Dynamic Modeling and Control of Multi-Machine Power System with FACTS Devices for Stability Enhancement

Transcription

1 Dynamc Modelng and Control of Mult-Machne Power System wth FACTS Devces for Stablty Enhancement A thess submtted n partal fulfllment of the requrements for the degree of Doctor of Phlosophy n Electrcal Engneerng by Jose P. Therattl ROLL NO. 509EE703 Under the Gudance of Prof. P. C. Panda Department of Electrcal Engneerng Natonal Insttute of Technology Rourkela (Odsha) July 2012

2 DEPARTMENT OF ELECTRICAL ENGINEERING NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA ODISHA, INDIA CERTIFICATE Ths s to certfy that the thess enttled Dynamc Modellng and Control of Mult-machne Power System wth FACTS Devces for Stablty Enhancement, beng submtted by Shr Jose P. Therattl, s a record of bonafde research carred out by hm at Electrcal Engneerng Department, Natonal Insttute of Technology, Rourkela, under my gudance and supervson. The work ncorporated n ths thess has not been, to the best of my knowledge, submtted to any other unversty or nsttute for the award of any degree or dploma. Dr. P. C. Panda Professor Department of Electrcal Engneerng Natonal Insttute of Technology Rourkela (Odsha)

3 Acknowledgements Ths thess s a result of research that has been carred out at Natonal Insttute of Technology, Rourkela. Durng ths perod, I came across wth a great number of people whose contrbutons n varous ways helped my feld of research and they deserve specal thanks. It s a pleasure to convey my grattude to all of them. In the frst place, I would lke to express my deep sense of grattude and ndebtedness to my supervsor Prof. P. C. Panda for hs advce, and gudance from early stage of ths research and provdng me extraordnary experences throughout the work. Above all, he provded me unflnchng encouragement and support n varous ways whch exceptonally nspre and enrch my growth as a student, a researcher and a scentst. I am proud to record that I had opportunty to work wth an exceptonally experenced scentst lke hm. I am grateful to Drector, Prof. S.K. Sarang and Prof. Bdyadhar Subudh, Head of Electrcal Engneerng Department, Natonal Insttute of Technology, Rourkela, for ther knd support and concern regardng my academc requrements. I am thankful for the opportunty to be a member of Natonal nsttute of technology of Electrcal Engneerng Department. I express my grattude to the members of Doctoral Scrutny Commttee, Prof. K.B. Mohanty and Prof. K.K. Mohapatra for ther advce and care. I express my thankfulness to the faculty and staff members of the Electrcal Engneerng Department for ther contnuous encouragement and suggestons. Thanks are also due to my co-scholars at Natonal Insttute of Technology, Rourkela, for ther whole hearted support and cooperaton durng the duraton of ths work. My parents deserve specal menton for ther nseparable support and prayers. They are the persons who show me the joy of ntellectual pursut ever snce I was a chld. I thank them for sncerely brngng up me wth care and love. The completon of ths work came at the expense of my long hours of absence from home. Words fal me to express my apprecaton to my wfe Jerry Jose and my sons Paul Therattl

4 and Anthony Therattl for ther understandng, patence and actve cooperaton throughout the course of my doctoral dssertaton. I thank them for beng supportve and carng. Last, but not the least, I thank the one above all of us, the omnpresent God, for gvng me the strength durng the course of ths research work. Jose P. Therattl Roll No. 509EE703

5 Abstract Due to envronmental and economcal constrants, t s dffcult to buld new power lnes and to renforce the exstng ones. The contnued growth n demand for electrc power must therefore to a great extent be met by ncreased loadng of avalable lnes. A consequence of ths s reducton of power system dampng, leadng to a rsk of poorly damped power oscllatons between generators. Ths thess proposes the use of controlled actve and reactve power to ncrease dampng of such electro-mechancal oscllatons. The focus of ths thess s a FACTS devce known as the Unfed Power Flow Controller (UPFC). Wth ts unque capablty to control smultaneously real and reactve power flows on a transmsson lne as well as to regulate voltage at the bus where t s connected, ths devce creates a tremendous qualty mpact on power system stablty. These features turn out to be even more sgnfcant because UPFC can allow loadng of the transmsson lnes close to ther thermal lmts, forcng the power to flow through the desred paths. Ths provddes the power system operators much needed flexblty n order to satsfy the demands. A power system wth UPFC s hghly nonlnear. The most effcent control method for such a system s to use nonlnear control technques to acheve system oscllaton dampng. The nonlnear control methods are ndependent of system operatng condtons. Advanced nonlnear control technques generally requre a system beng represented by purely dfferental equatons whereas a power system s normally represented by a set of dfferental and algebrac equatons. In ths thess, a new method to generate a dynamc modelng for power network s ntroduced such that the entre power system wth UPFC can be represented by purely dfferental equaton. Ths representaton helps us to convert the nonlnear power system equatons nto standard parametrc feedback form. Once the standard form s acheved, conventonal and advanced nonlnear control technques can be easly mplemented.

