ou das instalações a ele conectadas, que causa distorção harmônica da forma de onda da corrente e / ou tensão. tradução livre - IEC 60050.

Fonte de corrente harmônica no PSP-UFU

As fontes de corrente harmônica são responsáveis pela injeção de correntes harmônicas e são utilizadas pela ferramenta de cálculo de distorções harmônicas. Uma lista de correntes harmônicas pode ser inserida em um mesmo elemento, conforme é exibido na o formulário de edição de dados.

Atenção!

A presença da fonte de corrente harmônica não é considerada nos estudos de fluxo de carga, curto-circuito e estabilidade.

Formulário de edição das fontes de corrente harmônica

A imagem abaixo apresenta o formulário de inserção/alteração de dados da fonte de corrente harmônica:

Formulário dos indutores no PSP-UFU

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Ordem

Especifica a ordem harmônica a ser inserida na lista de correntes harmônicas do elemento. Caso a ordem harmônica já exista na lista, ela será substituída pelos novos parâmetros.

Corrente

Módulo da corrente harmônica.

Unidade

Unidade do módulo de corrente harmônica, em A ou p.u.p.u.

Ângulo

Ângulo da corrente harmônica, em graus.

Adicionar / Remover

Insere ou modifica a nova ordem harmônica ao clicar em “Adicionar”. Retira a ordem harmônica selecionada da lista ao clicar em “Remover”.

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Harmônicos

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Harmônicos

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Mapa de Tensão

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Motor de Indução

Uma máquina assíncrona da qual apenas um enrolamento é energizado. tradução livre - IEC 60050.

Motor de indução trifásico no PSP-UFU

No PSP-UFU, os motores de indução são contemplados nos estudos de fluxo de carga e no estudo de estabilidade.

Informação

Os dados de estabilidade da máquina de indução são utilizados em conjunto com o fluxo de carga, calculando de forma correta a potência reativa das máquinas e consequentemente a tensão no barramento conectado.

Cuidado!

Ao marcar a opção "Calcular a potência reativa no fluxo de carga", devem ser inseridos os dados corretos na aba "Estabilidade", caso contrário, será atribuída uma potência reativa incorreta no motor.

Motor de indução trifásico no cálculo do fluxo de carga

A figura abaixo apresenta o modelo do motor de indução trifásico (MIT) de gaiola simples.

Circuito equivalente do motor de indução

As potências ativa e reativa podem ser calculadas em relação às variáveis e parâmetros do motor em p.u.p.u. como:

P=V2{(r2s)[(r2s)r1−x1K1−x2xm]+K1[(r2s)(xm+x1)+r1K1]}[(r2s)r1−x1K1−x2xm]2+[(r2s)(xm+x1)+r1K1]2Q=−V2{K1[(r2s)r1−x1K1−x2xm]−(r2s)[(r2s)(xm+x1)+r1K1]}[(r2s)r1−x1K1−x2xm]2+[(r2s)(xm+x1)+r1K1]2 K1=x2+xmP = \frac{V^2 \left\{ \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]+K_1 \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ Q = \frac{-V^2 \left\{ K_1 \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]- \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ ~\\ K_1=x_2+x_m

Como pode ser observado nas equações acima, existem quatro variáveis e somente duas equações. Na prática, as variáveis podem ser reduzidas a três, uma vez que o módulo da tensão (V) é obtido nos resultados do fluxo de potência. Para resolver as equações é necessário definir uma variável adicional. A variável escolhida como fixa no PSP-UFU é a potência ativa (P), por fornecer resultados numericamente corretos e adequados para motores em situações de estabilidade.

Portanto, nesse modelo estático, a potência ativa é mantida constante durante o cálculo do fluxo de carga e o escorregamento (s) é atualizado em cada iteração. A equação da potência ativa pode ser reescrita em relação ao escorregamento:

(r2s)2A+(r2s)B+C=0\left(\frac{r_2}{s} \right)^2 A + \left(\frac{r_2}{s} \right) B + C = 0

Em que:

A=P(r12+K32)−V2r1B=2P(r1K2+K3K4)−V2(K2+K1K3)C=P(K22+K42)−V2K1K4K2=−x1K1−x2xmK3=xm+x1K4=r1K1A = P \left( r_1^2 + K_3^2 \right) - V^2 r_1\\ B = 2P(r_1 K_2 + K_3 K_4) - V^2 \left(K_2 + K_1 K_3 \right)\\ C = P \left( K_2^2 + K_4^2 \right) - V^2 K_1 K_4\\ K_2 = -x_1 K_1 -x_2 x_m\\ K_3 = x_m + x_1\\ K_4 = r_1 K_1

Esse modelo pode ser inserido na solução do fluxo de carga seguindo os seguintes passos:

  1. As constantes K1K_1 a K4K_4 são inicialmente calculadas . Esses valores são mantidos constantes durante toda a solução;
  2. Em cada iteração são calculados os coeficientes AA, BB e CC utilizando o valor atualizado de VV;
  3. A equação quadrática é resolvida e dois valores de (r2s)\left(\frac{r_2}{s} \right) são obtidos, em que o maior deles é escolhido por estar na região estável da característica toque-escorregamento do motor;
  4. Utilizando o novo valor de (r2s)\left(\frac{r_2}{s} \right), a potência reativa (QQ) é obtida. O vetor de potências é então atualizado e os procedimentos convencionais de solução do fluxo de potência são realizados.

Os passos de 2 a 4 são repetidos até que se obtenha a convergência.

Atenção!

No PSP-UFU, os motores de indução não são considerados no cálculo de curto-circuito.

Motor de indução trifásico no estudo de estabilidade

Uma importante carga dinâmica são os motores de indução, uma vez que correspondem a uma parcela significativa das cargas presentes no sistema elétrico. O modelo da máquina de indução apresentado anteriormente, a qual pode ser utilizada tanto como motor quanto como gerador, é bem estabelecida na literatura.

Como descrito na seção anterior, a inicialização dessa máquina é realizada em conjunto com o fluxo de potência, visto que a potência reativa exigida pela máquina de indução é dependente dos parâmetros do motor, assim como a tensão do seu barramento. Essa abordagem é necessária, pois métodos convencionais conduzem a resultados errôneos em sistemas altamente carregados.

É necessário expressar a equação de movimento da máquina de indução em termos de torque e não potência, como é realizado com as máquinas síncronas. A simetria do rotor também faz com que a posição angular não seja importante e o escorregamento (ss) é utilizado no lugar da velocidade (ω\omega), em que:

s=fracΩ0−ωΩ0s = frac{\Omega_0 - \omega}{\Omega_0}

Desprezando as perdas por atrito e ventilação e a potência no eixo suave, as equações mecânicas do motor são expressas da seguinte forma:

Tm=A−Bs+Cs2Te=Re{E˙I˙∗}Ωbdsdt=(Tm−Te)2HT_m = A -Bs + Cs^2\\ T_e = \frac{Re\left\{ \dot{E}\dot{I}^* \right\}}{\Omega_b}\\ \frac{ds}{dt} = \frac{\left( T_m - T_e \right)}{2H}

Em que:

  • TmT_m é o torque mecânico;
  • TeT_e é o torque elétrico;
  • HH é a inércia do conjunto motor - carga mecânica

Os termos AA, BB e CC são termos que definem o comportamento do torque mecânico da carga de acordo com o escorregamento. O torque mecânico normalmente varia com a velocidade, podendo ser expressa proporcionalmente com a seguinte equação quadrática:

Tm∝a+bω+cω2T_m \propto a + b\omega + c\omega^2

Em que:

{A∝a+b+cB∝b+2cC∝c\begin{cases} A \propto a + b + c \\ B \propto b + 2c \\ C \propto c \end{cases}

As equações elétricas do motor de indução de gaiola simples são baseadas no circuito equivalente da figura anterior. De forma semelhante ao modelo transitório da máquina síncrona, o motor de indução pode ser modelado pelo circuito equivalente de Thevenin de tensão transitória E′E' atrás de uma resistência do estator r1r_1 e uma reatância transitória x′x'. A reatância transitória aparente de rotor bloqueado é dada por:

x′=x1+x2xmx2+xmx' = x_1 + \frac{x_2 x_m}{x_2 + x_m}

A constante de tempo de circuito aberto do rotor (T0′T_0') é:

T0′=x2+xmΩbr2T_0' = \frac{x_2 + x_m}{\Omega_b r_2}

E a reatância de circuito aberto é:

x0=x1+xmx_0 = x_1 + x_m

Uma vez que as reatâncias não são afetadas pela posição do rotor, as EADs do motor de indução podem ser expressar diretamente por componentes reais (rr) e imaginárias (mm). Portanto, a descrição completa desse modelo é representada pelo seguinte sistema de equações algébrico-diferenciais:

Vr−Er′=r1Ir−x′ImVm−Em′=r1Im−x′ImdEr′dt=ΩbsEm′−Er′+(x0−x′)ImT0′dEm′dt=ΩbsEr′−Em′i(x0−x′)IrT0′V_r - E_r' = r_1 I_r - x' I_m\\ V_m - E_m' = r_1 I_m - x' I_m\\ \frac{dE_r'}{dt} = \Omega_b s E_m' - \frac{E_r' + \left( x_0 - x' \right) I_m}{T_0'}\\ \frac{dE_m'}{dt} = \Omega_b s E_r' - \frac{E_m' i \left( x_0 - x' \right) I_r}{T_0'}

Formulário de edição dos geradores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos motores de indução:

Formulário dos motores de indução no PSP-UFU

No formulário pode ser observado o botão "Chaveamento" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do motor durante o estudo de estabilidade.

Formulário de chaveamento do motores de indução

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do gerador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.p.u.) do motor.

Atenção!

Caso a opção “Calcular a potência reativa no fluxo de carga” esteja ativada, o campo de potência reativa é desativado para edição.

Calcular a potência reativa no fluxo de carga

Caso essa opção seja marcada, o programa irá utilizar os dados fornecidos no formulário de estabilidade para calcular a potência reativa do motor durante o processo iterativo do fluxo de carga.

Cuidado!

Caso essa opção não seja utilizada o motor será considerado uma carga de potência constante no estudo de fluxo de carga.

A não utilização dessa opção poderá gerar erros de regime permamente no estudo de estabilidade.

Utilizar potência nominal como base -Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.

Estabilidade

Imprimir dados da máquina de indução

Exibe os dados do gerador síncrono nos gráficos no tempo. Os seguintes dados são exibidos:

  • tensão terminal
  • potências ativa e reativas
  • corrente, torque elétrico
  • torque mecânico
  • velocidade
  • escorregamento

Inércia

Inércia do conjunto motor-carga, em s.

Resistência e reatância do estator

Resistência e reatância do estator do motor de indução, em p.u.p.u.

Resistência e reatância do rotor

Resistência e reatância do rotor do motor de indução, em p.u.p.u.

Reatância de magnetização

Reatância do ramo de magnetização do motor de indução, em p.u.p.u.

Utilizar fator de gaiola

Permite a inserção de um fator de gaiola (KgK_g) no motor de indução. Tal fator eleva o valor da resistência do rotor em condições de grande escorregamento, como ocorre em motores de gaiola dupla ou gaiola profunda. A resistência do rotor segue a seguinte equação:

r2=r20(1+Kgs)r_2 = r_{2_0} \left( 1+K_g s \right)

Em que:

  • r20r_{2_0} é a resistência do rotor inserida no formulário.

Característica da carga

Descreve a característica do torque da carga mecânica no eixo do motor seguindo a equação do torque mecânico.

Tm∝a+bω+cω2T_m \propto \bold{a} + \bold{b}\omega + \bold{c}\omega^2
Cuidado!

A soma dos coeficientes (a+b+ca + b + c) deve ser unitária.

Botão Chaveamento

O botão "Chaveamento" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do gerador durante o estudo de estabilidade.

Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.

Referências

  1. SÁNCHEZ, J. C.; OLIVARES, T. I. A.; ORTIZ, G. R.; VEGA, D. R. Induction Motor Static Models for Power Flow and Voltage Stability Studies. In: IEEE Power and Energy Society General Meeting, 2012, San Diego. doi: https://doi.org/10.1109/PESGM.2012.6345618
  2. IEEE Std 399-1997. IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book). IEEE, New York, ago. 1998. doi: https://doi.org/10.1109/IEEESTD.1998.88568
  3. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  4. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
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Motor de Indução

Uma máquina assíncrona da qual apenas um enrolamento é energizado. tradução livre - IEC 60050.

Motor de indução trifásico no PSP-UFU

No PSP-UFU, os motores de indução são contemplados nos estudos de fluxo de carga e no estudo de estabilidade.

Informação

Os dados de estabilidade da máquina de indução são utilizados em conjunto com o fluxo de carga, calculando de forma correta a potência reativa das máquinas e consequentemente a tensão no barramento conectado.

Cuidado!

Ao marcar a opção "Calcular a potência reativa no fluxo de carga", devem ser inseridos os dados corretos na aba "Estabilidade", caso contrário, será atribuída uma potência reativa incorreta no motor.

Motor de indução trifásico no cálculo do fluxo de carga

A figura abaixo apresenta o modelo do motor de indução trifásico (MIT) de gaiola simples.

Circuito equivalente do motor de indução

As potências ativa e reativa podem ser calculadas em relação às variáveis e parâmetros do motor em p.u.p.u. como:

P=V2{(r2s)[(r2s)r1−x1K1−x2xm]+K1[(r2s)(xm+x1)+r1K1]}[(r2s)r1−x1K1−x2xm]2+[(r2s)(xm+x1)+r1K1]2Q=−V2{K1[(r2s)r1−x1K1−x2xm]−(r2s)[(r2s)(xm+x1)+r1K1]}[(r2s)r1−x1K1−x2xm]2+[(r2s)(xm+x1)+r1K1]2 K1=x2+xmP = \frac{V^2 \left\{ \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]+K_1 \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ Q = \frac{-V^2 \left\{ K_1 \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]- \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ ~\\ K_1=x_2+x_m

Como pode ser observado nas equações acima, existem quatro variáveis e somente duas equações. Na prática, as variáveis podem ser reduzidas a três, uma vez que o módulo da tensão (V) é obtido nos resultados do fluxo de potência. Para resolver as equações é necessário definir uma variável adicional. A variável escolhida como fixa no PSP-UFU é a potência ativa (P), por fornecer resultados numericamente corretos e adequados para motores em situações de estabilidade.

Portanto, nesse modelo estático, a potência ativa é mantida constante durante o cálculo do fluxo de carga e o escorregamento (s) é atualizado em cada iteração. A equação da potência ativa pode ser reescrita em relação ao escorregamento:

(r2s)2A+(r2s)B+C=0\left(\frac{r_2}{s} \right)^2 A + \left(\frac{r_2}{s} \right) B + C = 0

Em que:

A=P(r12+K32)−V2r1B=2P(r1K2+K3K4)−V2(K2+K1K3)C=P(K22+K42)−V2K1K4K2=−x1K1−x2xmK3=xm+x1K4=r1K1A = P \left( r_1^2 + K_3^2 \right) - V^2 r_1\\ B = 2P(r_1 K_2 + K_3 K_4) - V^2 \left(K_2 + K_1 K_3 \right)\\ C = P \left( K_2^2 + K_4^2 \right) - V^2 K_1 K_4\\ K_2 = -x_1 K_1 -x_2 x_m\\ K_3 = x_m + x_1\\ K_4 = r_1 K_1

Esse modelo pode ser inserido na solução do fluxo de carga seguindo os seguintes passos:

  1. As constantes K1K_1 a K4K_4 são inicialmente calculadas . Esses valores são mantidos constantes durante toda a solução;
  2. Em cada iteração são calculados os coeficientes AA, BB e CC utilizando o valor atualizado de VV;
  3. A equação quadrática é resolvida e dois valores de (r2s)\left(\frac{r_2}{s} \right) são obtidos, em que o maior deles é escolhido por estar na região estável da característica toque-escorregamento do motor;
  4. Utilizando o novo valor de (r2s)\left(\frac{r_2}{s} \right), a potência reativa (QQ) é obtida. O vetor de potências é então atualizado e os procedimentos convencionais de solução do fluxo de potência são realizados.

Os passos de 2 a 4 são repetidos até que se obtenha a convergência.

Atenção!

No PSP-UFU, os motores de indução não são considerados no cálculo de curto-circuito.

Motor de indução trifásico no estudo de estabilidade

Uma importante carga dinâmica são os motores de indução, uma vez que correspondem a uma parcela significativa das cargas presentes no sistema elétrico. O modelo da máquina de indução apresentado anteriormente, a qual pode ser utilizada tanto como motor quanto como gerador, é bem estabelecida na literatura.

Como descrito na seção anterior, a inicialização dessa máquina é realizada em conjunto com o fluxo de potência, visto que a potência reativa exigida pela máquina de indução é dependente dos parâmetros do motor, assim como a tensão do seu barramento. Essa abordagem é necessária, pois métodos convencionais conduzem a resultados errôneos em sistemas altamente carregados.

É necessário expressar a equação de movimento da máquina de indução em termos de torque e não potência, como é realizado com as máquinas síncronas. A simetria do rotor também faz com que a posição angular não seja importante e o escorregamento (ss) é utilizado no lugar da velocidade (ω\omega), em que:

s=fracΩ0−ωΩ0s = frac{\Omega_0 - \omega}{\Omega_0}

Desprezando as perdas por atrito e ventilação e a potência no eixo suave, as equações mecânicas do motor são expressas da seguinte forma:

Tm=A−Bs+Cs2Te=Re{E˙I˙∗}Ωbdsdt=(Tm−Te)2HT_m = A -Bs + Cs^2\\ T_e = \frac{Re\left\{ \dot{E}\dot{I}^* \right\}}{\Omega_b}\\ \frac{ds}{dt} = \frac{\left( T_m - T_e \right)}{2H}

Em que:

  • TmT_m é o torque mecânico;
  • TeT_e é o torque elétrico;
  • HH é a inércia do conjunto motor - carga mecânica

Os termos AA, BB e CC são termos que definem o comportamento do torque mecânico da carga de acordo com o escorregamento. O torque mecânico normalmente varia com a velocidade, podendo ser expressa proporcionalmente com a seguinte equação quadrática:

Tm∝a+bω+cω2T_m \propto a + b\omega + c\omega^2

Em que:

{A∝a+b+cB∝b+2cC∝c\begin{cases} A \propto a + b + c \\ B \propto b + 2c \\ C \propto c \end{cases}

As equações elétricas do motor de indução de gaiola simples são baseadas no circuito equivalente da figura anterior. De forma semelhante ao modelo transitório da máquina síncrona, o motor de indução pode ser modelado pelo circuito equivalente de Thevenin de tensão transitória E′E' atrás de uma resistência do estator r1r_1 e uma reatância transitória x′x'. A reatância transitória aparente de rotor bloqueado é dada por:

x′=x1+x2xmx2+xmx' = x_1 + \frac{x_2 x_m}{x_2 + x_m}

A constante de tempo de circuito aberto do rotor (T0′T_0') é:

T0′=x2+xmΩbr2T_0' = \frac{x_2 + x_m}{\Omega_b r_2}

E a reatância de circuito aberto é:

x0=x1+xmx_0 = x_1 + x_m

Uma vez que as reatâncias não são afetadas pela posição do rotor, as EADs do motor de indução podem ser expressar diretamente por componentes reais (rr) e imaginárias (mm). Portanto, a descrição completa desse modelo é representada pelo seguinte sistema de equações algébrico-diferenciais:

Vr−Er′=r1Ir−x′ImVm−Em′=r1Im−x′ImdEr′dt=ΩbsEm′−Er′+(x0−x′)ImT0′dEm′dt=ΩbsEr′−Em′i(x0−x′)IrT0′V_r - E_r' = r_1 I_r - x' I_m\\ V_m - E_m' = r_1 I_m - x' I_m\\ \frac{dE_r'}{dt} = \Omega_b s E_m' - \frac{E_r' + \left( x_0 - x' \right) I_m}{T_0'}\\ \frac{dE_m'}{dt} = \Omega_b s E_r' - \frac{E_m' i \left( x_0 - x' \right) I_r}{T_0'}

Formulário de edição dos geradores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos motores de indução:

Formulário dos motores de indução no PSP-UFU

No formulário pode ser observado o botão "Chaveamento" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do motor durante o estudo de estabilidade.

