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Power System State Estimation and Contingency Constrained OptimalPowerFlow - A Numerically Robust ImplementationbySlobodan Pajic

A !issertationSubmitted to t"e Facultyo# t"e$ORCES%ER PO&'%EC(NIC INS%I%)%Ein partial #ul*llment o# t"e re+uirements #or t"e!egree o# !octor o# P"ilosop"yinElectrical and Computer EngineeringbyApril ,.APPRO/E!0

!r1 2e3in A1 Clements4 Ad3isor!r1 Paul $1 !a3is!r1 5arija Ilic!r1 (omer F1 $al6er!r1 Ale7ander E1 Emanuel

Abstract%"e researc" conducted in t"is dissertation is di3ided into two main parts1 %"e*rst part pro3ides#urt"er impro3ements in power system state estimation and t"e second partimplements ContingencyConstrained Optimal Power Flow 8CCOPF9 in a stoc"astic multiple contingency#ramewor61As a real-time application in modern power systems4 t"e e7isting Newton-:Rstate estimationalgorit"ms are too slow and too #ragile numerically1 %"is dissertation presents anew and morerobust met"od t"at is based on trust region tec"ni+ues1 A #aster met"od was#ound among t"eclass o# 2rylo3 subspace iterati3e met"ods4 a robust implementation o# t"econjugate gradientmet"od4 called t"e &S:R met"od1;ot" algorit"ms "a3e been tested against t"e widely used Newton-:R stateestimator on t"e

standard IEEE test networ6s1 %"e trust region met"od-based state estimatorwas #ound to be3ery reliable under se3ere conditions 8bad data4 topological and parametererrors91 %"is en"ancedreliability justi*es t"e additional time and computational e

8/9/2019 Power System State Estimation and Contingency Constrained Optimal Power

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wit" classical direct Newton-:R1 %"e gain in computational e=ciency "as notcome at t"e cost o#solution reliability1

%"e second part o# t"e dissertation combines Se+uential :uadraticProgramming 8S:P9-basedCCOPF wit" 5onte Carlo importance sampling to estimate t"e operating cost o#

multiple contingencies1$e also de3eloped an &P-based #ormulation #or t"e CCOPF t"at can e=cientlycalculate&ocational 5arginal Prices 8&5Ps9 under multiple contingencies1 ;ased on5onte Carlo importancesampling idea4 t"e proposed algorit"m can stoc"astically assess t"e impact o#multiple contingencieson &5P-congestion prices1iii

Ac6nowledgementsI would li6e to e7press my deepest appreciation and gratitude to my ad3isor4!r1 2e3in A1Clements1 (is guidance and support were essential #or t"e de3elopment o# t"isdissertation1 I couldnot "a3e imagined a better mentor t"an !r1 Clements1 (is insig"t#ul e7perienceand editorialassistance "a3e always been immensely "elp#ul1I grate#ully ac6nowledge !r1 Paul $1 !a3is #or "is in3aluable comments w"ilepatiently goingo3er dra#ts and dra#ts o# my dissertation1 $it"out !r1 !a3is>s re3isions4 clarityo# t"e presentedresearc" would "a3e not been t"e same1Additionally4 I would li6e to t"an6 !r1 (omer F1 $al6er #or teac"ing me t"e art o#

numericalanalysis1 I am also obliged to !r1 $al6er #or t"e numerous discussions andguidance o3er t"e courseo# t"is dissertation1I am deeply indebted to !r1 Ale7ander E1 Emanuel #or "is tremendousassistance on many le3els1Our ric" collaboration was not only scienti*cally rewarding4 but alsoinspirational on a personalle3el1I>m e3er t"an6#ul to !r1 5arija Ilic #or encouraging me to pursue my graduatestudies inelectrical engineering1 $it"out "er4 t"is scienti*c journey may not "a3e

occurred1From t"e bottom o# my "eart4 I wis" to t"an6 my mot"er &jiljana ?Cola6 and mysister @elenaPajic4 #or t"eir endless lo3e4 support and understanding1Financial support #or a part o# t"is researc" was pro3ided by t"e NationalScience Foundationunder grant ECS-B.B1i3

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D11, Importance Sampling 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 G.D11 Numerical e7ample 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ,D11D Conclusion 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A Formulation o# t"e !C Contingency Constrained OPF #or &5PCalculationsD1 Introduction 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 D

1, Initial problem #ormulation 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5odeling o# Ine+uality Constraints 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 G11 %ransmission line Jow limits using distribution #actors 1 1 1 1 1 1 1 1 1 1 1 1 1G11, Henerator output limits 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ,11 &oad s"edding limits 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11D Ramp-rate constraints 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 D1D An Interior Point Solution Algorit"m 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 D1D1 Solution o# t"e reduced system 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ,1 Formulation o# t"e !C Contingency Constrained OPF 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1,,11 Solution o# t"e upper ;ordered-diagonal system 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ,.

1B Importance sampling #or &5P-based congestion prices 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1,GB Conclusions and Future $or6 B1 Conclusions 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 B1, Future $or6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ,A Networ6 %est Cases A1 Introduction 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A1, IEEE D bus networ6 case 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A1 IEEE bus networ6 case 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A1D Non-con3erging cases 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 .; ; 5atri7 %"eorems G;ibliograp"y DB

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