6 A comprehensve approach to the desgn of UPFC controllers (AC voltage control, DC voltage control and dampng control) s presented. The dampng controller s desgned usng nonlnear control technque by defnng an approprate Lyapunov functon. The analytcal expresson of the nonlnear control law for the UPFC s obtaned usng back steppng method. Then, combnng the nonlnear control strategy wth the lnear one for the other varables, a complete lnear and nonlnear stablzng controller s developed. Fnally, an adaptve method for estmatng the uncertan parameters s derved. Ths relaxes the need for approxmatng the uncertan parameters lke dampng coeffcent, transent synchronous reactance etc., whch are dffcult to be measured precsely. The developed controller provdes robust dynamc performance under wde varatons n loadng condton and system parameters, and provdes a sgnfcant mprovement n dynamc performance n terms of peak devatons. The proposed controller s tested on dfferent mult-machne power systems and found to be more effectve than exstng ones.

7 Dedcated to My Wfe and Chldren

8 Contents Certfcate Acknowledgements Abstract Contents Lst of Fgures Nomenclature Abbrevaton v v x xv xx 1 Introducton Revew of lterature Research objectve Thess outlne Conclusons 16 2 Basc Operaton, Modelng and Interfacng of Power System Components Introducton Basc operaton of UPFC Modelng of power system components Interfacng UPFC wth power network Concluson 47 3 Lead-Lag Control Desgn for Mult-Machne Power System wth UPFC Introducton Lnearzaton Lnearzed model for a two-machne power system Partcpaton factor Controllablty ndex Genetc algorthm 62 v

9 3.7 Phllps-Heffron model Results and dscusson Concluson 73 4 Dynamc Modelng and Adaptve Control of Sngle Machne-Infnte Bus System wth UPFC Introducton Power system modelng Controller desgn Results and dscusson Concluson 95 5 Dynamc Modelng and Nonlnear Control of Mult-Machne Power System wth UPFC Introducton Nonlnear dynamc representaton Nonlnear control desgn Results and dscusson Concluson Integrated Lnear-Nonlnear Control of Mult-Machne Power System wth UPFC Introducton System under study Results and dscusson Conclusons and Future Work 140 References 143 Appendx A 152 Appendx B 153 Appendx C 154 Dssemnaton of the Work 158 x

10 Lst of Tables Table 1.1 Performance Analyss of FACTS devces [20] 12 Table 3.1 Stablty crtera for a lnear system [64] 54 Table 3.2 System parameters and ntal condtons 56 Table 3.3 System states and egen-values 58 Table 3.4 Computatonal results to select the best nput control sgnal 61 Table 3.5 Parameters used n Genetc Algorthm 63 Table 3.6 Egen-values for the electromechancal modes 64 Table 4.1 System parameters and ntal condtons 78 Table 6.1 System egen-values for the electromechancal modes 130 Table 6.2 System egen-values for the electromechancal modes 136 x

11 Lst of Fgures Fgure 1.1 Block dagram of conventonal power system stablzer 5 Fgure 1.2 Statstcs for FACTS applcatons to power system stablty 12 Fgure 2.1 Basc Crcut Confguraton of the UPFC 19 Fgure 2.2 Three Phase Voltage Source-Converter 21 Fgure 2.3 A Phase-leg 23 Fgure 2.4 PWM Waveforms 23 Fgure 2.5 Transmsson Lne 24 Fgure 2.6 Phasor Dagrams 27 Fgure 2.7 Transmsson lne wth UPFC 28 Fgure 2.8 P-Q relatonshp wth a UPFC 30 Fgure 2.9 P-Q relatonshp wth a UPFC at = 00, 300, 600 and Fgure 2.10 Axs-Transformaton Phasor dagram 36 Fgure 2.11 UPFC sngle-lne dagram 37 Fgure 2.12 Steady-state dagram of two-machne system 37 Fgure 2.13 UPFC power flow model 38 Fgure 2.14 Equvalent crcut and Phasor dagram of UPFC 40 Fgure 2.15 Injecton model for UPFC 40 Fgure 2.16 Transmsson lne wth UPFC 42 Fgure 2.17 Interface of UPFC wth power network 44 Fgure 3.1 Sample power system wth UPFC 55 Fgure 3.2 Block dagram of dampng controller 62 Fgure 3.3 Lnearzed Phllps-Heffron model of power system wth UPFC 64 x