Formulário de chaveamento do motores de indução

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do gerador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.p.u.) do motor.

Atenção!

Caso a opção “Calcular a potência reativa no fluxo de carga” esteja ativada, o campo de potência reativa é desativado para edição.

Calcular a potência reativa no fluxo de carga

Caso essa opção seja marcada, o programa irá utilizar os dados fornecidos no formulário de estabilidade para calcular a potência reativa do motor durante o processo iterativo do fluxo de carga.

Cuidado!

Caso essa opção não seja utilizada o motor será considerado uma carga de potência constante no estudo de fluxo de carga.

A não utilização dessa opção poderá gerar erros de regime permamente no estudo de estabilidade.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.

Referências

  1. SÁNCHEZ, J. C.; OLIVARES, T. I. A.; ORTIZ, G. R.; VEGA, D. R. Induction Motor Static Models for Power Flow and Voltage Stability Studies. In: IEEE Power and Energy Society General Meeting, 2012, San Diego. doi: https://doi.org/10.1109/PESGM.2012.6345618
  2. IEEE Std 399-1997. IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book). IEEE, New York, ago. 1998. doi: https://doi.org/10.1109/IEEESTD.1998.88568
  3. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  4. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
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PSP-UFU

important

This user guide was written in Brazilian Portuguese. If you want to help me translate this guide, contact-me on GitHub or Twitter.

Sobre o PSP-UFU

O PSP-UFU (Plataforma de Sistemas de Potência da Universidade Federal de Uberlândia) é um software multi-plataforma, multilíngue, livre e de código aberto (FOSS) com recursos avançados de GUI (Graphical User Interface) e ferramentas CAD (Computer Aided Design) para estudos de sistemas elétricos de potência.

O software permite a construção de qualquer rede de transmissão elétrica e sistemas de controle através da inserção de elementos visuais. Para a visualização dos resultados, o programa oferece elementos de texto vinculados na tela principal e também editores de tabelas e gráficos.

O PSP-UFU tem como objetivo fornecer ferramentas eficientes de simulação para fins de pesquisa e educação, além de aplicações industriais em sistemas elétricos de potência.

Resumidamente, o software pode executar os seguintes estudos:

  • Fluxo de potência
  • Cálculo de curto-circuito
  • Harmônicos
  • Estabilidade transitória e dinâmica

Publicações

Os artigos abaixo possuem maiores detalhes a respeito do PSP-UFU:

Oliveira, T. L., Guimarães, G. C., & Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. International Transactions on Electrical Energy Systems, e12185. doi: 10.1002/2050-7038.12185

Oliveira, T. L., Guimarães, G. C., Silva, L. R., & Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. The International Journal of Electrical Engineering & Education, 0020720919879058. doi: 10.1177/0020720919879058

A Tese de Doutorado abaixo detalha em profundidade os cálculos envolvidos, arquitetura de software e ferramentas implementadas no PSP-UFU:

Oliveira, T. L. (2019). Desenvolvimento de um programa computacional livre, gráfico, e multiplataforma para analisar sistemas elétricos de potência em regime permanente e dinâmico. doi: 10.14393/ufu.te.2019.2444

Contribuindo com o projeto

Se você está interessado em contribuir com o PSP-UFU de alguma forma (desenvolvimento, críticas, sugestões, etc.), entre em contato pelo GitHub ou Twitter.

Desenvolvedores

Thales Lima Oliveira

Edit this page
- - - - - - - - - - +

PSP-UFU

important

This user guide was written in Brazilian Portuguese. If you want to help me translate this guide, contact-me on GitHub or Twitter.

Sobre o PSP-UFU

O PSP-UFU (Plataforma de Sistemas de Potência da Universidade Federal de Uberlândia) é um software multi-plataforma, multilíngue, livre e de código aberto (FOSS) com recursos avançados de GUI (Graphical User Interface) e ferramentas CAD (Computer Aided Design) para estudos de sistemas elétricos de potência.

O software permite a construção de qualquer rede de transmissão elétrica e sistemas de controle através da inserção de elementos visuais. Para a visualização dos resultados, o programa oferece elementos de texto vinculados na tela principal e também editores de tabelas e gráficos.

O PSP-UFU tem como objetivo fornecer ferramentas eficientes de simulação para fins de pesquisa e educação, além de aplicações industriais em sistemas elétricos de potência.

Resumidamente, o software pode executar os seguintes estudos:

  • Fluxo de potência
  • Cálculo de curto-circuito
  • Harmônicos
  • Estabilidade transitória e dinâmica

Publicações

Os artigos abaixo possuem maiores detalhes a respeito do PSP-UFU:

Oliveira, T. L., Guimarães, G. C., & Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. International Transactions on Electrical Energy Systems, e12185. doi: 10.1002/2050-7038.12185

Oliveira, T. L., Guimarães, G. C., Silva, L. R., & Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. The International Journal of Electrical Engineering & Education, 0020720919879058. doi: 10.1177/0020720919879058

A Tese de Doutorado abaixo detalha em profundidade os cálculos envolvidos, arquitetura de software e ferramentas implementadas no PSP-UFU:

Oliveira, T. L. (2019). Desenvolvimento de um programa computacional livre, gráfico, e multiplataforma para analisar sistemas elétricos de potência em regime permanente e dinâmico. doi: 10.14393/ufu.te.2019.2444

Contribuindo com o projeto

Se você está interessado em contribuir com o PSP-UFU de alguma forma (desenvolvimento, críticas, sugestões, etc.), entre em contato pelo GitHub ou Twitter.

Desenvolvedores

Thales Lima Oliveira

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+ + + + + + + + + + \ No newline at end of file diff --git a/docs/docs/inductor/index.html b/docs/docs/inductor/index.html index f286613..8f2539f 100644 --- a/docs/docs/inductor/index.html +++ b/docs/docs/inductor/index.html @@ -4,30 +4,30 @@ -Indutor | PSP-UFU - - - - - - - - - - +Indutor | PSP-UFU + + + + + + + + + +
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Indutor

Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. tradução livre - IEC 60050.

Indutor no PSP-UFU

O elemento indutor (ou reator) representa, geralmente, reator shunt no circuito do PSP-UFU.

Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.

Formulário de edição dos indutores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos indutores:

Formulário dos indutores no PSP-UFU

Além do único contexto geral, pode ser observado o botão "Estabilidade" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do indutor durante o estudo de estabilidade.

Formulário de chaveamento do indutor

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência reativa

Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou p.u.p.u. (na base de potência do sistema).

Botão Estabilidade

O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do indutor durante o estudo de estabilidade.

Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.

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- - - - - - - - - - +

Indutor

Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. tradução livre - IEC 60050.

Indutor no PSP-UFU

O elemento indutor (ou reator) representa, geralmente, reator shunt no circuito do PSP-UFU.

Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.

Formulário de edição dos indutores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos indutores:

Formulário dos indutores no PSP-UFU

Além do único contexto geral, pode ser observado o botão "Estabilidade" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do indutor durante o estudo de estabilidade.

Formulário de chaveamento do indutor

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência reativa

Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou p.u.p.u. (na base de potência do sistema).

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+ + + + + + + + + + \ No newline at end of file diff --git a/docs/docs/installation/index.html b/docs/docs/installation/index.html index 1415e17..66b5db9 100644 --- a/docs/docs/installation/index.html +++ b/docs/docs/installation/index.html @@ -4,31 +4,31 @@ -Instalação | PSP-UFU - - - - - - - - - - +Instalação | PSP-UFU + + + + + + + + + +
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Instalação

Download

O download do PSP-UFU pode ser realizado pelo "last release" do repositório do PSP-UFU no GitHub.

Ao acessar ao link, role a página até encontrar os Assets:

Assets download

Como o PSP-UFU é um software multiplataforma, você deve baixar o arquivo correto:

  • Para o sistema operacional Windows baixe os arquivos .exe (recomendado) ou .zip.
  • Para os sistemas Linux baseados no Debian (por exemplo, Ubuntu, Mint) 64 bits baixe o pacote de instalação .deb.
Dica

Se você está interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo GitHub ou Twitter.

Na sequência são apresentados o passo-a-passo para instalação dos SOs Windows e Linux. Também são apresentadas as soluções para os erros mais recorrentes.

Windows

Após baixar o arquivo .exe avance em cada passo do instalador. O executável irá solicitar automaticamente a instalação do Microsoft Visual C++ Redistribuível e, caso não esteja instalado no seu computador, realize os procedimentos do programa.

Caso o executável falhe em abrir, baixe o arquivo .zip e descompacte em alguma pasta do seu sistema. Nesse caso é necessário baixar e instalar manualmente o Microsoft Visual C++ Redistribuível 32 bits.

Após a conclusão da instalação abra o PSP-UFU para verificar a correta instalação. O executável está presente na pasta "<local de instalação>/PSP-UFU/bin/PSP-UFU.exe".

Problemas recorrentes no Windows

  • Ao baixar o navegador pode falsamente sinalizar que é um arquivo perigoso, basta clicar em "Manter arquivo";
  • Ao abrir o instalador, novamente o Windows sinaliza que o arquivo é perigoso, basta clicar em "Executar assim mesmo";
  • Ao abrir o programa e alterar o seu idioma, uma mensagem de erro é exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com botão direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;
  • Ao criar um novo projeto a tela de trabalho não é exibida ou é exibida uma tela preta. Vá nas opções gerais e altere o renderizador para "Device Context". Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.

Linux

A instalação no sistema Linux é facilmente realizado pelo pacote de instalação automático .deb.

Atenção!

Note que essa versão para Linux está defasada e algumas funcionalidades do programa podem não estar presentes.

Caso queira contribuir com o projeto e construir a versão atual no sistema Linux baseado em Debian ou em outras distribuições entre em contato pelo GitHub ou Twitter.

Problemas recorrentes no Linux

Pode ser necessário adicionar o diretório das bibliotecas do wxWidgets nas variáveis de ambiente. +

Instalação

Download

O download do PSP-UFU pode ser realizado pelo "last release" do repositório do PSP-UFU no GitHub.

Ao acessar ao link, role a página até encontrar os Assets:

Assets download

Como o PSP-UFU é um software multiplataforma, você deve baixar o arquivo correto:

  • Para o sistema operacional Windows baixe os arquivos .exe (recomendado) ou .zip.
  • Para os sistemas Linux baseados no Debian (por exemplo, Ubuntu, Mint) 64 bits baixe o pacote de instalação .deb.
Dica

Se você está interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo GitHub ou Twitter.

Na sequência são apresentados o passo-a-passo para instalação dos SOs Windows e Linux. Também são apresentadas as soluções para os erros mais recorrentes.

Windows

Após baixar o arquivo .exe avance em cada passo do instalador. O executável irá solicitar automaticamente a instalação do Microsoft Visual C++ Redistribuível e, caso não esteja instalado no seu computador, realize os procedimentos do programa.

Caso o executável falhe em abrir, baixe o arquivo .zip e descompacte em alguma pasta do seu sistema. Nesse caso é necessário baixar e instalar manualmente o Microsoft Visual C++ Redistribuível 32 bits.

Após a conclusão da instalação abra o PSP-UFU para verificar a correta instalação. O executável está presente na pasta "<local de instalação>/PSP-UFU/bin/PSP-UFU.exe".

Problemas recorrentes no Windows

  • Ao baixar o navegador pode falsamente sinalizar que é um arquivo perigoso, basta clicar em "Manter arquivo";
  • Ao abrir o instalador, novamente o Windows sinaliza que o arquivo é perigoso, basta clicar em "Executar assim mesmo";
  • Ao abrir o programa e alterar o seu idioma, uma mensagem de erro é exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com botão direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;
  • Ao criar um novo projeto a tela de trabalho não é exibida ou é exibida uma tela preta. Vá nas opções gerais e altere o renderizador para "Device Context". Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.

Linux

A instalação no sistema Linux é facilmente realizado pelo pacote de instalação automático .deb.

Atenção!

Note que essa versão para Linux está defasada e algumas funcionalidades do programa podem não estar presentes.

Caso queira contribuir com o projeto e construir a versão atual no sistema Linux baseado em Debian ou em outras distribuições entre em contato pelo GitHub ou Twitter.

Problemas recorrentes no Linux

Pode ser necessário adicionar o diretório das bibliotecas do wxWidgets nas variáveis de ambiente. Para isso, siga UM dos métodos apresentados abaixo:

Método I (recomendado)

Insira o seguinte comando no arquivo ~/.bashrc:

echo "export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib" >> ~/.bashrc

Método II (não recomendado)

Cuidado!

Utilizando esse método os passos abaixo devem ser executados todas as vezes que você quiser abrir o PSP-UFU.

  1. Abra o terminal e acesse o diretório onde está instalado o PSP-UFU:
cd /usr/local/bin
  1. Insira as bibliotecas compartilhadas do wxWidgets nas variáveis de ambiente:
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib
  1. Então, execute o PSP-UFU na mesma seção do terminal:
./PSP-UFU
Atenção!

Verifique se o computador possui as unidades de vídeo instaladas corretamente, caso contrário, o programa não exibirá a área de trabalho para criar e editar diagramas de linha única ou diagramas de blocos de controle.

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Entrada / Saída

As entradas e saída são variáveis relacionadas às máquinas síncronas. Cada tipo de entrada e saída está relacionada a um regulador da máquina: Regulador de Tensão (AVR, do inglês Automatic Voltage Regulator) e Regulador de Velocidade (RV).

Cuidado!

O sistema de controle deve ter ao menos uma entrada e uma saída.

As entradas e saídas do sistema de controle são definidas por esses blocos, os quais são distintos para cada tipo de escopo. A figura abaixo apresenta um exemplo de um formulário de edição das entradas e saídas de um AVR:

Formulário de edição de entradas e saídas de sistemas de controle de um AVR

Variáveis de entrada e saída

O usuário deve sinalizar o tipo de bloco entre entrada e saída e, então, selecionar em uma lista a variável desejada. As seguintes variáveis de controle estão atualmente disponíveis no programa:

  • Tensão terminal (entrada: AVR): Módulo da tensão no barramento da máquina síncrona, em p.u.p.u., variável no tempo. Essa variável é normalmente utilizada no cálculo do erro da tensão de referência do AVR;

  • Velocidade (entrada: AVR e RV): Velocidade da máquina síncrona, em rad/s, variável no tempo. Normalmente utilizada no cálculo do erro de velocidade nos reguladores de velocidade, além de entrada do PSS em AVRs;

  • Potência ativa e reativa (entrada: AVR): Potência ativa fornecida pela máquina síncrona, em p.u.p.u., variável no tempo. Normalmente utilizada como entrada do PSS (potência ativa) e controle de sub e sobrecorrente de excitação nos AVRs;

  • Tensão terminal inicial (entrada: AVR): Módulo da tensão no barramento da máquina síncrona prévia ao estudo dinâmico originado do fluxo de carga, em p.u.p.u., fixo no tempo. Essa variável está normalmente associada à referência de tensão do AVR;

  • Velocidade inicial (entrada: AVR e RV): Velocidade do sistema (2πf_ref), definida nas opções de simulação, em rad/s, fixa no tempo. Normalmente utiliza-se essa variável como referência de velocidade em RVs e normalização da velocidade;

  • Potência mecânica inicial (entrada: RV): Potência mecânica inicial, calculada após a inicialização das máquinas síncronas com os dados originados do fluxo de carga, em p.u.p.u., fixa no tempo. Normalmente é utilizada como referência de potência mecânica nos reguladores de velocidade;

  • Variação de velocidade e potência ativa (entrada: AVR): Cálculo da variação dessas entradas entre os passos de integração normalizada pelo passo de integração, conforme a equação:

    Δx=xn−xn−1h\Delta x = \frac{x_n-x_{n-1}}{h}

    Em que:

    • Δx\Delta x é a variação da entrada (velocidade ou potência ativa);
    • xnx_n e xn−1x_{n-1} é a variável no passo atual e anterior, respectivamente;
    • hh é o passo de integração.
    Nota

    A normalização é necessária para a correta utilização da razão de passo de controle, definida nas configurações de simulação.

  • Tensão de campo (saída: AVR): Define a tensão aplicada ao campo na máquina síncrona, em p.u.p.u. Utilizada como saída dos AVRs, controlando principalmente tensão no barramento conectado e/ou fator de potência da máquina;

  • Potência mecânica (saída: RV): Define qual a potência mecânica aplicada no eixo da máquina síncrona. Utilizada como saída dos reguladores de velocidade, controlando principalmente a potência ativa injetada pela máquina e sua frequência.

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Entrada / Saída

As entradas e saída são variáveis relacionadas às máquinas síncronas. Cada tipo de entrada e saída está relacionada a um regulador da máquina: Regulador de Tensão (AVR, do inglês Automatic Voltage Regulator) e Regulador de Velocidade (RV).

Cuidado!

O sistema de controle deve ter ao menos uma entrada e uma saída.

