Fuerte Esquivel, Claudio Rubén (1997) Steady State .
Fuerte Esquivel, Claudio Rubén (1997) Steady state modelling andanalysis of flexible AC transmission systems. PhD thesis.http://theses.gla.ac.uk/4616/Copyright and moral rights for this thesis are retained by the authorA copy can be downloaded for personal non-commercial research orstudy, without prior permission or chargeThis thesis cannot be reproduced or quoted extensively from without firstobtaining permission in writing from the AuthorThe content must not be changed in any way or sold commercially in anyformat or medium without the formal permission of the AuthorWhen referring to this work, full bibliographic details including theauthor, title, awarding institution and date of the thesis must be givenGlasgow Theses Servicehttp://theses.gla.ac.uk/theses@gla.ac.uk
Steady State Modelling and Analysisof Flexible AC Transmission SystemsbyClaudio Rubén Fuerte EsquivelB.Eng. (Summa Cum Laude) Instituto Tecnológico de Morelia, México, 1990M.Sc. (Summa Cum Laude) Instituto Politécnico Nacional, México, 1993A Thesis submitted to theDepartment of Electronics and Electrical EngineeringofThe University of Glasgowfor the degree ofDoctor of PhilosophyAugust 1997 Claudio Rubén Fuerte Esquivel, 1997
To my wife Monica, who put aside her own career, interest and a comfortable standard ofliving to kindly accompany me in this rewarding but often painful endeavour. Her love andwholehearted support, encouragement and understanding throughout these past three yearsmake our dream possible.To our wee son Claudio, who made our life a little more complicated but full of love andfun.To my mother for her love, encouragement, unconditional support and for always giving methe freedom and opportunity to pursue my aspirations.To my brother whose example has been a source of my strength and confidence to make thisundertaking possible.ii
AbstractAs electric utilities move into more competitive generation supply regimes, with limitedscope to expand transmission facilities, the optimisation of existing transmission corridorsfor power transfer becomes of paramount importance. In this scenario, Flexible ACTransmission System (FACTS) technology, which aims at increasing system operationflexibility, appear as an attractive alternative.Many of the ideas upon which the foundations of FACTS rest were conceived some timeago. Nevertheless, FACTS as a single coherent integrated philosophy is a newly developedconcept in electrical power systems which has received the backing of the majormanufacturers of electrical equipment and utilities around the world. It is looking at ways ofcapitalising on the new developments taking place in the area of high-voltage and highcurrent power electronics in order to increase the control of the power flows in the highvoltage side of the network during both steady state and transient conditions, so as to makethe network electronically controllable.In order to examine the applicability and functional specifications of FACTS devices, it isnecessary to develop accurate and flexible digital models of these controllers and to upgrademost of the software tools used by planners and operators of electric power systems.The aim of this work is to develop general steady-state models FACTS devices, suitable forthe analysis of positive sequence power flows in, large-scale real life electric power systems.Generalised nodal admittance models are developed for the Advance Series Compensator(ASC), Phase Shifter (PS), Static Var Compensator (SVC), Load Tap Changer (LTC) andUnified Power Flow Controller (UPFC). In the case of the ASC, two models are presented,the Variable Series Compensator (VSC) and the Thyristor Controlled Series CapacitorFiring Angle (TCSC-FA). An alternative UPFC model based on the concept of SynchronousVoltage Source (SVS) is also developed. The Interphase Power Controller (IPC) is modelledby combining PSs and VSCs nodal admittance models.The combined solution of the power flow equations pertaining to the