12 Fgure 3.4 Load angle varaton 65 Fgure 3.5 Angular speed varaton 66 Fgure 3.6 Termnal voltage varaton 66 Fgure 3.7 Termnal voltage varaton 67 Fgure 3.8 Injected UPFC real power varaton 67 Fgure 3.9 Load angle varaton 68 Fgure 3.10 Load angle varaton 68 Fgure 3.11 Load angle varaton 69 Fgure 3.12 Load angle varaton 69 Fgure 3.13 Load angle varaton 69 Fgure 3.14 Load angle varaton 70 Fgure 3.15 Load angle varaton 71 Fgure 3.16 Load angle varaton 71 Fgure 3.17 Load angle varaton 72 Fgure 3.18 Load angle varaton 72 Fgure 3.19 Load angle varaton 72 Fgure 4.1 Sngle machne Infnte bus power system 76 Fgure 4.2 structure of parameter estmater 83 Fgure 4.3 Block dagram representaton of nonlnear adaptve control 85 Fgure 4.4 Conventonal controller 86 Fgure 4.5 Dynamc performance of generator at Pe = 1.2 pu 87 Fgure 4.6 Dynamc performance of generator at Pe=1.2 pu 88 Fgure 4.7 Varaton of termnal voltage 89 Fgure 4.8 Varaton of real power transfer 89 x

13 Fgure 4.9 Injected UPFC real power 90 Fgure 4.10 Injected UPFC voltage 90 Fgure 4.11 Uncertan parameter 2 91 Fgure 4.12 Uncertan parameter 3 91 Fgure 4.13 Dynamc performance of the generator at Pe =0.1 pu 92 Fgure 4.14 Dynamc performance of the generator at Pe =0.1 pu 92 Fgure 4.15 Load angle varaton wth dfferent topologes 93 Fgure 4.16 Load angle varaton at a dfferent fault locaton wth Pe =1.2pu 94 Fgure 4.17 Dynamc performance wth dfferent control sgnals 94 Fgure 5.1 Sample two area power system 99 Fgure 5.2 Varaton of load angle n degrees 105 Fgure 5.3 Varaton of speed of generator Fgure 5.4 Varaton of actve power of generator Fgure 5.5 Termnal voltage varaton of generator Fgure 6.1 Proposed hybrd controller 110 Fgure 6.2 Sample two generator power system 110 Fgure 6.3 Control performance of PI AC voltage regulator 121 Fgure 6.4 Load angle varaton durng AC voltage regulaton 121 Fgure 6.5 Control performance of PI DC voltage controller 121 Fgure 6.6 Load angle varaton durng DC voltage regulaton 122 Fgure 6.7 Performance of dampng controller at Pe = 0.5pu 122 Fgure 6.8 Performance of dampng controller at Pe = 0.5pu 123 Fgure 6.9 Performance of dampng controller at Pe = 0.5pu 123 x

14 Fgure 6.10 Performance of dampng controller at Pe = 0.5pu 123 Fgure 6.11 Performance of dampng controller at Pe = 0.5pu 124 Fgure 6.12 DC voltage at Pe = 0.5pu 124 Fgure 6.13 Performance of dampng controllers at Pe = 1.2pu 125 Fgure 6.14 Performance of dampng controllers at Pe = 1.0pu 125 Fgure 6.15 Performance of dampng controllers at Pe = 0.8pu 126 Fgure 6.16 Performance of dampng controllers at Pe = 0.5pu 126 Fgure 6.17 Performance of dampng controllers at Pe = 0.2pu 126 Fgure 6.18 Load angle varaton 127 Fgure 6.19 Load angle varaton 127 Fgure 6.20 Load angle varaton 128 Fgure 6.21 Load angle varaton 128 Fgure 6.22 Load angle varaton 128 Fgure 6.23 Load angle varaton 129 Fgure 6.24 Three machne nne bus system 131 Fgure 6.25 Angular speed varaton of generator Fgure 6.26 Angular speed varaton of generator Fgure 6.27 Angular speed varaton of generator Fgure 6.28 Real power varaton of generator Fgure 6.29 Real power varaton of generator Fgure 6.30 Real power varaton of generator Fgure 6.31 Load angle varaton (δ12) 134 Fgure 6.32 Load angle varaton (δ13) 134 Fgure 6.33 Four generator power system 135 xv