As entradas e saídas do sistema de controle são definidas por esses blocos, os quais são distintos para cada tipo de escopo. A figura abaixo apresenta um exemplo de um formulário de edição das entradas e saídas de um AVR:

Formulário de edição de entradas e saídas de sistemas de controle de um AVR

Variáveis de entrada e saída

O usuário deve sinalizar o tipo de bloco entre entrada e saída e, então, selecionar em uma lista a variável desejada. As seguintes variáveis de controle estão atualmente disponíveis no programa:

  • Tensão terminal (entrada: AVR): Módulo da tensão no barramento da máquina síncrona, em p.u.p.u., variável no tempo. Essa variável é normalmente utilizada no cálculo do erro da tensão de referência do AVR;

  • Velocidade (entrada: AVR e RV): Velocidade da máquina síncrona, em rad/s, variável no tempo. Normalmente utilizada no cálculo do erro de velocidade nos reguladores de velocidade, além de entrada do PSS em AVRs;

  • Potência ativa e reativa (entrada: AVR): Potência ativa fornecida pela máquina síncrona, em p.u.p.u., variável no tempo. Normalmente utilizada como entrada do PSS (potência ativa) e controle de sub e sobrecorrente de excitação nos AVRs;

  • Tensão terminal inicial (entrada: AVR): Módulo da tensão no barramento da máquina síncrona prévia ao estudo dinâmico originado do fluxo de carga, em p.u.p.u., fixo no tempo. Essa variável está normalmente associada à referência de tensão do AVR;

  • Velocidade inicial (entrada: AVR e RV): Velocidade do sistema (2πfref2 \pi f_{ref}), definida nas opções de simulação, em rad/s, fixa no tempo. Normalmente utiliza-se essa variável como referência de velocidade em RVs e normalização da velocidade;

  • Potência mecânica inicial (entrada: RV): Potência mecânica inicial, calculada após a inicialização das máquinas síncronas com os dados originados do fluxo de carga, em p.u.p.u., fixa no tempo. Normalmente é utilizada como referência de potência mecânica nos reguladores de velocidade;

  • Variação de velocidade e potência ativa (entrada: AVR): Cálculo da variação dessas entradas entre os passos de integração normalizada pelo passo de integração, conforme a equação:

    Δx=xn−xn−1h\Delta x = \frac{x_n-x_{n-1}}{h}

    Em que:

    • Δx\Delta x é a variação da entrada (velocidade ou potência ativa);
    • xnx_n e xn−1x_{n-1} é a variável no passo atual e anterior, respectivamente;
    • hh é o passo de integração.
    Nota

    A normalização é necessária para a correta utilização da razão de passo de controle, definida nas configurações de simulação.

  • Tensão de campo (saída: AVR): Define a tensão aplicada ao campo na máquina síncrona, em p.u.p.u. Utilizada como saída dos AVRs, controlando principalmente tensão no barramento conectado e/ou fator de potência da máquina;

  • Potência mecânica (saída: RV): Define qual a potência mecânica aplicada no eixo da máquina síncrona. Utilizada como saída dos reguladores de velocidade, controlando principalmente a potência ativa injetada pela máquina e sua frequência.

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Limitador absoluto

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Limitador absoluto

Os blocos de limite absoluto cumprem a função de restringir os valores de entrada de acordo com os limites máximos e mínimos inseridos pelo usuário. Caso a entrada ultrapasse algum dos limites impostos, a saída será igual a esse valor limite até que a entrada retorne para a faixa permitida.

As restrições máximas e mínimas de valores dos sistemas de controle são modeladas utilizando um Limitador, cuja implementação é bastante simples e segue a seguinte expressão:

yn={Lsup,se un>Lsupun,se Linf≤un≤LsupLinf,se un<Linfy_n = \begin{cases} L_{sup}{,} & \text{se } u_n > L_{sup} \\ u_n{,} & \text{se } L_{inf} \le u_n \le L_{sup}\\ L_{inf}{,} & \text{se } u_n < L_{inf} \end{cases}

Em que:

  • yny_n Éé o valor de saída atual do bloco
  • LsupL_{sup} e LinfL_{inf} são os limites superior e inferior, respectivamente
  • unu_n é o valor de entrada atual do bloco

Formulário de edição do bloco Limitador

A figura abaixo apresenta o formulário de edição de dados do bloco limitador.

Formulário de edição de dados do bloco limitador no PSP-UFU

Esse bloco não linear é definido pelo limite superior e inferior, inseridos pelo usuário.

Informação

Tais blocos são bastante encontrados nos sistemas de controle para limitar a atuação do controlador, além de representar limites físicos de modelos implementados, como, por exemplo, valores máximos de corrente de excitação ou potência mecânica fornecida pelas turbinas.

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Linha

Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. tradução livre - IEC 60050.

Linha no PSP-UFU

As linhas no PSP-UFU são modelos π\pi equilibradas. Podem ser utilizadas como linhas de transmissão e distribuição de sistemas elétricos de potência.

A figura abaixo mostra o modelo π\pi implementado no PSP-UFU:

Modelo PI da linha

Em que:

  • rL\bold{r_L} é a resistência da linha;
  • xL\bold{x_L} é a reatância indutiva da linha;
  • bLd\bold{b_{L}^{d}} é a susceptância capacitiva shunt da linha.
Atenção

O modelo utilizado no PSP-UFU é equilibrado e não possui impedâncias mútuas entre as fases.

A linha pode ser inseridas com pontos de ancoragem, ou "nós", para maior personalização gráfica do elemento, como apresentado nas Ferramentas CAD.

Cuidado!

A linha deve ser inserida entre duas barras de mesma tensão nominal. Caso você tente inseri-la entre barras de tensão diferentes, uma mensagem de erro será exibida.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

Formulário de edição das linhas

A imagem abaixo apresenta o formulário de inserção/alteração de dados das linhas de transmissão:

Formulário das linhas no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais da linha e informações do fluxo de carga;
  • Falta: local onde as impedâncias de sequência zero são inseridas.
Nota

Os parâmetros necessários para construção da linha segundo seu modelo π\pi são inseridos na aba Geral, utilizados para construção da matriz admitância de sequência positiva e negativa.

Dados adicionais de impedâncias de sequência zero necessário para o cálculo de curtos-circuitos desbalanceados são editados na aba Falta, utilizados na construção da matriz admitância de sequência zero.

Além desses dois contextos, pode ser observado o botão "Estabilidade" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da linha durante o estudo de estabilidade.

Formulário de chaveamento da linha

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Campo de informação não editável que apresenta a tensão nominal da linha. Para alterar esse campo é necessário editar o campo correspondente do barramento conectado.

Potência nominal

Potência nominal da linha, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Parâmetros do modelo π\pi

Resistência (rLr_L), Reatância indutiva (xLx_L) série e Susceptância capacitiva shunt total (2bLd2b_{L}^{d}) presentes no modelo π\pi da linha.

Esses parâmetros são inseridos em p.u.p.u., Ω\Omega ou Ω/km\Omega/km (SS ou S/kmS/km para bLdb_{L}^{d}).

Comprimento da linha

Utilizado para calcular o valor dos parâmetros da linha inseridos em Ω/km\Omega/km (ou S/kmS/km).

Informação

O comprimento da linha é ignorado caso não sejam utilizadas as unidades por quilometro.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal da linha como base para a conversão das unidades, caso contrário será usada a potência base do sistema.

Falta

Parâmetros do modelo π\pi de sequência zero

Esses parâmetros são necessários para o correto cálculo das correntes de falta desbalanceadas (fase-fase, fase-fase-terra e fase-terra) e devem ser inseridos em p.u.p.u.

Cuidado!

A não inserção desses dados acarretarão em resultados incorretos para faltas desbalanceadas.

Botão Estabilidade

O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção da linha durante o estudo de estabilidade.

Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.

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Linha

Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. tradução livre - IEC 60050.

Linha no PSP-UFU

As linhas no PSP-UFU são modelos π\pi equilibradas. Podem ser utilizadas como linhas de transmissão e distribuição de sistemas elétricos de potência.

A figura abaixo mostra o modelo π\pi implementado no PSP-UFU:

Modelo PI da linha

Em que:

  • rL\bold{r_L} é a resistência da linha;
  • xL\bold{x_L} é a reatância indutiva da linha;
  • bLd\bold{b_{L}^{d}} é a susceptância capacitiva shunt da linha.
Atenção

O modelo utilizado no PSP-UFU é equilibrado e não possui impedâncias mútuas entre as fases.

A linha pode ser inseridas com pontos de ancoragem, ou "nós", para maior personalização gráfica do elemento, como apresentado nas Ferramentas CAD.

Cuidado!

A linha deve ser inserida entre duas barras de mesma tensão nominal. Caso você tente inseri-la entre barras de tensão diferentes, uma mensagem de erro será exibida.

Dica

Um arranjo série de uma linha sem as susceptâncias shunt, um barramento e um capacitor pode ser utilizado para fabricar um filtro passivo nos estudos harmônicos. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.

Formulário de edição das linhas

A imagem abaixo apresenta o formulário de inserção/alteração de dados das linhas de transmissão:

Formulário das linhas no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais da linha e informações do fluxo de carga;
  • Falta: local onde as impedâncias de sequência zero são inseridas.
Nota

Os parâmetros necessários para construção da linha segundo seu modelo π\pi são inseridos na aba Geral, utilizados para construção da matriz admitância de sequência positiva e negativa.

Dados adicionais de impedâncias de sequência zero necessário para o cálculo de curtos-circuitos desbalanceados são editados na aba Falta, utilizados na construção da matriz admitância de sequência zero.

Além desses dois contextos, pode ser observado o botão "Estabilidade" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da linha durante o estudo de estabilidade.

Formulário de chaveamento da linha

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Campo de informação não editável que apresenta a tensão nominal da linha. Para alterar esse campo é necessário editar o campo correspondente do barramento conectado.

Potência nominal

Potência nominal da linha, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Parâmetros do modelo π\pi

Resistência (rLr_L), Reatância indutiva (xLx_L) série e Susceptância capacitiva shunt total (2bLd2b_{L}^{d}) presentes no modelo π\pi da linha.

Esses parâmetros são inseridos em p.u.p.u., Ω\Omega ou Ω/km\Omega/km (SS ou S/kmS/km para bLdb_{L}^{d}).

Comprimento da linha

Utilizado para calcular o valor dos parâmetros da linha inseridos em Ω/km\Omega/km (ou S/kmS/km).

Informação

O comprimento da linha é ignorado caso não sejam utilizadas as unidades por quilometro.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal da linha como base para a conversão das unidades, caso contrário será usada a potência base do sistema.

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Carga

  1. a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;
  2. a potência demandada por um grupo de consumidores classificados de acordo com suas particularidades e características, por exemplo, carga de aquecimento, carga reativa diurna, etc. tradução livre - IEC 60050.

Carga no PSP-UFU

As cargas são os elementos de potência consumidores de potência genéricos. Nos estudos de fluxo de carga é possível modelar a carga como potência ou impedância constante e em estabilidade pode-se compor a carga na proporção desejada em três tipos (carga ZIP): potência constante, impedância constante e corrente constante.

As cargas de potência constante nos estudos de fluxo de carga são inseridos no vetor de potências e permanecem fixos durante toda a simulação.

Os elementos shunt, como reatores, banco de capacitores e cargas de impedância constante, são representados simplesmente por suas admitâncias em derivação. Como os parâmetros de entrada geralmente se constituem de suas potências ativa (P) e reativa (Q) nominais (no caso de reatores e capacitores, P=0), deve-se, portanto, encontrar sua admitância com a equação abaixo para inseri-la na matriz admitância:

y‾=P−jQV˙2\overline{y} = \frac{P-jQ}{\dot{V}^2}
Atenção!

Para os estudos de curto-circuito e harmônicos as cargas são modeladas como impedância constante, independentemente da sinalização indicada em seu formulário de edição de dados.

Carga no estudo de estabilidade

A modelagem das cargas do sistema de forma exata se torna impraticável em um problemas de estabilidade, visto à grande quantidade e variedade dos componentes envolvidos, além de apresentar modificações em suas composições causado por vários fatores, como tempo, condições climáticas e economia. Portanto várias aproximações devem ser utilizadas na formulação de um modelo de carga nos estudos aqui postos.

Uma forma interessante de se representar cargas dependentes da tensão são as cargas ZIP, as quais são funções quadráticas, possuindo três parcelas: impedância constante (Z), corrente constante (I) e potência constante (P). As potências ativa e reativa são obtidas pelas seguintes equações:

PL=PZ0(ViVi0)2+PI0(ViVi0)+PP0P_L=P_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+P_{I0} \left(\frac{V_i}{V_i0} \right)+P_{P0}
QL=QZ0(ViVi0)2+QI0(ViVi0)+QP0Q_L=Q_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+Q_{I0} \left(\frac{V_i}{V_i0} \right)+Q_{P0}

Em que:

PLP_L e QLQ_L são as potências ativa e reativa da carga ZIP, respectivamente, conectadas em uma barra genérica i;

ViV_i é a tensão atual de uma barra genérica i;

Vi0V_{i0} é a tensão inicial de uma barra genérica i, obtida do estudo de fluxo de carga;

PZ0P_{Z0} e QZ0Q_{Z0} são as parcelas de impedância constante para potências ativa e reativa, respectivamente;

PI0P_{I0} e QI0Q_{I0} são as parcelas de corrente constante para potências ativa e reativa, respectivamente;

PP0P_{P0} e QP0Q_{P0} são as parcelas de potência constante para potências ativa e reativa, respectivamente.

Os valores das parcelas de potência da carga ZIP são obtidos utilizando as potências da carga após a convergência do cálculo do fluxo de carga (PL0P_{L0}, para a potência ativa e QL0Q_{L0}, para a potência reativa), utilizando as seguintes expressões:

{PZ0=kPZ100PL0Vi02PI0=kPI100PL0Vi0PP0=kPP100PL0\begin{cases} P_{Z0}=\displaystyle \frac{k_{PZ}}{100} \frac{P_{L0}}{V_{i0}^2}\\ P_{I0}=\displaystyle \frac{k_{PI}}{100} \frac{P_{L0}}{V_{i0}}\\ P_{P0}=\displaystyle \frac{k_{PP}}{100} P_{L0} \end{cases}

Os valores de kPZk_{PZ}, kPIk_{PI} e kPPk_{PP} representam a composição em impedância, corrente e potência constantes, respectivamente, da parcela ativa da carga, os quais são inseridos pelo usuário na forma de porcentagem, sendo a soma desses três valores necessariamente igual a 100%. Os parâmetros kQZk_{QZ}, kQIk_{QI} e kQPk_{QP} podem ser interpretados de forma análoga, porém compõe a parcela reativa da carga.

O comportamento das potências, retiradas de simulações no PSP-UFU, de cada parcela que compõe a carga ZIP são evidenciadas na figura abaixo.

Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente

Cargas de corrente e potência constantes possuem problemas em tensões muito baixas. À medida que a tensão diminui as correntes dessas cargas não reduz, como pode ser observado na figura acima, resultando em perda de precisão e problemas na convergência de processos iterativos. Para contornar esse problema utiliza-se uma tensão pré-definida pelo usuário (VlowV_{low}), a qual as cargas (ou parcelas) de corrente e potência constantes são modeladas como impedância constante, resultando no comportamento de potência e corrente apresentados na figura acima.

Formulário de edição das cargas

A imagem abaixo apresenta o formulário de inserção/alteração de dados das cargas:

Formulário das cargas no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais das cargas, informações e o tipo de carga no fluxo de carga;
  • Estabilidade: contendo opções de visualização de dados da carga em gráficos no tempo e opções de parametrização da carga ZIP.

Além desses dois contextos, pode ser observado o botão "Chaveamento" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da carga durante o estudo de estabilidade.

Formulário de chaveamento da carga

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência ativa

Parcela de potência ativa da carga. Pode ser inserido em MW, kW W ou p.u.p.u. (na base do sistema).

Potência reativa

Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou p.u.p.u. (na base do sistema).

Tipo de carga (fluxo de carga)

Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Potência constante e Impedância constante. As cargas de potência constantes são inseridas nos vetores de potência e permanecem invariantes no cálculo, enquanto que para as cargas de impedância constante determina-se o valor da impedância utilizando a potência e tensão nominal, a qual é inserida na matriz admitância.

Estabilidade

Imprimir dados

Exibe os dados da carga nos gráficos no tempo. -Os seguintes dados são exibidos:

  • módulo da tensão
  • corrente
  • potências ativa e reativa.

Utilizar composição de carga ZIP

Permite compor a carga ZIP para estudos de estabilidade. Caso essa opção não esteja selecionada é usada a composição global definida nas configurações de simulação.

Atenção

Por padrão, todas as cargas no PSP-UFU são definidas como impedância constante no estudo de estabilidade.

Dica

Caso todas as barras possuírem o mesmo comportamento de carga ZIP, a parametrização poderá ser realizada nas configurações de simulação para todas as cargas, sem a necessidade de parametrização individual.

Composição de potência ativa e reativa

Valores da composição da carga ZIP, inseridas para potência ativa e reativa separadamente, em porcentagem. A soma da composição deve ser igual a 100%, caso contrário será exibida uma mensagem de erro ao usuário.

Botão Chaveamento

O botão "Chaveamento" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de estabilidade.

Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.

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Carga

  1. a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;
  2. a potência demandada por um grupo de consumidores classificados de acordo com suas particularidades e características, por exemplo, carga de aquecimento, carga reativa diurna, etc. tradução livre - IEC 60050.

Carga no PSP-UFU

As cargas são os elementos de potência consumidores de potência genéricos. Nos estudos de fluxo de carga é possível modelar a carga como potência ou impedância constante e em estabilidade pode-se compor a carga na proporção desejada em três tipos (carga ZIP): potência constante, impedância constante e corrente constante.

As cargas de potência constante nos estudos de fluxo de carga são inseridos no vetor de potências e permanecem fixos durante toda a simulação.

Os elementos shunt, como reatores, banco de capacitores e cargas de impedância constante, são representados simplesmente por suas admitâncias em derivação. Como os parâmetros de entrada geralmente se constituem de suas potências ativa (P) e reativa (Q) nominais (no caso de reatores e capacitores, P=0), deve-se, portanto, encontrar sua admitância com a equação abaixo para inseri-la na matriz admitância:

y‾=P−jQV˙2\overline{y} = \frac{P-jQ}{\dot{V}^2}
Atenção!

Para os estudos de curto-circuito e harmônicos as cargas são modeladas como impedância constante, independentemente da sinalização indicada em seu formulário de edição de dados.

Carga no estudo de estabilidade

A modelagem das cargas do sistema de forma exata se torna impraticável em um problemas de estabilidade, visto à grande quantidade e variedade dos componentes envolvidos, além de apresentar modificações em suas composições causado por vários fatores, como tempo, condições climáticas e economia. Portanto várias aproximações devem ser utilizadas na formulação de um modelo de carga nos estudos aqui postos.