FACTS devicesmodels and the power network is described in this thesis. The set of non-linear equations issolved through a Newton-Rapshon technique. In this unified iterative environment, theFACTS device state variables are adjusted automatically together with the nodal networkstate variables so as to satisfy a specified nodal voltage magnitudes and specified powerflows.Guidelines and methods for implementing FACTS devices and their adjustments within theNewton-Rapshon algorithm are described. It is shown that large increments in theadjustments of FACTS devices and nodal network state variables during the backwardsubstitution may dent the algorithm’s quadratic convergence. Suitable strategies are givenwhich avoid large changes in these variables and retain the Newton-Rapshon method'squadratic convergence.The influence of initial conditions of FACTS devices state variables on the iterative processis investigated. Suitable initialisation guidelines are recommended. Where appropriate,analytical equations are given to assure good initial conditions.iii
In order to investigate the issue of ‘number crunching’ Object Oriented Programming (OOP)power engineering applications, a power flow program written in C is developed usingthe OOP philosophy. The algorithm is a Newton-Raphson load flow which includescomprehensive control facilities and yet exhibits very strong convergence characteristics.The software is fast and reliable. It can be used for the analysis and control of large-scalepower networks containing FACTS-controlled devices. The methodology used in thedevelopment of the software is also given. Comparisons of the newly developed C powerflow program with a sequential N-R load flow program written in FORTRAN are made andsome finding are reported.Using the newly developed program, an extensive number of simulations are carried out inorder to investigate the interaction between FACTS devices and the network. Theapplication of FACTS devices to solve current issues in real life power networks is alsopresented. FACTS devices are used to redistribute power flow in an interconnected powernetwork, to eliminate loop flows and to increase margins of voltage collapse. Moreover, theeffect of the transformer magnetising branch on system losses is quantified. A general powerflow tracing algorithm to compute the individual generator contributions to the active andreactive power flows and losses is also proposed.iv
AcknowledgementsDuring this research I have had interaction with many people whose attitude, enthusiasmand willingness have enriched, in many forms, my knowledge and/or my experience to giveme encouragement to make this dream possible. To all of them I express my sincere thanks.Despite the above sentiments, there are few persons and organisations who deserve specialmention.I would like to extend my warmest thanks and gratitude to my supervisor Dr. Enrique Acha,for his invaluable technical support, incessant encouragement, sincere friendship andunderstanding. Dr. Acha has always generously given me his time and expertise in advisingme throughout my research. The past three years of working together has given me faith andconfidence to become an independent research for which I am thankful.I am indebted to my friend Dr. Horacio Tovar for his help with all legal matters of my studyleave at Instituto Tecnológico de Morelia, México.I gratefully acknowledge the financial assistance given by the Consejo Nacional de Cienciay Tecnología, México during my PhD studies.Thanks are also due to Instituto Tecnológico de Morelia, México for granting me study leaveto carry out my PhD research.I would like to express my appreciation to my postgraduate colleagues who made life somuch enjoyable.I thank my family, especially my uncle Fernando, my aunts Mary and Anita and my cousinsChela and Licha, for their love and kindness.Last, but not least, to my cousin Juan for his love, encouragement and help during myformative education in México. To him I also dedicate this work. I wish you were here.v