15 Fgure 6.34 Load angle varaton (δ13) 135 Fgure 6.35 Load angle varaton (δ23) 136 Fgure 6.36 Termnal voltage varaton (V9) 137 Fgure 6.37 Capactor DC voltage (Vdc) 137 Fgure 6.38 Load angle varaton 138 Fgure 6.39 Capactor DC voltage (Vdc) 138 xv

16 Nomenclature δ, ω : Rotor angle and angular speed of the th machne P m : Input mechancal power of the th machne E g : Internal generator voltage of the th machne M : Machne nerta of the th machne D : Dampng coeffcent H : Inerta constant P e : Electrcal power of the generator X d X q :Drect axs steady state reactance of the generator : Quadrature axs steady state reactance of the generator X d : Drect axs transent reactance of the generator T do : Drect axs open crcut tme constant of the generator C dc : DC lnk capactor V dc : Voltage at DC lnk m SH : Modulaton ndex of shunt converter φ SH : Phase angle of shunt-converter voltage m : Modulaton ndex of seres converter φ I SH : Phase angle of seres-converter voltage : Current through shunt converter xv

17 T 1,T 2,T 3,T 4 f P L, Q L : Tme constants of Lead-Lag controller : Frequency : Actve and reactve load at each bus V : Voltage magntude of the th bus Ф : Phase angle of the th bus voltage X L : Reactance of transmsson lne X SH, X V T X t V B E fd K A T A T W Ψ : Reactance of shunt and seres transformer : Termnal voltage at bus : Reactance of the step-up transformer : System sde base voltage n KV : Feld voltage of generator : Exctaton system gan : Exctaton system tme constant : Incremental operator : Wash out flter tme constant : Uncertan parameters xv

18 xv

19 Abbrevaton FACTS SVC TCSC STATCOM SSSC UPFC IPFC PSS HVDC EPRI QFT CSC S GTO SVD PWM VSC SISO : Flexble AC Transmsson Systems : Statc VAR Compensator : Thyrstor Controlled Seres Capactor : Statc Synchronous Compensators : Statc Synchronous Seres Compensators : Unfed Power Flow Controllers : Interlne Power Flow Controllers : Power System Stablzer : Hgh Voltage Drect Current : Electrc Power Research Insttute : Quanttatve feedback theory : Controllable Seres Capactor : Sub-synchronous Resonance : Gate Turn Off : Sngular Value Decomposton : Pulse Wdth Modulaton : Voltage Source Converter : Sngle-nput Sngle-output xx

20 MIMO PI COI SMIB GA : Mult-nput Mult-output : Proportonal and Integral : Center of Inerta : Sngle Machne Infnte Bus : Genetc Algorthm xx

21 Chapter 1 Introducton xx

22 Chapter 1 Introducton The avalable power generatng plants are often located at dstant locatons for economc, envronmental and safety reasons. For nstance, t becomes cheaper to nstall a thermal power staton at pt-head nstead of transportng coal to load centers. Hydro power s generally avalable n remote areas and a nuclear plant may be located at a place away from urban areas. Addtonally, modern power systems are hghly nterconnected. Sharng of generaton reserves, explotng load dversty and economy ganed from the use of large effcent unts wthout sacrfcng relablty are the advantages of nterconnecton. Thus power must consequently be transmtted over long dstances. To meet the load and electrc market demands, new lnes should be added to the system, but due to envronmental reasons, the nstallaton of electrc power transmsson lnes are often restrcted. Hence, the utltes are forced to rely on already exstng nfra-structure nstead of buldng new transmsson lnes. In order to maxmze the effcency of generaton, transmsson and dstrbuton of electrc power, the transmsson networks are very often pushed to ther physcal lmts, where outage of lnes or other equpment could result n the rapd falure of the entre system. The power system may be thought of as a nonlnear system wth many lghtly damped electromechancal modes of oscllaton. The three modes of electromechancal oscllatons are: Local plant mode oscllatons Inter-area mode oscllatons Torsonal modes between rotatng plant In local mode, one generator swngs aganst the rest of the system at 1.0 to 2.0 Hz. The mpact of the oscllaton s localzed to the generator and the lne connectng t to the