Uma forma interessante de se representar cargas dependentes da tensão são as cargas ZIP, as quais são funções quadráticas, possuindo três parcelas: impedância constante (Z), corrente constante (I) e potência constante (P). As potências ativa e reativa são obtidas pelas seguintes equações:

PL=PZ0(ViVi0)2+PI0(ViVi0)+PP0P_L=P_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+P_{I0} \left(\frac{V_i}{V_i0} \right)+P_{P0}
QL=QZ0(ViVi0)2+QI0(ViVi0)+QP0Q_L=Q_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+Q_{I0} \left(\frac{V_i}{V_i0} \right)+Q_{P0}

Em que:

PLP_L e QLQ_L são as potências ativa e reativa da carga ZIP, respectivamente, conectadas em uma barra genérica i;

ViV_i é a tensão atual de uma barra genérica i;

Vi0V_{i0} é a tensão inicial de uma barra genérica i, obtida do estudo de fluxo de carga;

PZ0P_{Z0} e QZ0Q_{Z0} são as parcelas de impedância constante para potências ativa e reativa, respectivamente;

PI0P_{I0} e QI0Q_{I0} são as parcelas de corrente constante para potências ativa e reativa, respectivamente;

PP0P_{P0} e QP0Q_{P0} são as parcelas de potência constante para potências ativa e reativa, respectivamente.

Os valores das parcelas de potência da carga ZIP são obtidos utilizando as potências da carga após a convergência do cálculo do fluxo de carga (PL0P_{L0}, para a potência ativa e QL0Q_{L0}, para a potência reativa), utilizando as seguintes expressões:

{PZ0=kPZ100PL0Vi02PI0=kPI100PL0Vi0PP0=kPP100PL0\begin{cases} P_{Z0}=\displaystyle \frac{k_{PZ}}{100} \frac{P_{L0}}{V_{i0}^2}\\ P_{I0}=\displaystyle \frac{k_{PI}}{100} \frac{P_{L0}}{V_{i0}}\\ P_{P0}=\displaystyle \frac{k_{PP}}{100} P_{L0} \end{cases}

Os valores de kPZk_{PZ}, kPIk_{PI} e kPPk_{PP} representam a composição em impedância, corrente e potência constantes, respectivamente, da parcela ativa da carga, os quais são inseridos pelo usuário na forma de porcentagem, sendo a soma desses três valores necessariamente igual a 100%. Os parâmetros kQZk_{QZ}, kQIk_{QI} e kQPk_{QP} podem ser interpretados de forma análoga, porém compõe a parcela reativa da carga.

O comportamento das potências, retiradas de simulações no PSP-UFU, de cada parcela que compõe a carga ZIP são evidenciadas na figura abaixo.

Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente

Cargas de corrente e potência constantes possuem problemas em tensões muito baixas. À medida que a tensão diminui as correntes dessas cargas não reduz, como pode ser observado na figura acima, resultando em perda de precisão e problemas na convergência de processos iterativos. Para contornar esse problema utiliza-se uma tensão pré-definida pelo usuário (VlowV_{low}), a qual as cargas (ou parcelas) de corrente e potência constantes são modeladas como impedância constante, resultando no comportamento de potência e corrente apresentados na figura acima.

Formulário de edição das cargas

A imagem abaixo apresenta o formulário de inserção/alteração de dados das cargas:

Formulário das cargas no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais das cargas, informações e o tipo de carga no fluxo de carga;
  • Estabilidade: contendo opções de visualização de dados da carga em gráficos no tempo e opções de parametrização da carga ZIP.

Além desses dois contextos, pode ser observado o botão "Chaveamento" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da carga durante o estudo de estabilidade.

Formulário de chaveamento da carga

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência ativa

Parcela de potência ativa da carga. Pode ser inserido em MW, kW W ou p.u.p.u. (na base do sistema).

Potência reativa

Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou p.u.p.u. (na base do sistema).

Tipo de carga (fluxo de carga)

Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Potência constante e Impedância constante. As cargas de potência constantes são inseridas nos vetores de potência e permanecem invariantes no cálculo, enquanto que para as cargas de impedância constante determina-se o valor da impedância utilizando a potência e tensão nominal, a qual é inserida na matriz admitância.

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Tela Principal

Organização da tela principal

A tela principal do PSP-UFU é dividida em três seções: Menu "Ribbon", Área de Trabalho e Barra de Status.

Tela principal

Resumidamente, no Menu Ribbon são acessadas as ferramentas do PSP-UFU; na Área de Trabalho são criados os diagramas unifilares de potência; e na Barra de Status são exibidas importantes informações acerca do estado da Área de Trabalho.

Menu Ribbon

Em informática o ribbon (faixa, em inglês) é um formato de apresentação de interface baseada na GUI onde a barra de ferramentas é mostrada através de uma barra mais larga com icones maiores possibilitando o uso dos aplicativos por dispositivos touch screen. +

Tela Principal

Organização da tela principal

A tela principal do PSP-UFU é dividida em três seções: Menu "Ribbon", Área de Trabalho e Barra de Status.

Tela principal

Resumidamente, no Menu Ribbon são acessadas as ferramentas do PSP-UFU; na Área de Trabalho são criados os diagramas unifilares de potência; e na Barra de Status são exibidas importantes informações acerca do estado da Área de Trabalho.

Menu Ribbon

Em informática o ribbon (faixa, em inglês) é um formato de apresentação de interface baseada na GUI onde a barra de ferramentas é mostrada através de uma barra mais larga com icones maiores possibilitando o uso dos aplicativos por dispositivos touch screen. Wikipedia

O menu Ribbon é composto de três submenus: “Arquivo”, “Ferramentas” e “Simulação”.

Menu Arquivo

Em Arquivo estão as ferramentas gerais do programa, as quais permitem ao usuário criar e salvar novos projetos, além daquelas que possibilitam carregar os projetos já existentes e importar arquivos de outros programas. Esse submenu também possui opções gerais do programa e acesso a informações sobre o programa.

Menu Ferramentas

Em Ferramentas estão presentes os itens específicos, os quais estão relacionados à criação e manipulação da rede elétrica de potência, relatórios tabulares de saída de dados e acesso ao formulário de criação de gráficos no tempo. Algumas configurações específicas do projeto ativo são acessadas por esse menu.

Menu Simulação

Finalmente, o submenu Simulação proporciona o acesso do usuário aos cálculos realizados pelo software e suas configurações, além da ferramenta de “solução contínua”, a qual resolve os cálculos estáticos (fluxo de potência, curto-circuito e harmônicos) após quaisquer mudanças na rede de potência, como remoção de componente ou alteração de seus dados. Todas as configurações de simulação do projeto ativo são acessadas por esse menu.

Área de Trabalho

Na área de trabalho estão presentes os projetos em execução, os quais são divididos por abas identificadas pelo nome do projeto (caso já esteja gravado no disco). É nessa área que são inseridos e excluídos os elementos elétricos, cujas ferramentas são acessadas por meio do Menu Ribbon.

As edições gráficas dos elementos, como posição, conexão e tamanho dos barramentos, são realizadas por meio da ação drag-and-drop (arrastar e soltar) com a utilização do mouse. A edição dos dados elétricos é feita por meio de formulários de dados acessados clicando duas vezes sobre os elementos.

Área de Trabalho

Barra de Status

A barra de status é responsável por informações interessantes sobre as circunstâncias atuais do programa: modo de operação do mouse (editar, mover, arrastar), zoom aplicado e posição do mouse na área de trabalho, além de dados sobre as ações dos usuários, como: inserção de elementos, informação sobre copiar e colar, etc.

Dica

Sempre fique atendo à barra de status, pois são fornecidas informações importantes acerca da operação do programa. Caso tenha alguma dúvida siga as instruções apresentadas nesse componente.

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Expressão Matemática

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Expressão Matemática

O bloco de expressão matemática utiliza a biblioteca externa fparser e permite ao usuário inserir expressões matemáticas genéricas de qualquer complexidade combinadas a estruturas condicionais em um diagrama de controle, aumentando significativamente a capacidade de generalização do programa.

Sintaxe das expressões matemáticas

As sintaxes das operações (para expressões A e B) são apresentadas na tabela abaixo:

OperadorExpressão
( )Expressão em parênteses primeiro
A unitUm multiplicador de unidade (se um estiver sido adicionado)
A^BExponenciação (A elevado à potência B)
-AOperação unária de oposto
!AOperação lógica unária de negação (resulta em 11 se int(A) é 00, senão 00)
A*B A/B A%BMultiplicação, divisão e módulo
A+B A-BAdição e subtração
A=B A<B A<=B A!=B A>B A>=BComparação entre A e B (resulta em 11 ou 00)
A&BResulta em 11 se int(A) e int(B) forem diferentes de 00, senão 00
A|BResulta em 11 se int(A) ou int(B) forem diferentes de 00, senão 00

As funções matemáticas suportadas pela biblioteca, as quais podem ser utilizadas na construção de diagrama de blocos, são descritas na tabela abaixo:

ExpressãoDescrição
abs(A)Valor absoluto de A. Para números reais, se A é negativo, retorna –A, senão retorna A. Para números complexos a expressão é equivalente a hypot(real(x),imag(x)).
acos(A)Arco cosseno de A. Retorna o ângulo em radianos.
acosh(A)O mesmo que acos() mas para cosseno hiperbólico
arg(A)Ângulo de fase de um número complexo A.
asin(A)Arco seno de A. Retorna o ângulo em radianos.
asinh(A)Mesmo que asin(), mas para seno hiperbólico
atan(A)Arco tangente de A. Retorna o ângulo em radianos.
atan2(A,B)Arco tangente de A/B, a qual os sinais dos dois argumentos para determinar o quadrante do resultado. Retorna a solução de do seguinte sistema: hypot(A,B)*sin(x)=A, hypot(A,B)*cos(x)=B. O valor retornado varia de −π-\pi a π\pi.
atanh(A)Mesmo que atan(), mas para tangente hiperbólica.
cbrt(A)Raiz cúbica de A.
conj(A)Conjugado complexo de A.
ceil(A)Teto de A. Arredonda para o próximo maior inteiro.
cos(A)Cosseno de A. Retorna o ângulo em radianos.
cosh(A)Mesmo que cos(), mas para cosseno hiperbólico
cot(A)Cotangente de A. Retorna o ângulo em radianos.
csc(A)Cossecante de A. Retorna o ângulo em radianos.
exp(A)Exponencial de A. Retorna o valor de e elevado a potência A.
exp2(A)Exponencial de A na base 22.
floor(A)Piso de A. Arredonda para o próximo menor inteiro.
hypot(A,B)Função de distância Euclidiana.
if(A,B,C)Se int(A) é diferente de 00, retorna o valor de B, senão retorna C.
imag(A)Retorna a parte imaginária do número complexo A.
int(A)Arredonda A para o inteiro mais próximo.
log(A)Logaritmo natural (base ee) de A.
log2(A)Logaritmo na base 22 de A.
log10(A)Logaritmo na base 1010 de A.
max(A,B)Se A>B, o resultado é A, senão é B.
min(A,B)Se A<B, o resultado é A, senão é B.
polar(A,B)Retorna o número complexo de magnitude A e ângulo de fase B (em radianos).
pow(A,B)Exponenciação (A elevado à potência B)
real(A,B)Retorna a parte real do número complexo A.
sec(A)Secante de A.
sin(A)Seno de A. Retorna o ângulo em radianos.
sinh(A)Mesmo que sin(), mas para seno hiperbólico.
sqrt(A)Raiz quadrada de A.
tan(A)Tangente de A. Retorna o ângulo em radianos.
tanh(A)Mesmo que tan(), mas para tangente hiperbólica.
trunc(A)Valor truncado de A. Retorna o número inteiro de A sem a parcela fracionada.

É possível atribuir novas variáveis utilizando a seguinte sintaxe:

<nome da variável> := <expressão>; <função>

Por exemplo:

comprimento := sqrt(x*x+y*y); 2*comprimento*sin(comprimento)
Dica

O caractere de espaço e de nova linha são ignorados na interpretação da expressão, portanto para maior organização, o código anterior pode ser escrito da seguinte forma:

comprimento := sqrt(x*x+y*y);
2*comprimento*sin(comprimento)
Cuidado!

Note que a expressão que determina o valor de saída do bloco não possui o caractere ; em seu final.

Formulário de edição de dados do bloco de Expressão Matemática

O formulário de inserção e edição das entradas do bloco e da expressão matemática genérica, assim como ferramentas de auxílio de sua construção é apresentado na figura abaixo.

Formulário de edição de dados do bloco de expressão matemática no PSP-UFU

No campo de “Variáveis de entrada” é inserida uma lista com os nomes das entradas separados por espaços. Um número qualquer de entrada pode ser definido nessa lista esses nomes são apresentados no ícone gráfico presente no editor de controle, além de serem destacados na expressão inserida pelo usuário. O número de entradas e saídas se comporta de forma semelhante aos blocos somadores.

Abaixo do campo das variáveis de entrada está presente o local para inserção da expressão matemática. A sintaxe da expressão inserida pelo usuário possui realce (por meio de diferentes formas e cores da fonte) para números, operadores, variáveis de entrada, funções e constantes, facilitando a criação, manipulação e identificação de erros de digitação e lógica.

Informação

Como ferramenta de auxílio ao usuário foi desenvolvida uma verificação da expressão inserida.

Tal ferramenta irá encontrar erros e indicará ao usuário qual o tipo do erro, além da sua localização, destacando-o. A figura anterior exemplifica a identificação automática do erro pelo PSP-UFU, assim como sua posição na expressão inserida.

Exemplo de Expressão Matemática

A corrente de campo em p.u.p.u. pode ser estimada de forma aproximada utilizando as potências ativa (PP) e reativa (QQ), assim como as reatâncias transitórias de eixo direto (xdx_d) e em quadratura (xqx_q) e o módulo da tensão terminal (VV) da máquina:

if≈(V+Q′)2+P2+(xdxq+1,0)×Q′(V+Q′)+P′2(V+Q′)2+P2i_f \approx \sqrt{ \left( V + Q' \right)^2 + P^2} + \left(\frac{x_d}{x_q} +1{,}0 \right) \times \frac{Q' \left( V + Q' \right) + {P'}^2}{\sqrt{\left( V + Q'\right)^2 + P^2}}

Em que:

  • P′=xq×PVP' = x_q \times \frac{P}{V}
  • Q′=xq×QVQ' = x_q \times \frac{Q}{V}

Primeiramente, deve-se inserir no campo "variáveis de entrada" as grandezas fornecidas pelo PSP-UFU. Nesse caso, como pode ser observado no bloco de entrada / saída, todas as variáveis necessárias são fornecidas: PP, QQ e VV. Essas variáveis devem ser inseridas separadas por espaço: p q v.

Utilizando três blocos de entrada / saída pode-se fornecer tais dados ao conectá-los ao bloco de expressão matemática.

As reatâncias transitórias de eixo direto (xdx_d) e em quadratura (xqx_q) podem ser definidas diretamente na expressão matemática:

xd := 0.146;
xq := 0.0969;

Os valores de P′P' e Q′Q' podem ser também calculados:

yp := xq * p / v;
yq := xq * q / v;

Com todos os dados necessários pode-se calcular a corrente de campo:

i_f := sqrt((v + yq)^2 + p^2) + (xd / xq + 1.0) *
((yq * (v + yq) + yp^2) / sqrt((v + yq)^2 + p^2));

Finalmente, pode-se definir a saída do bloco (não inserindo ;):

i_f

Portanto, para as entradas definidas como p q v, a expressão matemática total para cálculo da corrente de campo será:

xd := 0.146;
xq := 0.0969;
yp := xq * p / v;
yq := xq * q / v;
i_f := sqrt((v + yq)^2 + p^2) + (xd / xq + 1.0) *
((yq * (v + yq) + yp^2) / sqrt((v + yq)^2 + p^2));
i_f

Referências

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Multiplicador

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Multiplicador

Esse elemento é bastante simples e cumpre com a função matemáticas de seu nome.

Possui duas entradas de valores reais e sua saída é computada na sequência do nó superior pelo inferior, ou seja, a saída será o valor presente no nó 1 multiplicado pelo nó 2.

Atenção!

Nós não conectados no multiplicador são assumidos com o valor unitário e para o divisor é considerado valor nulo.

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Editor de Potência

O Editor de Elementos de Potência no PSP-UFU permite a inserção, manipulação e edição de elementos elétricos de potência por meio de um diagrama unifilar.

(Diagrama unifilar) Um diagrama do sistema no qual as linhas polifásicas são representados por sua única linha equivalente. tradução livre - IEC 60050.

Informação

Todos os elementos inseridos pode ser manipulados e editados utilizando as Ferramentas CAD.

Novo projeto

A criação de um novo projeto é realizada clicando no item Novo projeto no submenu Arquivo. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do submenu Ferramentas ou pelas teclas de atalho.

Abaixo são apresentados os elementos elétricos de potência que podem ser inseridos no PSP-UFU:

Elementos de potência

Inserindo elementos

Por meio do submenu Ferramentas pode-se inserir os elementos de potência, como é apresentado na imagem abaixo.

Adicionar elementos de potência

No caso de inserção de um barramento, o usuário deve apenas clicar na posição desejada, já para os outros componentes será solicitado que o usuário selecione em uma ou duas barras, o qual o novo componente será conectado.

Sempre que são inseridos novos elementos, um formulário de dados é exibido e pode-se editar os dados elétricos e acessar formulários adicionais, como dados de estabilidade.

Atenção

O primeiro elemento que a ser inserido no projeto deve ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.

Além dos elementos de potência pode-se inserir os elementos de texto vinculado, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na Área de Trabalho.

Cuidado!

Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos deve-se clicar em uma mais barras para exibir o elemento inserido.

Sempre fique atento às instruções da Barra de Status.

Teclas de atalho

É possível inserir todos os elementos de potência por meio de teclas de atalho, facilitando e agilizando a criação dos diagramas unifilares no PSP-UFU. A tabela abaixo apresenta tais atalhos:

ElementoAtalhoElementoAtalho
BarramentoBCargaShift + L
LinhaLCapacitorShift + C
TransformadorTIndutorShift + I
GeradorGCorrente harmônicaShift + H
Motor de induçãoITextoA
Compensador síncronoK

Editando dados elétricos

Ao inserir um elemento, seu respectivo formulário de edição é exibido para inserção dos dados elétricos d elemento. Todos os dados podem ser alterados ao clicar duas vezes sobre o elemento ou por opção do menu de contexto exibido ao clicar com o botão direito sobre o elemento.

Cada formulário de edição de dados elétricos dos elementos possuem suas particularidades e são descritos em documentação específica: Barramento, Linha, Transformador, Carga, Capacitor, Indutor, Fonte de Corrente Harmônica, Gerador Síncrono, Compensador Síncrono, Motor de Indução.