List of PublicationsThe following publications are associated with this research work:Transaction-Graded Papers: C.R. Fuerte-Esquivel and E. Acha.: ‘The Unified Power Flow Controller: A CriticalComparison of Newton-Rapshon UPFC Algorithms in Power Flow Studies’, accepted forpublication in IEE Proceedings on Generation, Transmission and Distribution, 1997. C.R. Fuerte-Esquivel and E. Acha.: ‘A Newton-type Algorithm for the Control of PowerFlow in Electrical Power Networks’, PE-159-PWRS-0-12-1997, To be published in IEEETransactions on Power Systems, 1997. C.R. Fuerte-Esquivel, E. Acha, S.G. Tan and J.J. Rico.: ‘Efficient Object Oriented PowerSystems Software for the Analysis of Large-scale Networks Containing FACTSControlled Branches’, PE-158-PWRS-0-12-1997, To be published in IEEE Transactionson Power Systems, 1997. C.R. Fuerte-Esquivel and E. Acha.: ‘Newton-Rapshon Algorithm for the ReliableSolution of Large Power Networks with Embedded FACTS Devices’, IEE Proceedingson Generation, Transmission and Distribution, Vol. 143, No. 5, September 1996, pp.447-454. C.R. Fuerte-Esquivel, E. Acha and H. Ambriz-Perez.: ‘A Thyristor Controlled SeriesCompensator Model for the Power Flow Solution of Practical Power Networks’,Submitted to IEEE Transactions on Power Systems, Summer 1997. C.R. Fuerte-Esquivel, E. Acha and H. Ambriz-Pérez.: ‘A Comprehensive NewtonRapshon UPFC for the Quadratic Power Flow Solution of Practical Power Networks’,Submitted to IEEE Transactions on Power Systems, Summer 1997. H. Ambriz-Pérez, E. Acha, C.R. Fuerte-Esquivel and A. De la Torre.: ‘The Incorporationof a UPFC model in an Optimal Power Flow by Newton’s Method’, Submitted to IEEProceedings on Generation, Transmission and Distribution, Summer 1997.Conference Papers: E. Acha, H. Ambriz-Pérez, S.G. Tan and C.R. Fuerte-Esquivel.: ‘A New Generation ofPower System Software Based on the OOP Paradigm’, International Power EngineeringConference 1997 (IPEC 97), Singapore 21-23 May 1997 pp. 68-73. H. Ambriz-Pérez, E. Acha, C.S. Chua and C.R. Fuerte-Esquivel.: ‘On the Auditing ofIndividual Generator Contributions to Optimal Power Flows and Losses in Large,Interconnected Power Networks’, International Power Engineering Conference 1997(IPEC 97), Singapore 21-23 May 1997 pp. 513-518. E. Acha, C.R. Fuerte-Esquivel and C.S. Chua.: ‘On the Auditing of Individual GeneratorContributions to Power Flows and Losses in Meshed Power Networks’, RVP 96-SIS-10,Power Summer Meeting IEEE Mexico Section, Acapulco Gro, Mexico, 21-26 July 1996,pp. 170-173. S.G. Tan, J.J. Rico, C.R. Fuerte-Esquivel and E. Acha: ‘C Object Oriented PowerSystems Software’, Proceedings of the 30th UPEC Conference, London UK, 5-7September 1995, pp. 339-342.vi
Table of ContentsAbstract.iiiAcknowledgements.vList of Publications.viTable of Contents.viiList of Figures.xiList of Tables.xviAbbreviations.xixChapter 11.11.21.31.41.5Background and motivation behind the present research.Objectives.Contributions.Thesis outline.Bibliography.Chapter 22.12.22.32.42.52.62.72.82.92.102.1123456A General Overview of Flexible AC Transmission SystemsIntroduction.Steady-state power flow and voltage control.Inherent limitations of conventional transmission systems.FACTS controllers.Power flow analysis of networks with FACTS devices.Initialisation of FACTS devices.Adjusted solution criterion.Truncated adjustments.FACTS applications.2.9.1 United Kingdom.2.9.2 Italy.2.9.3 France.2.9.4 Japan.2.9.5 Application of a thyristor series capacitor in theBonneville Power Administration system (USA).2.9.6 Application of a controllable series capacitor inthe American Electric Power system (USA).Conclusions.Bibliography.Chapter 0Power Flow Series ControllerIntroduction.Thyristor controlled series capacitor.3.2.1 TCSC voltage and current steady-state equations.3.2.2 TCSC fundamental frequency impedance.3.2.3 Operating modes of TCSCs.3.2.4 ASC steady-state power flow model.3.2.5 VSC initialisation.3.2.6 VSC active power flow control test case.3.2.7 Feasible active power flow control region.vii222223273032343537