23 grd. The rest of the system s normally modeled as a constant voltage source whose frequency s assumed to reman constant. Ths s known as the SIMB model Inter-area mode of oscllatons s observed over a large part of the network. It nvolves two coherent groups of generators swngng aganst each other at 1Hz or less. Ths complex phenomenon nvolves many parts of the system wth hghly non-lnear dynamc behavor. The dampng characterstc of the nter-area mode s dctated by the te-lne strength, the nature of the loads and the power flow through the nterconnecton and the nteracton of loads wth the dynamcs of generators and ther assocated controls. Torsonal mode oscllatons s assocated wth a turbne generator shaft system n the frequency range of Hz. Usually these modes are excted when a mult-stage turbne generator s connected to the grd system through a seres compensated lne. A mechancal torsonal mode of the shaft system nteracts wth the seres capactor at the natural frequency of the electrcal network. The shaft resonance appears when network natural frequency equals synchronous frequency mnus torsonal frequency. If the dampng of these modes becomes too small, t can mpose severe constrants on the system s operaton. It s thus mportant to be able to determne the nature of those modes, fnd stablty lmts and n many cases use controls to prevent nstablty. The poorly damped low frequency electromechancal oscllatons occur due to nadequate dampng torque n some generators, causng both local-mode oscllatons and nter-area oscllatons (0.2 Hz to 2.5 Hz) [1], [2]. The basc functon of an exctaton system s to provde drect current to the synchronous machne feld wndng. In addton, the exctaton system performs control functons essental to the satsfactory performance of the power system by controllng the feld voltage and there by the feld current. The control functons nclude the control of voltage and reactve power flow, and the enhancement of system stablty. Exctaton system helps to mprove synchronzng torque where as under heavy loadng condtons t ntroduces negatve dampng. Ths s because the exctaton system ntroduces a large 2

24 phase lag at low system frequences just above the natural frequency of the exctaton system. Thus t can often be assumed that the voltage regulator ntroduces negatve dampng. These are the stuatons n whch dynamc stablty s of concern. The tradtonal approach employs power system stablzers (PSS) on generator exctaton control systems n order to damp those oscllatons. PSSs are effectve but they are usually desgned for dampng local modes. In large power systems, they may not provde enough dampng for nter-area modes. So, more effcent substtutes are needed other than PSS. In late 1980s, the Electrc Power Research Insttute (EPRI) had ntroduced a new technology program known as Flexble AC Transmsson System (FACTS) [3]. The man dea behnd ths program s to ncrease controllablty and optmze the utlzaton of the exstng power system capactes by relable and hgh-speed power electronc devces. The latest generaton of FACTS controllers s based on the concept of the sold state synchronous voltage sources (SVSs) ntroduced by L. Gyugy n the late 1980s [4]. The SVS behaves as an deal synchronous machne,.e., t generates three-phase balanced snusodal voltages of controllable ampltude and phase angle wth fundamental frequency. It can nternally generate both nductve and capactve reactve power. If coupled wth an approprate energy storage devce,.e., DC storage capactor, battery etc., SVS can exchange real power wth the AC system. The SVS can be mplemented by the use of the voltage source converters (VSC). The major advantages of SVS-based compensators over mechancal and conventonal thyrstor compensators are: Improved operatng and performance characterstcs Unform use of same power electronc devce n dfferent compensaton and control applcatons Reduced equpment sze and nstallaton labor. 3

25 The SVS can be used as shunt or seres compensator. If operated as a reactve shunt compensator, t s called statc synchronous compensator (STATCOM); and f operated as a reactve seres compensator, t s called statc synchronous seres compensator (SSSC). A specal arrangement of two SVSs, one connected n seres wth the AC system and the other one connected n shunt wth common DC termnals, s called Unfed Power Flow Controller (UPFC). The UPFC s a combnaton of the two n a sngle devce. UPFC s the most promsng devce n the FACTS concept. It has the ablty to adjust all the three control parameters,.e., the bus voltage, transmsson lne reactance and phase angle between two buses, ether smultaneously or ndependently. A UPFC performs ths through the control of the n-phase voltage, quadrature voltage and shunt compensaton. 1.1 Revew of lterature In ths secton a lterature survey of topcs related to power system operaton, modelng and control s hghlghted. A power system may be thought to be a large nterconnected system wth many lghtly damped electro-mechancal oscllatons. Durng such oscllatons, mechancal knetc energy s exchanged between synchronous generators as electrc power flows through the network. The oscllatons can be seen n many varables, where the rotor veloctes of the generators and the power flows n the network are the most mportant. The rotor velocty varaton causes stran to mechancal parts n the power plant and should be lmted. The power flow oscllatons may amount to the entre ratng of a power lne. As they are supermposed on the statonary lne flow, they lmt the transfer capacty by requrng ncreased safety margns. Power system stablty s defned as the ablty of an electrcal power system, for a gven ntal operatng condton, to regan a state of operatng equlbrum after beng subjected to physcal dsturbance [1], [6]. 4