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Editor de Potência

O Editor de Elementos de Potência no PSP-UFU permite a inserção, manipulação e edição de elementos elétricos de potência por meio de um diagrama unifilar.

(Diagrama unifilar) Um diagrama do sistema no qual as linhas polifásicas são representados por sua única linha equivalente. tradução livre - IEC 60050.

Informação

Todos os elementos inseridos pode ser manipulados e editados utilizando as Ferramentas CAD.

Novo projeto

A criação de um novo projeto é realizada clicando no item Novo projeto no submenu Arquivo. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do submenu Ferramentas ou pelas teclas de atalho.

Abaixo são apresentados os elementos elétricos de potência que podem ser inseridos no PSP-UFU:

Elementos de potência

Inserindo elementos

Por meio do submenu Ferramentas pode-se inserir os elementos de potência, como é apresentado na imagem abaixo.

Adicionar elementos de potência

No caso de inserção de um barramento, o usuário deve apenas clicar na posição desejada, já para os outros componentes será solicitado que o usuário selecione em uma ou duas barras, o qual o novo componente será conectado.

Sempre que são inseridos novos elementos, um formulário de dados é exibido e pode-se editar os dados elétricos e acessar formulários adicionais, como dados de estabilidade.

Atenção

O primeiro elemento que a ser inserido no projeto deve ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.

Além dos elementos de potência pode-se inserir os elementos de texto vinculado, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na Área de Trabalho.

Cuidado!

Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos deve-se clicar em uma mais barras para exibir o elemento inserido.

Sempre fique atento às instruções da Barra de Status.

Teclas de atalho

É possível inserir todos os elementos de potência por meio de teclas de atalho, facilitando e agilizando a criação dos diagramas unifilares no PSP-UFU. A tabela abaixo apresenta tais atalhos:

ElementoAtalhoElementoAtalho
BarramentoBCargaShift + L
LinhaLCapacitorShift + C
TransformadorTIndutorShift + I
GeradorGCorrente harmônicaShift + H
Motor de induçãoITextoA
Compensador síncronoK

Editando dados elétricos

Ao inserir um elemento, seu respectivo formulário de edição é exibido para inserção dos dados elétricos d elemento. Todos os dados podem ser alterados ao clicar duas vezes sobre o elemento ou por opção do menu de contexto exibido ao clicar com o botão direito sobre o elemento.

Cada formulário de edição de dados elétricos dos elementos possuem suas particularidades e são descritos em documentação específica: Barramento, Linha, Transformador, Carga, Capacitor, Indutor, Fonte de Corrente Harmônica, Gerador Síncrono, Compensador Síncrono, Motor de Indução.

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Fluxo de Potência

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Fluxo de Potência

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Limitador de taxa

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Limitador de taxa

Os blocos de limite de taxa têm como objetivo conter a taxa de crescimento ou decrescimento da sua entrada a valores inseridos pelo usuário. A taxa de variação é calculada a partir dos valores de entrada atual e passado e, caso seja violada, será definida uma saída que respeite essas taxas (de crescimento ou decrescimento).

A taxa (rr) é calculada de acordo com a equação:

r=un−yn−1hr = \frac{u_n - y_{n-1}}{h}

Em que:

  • unu_n é a entrada atual do bloco
  • yn−1y_{n-1} é o valor de saída anterior do bloco
  • hh é o passo de integração

Obtida a taxa, o bloco irá resultar em um valor calculado pelas seguintes condições:

{h×Rcre,se r>Rcreun,se Rdec≤r≤Rcreh×Rdec,se r<Rdec\begin{cases} h \times R_{cre}{,} & \text{se } r > R_{cre} \\ u_n{,} & \text{se } R_{dec} \le r \le R_{cre}\\ h \times R_{dec}{,} & \text{se } r < R_{dec} \end{cases}

Em que:

  • RcreR_{cre} e RdecR_{dec} são as taxas de crescimento e decaimento, respectivamente

Formulário de edição de dados do Limitador de taxa

A figura abaixo apresenta o formulário de edição de dados do bloco limitador de taxa.

Formulário de edição de dados do bloco limitador de taxa no PSP-UFU

Esse bloco é definido pelo limite superior (taxa de crescimento máxima) e inferior (taxa de decrescimento máxima), inseridos pelo usuário.

Informação

Esses blocos são úteis para limitar variações bruscas na entrada que possam comprometer o controle ou limites físicos de modelos de turbina, por exemplo.

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Configurações da Simulação

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Configurações da Simulação

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Estabilidade

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Estabilidade

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Somador

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Somador

Como o próprio nome sugere, os somadores são elementos de controle capazes de somar qualquer quantidade de valores reais.

Formulário de edição de dados do somador

A quantidade de entradas, assim como seus sinais são definidas pelo usuário, como mostra a figura abaixo.

Formulário de edição de dados do somador no PSP-UFU

No seu único campo “Sinais” é inserida uma lista de sinais separados por espaços contendo os símbolos “+” para uma entrada positiva e “-” para negativa.

Informação

O usuário pode inserir duas ou mais entradas de sinais no bloco.

Uma vez inseridas novas entradas, nós correspondentes serão incluídos no elemento gráfico do somador, o qual poderá ser conectado por meio das linhas de conexão.

De forma semelhante, o usuário poderá excluir entradas de sinais pré-existentes, as quais serão removidas no ícone gráfico pela remoção do nó e da linha (caso exista alguma conectada).

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Gerador Síncrono

Uma máquina de corrente alternada na qual a frequência das tensões geradas e a velocidade da máquina estão em uma proporção constante. tradução livre - IEC 60050.

Gerador Síncrono no PSP-UFU

Os geradores síncronos são a fonte de potência para o cálculo do fluxo de carga e estabilidade, além de serem um dos principais contribuintes para as correntes de falta.

Atenção!

Somente barramentos que possuem esse elemento conectado podem ser considerados barras de referência. Barras do tipo PV devem conter um gerador síncrono ou um motor síncrono (compensador síncrono).

O formulário de dados é dividido em dois, sendo o primeiro responsável pelos dados gerais, de fluxo de carga e de falta e um segundo pelos dados de estabilidade . Esse último também permite o acesso aos controles das máquinas síncronas manipulados pelo editor de controle.

Informação

Os dados referentes às impedâncias de sequência positiva do gerador síncrono inseridas no contexto (aba) "Falta" são utilizados tanto para os estudos de curto-circuito quanto para os estudos de harmônicos.

Esses dados são ignorados nos estudos de fluxo de carga (não são utilizado nesse estudo) e estabilidade (são utilizados dados inseridos em formulário específico).

Gerador Síncrono no fluxo de carga

O gerador síncrono é a fonte de potência do PSP-UFU no estudo de fluxo de carga. Seu comportamento difere de acordo com o tipo de barra conectada:

  • Barra de referência: Os dados de potência ativa e reativa inseridos são desprezados, uma vez que esse elemento será utilizado para completar o balanço de potência do estudo de fluxo d carga;
  • Barra PV: O dado de potência ativa é considerado, porém o dados de potência reativa são desprezados. O valor da potência reativa é utilizado para manter o módulo da tensão constante no barramento conectado;
  • Barra PQ: Para os geradores conectados a essa barra tanto a potência ativa quanto reativa inseridas são consideradas.
Atenção

Caso o limite de potência reativa seja excedido, o programa automaticamente transforma a Barra PV conectada em uma Barra PQ, utilizando o valor limite de potência reativa que seria ultrapassado.

Gerador Síncrono no estudo de curto-circuito

Enquanto os geradores no estudo de fluxo de carga são modelados somente por correntes injetadas nas barras, para o curto-circuito utiliza-se uma tensão atrás de uma impedância. A figura abaixo mostra o caminho da corrente e o circuito equivalente de cada sequência nos geradores.

Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero

As tensões geradas são somente de sequência positiva, uma vez que o gerador fornece sempre tensões trifásicas equilibradas. Portanto a rede de sequência positiva é composta de uma tensão pré-falta atrás de uma impedância de sequência positiva. As redes de sequência negativa e zero não contêm forças eletromotrizes, porém incluem as impedâncias do gerador de sequência negativa e zero.

A corrente que circula na impedância z‾n\overline{z}_n entre o neutro e a terra é 3I˙a03\dot{I}_{a0}. Pela figura acima (c), observa-se que a queda de tensão de sequência zero do ponto a para terra (V˙a0\dot{V}_{a0}) é:

V˙a0=−3I˙a0z‾n−I˙a0z‾g0\dot{V}_{a0} = -3\dot{I}_{a0}\overline{z}_n - \dot{I}_{a0}\overline{z}_{g0}

A rede de sequência zero, que é um circuito monofásico pelo qual se supõe que circule apenas corrente de sequência zero e deve, portanto, ter uma impedância definida pela seguinte equação:

z‾0=3z‾n+z‾g0\overline{z}_{0} = 3\overline{z}_n + \overline{z}_{g0}
Dica

Caso o gerador não seja aterrado, não circulará corrente de sequência zero por ele. Nesse caso, dependendo da conexão do transformador próximo ao gerador sem aterramento, a seguinte mensagem de erro pode ser exibida:

"Falha ao inverter a matriz admitância de sequência zero"

Isso ocorre porque a matriz admitância de sequência zero é singular. Para contornar esse problema escolha uma das duas soluções abaixo:

  1. Marque a opção "Neutro aterrado" e insira um alto valor de reatância de aterramento (j9999 p.u.j9999~p.u., por exemplo);
  2. Ou, na barra do gerador, insira um reator de baixo valor de potência reativa (1,0 var1,0~var, por exemplo).

Gerador Síncrono no estudo de estabilidade

A relação de valores observados em testes adequados (definidos na IEEE Std. 115-2019), denominados parâmetros padrões, são utilizados para modelar a máquina síncrona no estudo de estabilidade do PSP-UFU.

Os parâmetros da máquina síncrona que influenciam rapidamente no decaimento de valores são chamados subtransitórios (indicados por ′′''), aqueles que influenciam mais lentamente são chamados transitórios (indicados por ′') e, finalmente, aqueles que influenciam continuamente são chamados de parâmetros síncronos (sem indicação de sobrescrito).

Um conjunto de equações algébrico-diferenciais determinam o comportamento da máquina síncrona no estudo de estabilidade:

Eq′−Vq=raIq−xds′IdEd′−Vd=raId−xqs′IqEq′′−Vq=raIq−xds′′IdEd′′−Vd=raId−xqs′′Iq dEq′dt=Vfd+(xd−xd′)Id−sdEq′Td0′dEd′dt=−(xq−xq′)Iq−sqEd′Tq0′dEq′′dt=sdEq′+(xd′−xd′′)Id−sdEq′′Td0′′dEd′′dt=sdEd′+(xq′−xq′′)Iq−sdEd′′Tq0′′ dωdt=ωr2H[Pm−Pe−Da(ω−ωr)]dδdt=Ωb(ω−ωr)E_{q}' - V_q = r_aI_q - x_{ds}'Id\\ E_{d}' - V_d = r_aI_d - x_{qs}'Iq\\ E_{q}'' - V_q = r_aI_q - x_{ds}''Id\\ E_{d}'' - V_d = r_aI_d - x_{qs}''Iq\\ ~\\ \frac{dE_{q}'}{dt} = \frac{V_{fd} + \left( x_d - x_{d}' \right)I_d - s_d E_{q}'}{T_{d0}'}\\ \frac{dE_{d}'}{dt} = \frac{- \left( x_q - x_{q}' \right)I_q - s_q E_{d}'}{T_{q0}'}\\ \frac{dE_{q}''}{dt} = \frac{s_dE_{q}' + \left( x_{d}' - x_{d}'' \right)I_d - s_d E_{q}''}{T_{d0}''}\\ \frac{dE_{d}''}{dt} = \frac{s_dE_{d}' + \left( x_{q}' - x_{q}'' \right)I_q - s_d E_{d}''}{T_{q0}''}\\ ~\\ \frac{d\omega}{dt} = \frac{\omega_r}{2H} \left[ P_m - P_e - D_a \left( \omega - \omega_r \right) \right]\\ \frac{d\delta}{dt} = \Omega_b\left( \omega - \omega_r \right)

As duas últimas equações diferenciais são as equações mecânicas da máquina; e as demais são equações elétricas (consulte essa tese para maiores detalhes acerca dos parâmetros dessas equações).

Utilizando as equações transitórias e subtransitórias podem-se definir cinco modelos de distintas complexidades.

Atenção!

O modelo da máquina síncrona é selecionado automaticamente de acordo com os dados fornecidos ao programa.

Na sequência são apresentados tais modelos, incluídos os efeitos da saturação magnética, em conjunto com seus diagramas de blocos:

  • Modelo 1: Corresponde a uma tensão constante atrás de uma reatância transitória de eixo direto (xd′x_{d}'), não exigindo equações diferenciais;
  • Modelo 2: São representados os efeitos transitórios de eixo direto, sendo necessária a solução de uma equação diferencial (dEq′dt\frac{dE_{q}'}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 2 das máquinas síncronas
  • Modelo 3: São representados os efeitos transitórios de eixo direto e em quadratura, exigindo duas equações diferenciais (dEq′dt\frac{dE_{q}'}{dt} e dEd′dt\frac{dE_{d}'}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 3 das máquinas síncronas
  • Modelo 4: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de três equações diferenciais (dEq′dt\frac{dE_{q}'}{dt}, dEq′′dt\frac{dE_{q}''}{dt} e dEd′′dt\frac{dE_{d}''}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 4 das máquinas síncronas
  • Modelo 5: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de quatro equações diferenciais (dEq′dt\frac{dE_{q}'}{dt}, dEd′dt\frac{dE_{d}'}{dt}, dEq′′dt\frac{dE_{q}''}{dt} e dEd′′dt\frac{dE_{d}''}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 4 das máquinas síncronas
Nota

Em todos os modelos as equações diferenciais mecânicas são solucionadas.

Barramento infinito

Algumas referências incluem um modelo sem equações diferenciais, em que a máquina é somente representada por uma tensão constante atrás de uma reatância transitória de eixo direto. Tal é utilizado na representação de um barramento infinito, o qual é normalmente constituído de um subsistema muito maior àquele simulado.

No PSP-UFU a representação de um barramento infinito pode ser obtido por meio da utilização de uma máquina representada pelo Modelo 1 cujo valor da constante de inércia (H) é infinito ou muito grande (9999 s9999~s, por exemplo) em relação às demais máquinas do sistema, e o valor de xd′x_{d}' deve ser um valor muito pequeno (10−3 p.u.10^{-3}~p.u., por exemplo).

Centro de inércia

Normalmente utiliza-se a velocidade de referência como sendo a síncrona e portanto, nesse caso, ωr=ωb=1,0 p.u.\omega_r = \omega_b = 1,0~p.u. Essa abordagem, adotada por vários livros de estabilidade, considera como referência uma máquina fictícia girando sempre na velocidade síncrona independente das perturbações aplicadas no sistema. No PSP-UFU foi implementado o conceito de centro de inércia (COI, do inglês, Center of Inertia), que constitui uma soma ponderada das velocidades das máquinas presentes no sistema:

ωr=(∑i=1nHiωi)(∑i=1nHi)\omega_r=\frac{\left( \sum_{i=1}^{n} H_i \omega_i \right)}{\left( \sum_{i=1}^{n} H_i \right)}

Em que: -nn é o número de máquinas síncronas conectadas no sistema.

A aplicação do COI resulta em dados de saída, como o ângulo do rotor, mais fáceis de serem analisados. Na implementação realizada no programa a utilização ou não desse recurso é opcional e pode ser definida pelo usuário.

Formulário de edição dos geradores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos geradores síncronos:

Formulário dos geradores síncronos no PSP-UFU

Um segundo pelos dados de estabilidade, como mostra a figura abaixo, acessado ao clicar no botão "Estabilidade" do formulário principal. Nele é possível também acessar aos controles das máquinas síncronas manipulados pelo editor de controle.

Formulário de estabilidade dos geradores síncronos no PSP-UFU

No formulário de estabilidade pode ser observado o botão "Chaveamento" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do gerador durante o estudo de estabilidade.

Formulário de chaveamento do gerador síncrono

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do gerador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador.

Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.

Atenção!

Caso mais de um gerador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.

Potências reativas máxima e mínima

Limites de potência reativa máxima e mínima do gerador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.

Falta

Impedâncias de sequência

Valores de resistência e reatância para cálculo das correntes de falta. São inseridos dados de sequência positiva, negativa e zero.

Impedância de aterramento

Valores utilizados para o cálculo das correntes de falta do tipo fase-terra e fase-fase-terra. Caso o neutro do gerador não seja aterrado, o valor inserido nesse campo é ignorado.

Neutro aterrado

Indica se o neutro do gerador é aterrado.

Botão Estabilidade

Imprimir dados da máquina síncrona

Exibe os dados do gerador síncrono nos gráficos no tempo. Os seguintes dados são exibidos:

  • tensão terminal
  • potências ativa e reativas
  • potência mecânica
  • frequência
  • tensão de campo
  • ângulo δ\delta.

Utilizar AVR e regulador de velocidade

Esses campos acionam ou inibem os controles da máquina síncrona, assim como modelos de turbina e excitatrizes.

Caso selecionadas os controles podem ser inseridos e modificados pelos botões “Editar AVR” e “Editar regulador de velocidade”, os quais acessam o editor de controle do PSP-UFU.

Resistência de armadura

Resistência de armadura da máquina síncrona, em p.u.p.u.

Reatância de Potier

Reatância de Potier para cálculo da saturação da máquina, em p.u.p.u.

Fator de saturação

Valor utilizado no cálculo da curva de saturação.

Representa o valor (em p.u.p.u.) de corrente de campo necessária para atingir 1,2 p.u. de tensão terminal.

Atenção!

Esse valor deve ser maior que 1,2, ou irá gerar erros na simulação. Caso não seja informado, a saturação da máquina não é considerada nos cálculos.

Reatâncias síncronas

Valores de reatância síncrona (regime permanente) da máquina. Os valores de eixo direto e em quadratura devem ser iguais ou muito próximos para representação de uma máquina de polos lisos, enquanto para polos salientes esses valores são distintos.

Reatâncias e constantes de tempo transitórias

Parâmetros transitórios da máquina síncrona em p.u.p.u. ou segundos.

Cuidado!

O valor da reatância transitória de eixo direto deve ser diferente de zero ou levará o programa a erro.

De acordo com a quantidade de parâmetros inseridos é definido internamente pelo programa qual o modelo a ser utilizado.

Reatâncias e constantes de tempo subtransitórias

Parâmetros subtransitórios da máquina síncrona em p.u.p.u. ou segundos, representando em detalhes a presença de enrolamentos amortecedores. Assim como os dados transitórios, esses parâmetros definem o modelo da máquina.