3.33.43.53.63.2.8 Convergence test and VSC model validation.3.2.9 VSC active power flow control in a real power system.3.2.10 TCSC power flow model as function of the firing angle.3.2.11 TCSC’s firing angle initial condition.3.2.12 Numerical properties of the TCSC-FA model.3.2.13 Limit revision of TCSC’s firing angle.3.2.14 TCSC-FA active power flow control test case.3.2.15 Effect of the firing angle truncated adjustment.3.2.16 Multiple solutions due to multiple resonant points.3.2.17 TCSC-FA control near a resonance point.3.2.18 Power flow control by TCSC-FA in a real power system.3.2.19 Comparison of VSC and TCSC-FA models.Phase shifter.3.3.1 Phase shifter steady-state power flow model.3.3.2 PS initialisation and adjusted solution.3.3.3 PS active power flow control test case.3.3.4 PS feasible active power flow control region.3.3.5 Effect of PS’s impedance on phase angle value.3.3.6 Active power flow control by PSs and VSCs.3.3.7 Active power flow control in a real power system.Interphase power controller.3.4.1 IPC steady-state power flow model.3.4.2 IPC active power flow control test case.3.4.3 IPC feasible power flow control region.3.4.4 Effect of IPC reactances.3.4.5 Feasible active power control region of two IPCs.3.4.6 Active power flow control in a real power system.Conclusions.Bibliography.Chapter 727375767980838384Voltage magnitude controllers.Introduction.Static Var Compensator.4.2.1 SVC voltage-current characteristic and operation.4.2.2 SVC voltage-current equations.4.2.3 SVC fundamental frequency impedance.4.2.4 Conventional SVC power flow models.4.2.5 Proposed SVC power flow model.4.2.6 Control co-ordination between reactive sources.4.2.7 Revision of SVC limits.4.2.8 SVC nodal voltage magnitude test case.4.2.9 Control co-ordination between generators and SVCs.Load tap-changer.4.3.1 LTC power flow model for control of nodal voltage magnitude.4.3.2 Special control system configurations of LTCs.4.3.3 Simultaneous nodal voltage magnitude control by meansof reactive sources and LTCs.4.3.4 Initial conditions and adjusted solutions criterion of LTCs.4.3.5 LTC nodal voltage magnitude test case.4.3.6 Effect of LTC impedance on the tap magnitude value.4.3.7 Convergence test.4.3.8 Effect of sensitivity factors in the parallel control 106107108
4.44.54.3.9 Effect of truncated adjustments in the state variables.1084.3.10 Control co-ordination between LTCs and reactive sources.1144.3.11 Solution of a large power network with embedded FACTS devices. 116Conclusions.116Bibliography.117Chapter ised UPFC model.1205.2.1 UPFC equivalent circuit.1215.2.2 UPFC power equations.1215.2.3 UPFC jacobian equations.123Criterion control.1265.3.1 Shunt converter control criterion.1275.3.2 Series converter control criterion.1275.3.3 Special UPFC control configurations.127UPFC initial conditions and limits revisions.1285.4.1 Series source initial conditions.1285.4.2 Shunt source initial conditions.1285.4.3 Limit revision of UPFC controllable variables.129Synchronous voltage source UPFC model.1295.5.1 SVS initial conditions.130Load flow test cases.1325.6.1 Power flow control by means of UPFCs.1325.6.2 Effect of initial conditions.1335.6.3 Effect of UPFC transformer coupling reactances.1345.6.4 Effect of UPFC transformer coupling losses.1355.6.5 UPFC model validation.1365.6.6 Power flow control by means of SVSs.1375.6.7 Effect of SVS initial conditions.1385.6.8 Comparison of UPFC and SVS devices.1385.6.9 Interaction of UPFC and SVS with other FACTS devices.1395.6.10 Solution of a large power network with embedded FACTS devices. 1415.6.11 Power flow control by means of UPFCs in a real power system.142Conclusions.144Bibliography.144Chapter 66.1.6.2Unified power flow controllersApplications of FACTS DevicesIntroduction.Auditing of individual generator contributions to power flows,losses and cost in interconnected power networks.6.2.1 Tracing generators’ costs.6.2.2 Dominion’s contributions to active power flows.6.2.3 Dominion’s contributions to reactive power flows.6.2.4 Dominion’s contributions to loads.6.2.5 Source’s dominions.6.2.6 Numeric example of active power flow auditing.6.2.7 Numeric example of reactive power flow auditing.6.2.8 Effect of FACTS devices on active power source’s dominions.6.2.9 Numeric examples of use of line charges.6.2.10 Allocating generation costs and ULCs in a real lifepower network.ix146146147147148149149151154157158160