26 A. Conventonal methods As a convenent approach to control synchronous generator and stablze power systems, exctaton controller desgn has drawn szable consderaton [7], [8]. The operaton of exctaton control contnues to mantan generator voltage and reactve power output. A hgh response excter s helpful n addng synchronzng torque. However, on account of performng, t ntroduces negatve dampng. An effcent method to meet the conflctng excter behavor wth respect to system stablty s to assgn a PSS. The elementary usage of power system stablzer s to supplement dampng to the generator rotor oscllatons by governng ts exctaton employng auxlary stablzng sgnals [9], [10], [11]. The PSS classcally uses shaft speed, actve power output or bus frequency as nput [12]. The stablzer shown n Fgure 1.1 conssts of two lead-lag flters. These are used to compensate for the phase lag ntroduced by the AVR and the feld crcut of the generator. Other flter sectons are usually added to reduce the mpact on torsonal dynamcs of the generator, and to prevent voltage errors due to a frequency offset. The lead-lag flters are tuned so that speed oscllatons gve a dampng torque on the rotor. By varyng the termnal voltage the PSS affects the power flow from the generator, whch effcently damps local modes. Fgure 1.1 shows the block dagram representaton of a conventonal PSS. Where K S s the stablzer gan, whle T w and T1 to T 4 are the tme constants of washout and lead-lag flters respectvely. The PSS output s added to the dfference between reference V ref and actual value V act of the termnal voltage. Fgure 1.1: Block dagram of conventonal power system stablzer 5

27 A dffculty of PSS tunng, except for the trade-off wth voltage regulaton, s that the dynamcs that should be compensated by the lead-lag flters vary wth the operatng pont and the network reactance [12]. The effect of PSS on nter-area modes dffers from the local modes n two ways. Frstly, the achevable dampng of nter-area modes s less than that of local modes. Secondly, nter-area modes are affected manly through modulaton of voltage senstve loads. Ths makes assumptons on load characterstcs crtcal both for nvestgatons and for feld tunng [13], [14]. Dampng of both local and nter-area modes requres sutable phase compensaton over a wder frequency range, whch may be dffcult to acheve and therefore, other effcent substtutes are needed n addton to PSS. B. FACTS devces In the late 1980s, the Electrc Power Research Insttute (EPRI) formulated the vson of the FACTS n whch varous power-electroncs based controllers regulate power flow and transmsson voltage, and they mtgate dynamc dsturbances. Generally, the man objectves of FACTS are to ncrease the useable transmsson capacty of lnes and control power flow over desgnated transmsson routes. Hngoran and Gyugy [5] and Hngoran [15], [16] proposed the concept of FACTS and Edrs et al. [17] proposed terms and defntons for dfferent FACTS controllers. Due to recent advances n power electroncs, the FACTS devces have ganed a great nterest durng the last few years. There are two generatons for realzaton of power electroncs-based FACTS controllers: the frst generaton employs conventonal thyrstor-swtched capactors and reactors, and quadrature tap-changng transformers, and the second generaton employs gate turn-off (GTO) thyrstor-swtched converters as voltage source converters (VSCs). The frst generaton has resulted n the Statc VAR Compensator (SVC), the Thyrstor- Controlled Seres Capactor (TCSC), and the Thyrstor-Controlled Phase Shfter (TCPS) [18], [19]. The second generaton has produced the Statc Synchronous Compensator (STATCOM), the Statc Synchronous Seres Compensator (SSSC), the Unfed Power Flow Controller 6