Botão Chaveamento

O botão "Chaveamento" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do gerador durante o estudo de estabilidade.

Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.

Referências

  1. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  2. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
  3. KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.
  4. DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: https://doi.org/10.1109/TPAS.1972.293341
  5. IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: https://doi.org/10.1109/IEEESTD.2003.94408
  6. KIMBARK, E. W. Power System Stability: Volume III – Synchronous Machine. New York: Wiley-IEEE Press, 1995.
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Gerador Síncrono

Uma máquina de corrente alternada na qual a frequência das tensões geradas e a velocidade da máquina estão em uma proporção constante. tradução livre - IEC 60050.

Gerador Síncrono no PSP-UFU

Os geradores síncronos são a fonte de potência para o cálculo do fluxo de carga e estabilidade, além de serem um dos principais contribuintes para as correntes de falta.

Atenção!

Somente barramentos que possuem esse elemento conectado podem ser considerados barras de referência. Barras do tipo PV devem conter um gerador síncrono ou um motor síncrono (compensador síncrono).

O formulário de dados é dividido em dois, sendo o primeiro responsável pelos dados gerais, de fluxo de carga e de falta e um segundo pelos dados de estabilidade . Esse último também permite o acesso aos controles das máquinas síncronas manipulados pelo editor de controle.

Informação

Os dados referentes às impedâncias de sequência positiva do gerador síncrono inseridas no contexto (aba) "Falta" são utilizados tanto para os estudos de curto-circuito quanto para os estudos de harmônicos.

Esses dados são ignorados nos estudos de fluxo de carga (não são utilizado nesse estudo) e estabilidade (são utilizados dados inseridos em formulário específico).

Gerador Síncrono no fluxo de carga

O gerador síncrono é a fonte de potência do PSP-UFU no estudo de fluxo de carga. Seu comportamento difere de acordo com o tipo de barra conectada:

  • Barra de referência: Os dados de potência ativa e reativa inseridos são desprezados, uma vez que esse elemento será utilizado para completar o balanço de potência do estudo de fluxo d carga;
  • Barra PV: O dado de potência ativa é considerado, porém o dados de potência reativa são desprezados. O valor da potência reativa é utilizado para manter o módulo da tensão constante no barramento conectado;
  • Barra PQ: Para os geradores conectados a essa barra tanto a potência ativa quanto reativa inseridas são consideradas.
Atenção

Caso o limite de potência reativa seja excedido, o programa automaticamente transforma a Barra PV conectada em uma Barra PQ, utilizando o valor limite de potência reativa que seria ultrapassado.

Gerador Síncrono no estudo de curto-circuito

Enquanto os geradores no estudo de fluxo de carga são modelados somente por correntes injetadas nas barras, para o curto-circuito utiliza-se uma tensão atrás de uma impedância. A figura abaixo mostra o caminho da corrente e o circuito equivalente de cada sequência nos geradores.

Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero

As tensões geradas são somente de sequência positiva, uma vez que o gerador fornece sempre tensões trifásicas equilibradas. Portanto a rede de sequência positiva é composta de uma tensão pré-falta atrás de uma impedância de sequência positiva. As redes de sequência negativa e zero não contêm forças eletromotrizes, porém incluem as impedâncias do gerador de sequência negativa e zero.

A corrente que circula na impedância z‾n\overline{z}_n entre o neutro e a terra é 3I˙a03\dot{I}_{a0}. Pela figura acima (c), observa-se que a queda de tensão de sequência zero do ponto a para terra (V˙a0\dot{V}_{a0}) é:

V˙a0=−3I˙a0z‾n−I˙a0z‾g0\dot{V}_{a0} = -3\dot{I}_{a0}\overline{z}_n - \dot{I}_{a0}\overline{z}_{g0}

A rede de sequência zero, que é um circuito monofásico pelo qual se supõe que circule apenas corrente de sequência zero e deve, portanto, ter uma impedância definida pela seguinte equação:

z‾0=3z‾n+z‾g0\overline{z}_{0} = 3\overline{z}_n + \overline{z}_{g0}
Dica

Caso o gerador não seja aterrado, não circulará corrente de sequência zero por ele. Nesse caso, dependendo da conexão do transformador próximo ao gerador sem aterramento, a seguinte mensagem de erro pode ser exibida:

"Falha ao inverter a matriz admitância de sequência zero"

Isso ocorre porque a matriz admitância de sequência zero é singular. Para contornar esse problema escolha uma das duas soluções abaixo:

  1. Marque a opção "Neutro aterrado" e insira um alto valor de reatância de aterramento (j9999 p.u.j9999~p.u., por exemplo);
  2. Ou, na barra do gerador, insira um reator de baixo valor de potência reativa (1,0 var1,0~var, por exemplo).

Gerador Síncrono no estudo de estabilidade

A relação de valores observados em testes adequados (definidos na IEEE Std. 115-2019), denominados parâmetros padrões, são utilizados para modelar a máquina síncrona no estudo de estabilidade do PSP-UFU.

Os parâmetros da máquina síncrona que influenciam rapidamente no decaimento de valores são chamados subtransitórios (indicados por ′′''), aqueles que influenciam mais lentamente são chamados transitórios (indicados por ′') e, finalmente, aqueles que influenciam continuamente são chamados de parâmetros síncronos (sem indicação de sobrescrito).

Um conjunto de equações algébrico-diferenciais determinam o comportamento da máquina síncrona no estudo de estabilidade:

Eq′−Vq=raIq−xds′IdEd′−Vd=raId−xqs′IqEq′′−Vq=raIq−xds′′IdEd′′−Vd=raId−xqs′′Iq dEq′dt=Vfd+(xd−xd′)Id−sdEq′Td0′dEd′dt=−(xq−xq′)Iq−sqEd′Tq0′dEq′′dt=sdEq′+(xd′−xd′′)Id−sdEq′′Td0′′dEd′′dt=sdEd′+(xq′−xq′′)Iq−sdEd′′Tq0′′ dωdt=ωr2H[Pm−Pe−Da(ω−ωr)]dδdt=Ωb(ω−ωr)E_{q}' - V_q = r_aI_q - x_{ds}'Id\\ E_{d}' - V_d = r_aI_d - x_{qs}'Iq\\ E_{q}'' - V_q = r_aI_q - x_{ds}''Id\\ E_{d}'' - V_d = r_aI_d - x_{qs}''Iq\\ ~\\ \frac{dE_{q}'}{dt} = \frac{V_{fd} + \left( x_d - x_{d}' \right)I_d - s_d E_{q}'}{T_{d0}'}\\ \frac{dE_{d}'}{dt} = \frac{- \left( x_q - x_{q}' \right)I_q - s_q E_{d}'}{T_{q0}'}\\ \frac{dE_{q}''}{dt} = \frac{s_dE_{q}' + \left( x_{d}' - x_{d}'' \right)I_d - s_d E_{q}''}{T_{d0}''}\\ \frac{dE_{d}''}{dt} = \frac{s_dE_{d}' + \left( x_{q}' - x_{q}'' \right)I_q - s_d E_{d}''}{T_{q0}''}\\ ~\\ \frac{d\omega}{dt} = \frac{\omega_r}{2H} \left[ P_m - P_e - D_a \left( \omega - \omega_r \right) \right]\\ \frac{d\delta}{dt} = \Omega_b\left( \omega - \omega_r \right)

As duas últimas equações diferenciais são as equações mecânicas da máquina; e as demais são equações elétricas (consulte essa tese para maiores detalhes acerca dos parâmetros dessas equações).

Utilizando as equações transitórias e subtransitórias podem-se definir cinco modelos de distintas complexidades.

Atenção!

O modelo da máquina síncrona é selecionado automaticamente de acordo com os dados fornecidos ao programa.

Na sequência são apresentados tais modelos, incluídos os efeitos da saturação magnética, em conjunto com seus diagramas de blocos:

  • Modelo 1: Corresponde a uma tensão constante atrás de uma reatância transitória de eixo direto (xd′x_{d}'), não exigindo equações diferenciais;
  • Modelo 2: São representados os efeitos transitórios de eixo direto, sendo necessária a solução de uma equação diferencial (dEq′dt\frac{dE_{q}'}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 2 das máquinas síncronas
  • Modelo 3: São representados os efeitos transitórios de eixo direto e em quadratura, exigindo duas equações diferenciais (dEq′dt\frac{dE_{q}'}{dt} e dEd′dt\frac{dE_{d}'}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 3 das máquinas síncronas
  • Modelo 4: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de três equações diferenciais (dEq′dt\frac{dE_{q}'}{dt}, dEq′′dt\frac{dE_{q}''}{dt} e dEd′′dt\frac{dE_{d}''}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 4 das máquinas síncronas
  • Modelo 5: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de quatro equações diferenciais (dEq′dt\frac{dE_{q}'}{dt}, dEd′dt\frac{dE_{d}'}{dt}, dEq′′dt\frac{dE_{q}''}{dt} e dEd′′dt\frac{dE_{d}''}{dt}), cujo diagrama de blocos é apresentado na figura abaixo:
Diagrama de blocos do Modelo 4 das máquinas síncronas
Nota

Em todos os modelos as equações diferenciais mecânicas são solucionadas.

Saturação

Para representar matematicamente o efeito da saturação nas equações das máquinas síncronas são introduzidos “fatores de saturação” que modificam as impedâncias do circuito equivalente, os quais dependem de uma reatância de dispersão efetiva, chamada de reatância de Potier (xpx_p).

Tal reatância pode ser obtida por meio de ensaios (utilizando curvas de saturação de circuito aberto e carga de fator de potência zero) ou estimadas de forma aproximada por outros parâmetros da máquina. A reatância de dispersão (xlx_l), aqui substituída de forma aproximada por xpx_p, representa a parcela da reatância da máquina originados do fluxo magnético que percorrem o ar na maioria de seu caminho e, portanto, é independente da saturação.

O método implementado no programa permite reproduzir a saturação em ambos os eixos (direto e em quadratura), diferindo entre si devido à divergência no tamanho do entreferro. É assumido que a soma vetorial das duas componentes do fluxo magnético saturado está em fase com a f.m.m. e proporcional à Tensão de Potier (EpE_p, a qual é a tensão atrás da reatância de Potier).

Para isso, são utilizados internamente dois fatores de saturação, sendo um no eixo direto (sds_d) e outro no eixo em quadratura (sqs_q). Esses fatores de saturação são automaticamente calculados a cada passo de integração e dependem da curva de saturação da máquina definida pelo fator de saturação inserido no formulário de edição de dados.

Portanto as reatâncias saturadas, que devem ser inseridas nas equações algébricas da máquina, são definidas pelas seguintes equações:

xds=xd−xpsd+xpxqs=xq−xpsq+xpx_{ds}=\frac{x_d-x_p}{s_d +x_p}\\ x_{qs}=\frac{x_q-x_p}{s_q +x_p}

Essas equações também são utilizadas para as reatâncias transitórias e subtransitórias, visto que o valor da reatância de Potier (ou de dispersão) não é alterada.

Barramento infinito

Algumas referências incluem um modelo sem equações diferenciais, em que a máquina é somente representada por uma tensão constante atrás de uma reatância transitória de eixo direto. Tal é utilizado na representação de um barramento infinito, o qual é normalmente constituído de um subsistema muito maior àquele simulado.

No PSP-UFU a representação de um barramento infinito pode ser obtido por meio da utilização de uma máquina representada pelo Modelo 1 cujo valor da constante de inércia (H) é infinito ou muito grande (9999 s9999~s, por exemplo) em relação às demais máquinas do sistema, e o valor de xd′x_{d}' deve ser um valor muito pequeno (10−3 p.u.10^{-3}~p.u., por exemplo).

Centro de inércia

Normalmente utiliza-se a velocidade de referência como sendo a síncrona e portanto, nesse caso, ωr=ωb=1,0 p.u.\omega_r = \omega_b = 1,0~p.u. Essa abordagem, adotada por vários livros de estabilidade, considera como referência uma máquina fictícia girando sempre na velocidade síncrona independente das perturbações aplicadas no sistema. No PSP-UFU foi implementado o conceito de centro de inércia (COI, do inglês, Center of Inertia), que constitui uma soma ponderada das velocidades das máquinas presentes no sistema:

ωr=(∑i=1nHiωi)(∑i=1nHi)\omega_r=\frac{\left( \sum_{i=1}^{n} H_i \omega_i \right)}{\left( \sum_{i=1}^{n} H_i \right)}

Em que: +nn é o número de máquinas síncronas conectadas no sistema.

A aplicação do COI resulta em dados de saída, como o ângulo do rotor, mais fáceis de serem analisados. Na implementação realizada no programa a utilização ou não desse recurso é opcional e pode ser definida pelo usuário.

Formulário de edição dos geradores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos geradores síncronos:

Formulário dos geradores síncronos no PSP-UFU

Um segundo pelos dados de estabilidade, como mostra a figura abaixo, acessado ao clicar no botão "Estabilidade" do formulário principal. Nele é possível também acessar aos controles das máquinas síncronas manipulados pelo editor de controle.

Formulário de estabilidade dos geradores síncronos no PSP-UFU

No formulário de estabilidade pode ser observado o botão "Chaveamento" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do gerador durante o estudo de estabilidade.

Formulário de chaveamento do gerador síncrono

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do gerador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador.

Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.

Atenção!

Caso mais de um gerador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.

Potências reativas máxima e mínima

Limites de potência reativa máxima e mínima do gerador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.

Acesso aos controles da máquina síncrona

Como já mencionado anteriormente, os reguladores de velocidade e tensão da máquina síncrona podem ser acionados ou inibidos por meio das caixas de seleção "Utilizar AVR e regulador de velocidade". Ambas as opções irão acessar o editor de controles.

O acesso aos controles do AVR poderão então ser criados e manipulados ao clicar no botão "Editar AVR", assim como o Regulador de Velocidade é acessado no botão "Editar regulador de velocidade".

Atenção!

No PSP-UFU a opção de editar o AVR engloba mais que somente o controle de tensão da máquina. Nele deve ser inserida a malha de controle da máquina assim como a excitatriz da máquina síncrona. Outras estratégias de controle (opcionais), como PSS (Power System Stabilizer) e/ou controles de sobre e sub excitação, são também implementadas em conjunto.

Atenção!

Assim como no AVR, o Regulador de Velocidade engloba mais que a regulação primária da máquina. Nessa opção deve ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o modelo da turbina. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.

Referências

  1. MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: https://doi.org/10.1007/978-3-642-13669-6
  2. ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: https://doi.org/10.1002/9781118878286
  3. KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.
  4. DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: https://doi.org/10.1109/TPAS.1972.293341
  5. IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: https://doi.org/10.1109/IEEESTD.2003.94408
  6. KIMBARK, E. W. Power System Stability: Volume III – Synchronous Machine. New York: Wiley-IEEE Press, 1995.
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Compensador Síncrono

Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. tradução livre - IEC 60050.

Compensador Síncrono no PSP-UFU

O compensador síncrono nada mais é que um motor síncrono operando sem carga em seu eixo com o intuito de fornecer ou absorver potência reativa na rede. Em relação ao fluxo de carga, no PSP-UFU esse elemento tem comportamento idêntico ao gerador síncrono, porém a sua potência ativa é inserida nos algoritmos de solução com sinal negativo.

Sua parametrização para o estudo de fluxo de carga, falta e harmônicos é idêntica ao gerador síncrono.

Cuidado!

O compensador síncrono não foi implementado no estudo de estabilidade e sua presença no circuito pode causar erros durante os cálculos.

Não inclua esse elemento para os estudos de estabilidade. Versões futuras do PSP-UFU irão contemplar esse elemento para esse estudo.

Dica

É possível utilizar um gerador síncrono com potência ativa nula ou negativa para representar o compensador síncrono nos estudos de estabilidade.

Formulário de edição dos compensadores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos compensadores síncronos:

Formulário dos compensadores síncronos no PSP-UFU

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do compensador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador.

Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.

Atenção!

Caso mais de um compensador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.

Potências reativas máxima e mínima

Limites de potência reativa máxima e mínima do compensador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal do compensador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.

Falta

Impedâncias de sequência

Valores de resistência e reatância para cálculo das correntes de falta. São inseridos dados de sequência positiva, negativa e zero.

Impedância de aterramento

Valores utilizados para o cálculo das correntes de falta do tipo fase-terra e fase-fase-terra. Caso o neutro do gerador não seja aterrado, o valor inserido nesse campo é ignorado.

Neutro aterrado

Indica se o neutro do gerador é aterrado.

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Compensador Síncrono

Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. tradução livre - IEC 60050.

Compensador Síncrono no PSP-UFU

O compensador síncrono nada mais é que um motor síncrono operando sem carga em seu eixo com o intuito de fornecer ou absorver potência reativa na rede. Em relação ao fluxo de carga, no PSP-UFU esse elemento tem comportamento idêntico ao gerador síncrono, porém a sua potência ativa é inserida nos algoritmos de solução com sinal negativo.

Sua parametrização para o estudo de fluxo de carga, falta e harmônicos é idêntica ao gerador síncrono.

Cuidado!

O compensador síncrono não foi implementado no estudo de estabilidade e sua presença no circuito pode causar erros durante os cálculos.

Não inclua esse elemento para os estudos de estabilidade. Versões futuras do PSP-UFU irão contemplar esse elemento para esse estudo.

Dica

É possível utilizar um gerador síncrono com potência ativa nula ou negativa para representar o compensador síncrono nos estudos de estabilidade.

Formulário de edição dos compensadores síncronos

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos compensadores síncronos:

Formulário dos compensadores síncronos no PSP-UFU

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Potência nominal

Potência nominal do compensador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Potências ativa e reativa

Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador.

Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.

Atenção!

Caso mais de um compensador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.

Potências reativas máxima e mínima

Limites de potência reativa máxima e mínima do compensador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal do compensador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.

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Relatórios Tabulares

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Texto Vinculado

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Função Transferência

A Função Transferência é um importante bloco elementar e essencial em um sistema de controle, visto que esse componente possibilita a representação de sistemas dinâmicos por meio de equações algébricas no domínio da frequência.

Informação

Nesses blocos é utilizado a letra “s” para representação no domínio da frequência, pois essa é a terminologia mais utilizada em sistemas de controle.

Função Transferência no PSP-UFU

Após a inserção da função transferência, o programa a transforma na representação em espaço de estado, visto que sua solução é sistemática tornando-a, assim, mais eficiente computacionalmente.