6.36.46.56.66.76.2.11 Tracing of reactive power flows.Loop flows.Effect of the transformer magnetising branch.6.4.1 Case 1.6.4.2 Case 2.Voltage collapse.6.5.1 Analysis of voltage collapse by a static approach.6.5.2 Analysis of maximum loadability and voltage collapsein the presence of FACTS devices.Conclusions.Bibliography.Chapter 3185186188190192193195195Conclusions and RecommendationsGeneral conclusions.Suggestions for further research work.Appendix I173178179Application of the Object Oriented Programming philosophy tothe analysis of electric power systems containing FACTS devicesIntroduction.Objective modelling of power networks.Derived types and data abstraction.Class hierarchy and inheritance.Sparsity techniques.Load flow analysis.Controllable devices.Load flow test case and validation.Solution of ill-conditioned networks.Conclusions.Bibliography.Chapter 8163164168168168170171197198200Data filesAppendix II General current equation of the TCSC215Appendix III Phase shifter transformer219x
List of FiguresFigure 2.1.Figure 2.2.Figure 2.3.Figure 3.1.Figure 3.2.Figure 3.3.Figure 3.4.Figure 3.5.Figure 3.6.Figure 3.7.Figure 3.8.Figure 3.9.Figure 3.10.Figure 3.11.Figure 3.12.Figure 3.13.Figure 3.14.Figure 3.15.Figure 3.16.Figure 3.17.Figure 3.18.Figure 3.19.Figure 3.20.Figure 3.21.Figure 3.22.Figure 3.23.Figure 3.24.Figure 3.25.Figure 3.26.Figure 3.27.Figure 3.28.Figure 3.29.Figure 3.30.Figure 3.31.Figure 3.32.Figure 3.33.Figure 3.34.Figure 3.35.Figure 3.36.Figure 3.37.Figure 3.38.Figure 3.39.Figure 3.40.Overhead transmission line.Organisation for implementation of FACTS Research programs.One-line diagram of Slatt substation’s TCSC.TCSC module.Equivalent electric circuit of a TCSC module.Asymmetrical thyristor current pulse.TCSC thyristor current in steady-state.Voltage and currents waveforms in the TCSC capacitor.Voltage and currents waveforms in the TCSC inductor.Voltage and currents waveforms in the TCSCbi-directional thyristors.TCSC fundamental impedance.TCSC module operating in thyristor blocked mode.TCSC module operating in thyristor-bypassed mode(full thyristor conduction).TCSC module operating in vernier mode.TCSC capacitor voltage in vernier mode operation.TCSC thyristor current in vernier mode operation.TCSC capacitor current in vernier mode operation.Advanced Series compensator.Original test network and load flow results.Modified test network and load flow results.Increments of active power flow as functionof series compensation.Feasible active power control region for 60%series compensation.Comparison of feasible active power control region sizes.Relevant part of the AEP 30 bus system.Relevant part of the modified AEP 30 bus system.Comparison of mismatches corresponding to unifiedand sequential methods as function of the number of iterations.Comparison of TCSC equivalent reactance.TCSC-FA module.TCSC susceptance profile as function of firing angle.Modified test network and load flow results.Multiple resonant points in the TCSC equivalent reactance.Relevant part of the 2172-nodes system.Phase shifter transformer.Phasor diagram showing the phase-shifting mechanism.A two winding transformer.Modified test network and load flow results.Eff
Steady State Modelling and Analysis of Flexible AC Transmission Systems by Claudio Rubén Fuerte Esquivel B.Eng. (Summa Cum Laude) Instituto Tecnológico de Morelia, México, 1990 M.Sc. (Summa Cum Laude) Instituto Politécnico Nacional, México, 1993 A Thesis submitted to the Department of Electronics and Electrical Engineering of
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