28 (UPFC), and the Interlne Power Flow Controller (IPFC) [20], [21], [22], [23]. The two groups of FACTS controllers have dstnctly dfferent operatng and performance characterstcs. (a) Frst generaton FACTS Frst generaton FACTS employs capactor and reactor banks wth fast sold-state swtches n tradtonal shunt or seres crcut arrangements. The thyrstor swtches control the on and off perods of the fxed capactor and reactor banks and thereby realze a varable reactve mpedance. Except for losses, they cannot exchange real power wth the system. Statc VAR Compensator (SVC) The SVC s a reactve shunt devce that uses ts reactve capablty to alter the bus voltage. It enables a regulated voltage support. An SVC for contnuous control contans a thyrstor swtched capactor bank n parallel wth a bank of phase angle controlled reactors and s connected to the transmsson voltage level va a transformer. The SVC nfluences electro-mechancal oscllatons lke the PSS: t changes the lne transfer (by controllng V ) as well as modulates voltage senstve loads. Dependng on whch of these effects domnate, the SVC s placed ether at the mdpont of a long transmsson lne or near the load centre. It s known that the SVCs wth an auxlary njecton of a sutable sgnal can consderably mprove the dynamc stablty performance of a power system [24] [36]. In the lterature, SVCs have been appled successfully to mprove the transent stablty of a synchronous machne [24]. Hammad [25] presented a fundamental analyss of the applcaton of SVC for enhancng the power systems stablty. Then, the low frequency oscllaton dampng enhancement va SVC has been analyzed [26], [27], [28], [29]. It shows that the SVC enhances the system dampng of local as well as nter-area oscllaton modes. Self-tunng and model reference adaptve stablzers for SVC control 7

29 have been also proposed and desgned [30], [31], [32]. Robust SVC controllers based on H, uncertanty representaton cannot treat stuatons where a nomnal stable system becomes unstable after beng perturbed [35]. Moreover, the pole-zero cancellaton structured sngular value, and Quanttatve Feedback Theory QFT has been presented to enhance system dampng [33], [34]. However, the mportance and dffcultes n the selecton of weghtng functons of H optmzaton problem have been reported. In addton, the addtve and/or multplcatve phenomenon assocated wth ths approach produces closed loop poles whose dampng s drectly dependent on the open loop system (nomnal system) [36]. Apart from the above-mentoned dsadvantage, the major dsadvantage of SVC s that ts maxmum compensaton current depends upon the system voltage. Durng fault, compensaton decreases due to voltage drop whch s an unhealthy stuaton. Maxmum capactve VAR output decreases wth the square of voltage decrease. Controllable Seres Capactor (CSC) The Controllable Seres Capactor (CSC) s connected n seres wth long transmsson lnes. In the frst place ts presence s motvated by the need to effectvely shorten the lne electrcally, whch ncreases the power transfer capablty. A CSC affects electro-mechancal oscllatons by modulatng the transfer reactance of a lne. The mpact of ths control acton ncreases wth lne loadng [37], whch s a desrable property. The CSC s more effectve than the SVC for dampng purposes [37], whch s explaned by how they are connected. The seres devce affects the entre lne flow, and the shunt devce only changes a part [38]. Whle fxed seres capactors are common, only a few CSCs are currently n operaton. An mportant reason s the constructonal dffcultes wth a man crcut on lne potental. The voltage ratng of a CSC s typcally a fracton of the normal voltage drop over the lne where t s nstalled. As ths s far less than the voltage resultng from a three-phase short-crcut on the lne, protecton crcuts that by-pass the compensator are crtcally mportant. Due to the low 8

30 number of CSCs n operaton, no statements about the measurements commonly used by dampng controllers can be made. The major dsadvantage s that sustaned oscllaton below the fundamental system frequency can be caused by seres capactve compensaton. The phenomenon, referred to as sub-synchronous resonance (S). Hgh Voltage Drect Current Lnk In a Hgh Voltage Drect Current (HVDC) lnk the AC voltage s rectfed, transmtted as DC, and converted back to AC. The absence of reactve transmsson losses makes HVDC the preferred technque for connectons wth submarne cables longer than 30 km and for overhead lnes longer than 600 km [1]. The DC transmsson also provdes an asynchronous connecton between two power systems, whch s of partcular value when the systems have dfferent frequences such as 50 and 60 Hz. An HVDC lnk s controlled at the rectfer and the nverter through ther frng angles and through the tap changer of the transformer at each converter staton. The control system operates n a number of control modes, where certan varables are held constant. The ablty to drectly affect power flow makes HVDC lnks very powerful for dampng of electro-mechancal oscllatons. The actve power modulaton s typcally controlled by the frequency at the converter staton(s) [40], [41], the frequency of a nearby generator [13] or a lne flow [1]. Snce the converters are lne commutated, reactve power consumpton s assocated wth the actve power flows. The dependence between the modulatons of actve and reactve power s governed by the control mode. It may ether support the actve power modulaton or counteract t [41]. (b) Second generaton of FACTS The technologes descrbed above are n operaton today, but new power electronc devces wth a potental for dampng of electro-mechancal oscllatons are constantly suggested [3]. The voltage source converter (VSC) type FACTS controller group 9