Dada uma função transferência genérica abaixo:

Y(s)U(s)=b0sk+b1sk−1+⋯+bk−1s+bksk+a1sk−1+⋯+ak−1s+ak\frac{Y(\bold{s})}{U(\bold{s})} = \frac{b_0 \bold{s}^k + b_1 \bold{s}^{k-1} + \cdots + b_{k-1} \bold{s} + b_k}{\bold{s}^k + a_1 \bold{s}^{k-1} + \cdots + a_{k-1} \bold{s} + a_k}

A transformação em espaço de estado na forma canônica controlável ficará da seguinte forma:

[sx1sx2⋮sxk−1sxk]=[010⋯0001⋯0⋮⋮⋮⋱⋮000⋯1−ak−ak−1−ak−2⋯−a1][x1x2⋮xk−1xk]+[00⋮01]unyn=[(bn−anb0)(bn−1−an−1b0)⋯(b1−a1b0)][x1x2⋮xk]+b0un\begin{bmatrix} \bold{s}x_1\\ \bold{s}x_2\\ \vdots\\ \bold{s}x_{k-1}\\ \bold{s}x_k \end{bmatrix} = \begin{bmatrix} 0 & 1 & 0 & \cdots & 0\\ 0 & 0 & 1 & \cdots & 0\\ \vdots & \vdots & \vdots & \ddots & \vdots\\ 0 & 0 & 0 & \cdots & 1\\ -a_k & -a_{k-1} & -a_{k-2} & \cdots & -a_1 \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_{k-1}\\ x_k \end{bmatrix} + \begin{bmatrix} 0\\ 0\\ \vdots\\ 0\\ 1 \end{bmatrix} u_n\\ y_n = \begin{bmatrix} \left( b_n - a_n b_0 \right) & \left( b_{n-1} - a_{n-1} b_0 \right) & \cdots & \left( b_1 - a_1 b_0 \right) \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_k \end{bmatrix} + b_0 u_n

A equação diferencial matricial é resolvida pelo método Trapezoidal Implícito. Um processo iterativo é realizado até que o erro entre os cálculos se torne menor que uma tolerância pré-estipulada e caso as iterações se tornem excessivas, ultrapassando um número máximo definido pelo usuário, o processo é interrompido com erro. Com os valores do vetor de estado (xx) calculados obtém-se o valor da saída do bloco (yny_n).

Formulário de edição de dados da Função Transferência

A figura abaixo apresenta o formulário de edição de dados da função transferência.

Formulário de edição de dados da função transferência no PSP-UFU

A função transferência é definida pelos coeficientes do numerador e denominador, separados por espaço.

Atenção!

Os elementos não presentes são representados como coeficientes de valor zero.

Por exemplo, um parâmetro inserido igual a “10,502\begin{matrix} 1 & 0{,}5 & 0 & 2 \end{matrix}” irá gerar: “s3+0,5s2+2s^3+0{,}5s^2+2”.

Referências

  1. OGATA, K. Modern Control Engineering. Prentice Hall Inc., New Jersey, 2004.
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Função Transferência

A Função Transferência é um importante bloco elementar e essencial em um sistema de controle, visto que esse componente possibilita a representação de sistemas dinâmicos por meio de equações algébricas no domínio da frequência.

Informação

Nesses blocos é utilizado a letra “s” para representação no domínio da frequência, pois essa é a terminologia mais utilizada em sistemas de controle.

Função Transferência no PSP-UFU

Após a inserção da função transferência, o programa a transforma na representação em espaço de estado, visto que sua solução é sistemática tornando-a, assim, mais eficiente computacionalmente.

Dada uma função transferência genérica abaixo:

Y(s)U(s)=b0sk+b1sk−1+⋯+bk−1s+bksk+a1sk−1+⋯+ak−1s+ak\frac{Y(\bold{s})}{U(\bold{s})} = \frac{b_0 \bold{s}^k + b_1 \bold{s}^{k-1} + \cdots + b_{k-1} \bold{s} + b_k}{\bold{s}^k + a_1 \bold{s}^{k-1} + \cdots + a_{k-1} \bold{s} + a_k}

A transformação em espaço de estado na forma canônica controlável ficará da seguinte forma:

[sx1sx2⋮sxk−1sxk]=[010⋯0001⋯0⋮⋮⋮⋱⋮000⋯1−ak−ak−1−ak−2⋯−a1][x1x2⋮xk−1xk]+[00⋮01]unyn=[(bn−anb0)(bn−1−an−1b0)⋯(b1−a1b0)][x1x2⋮xk]+b0un\begin{bmatrix} \bold{s}x_1\\ \bold{s}x_2\\ \vdots\\ \bold{s}x_{k-1}\\ \bold{s}x_k \end{bmatrix} = \begin{bmatrix} 0 & 1 & 0 & \cdots & 0\\ 0 & 0 & 1 & \cdots & 0\\ \vdots & \vdots & \vdots & \ddots & \vdots\\ 0 & 0 & 0 & \cdots & 1\\ -a_k & -a_{k-1} & -a_{k-2} & \cdots & -a_1 \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_{k-1}\\ x_k \end{bmatrix} + \begin{bmatrix} 0\\ 0\\ \vdots\\ 0\\ 1 \end{bmatrix} u_n\\ y_n = \begin{bmatrix} \left( b_n - a_n b_0 \right) & \left( b_{n-1} - a_{n-1} b_0 \right) & \cdots & \left( b_1 - a_1 b_0 \right) \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_k \end{bmatrix} + b_0 u_n

A equação diferencial matricial é resolvida pelo método Trapezoidal Implícito. Um processo iterativo é realizado até que o erro entre os cálculos se torne menor que uma tolerância pré-estipulada e caso as iterações se tornem excessivas, ultrapassando um número máximo definido pelo usuário, o processo é interrompido com erro. Com os valores do vetor de estado (xx) calculados obtém-se o valor da saída do bloco (yny_n).

Formulário de edição de dados da Função Transferência

A figura abaixo apresenta o formulário de edição de dados da função transferência.

Formulário de edição de dados da função transferência no PSP-UFU

A função transferência é definida pelos coeficientes do numerador e denominador, separados por espaço.

Atenção!

Os elementos não presentes são representados como coeficientes de valor zero.

Por exemplo, um parâmetro inserido igual a “10,502\begin{matrix} 1 & 0{,}5 & 0 & 2 \end{matrix}” irá gerar: “s3+0,5s2+2s^3+0{,}5s^2+2”.

Referências

  1. OGATA, K. Modern Control Engineering. Prentice Hall Inc., New Jersey, 2004.
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Transformador

Aparelho estático com dois ou mais enrolamentos que, por indução eletromagnética, transforma um sistema de tensão e corrente alternada em outro sistema de tensão e corrente geralmente de valores diferentes e na mesma frequência com o objetivo de transmitir energia elétrica. tradução livre - IEC 60050.

Transformador no PSP-UFU

Transformadores com quaisquer conexões e defasagens entre as tensões primárias e secundárias podem ser inseridos no PSP-UFU. Para isso, os transformadores devem ser modelados representando seu tape (tt) e defasagem (ϕ\phi), utilizando um transformador ideal de relação de transformação t‾:1\overline{t}:1 em série com sua impedância (y‾T=rT+jxT\overline{y}_T = r_T + jx_T), em que t‾\overline{t} é um número complexo (t∠ϕt\angle\phi)

Atenção

O modelo utilizado no PSP-UFU não considera o ramo magnetizante ou impedâncias mútuas entre as fases.

A figura abaixo mostra o modelo do transformador implementado no PSP-UFU:

Modelo PI da linha

Em que:

  • rT\bold{r_T} é a resistência total do transformador;
  • xT\bold{x_T} é a reatância indutiva total do transformador;
  • t‾\bold{\overline{t}} é a o tape complexo do transformador.

A relação entre as tensões e correntes das barras genéricas ii e jj é obtida pela equação matricial:

[I˙ijI˙ji]=[y‾Tt2−y‾Tt‾∗−y‾Tt‾y‾T]×[V˙iV˙j]\begin{bmatrix} \dot{I}_{ij}\\ \dot{I}_{ji} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} & -\displaystyle \frac{\overline{y}_T}{\overline{t}^*}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}} & \overline{y}_T \end{bmatrix} \times \begin{bmatrix} \dot{V}_{i}\\ \dot{V}_{j} \end{bmatrix}

Assim como nas linhas, o transformador de dois enrolamentos deve ser inserido entre barras, porém não há a necessidade das tensões nominais desses barramentos serem idênticas.

Atenção!

A primeira barra selecionada será o lado primário, o qual é indicado por um círculo. Para alterar o lado primário após a inserção basta desconectar os nós dos transformadores e reconectá-los alternando as barras, utilizando as ferramentas CAD.

Transformadores no estudo de curto-circuito

Da mesma forma que no estudo de fluxo de carga, a representação dos elementos do sistema para o estudo de curto-circuito é realizada por meio de circuitos equivalentes inseridos na matriz admitância de barras. Nas faltas desbalanceadas é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.

A matriz admitância de sequência positiva é construída da mesma forma que os estudos de fluxo de carga. Na sequência negativa o ângulo de defasagem entre tensões primária e secundária (ϕ\phi) deve ser invertido, uma vez que os fasores da sequência negativa são deslocados na direção oposta. Com isso, a matriz que representa as admitâncias da equação anterior deve ser substituída pela seguinte expressão:

[Y‾iiY‾ijY‾jiY‾jj]=[y‾Tt2−y‾Tt‾−y‾Tt‾∗y‾T]\begin{bmatrix} \overline{Y}_{ii} & \overline{Y}_{ij}\\ \overline{Y}_{ji} & \overline{Y}_{jj} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} & -\displaystyle \frac{\overline{y}_T}{\overline{t}}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}^*} & \overline{y}_T \end{bmatrix}

A impedância de sequência negativa nos transformadores deve ser tratada de maneira específica devido aos diferentes tipos de conexão. Na figura abaixo são mostrados os circuitos equivalentes para cada tipo de conexão de transformadores de dois enrolamentos. As setas indicam os caminhos possíveis para circulação da corrente de sequência zero.

Circuitos equivalentes de sequência zero dos transformadores

Para os transformadores com conexão estrela aterrado, se a ligação do neutro para a terra apresentar uma impedância z‾n\overline{z}_n, o circuito equivalente de sequência zero deve ter impedância de 3z‾n3\overline{z}_n em série com a resistência e reatância equivalentes do transformador.

Formulário de edição dos transformadores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos transformadores:

Formulário dos transformadores no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais dos transformadores, informações do fluxo de carga, sua conexão e defasagem;
  • Falta: local onde as impedâncias de sequência zero e impedâncias de aterramento são inseridas.

Além desses dois contextos, pode ser observado o botão "Estabilidade" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do transformador durante o estudo de estabilidade.

Formulário de chaveamento do transformador

Geral

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Campo de informação não editável que apresenta a tensão primária e secundária do transformador. Para alterar esse campo é necessário editar o campo correspondente dos barramento conectados.

Tensão base

Tensão utilizada para converter os parâmetros de impedância inseridos em Ω\Omega para p.u.p.u. As tensões selecionadas por uma caixa de escolha são editadas nos formulários dos barramentos conectados.

Informação

A tensão base é ignorada caso os dados inseridos estejam em p.u.p.u.

Potência nominal

Potência nominal do transformador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Impedância do transformador

Impedância série do transformador (resistência e reatância indutiva), inserida em p.u.p.u. ou Ω\Omega. Caso as impedâncias sejam inseridas em Ω\Omega será utilizada a tensão base selecionada para conversão para p.u.p.u.

Conexão

Conexão do transformador utilizada para cálculo das correntes de sequência zero nas faltas desbalanceadas com presença de terra (fase-terra e fase-fase-terra).

As seguintes conexões estão disponíveis:

  1. Yaterrado−YaterradoY_{aterrado}-Y_{aterrado}
  2. Y−YaterradoY-Y_{aterrado}
  3. Yaterrado−YY_{aterrado}-Y
  4. Y−YY-Y
  5. Δ−Yaterrado\Delta-Y_{aterrado}
  6. Δ−Y\Delta-Y
  7. Yaterrado−ΔY_{aterrado}-\Delta
  8. Y−ΔY-\Delta
  9. Δ−Δ\Delta-\Delta

TAP

Tape do transformador em relação ao primário.

Atenção!

O tape no PSP-UFU deve ser inserido pela relação entre a tensão primária nominal e a tensão de tape (TAP=VnominalVtape)\left(\text{TAP} = \frac{V_{nominal}}{V_{tape}}\right).

Defasagem

Defasagem do transformador em relação ao primário, em graus. Esse valor independe do tipo de conexão, portanto para conexões diferentes de Y−YY-Y(aterrado ou não) e Δ−Δ\Delta-\Delta, deve-se inserir o ângulo de defasagem correto.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal do transformador como base para a conversão das unidades, caso contrário será usada a potência base do sistema.

Falta

Impedância de sequência zero do transformador

Esses parâmetros são necessários para o correto cálculo das correntes de falta desbalanceadas (fase-fase, fase-fase-terra e fase-terra) e devem ser inseridos em p.u.p.u.

Cuidado!

A não inserção desses dados acarretarão em resultados incorretos para faltas desbalanceadas.

Impedâncias de aterramento

As impedâncias de aterramento são somente utilizadas para conexão YaterradoY_{aterrado} e devem ser inseridas em p.u.p.u.

Botão Estabilidade

O botão "Estabilidade" irá abrir um formulário, comum a vários outros elementos, que permite a inserção e/ou remoção do transformador durante o estudo de estabilidade.

Nesse formulário pode ser criada uma lista genérica de inserções e remoções da linha no tempo, personalizada por um contexto de propriedades de chaveamento que são editados o tipo de chaveamento (inserção ou remoção) e o instante (em segundos) do evento. Essas propriedades são atribuídas e retiradas da lista genérica por meio dos botões "Adicionar" e "Remover", respectivamente.

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Transformador

Aparelho estático com dois ou mais enrolamentos que, por indução eletromagnética, transforma um sistema de tensão e corrente alternada em outro sistema de tensão e corrente geralmente de valores diferentes e na mesma frequência com o objetivo de transmitir energia elétrica. tradução livre - IEC 60050.

Transformador no PSP-UFU

Transformadores com quaisquer conexões e defasagens entre as tensões primárias e secundárias podem ser inseridos no PSP-UFU. Para isso, os transformadores devem ser modelados representando seu tape (tt) e defasagem (ϕ\phi), utilizando um transformador ideal de relação de transformação t‾:1\overline{t}:1 em série com sua impedância (y‾T=rT+jxT\overline{y}_T = r_T + jx_T), em que t‾\overline{t} é um número complexo (t∠ϕt\angle\phi)

Atenção

O modelo utilizado no PSP-UFU não considera o ramo magnetizante ou impedâncias mútuas entre as fases.

A figura abaixo mostra o modelo do transformador implementado no PSP-UFU:

Modelo PI da linha

Em que:

  • rT\bold{r_T} é a resistência total do transformador;
  • xT\bold{x_T} é a reatância indutiva total do transformador;
  • t‾\bold{\overline{t}} é a o tape complexo do transformador.

A relação entre as tensões e correntes das barras genéricas ii e jj é obtida pela equação matricial:

[I˙ijI˙ji]=[y‾Tt2−y‾Tt‾∗−y‾Tt‾y‾T]×[V˙iV˙j]\begin{bmatrix} \dot{I}_{ij}\\ \dot{I}_{ji} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} & -\displaystyle \frac{\overline{y}_T}{\overline{t}^*}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}} & \overline{y}_T \end{bmatrix} \times \begin{bmatrix} \dot{V}_{i}\\ \dot{V}_{j} \end{bmatrix}

Assim como nas linhas, o transformador de dois enrolamentos deve ser inserido entre barras, porém não há a necessidade das tensões nominais desses barramentos serem idênticas.

Atenção!

A primeira barra selecionada será o lado primário, o qual é indicado por um círculo. Para alterar o lado primário após a inserção basta desconectar os nós dos transformadores e reconectá-los alternando as barras, utilizando as ferramentas CAD.

Transformadores no estudo de curto-circuito

Da mesma forma que no estudo de fluxo de carga, a representação dos elementos do sistema para o estudo de curto-circuito é realizada por meio de circuitos equivalentes inseridos na matriz admitância de barras. Nas faltas desbalanceadas é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.

A matriz admitância de sequência positiva é construída da mesma forma que os estudos de fluxo de carga. Na sequência negativa o ângulo de defasagem entre tensões primária e secundária (ϕ\phi) deve ser invertido, uma vez que os fasores da sequência negativa são deslocados na direção oposta. Com isso, a matriz que representa as admitâncias da equação anterior deve ser substituída pela seguinte expressão:

[Y‾iiY‾ijY‾jiY‾jj]=[y‾Tt2−y‾Tt‾−y‾Tt‾∗y‾T]\begin{bmatrix} \overline{Y}_{ii} & \overline{Y}_{ij}\\ \overline{Y}_{ji} & \overline{Y}_{jj} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} & -\displaystyle \frac{\overline{y}_T}{\overline{t}}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}^*} & \overline{y}_T \end{bmatrix}

A impedância de sequência negativa nos transformadores deve ser tratada de maneira específica devido aos diferentes tipos de conexão. Na figura abaixo são mostrados os circuitos equivalentes para cada tipo de conexão de transformadores de dois enrolamentos. As setas indicam os caminhos possíveis para circulação da corrente de sequência zero.

Circuitos equivalentes de sequência zero dos transformadores

Para os transformadores com conexão estrela aterrado, se a ligação do neutro para a terra apresentar uma impedância z‾n\overline{z}_n, o circuito equivalente de sequência zero deve ter impedância de 3z‾n3\overline{z}_n em série com a resistência e reatância equivalentes do transformador.

Formulário de edição dos transformadores

A imagem abaixo apresenta o formulário de inserção/alteração de dados dos transformadores:

Formulário dos transformadores no PSP-UFU

Esse formulário é subdividido em dois contextos distintos:

  • Geral: no qual são inseridas informações gerais dos transformadores, informações do fluxo de carga, sua conexão e defasagem;
  • Falta: local onde as impedâncias de sequência zero e impedâncias de aterramento são inseridas.

Além desses dois contextos, pode ser observado o botão "Estabilidade" na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do transformador durante o estudo de estabilidade.

Formulário de chaveamento do transformador

Nome

Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão Unicode.

Todos os componentes de potência do PSP-UFU possuem esse campo.

Tensão nominal

Campo de informação não editável que apresenta a tensão primária e secundária do transformador. Para alterar esse campo é necessário editar o campo correspondente dos barramento conectados.

Tensão base

Tensão utilizada para converter os parâmetros de impedância inseridos em Ω\Omega para p.u.p.u. As tensões selecionadas por uma caixa de escolha são editadas nos formulários dos barramentos conectados.

Informação

A tensão base é ignorada caso os dados inseridos estejam em p.u.p.u.

Potência nominal

Potência nominal do transformador, inserida em MVA, kVA ou VA.

Esse campo é especialmente importante caso a opção "Utilizar a potência nominal como base" esteja marcada.

