Power Flow Calculations.docx

Power Flow Calculations.docx

《Power Flow Calculations.docx》由会员分享，可在线阅读，更多相关《Power Flow Calculations.docx（12页珍藏版）》请在冰豆网上搜索。

PowerFlowCalculations

POWERFLOWCALCULATION

Name:

____郝攀_______________

Class:

____电气153班________

ID:

_____152247____________

POWERFLOWCALCULATION

Abstract：

Powerflowcalculationhasbeenvaluedasthebasisofpowersystemanalysis.Flowcalculationproblemsofcomplexpowersystemarecanbeincludedastosolveasetofmultivariatenonlinearequations.Andwecanusetheiterationtosolvemultivariatenonlinearequations.Threeapproacheswillbepresenttosolvethepowerflowcalculation.ThroughNewtonmethod,fast-decoupledmethod,DCpowerflowmethod,wecangetsomeconclusionswhichwillbenefitusonpoweranalysis.Differentmethodshavedifferentcharacteristicsandadvantagesandshortcomings.

Keywords:

Powerflowcalculation;Newtoniteration;fast-decoupled;DCmethod.

Introduction:

Thepowerflowproblemisaverywell-knownprobleminthefieldofpowersystemsengineering,wherevoltagemagnitudesandanglesforonesetofbusesaredesired,giventhatvoltagemagnitudesandpowerlevelsforanothersetofbusesareknownandthatamodelofthenetworkconfiguration（unitcommitmentandcircuittopology）isavailable.

Thepowerflowsolutioncontainsthevoltagesandanglesatallbuses,andfromthisinformation,wemaycomputetheactiveandreactivegenerationandloadlevelsatallbusesandtheactiveandreactiveflowsacrossallcircuits.

Powerbalanceequationsandtypesofbuses:

Whenanalyzingpowersystemsweknowneitherthecomplexbusvoltagesnorthecomplexcurrentinjections.However,weknowthecomplexpowerbeingconsumedbytheloadandthepowerbeinginjectedbythegeneratorsplustheirvoltagemagnitudes.Therefore,wecan’tdirectlyusetheY-busequations,butwemayusethepowerbalanceequations.

Where,

Therearethreemaintypesofpowerflowbuses:

PQ,PV,Slackbus.

Load（PQ）atwhichP/Qarefixed;iterationsolvesforvoltagemagnitudeandangle.Generator（PV）atwhichPandVarefixed;iterationsolvesforvoltageangleandQinjection.Slackatwhichthevoltagemagnitudeandanglearefixed;iterationsolvesforP/Qinjections.

Basicprinciplesofthreealgorithms:

Threemainmethodsareusedintheprojecttosolvethepowerflowcalculationsofthis24-Yus-network:

afullACNewtonapproach,afast-decoupledACNewtonapproachandaDCpowerflowapproach.

（a）Newtonapproach

IfweusetheNewtonapproach,weneedtogettheJacobianmatrix,andthecorrectionequation:

Where,

（b）fast-decoupledNewtonapproach

Ifweusethefast-decoupledACNewtonapproach,weneedtogettheB’andB’’matrix,andthecorrectionequation:

WhenwecalculateB’matrix,weignoretheeffectoftransformersandtheadmittance.ButwetakethemintoconsiderationwhenwecalculatetheB’’matrix.

（c）DCpowerflowapproach

IfweusetheDCpowerflowapproach,weneedtogettheBmatrix,andthecorrectionequation:

Powerofbranch:

Whenwegetallthevoltagesandanglesofeachbus,weshouldcalculatethepowerflowofeachbranch.

Howtocopewiththetransformer:

Weusethe

equivalentcircuitdiagramtoshowtheinfluenceoftransformerstovoltage.

IfthereisatransformerbetweennodeIandnodej,theratioisk,andtheadmittanceof1sideis

.

Powersystemstructureandthebusandbranchdata:

Busdata:

Branchdata:

Mainresults:

Aswecanseefromthetable,it’sthevoltagesandanglesofeachbus,andalsotheactiveandreactivepowerofthegeneratorsandtheload.

Thisisacomparisonbetweenthe3methods.AswecanseefromtheresultsofMATLABcode,theNewtonapproachhasthesameaccuracywiththePQapproach.

（withtheabove）

Thisisthepowerofeachbranch:

（withtheabove）

Conclusions:

Fromtheresultsoftheproject,wecandrawalotofconclusions:

First,theNewtonapproachhasthesameaccuracyofvoltagemagnitudes,voltageangles,activeflows,andreactiveflowswiththefast-decoupledACNewtonapproach.AndtheresultsfromtheDCpowerflowapproachisalittledifferentfromNewtonapproachandfast-decoupledACNewtonapproach.

Second,aswecanseefromthetable1,thePQ-methodhasmoreiterationsthantheNR-method,butitisfasterthantheNR-method.TheDC-methodisthefastestfromthethreemethods.Ifwewanttohaveafastcalculationandwecanallowsomeerror,wemustturntotheDC-methodfirstespeciallywhenthenetworkhasmanybuses.It’sbecausewedon’ttaketheto-groundcapacitorsandthetransformersintoconsideration.

Third,theparameterofBLhasagreatinfluenceonthevoltagephasors.

Table1

Accuracy（1e-7）

NR-method

PQ-method

DC-method

Iterations

5

12

1

Time

0.051502s

0.011400s

0.007457s

Alltheresultsisgivenintheattachment.Itincludesallinputandoutputdataofbusesandbranchesandacomparisontable（inDC-method）withvoltagephasorsandallcircuitflows（active&reactivepower）forallthreewaysofsolvingthenetwork.Tomakeareference,wealsogivetheresultsundera100%load.（Whenyouruntheprogramyoucanchangethepqtopq1andptop1togetresultsundera100%load.）

Attachment1:

NR-PQ（75%）

Attachment2:

DC（75%）（withacomparison）

Attachment3:

NR-PQ（100%）

Attachment4:

DC（100%）（withacomparison）