Impedância do transformador

Impedância série do transformador (resistência e reatância indutiva), inserida em p.u.p.u. ou Ω\Omega. Caso as impedâncias sejam inseridas em Ω\Omega será utilizada a tensão base selecionada para conversão para p.u.p.u.

Conexão

Conexão do transformador utilizada para cálculo das correntes de sequência zero nas faltas desbalanceadas com presença de terra (fase-terra e fase-fase-terra).

As seguintes conexões estão disponíveis:

  1. Yaterrado−YaterradoY_{aterrado}-Y_{aterrado}
  2. Y−YaterradoY-Y_{aterrado}
  3. Yaterrado−YY_{aterrado}-Y
  4. Y−YY-Y
  5. Δ−Yaterrado\Delta-Y_{aterrado}
  6. Δ−Y\Delta-Y
  7. Yaterrado−ΔY_{aterrado}-\Delta
  8. Y−ΔY-\Delta
  9. Δ−Δ\Delta-\Delta

TAP

Tape do transformador em relação ao primário.

Atenção!

O tape no PSP-UFU deve ser inserido pela relação entre a tensão primária nominal e a tensão de tape (TAP=VnominalVtape)\left(\text{TAP} = \frac{V_{nominal}}{V_{tape}}\right).

Defasagem

Defasagem do transformador em relação ao primário, em graus. Esse valor independe do tipo de conexão, portanto para conexões diferentes de Y−YY-Y(aterrado ou não) e Δ−Δ\Delta-\Delta, deve-se inserir o ângulo de defasagem correto.

Utilizar potência nominal como base

Caso essa opção seja marcada, o programa irá utilizar a potência nominal do transformador como base para a conversão das unidades, caso contrário será usada a potência base do sistema.

Edit this page
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",Object(m.b)("strong",{parentName:"p"},"harm\xf4nicos")," as cargas s\xe3o modeladas como imped\xe2ncia constante, independentemente da sinaliza\xe7\xe3o indicada em seu formul\xe1rio de edi\xe7\xe3o de dados."))),Object(m.b)("h3",{id:"carga-no-estudo-de-estabilidade"},"Carga no estudo de estabilidade"),Object(m.b)("p",null,"A modelagem das cargas do sistema de forma exata se torna impratic\xe1vel em um problemas de estabilidade, visto \xe0 grande quantidade e variedade dos componentes envolvidos, al\xe9m de apresentar modifica\xe7\xf5es em suas composi\xe7\xf5es causado por v\xe1rios fatores, como tempo, condi\xe7\xf5es clim\xe1ticas e economia. 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Corrente"}))),Object(m.b)("p",null,"Cargas de corrente e pot\xeancia constantes possuem problemas em tens\xf5es muito baixas. \xc0 medida que a tens\xe3o diminui as correntes dessas cargas n\xe3o reduz, como pode ser observado na figura acima, resultando em perda de precis\xe3o e problemas na converg\xeancia de processos iterativos. Para contornar esse problema utiliza-se uma tens\xe3o pr\xe9-definida pelo usu\xe1rio (",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("msub",{parentName:"mrow"},Object(m.b)("mi",{parentName:"msub"},"V"),Object(m.b)("mrow",{parentName:"msub"},Object(m.b)("mi",{parentName:"mrow"},"l"),Object(m.b)("mi",{parentName:"mrow"},"o"),Object(m.b)("mi",{parentName:"mrow"},"w")))),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"V_{low}")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.83333em",verticalAlign:"-0.15em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.22222em"}}),"V"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"msupsub"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.33610799999999996em"}}),Object(m.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-2.5500000000000003em",marginLeft:"-0.22222em",marginRight:"0.05em"}}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.01968em"}}),"l"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"o"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.02691em"}}),"w"))))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.15em"}}),Object(m.b)("span",{parentName:"span"})))))))))),"), a qual as cargas (ou parcelas) de corrente e pot\xeancia constantes s\xe3o modeladas como imped\xe2ncia constante, resultando no comportamento de pot\xeancia e corrente apresentados na figura acima."),Object(m.b)("h2",{id:"formul\xe1rio-de-edi\xe7\xe3o-das-cargas"},"Formul\xe1rio de edi\xe7\xe3o das cargas"),Object(m.b)("p",null,"A imagem abaixo apresenta o formul\xe1rio de inser\xe7\xe3o/altera\xe7\xe3o de dados das cargas:"),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/loadForm.png"),alt:"Formul\xe1rio das cargas no PSP-UFU",title:"Formul\xe1rio das cargas no PSP-UFU"}))),Object(m.b)("p",null,"Esse formul\xe1rio \xe9 subdividido em dois contextos distintos:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Geral"),": no qual s\xe3o inseridas informa\xe7\xf5es gerais das cargas, informa\xe7\xf5es e o tipo de carga no fluxo de carga;"),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Estabilidade"),": contendo op\xe7\xf5es de visualiza\xe7\xe3o de dados da carga em gr\xe1ficos no tempo e op\xe7\xf5es de parametriza\xe7\xe3o da carga ZIP.")),Object(m.b)("p",null,'Al\xe9m desses dois contextos, pode ser observado o bot\xe3o "Chaveamento" na parte inferior esquerda do formul\xe1rio. Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o da carga durante o estudo de ',Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/loadSw.png"),alt:"Formul\xe1rio de chaveamento da carga",title:"Formul\xe1rio de chaveamento da carga"}))),Object(m.b)("hr",null),Object(m.b)("h3",{id:"geral"},"Geral"),Object(m.b)("h4",{id:"nome"},"Nome"),Object(m.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(m.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(m.b)("h4",{id:"pot\xeancia-ativa"},"Pot\xeancia ativa"),Object(m.b)("p",null,"Parcela de pot\xeancia ativa da carga. 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Pode ser inserido em Mvar, kvar var ou ",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),".")))))," (na base do sistema)."),Object(m.b)("h4",{id:"tipo-de-carga-fluxo-de-carga"},"Tipo de carga (fluxo de carga)"),Object(m.b)("p",null,"Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Pot\xeancia constante e Imped\xe2ncia constante. As cargas de pot\xeancia constantes s\xe3o inseridas nos vetores de pot\xeancia e permanecem invariantes no c\xe1lculo, enquanto que para as cargas de imped\xe2ncia constante determina-se o valor da imped\xe2ncia utilizando a pot\xeancia e tens\xe3o nominal, a qual \xe9 inserida na matriz admit\xe2ncia."),Object(m.b)("hr",null),Object(m.b)("h3",{id:"estabilidade"},"Estabilidade"),Object(m.b)("h4",{id:"imprimir-dados"},"Imprimir dados"),Object(m.b)("p",null,"Exibe os dados da carga nos gr\xe1ficos no tempo.\nOs seguintes dados s\xe3o exibidos:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},"m\xf3dulo da tens\xe3o"),Object(m.b)("li",{parentName:"ul"},"corrente"),Object(m.b)("li",{parentName:"ul"},"pot\xeancias ativa e reativa.")),Object(m.b)("h4",{id:"utilizar-composi\xe7\xe3o-de-carga-zip"},"Utilizar composi\xe7\xe3o de carga ZIP"),Object(m.b)("p",null,"Permite compor a carga ZIP para estudos de estabilidade. 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Esse formul\xe1rio, comum a v\xe1rios outros elementos, permite a inser\xe7\xe3o e/ou remo\xe7\xe3o do motor durante o estudo de ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/indMotorSw.png"),alt:"Formul\xe1rio de chaveamento do motores de indu\xe7\xe3o",title:"Formul\xe1rio de chaveamento do motores de indu\xe7\xe3o"}))),Object(n.b)("hr",null),Object(n.b)("h3",{id:"geral"},"Geral"),Object(n.b)("h4",{id:"nome"},"Nome"),Object(n.b)("p",null,"Identifica\xe7\xe3o do elemento el\xe9trico. Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math 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considerado uma ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"load"}),"carga de pot\xeancia constante")," no estudo de ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),"."),Object(n.b)("p",{parentName:"div"},"A n\xe3o utiliza\xe7\xe3o dessa op\xe7\xe3o poder\xe1 gerar erros de regime permamente no estudo de ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."))),Object(n.b)("p",null,"Utilizar pot\xeancia nominal como base\nCaso essa op\xe7\xe3o seja marcada, o programa ir\xe1 utilizar a pot\xeancia nominal do gerador como base para a convers\xe3o das unidades, inclusive aqueles no formul\xe1rio de estabilidade, caso contr\xe1rio ser\xe1 usada a pot\xeancia base do sistema."),Object(n.b)("hr",null),Object(n.b)("h3",{id:"estabilidade"},"Estabilidade"),Object(n.b)("h4",{id:"imprimir-dados-da-m\xe1quina-de-indu\xe7\xe3o"},"Imprimir dados da m\xe1quina de indu\xe7\xe3o"),Object(n.b)("p",null,"Exibe os dados do 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Tal fator eleva o valor da resist\xeancia do rotor em condi\xe7\xf5es de grande escorregamento, como ocorre em motores de gaiola dupla ou gaiola profunda. 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PSP-UFU

Power System Platform of Federal University of Uberlândia

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User Guide
Samples
[object Object]

Complete Platform

PSP-UFU is a cross-platform, multilingual, Free and Open-Source Software (FOSS) with advanced GUI (Graphical User Interface) features and CAD (Computer-Aided Design) tools for electrical power system studies.

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Advanced CAD Features

The software allows the construction of any electric transmission network and control systems through the deployment of visual elements.

[object Object]

Easy Visualization

For the visualization of results, the program offers linked text elements in the main screen, voltage heatmap display, and also table and graph editors.

[object Object]

Application

The PSP-UFU aims to provide efficient computer simulation tools for research and education purposes, in addition to industrial applications in electrical power systems.

Studies Performed

Power Flow

  • Newton-Raphson
  • Gauss-Seidel
  • Hybrid Newton-Gauss
  • Three-phase induction motors included

Short-Circuit calculation

  • Balanced
  • Unbalanced
  • Short-Circuit power in all system buses

Harmonics

  • Harmonic voltages and THD (Total Harmonic Distortion) calculation
  • Frequency scan

Transient and Dynamic Stability

  • Several synchronous machine models automatically selected
  • Three-phase induction motors
  • User-defined machine controls, exciters and prime moves created using block diagrams (Exciters, AVR, PSS, Hydro and Thermal turbines, Speed Governor, etc.)

Published Papers

Further details can be found in the published papers:
Oliveira, T. L., Guimarães, G. C., & Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. International Transactions on Electrical Energy Systems, e12185. doi: 10.1002/2050-7038.12185
Oliveira, T. L., Guimarães, G. C., Silva, L. R., & Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. The International Journal of Electrical Engineering & Education, 0020720919879058. doi: 10.1177/0020720919879058

Code Documentation

All detailed descriptions of the source-code can be found at Online Documentation, generated by Doxygen.

Screenshots

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i.languages.go["class-name"],function(e){e.languages.handlebars={comment:/\{\{![\s\S]*?\}\}/,delimiter:{pattern:/^\{\{\{?|\}\}\}?$/i,alias:"punctuation"},string:/(["'])(?:\\.|(?!\1)[^\\\r\n])*\1/,number:/\b0x[\dA-Fa-f]+\b|(?:\b\d+\.?\d*|\B\.\d+)(?:[Ee][+-]?\d+)?/,boolean:/\b(?:true|false)\b/,block:{pattern:/^(\s*~?\s*)[#\/]\S+?(?=\s*~?\s*$|\s)/i,lookbehind:!0,alias:"keyword"},brackets:{pattern:/\[[^\]]+\]/,inside:{punctuation:/\[|\]/,variable:/[\s\S]+/}},punctuation:/[!"#%&'()*+,.\/;<=>@\[\\\]^`{|}~]/,variable:/[^!"#%&'()*+,.\/;<=>@\[\\\]^`{|}~\s]+/},e.hooks.add("before-tokenize",(function(t){e.languages["markup-templating"].buildPlaceholders(t,"handlebars",/\{\{\{[\s\S]+?\}\}\}|\{\{[\s\S]+?\}\}/g)})),e.hooks.add("after-tokenize",(function(t){e.languages["markup-templating"].tokenizePlaceholders(t,"handlebars")}))}(i),i.languages.json={property:{pattern:/"(?:\\.|[^\\"\r\n])*"(?=\s*:)/,greedy:!0},string:{pattern:/"(?:\\.|[^\\"\r\n])*"(?!\s*:)/,greedy:!0},comment:/\/\/.*|\/\*[\s\S]*?(?:\*\/|$)/,number:/-?\d+\.?\d*(e[+-]?\d+)?/i,punctuation:/[{}[\],]/,operator:/:/,boolean:/\b(?:true|false)\b/,null:{pattern:/\bnull\b/,alias:"keyword"}},i.languages.less=i.languages.extend("css",{comment:[/\/\*[\s\S]*?\*\//,{pattern:/(^|[^\\])\/\/.*/,lookbehind:!0}],atrule:{pattern:/@[\w-]+?(?:\([^{}]+\)|[^(){};])*?(?=\s*\{)/i,inside:{punctuation:/[:()]/}},selector:{pattern:/(?:@\{[\w-]+\}|[^{};\s@])(?:@\{[\w-]+\}|\([^{}]*\)|[^{};@])*?(?=\s*\{)/,inside:{variable:/@+[\w-]+/}},property:/(?:@\{[\w-]+\}|[\w-])+(?:\+_?)?(?=\s*:)/i,operator:/[+\-*\/]/}),i.languages.insertBefore("less","property",{variable:[{pattern:/@[\w-]+\s*:/,inside:{punctuation:/:/}},/@@?[\w-]+/],"mixin-usage":{pattern:/([{;]\s*)[.#](?!\d)[\w-]+.*?(?=[(;])/,lookbehind:!0,alias:"function"}}),i.languages.makefile={comment:{pattern:/(^|[^\\])#(?:\\(?:\r\n|[\s\S])|[^\\\r\n])*/,lookbehind:!0},string:{pattern:/(["'])(?:\\(?:\r\n|[\s\S])|(?!\1)[^\\\r\n])*\1/,greedy:!0},builtin:/\.[A-Z][^:#=\s]+(?=\s*:(?!=))/,symbol:{pattern:/^[^:=\r\n]+(?=\s*:(?!=))/m,inside:{variable:/\$+(?:[^(){}:#=\s]+|(?=[({]))/}},variable:/\$+(?:[^(){}:#=\s]+|\([@*%<^+?][DF]\)|(?=[({]))/,keyword:[/-include\b|\b(?:define|else|endef|endif|export|ifn?def|ifn?eq|include|override|private|sinclude|undefine|unexport|vpath)\b/,{pattern:/(\()(?:addsuffix|abspath|and|basename|call|dir|error|eval|file|filter(?:-out)?|findstring|firstword|flavor|foreach|guile|if|info|join|lastword|load|notdir|or|origin|patsubst|realpath|shell|sort|strip|subst|suffix|value|warning|wildcard|word(?:s|list)?)(?=[ 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i.languages.objectivec["class-name"],i.languages.ocaml={comment:/\(\*[\s\S]*?\*\)/,string:[{pattern:/"(?:\\.|[^\\\r\n"])*"/,greedy:!0},{pattern:/(['`])(?:\\(?:\d+|x[\da-f]+|.)|(?!\1)[^\\\r\n])\1/i,greedy:!0}],number:/\b(?:0x[\da-f][\da-f_]+|(?:0[bo])?\d[\d_]*\.?[\d_]*(?:e[+-]?[\d_]+)?)/i,type:{pattern:/\B['`]\w*/,alias:"variable"},directive:{pattern:/\B#\w+/,alias:"function"},keyword:/\b(?:as|assert|begin|class|constraint|do|done|downto|else|end|exception|external|for|fun|function|functor|if|in|include|inherit|initializer|lazy|let|match|method|module|mutable|new|object|of|open|prefix|private|rec|then|sig|struct|to|try|type|val|value|virtual|where|while|with)\b/,boolean:/\b(?:false|true)\b/,operator:/:=|[=<>@^|&+\-*\/$%!?~][!$%&*+\-.\/:<=>?@^|~]*|\b(?:and|asr|land|lor|lxor|lsl|lsr|mod|nor|or)\b/,punctuation:/[(){}\[\]|_.,:;]/},i.languages.python={comment:{pattern:/(^|[^\\])#.*/,lookbehind:!0},"string-interpolation":{pattern:/(?:f|rf|fr)(?:("""|''')[\s\S]+?\1|("|')(?:\\.|(?!\2)[^\\\r\n])*\2)/i,greedy:!0,inside:{interpolation:{pattern:/((?:^|[^{])(?:{{)*){(?!{)(?:[^{}]|{(?!{)(?:[^{}]|{(?!{)(?:[^{}])+})+})+}/,lookbehind:!0,inside:{"format-spec":{pattern:/(:)[^:(){}]+(?=}$)/,lookbehind:!0},"conversion-option":{pattern:/![sra](?=[:}]$)/,alias:"punctuation"},rest:null}},string:/[\s\S]+/}},"triple-quoted-string":{pattern:/(?:[rub]|rb|br)?("""|''')[\s\S]+?\1/i,greedy:!0,alias:"string"},string:{pattern:/(?:[rub]|rb|br)?("|')(?:\\.|(?!\1)[^\\\r\n])*\1/i,greedy:!0},function:{pattern:/((?:^|\s)def[ 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i.languages.reason.function,function(e){e.languages.sass=e.languages.extend("css",{comment:{pattern:/^([ \t]*)\/[\/*].*(?:(?:\r?\n|\r)\1[ \t]+.+)*/m,lookbehind:!0}}),e.languages.insertBefore("sass","atrule",{"atrule-line":{pattern:/^(?:[ \t]*)[@+=].+/m,inside:{atrule:/(?:@[\w-]+|[+=])/m}}}),delete e.languages.sass.atrule;var t=/\$[-\w]+|#\{\$[-\w]+\}/,n=[/[+*\/%]|[=!]=|<=?|>=?|\b(?:and|or|not)\b/,{pattern:/(\s+)-(?=\s)/,lookbehind:!0}];e.languages.insertBefore("sass","property",{"variable-line":{pattern:/^[ \t]*\$.+/m,inside:{punctuation:/:/,variable:t,operator:n}},"property-line":{pattern:/^[ \t]*(?:[^:\s]+ *:.*|:[^:\s]+.*)/m,inside:{property:[/[^:\s]+(?=\s*:)/,{pattern:/(:)[^:\s]+/,lookbehind:!0}],punctuation:/:/,variable:t,operator:n,important:e.languages.sass.important}}}),delete e.languages.sass.property,delete e.languages.sass.important,e.languages.insertBefore("sass","punctuation",{selector:{pattern:/([ \t]*)\S(?:,?[^,\r\n]+)*(?:,(?:\r?\n|\r)\1[ 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