31 employs self-commutated DC to AC converters, usng GTO thyrstors, whch can nternally generate capactve and nductve reactve power for transmsson lne compensaton, wthout the use of capactor or reactor banks. The converter wth energy storage devce can also exchange real power wth the system n addton to the ndependently controllable reactve power. The VSC can be used unformly to control transmsson lne voltage, mpedance, and angle by provdng reactve shunt compensaton, seres compensaton, and phase shftng, or to control drectly the real and reactve power flow n the lne [23]. Statc Synchronous Compensator (STATCOM) The emergence of FACTS devces and n partcular GTO thyrstor-based STATCOM has enabled such technology to be proposed as serous compettve alternatves to conventonal SVC [42]. From the vewpont of power system dynamc stablty, the STATCOM provdes better dampng characterstcs than the SVC as t s able to transently exchange actve power wth the system. The effectveness of the STATCOM to control the power system voltage was presented [43]. However, the effectveness of the STATCOM to enhance the angle stablty has not been addressed. Abdo [44] presented a sngular value decomposton (SVD) based approach to assess and measure the controllablty of the poorly damped electromechancal modes by STATCOM dfferent control channels. It was observed that the electromechancal modes are more controllable va phase modulaton channel. It was also concluded that the STATCOMbased dampng stablzers extend the crtcal clearng tme and enhance greatly the power system transent stablty. Haque [45] demonstrated that by the use of energy functon, a STATCOM can to provde addtonal dampng torque to the low frequency oscllatons n a power system. Statc Synchronous Seres Compensator (SSSC) The SSSC has been appled to dfferent power system studes to mprove the system performance. There has been some work done to utlze the characterstcs of the SSSC 10

32 to enhance power system stablty [46], [47]. Wang [46] nvestgated the dampng control functon of an SSSC nstalled n power systems. The lnearzed model of the SSSC ntegrated nto power systems was establshed and methods to desgn the SSSC dampng controller were proposed. Kumkratug and Haque [47] demonstrated the capablty of the SSSC to control the lne flow and to mprove the power system stablty. A control strategy of an SSSC to enlarge the stablty regon has been derved usng the drect method. The effectveness of the SSSC to extend the crtcal clearng tme has been confrmed though smulaton results on a sngle-machne nfnte bus system. Unfed Power Flow Controller (UPFC) The UPFC, whch was proposed by L. Gyugy n 1991 [5], [48], [49], s superor to the FACTS devces n terms of performance. UPFCs have been chosen n recent days to unfy the bus bar voltage regulaton ablty of STATCOM and power flow control capablty of SSSC n a sngle devce. It s prmarly used for ndependent control of real and reactve power n transmsson lnes for a flexble, relable and economc operaton and loadng of power system. Further, the UPFC can be used for voltage support, transent stablty mprovement and dampng of low frequency power system oscllatons. The elementary deas on how bus bar voltage regulaton, reactve power compensaton, and power flow control can be obtaned by a UPFC [49], [50]. The nterest measure of FACTS s shown n Fgure 1.2. The lterature survey carred out n [58] shows that the number of publcatons, applcatons of FACTS to power system stablty n partcular, has a tremendous ncrement. From Fgure 1.2, t s clear that the nterest n the 2 nd generaton of FACTS has drastcally ncreased whle the nterest n the 1 st generaton has decreased. The response tme of second generaton FACTS devces are shorter than that of frst generaton FACTS devces, manly due to the fast swtchng tmes provded by the IGBTs of voltage converter. The typcal dynamc response tmes of frst generaton FACTS devces are of the order of few mllseconds where as that of second generaton 11

33 FACTS devces are n the range of mcroseconds. Table 1.1 shows the performance analyss of FACTS devces. Frst column of Table 1.1 shows that seres compensator s good for load flow control. Second column of the same table shows shunt compensator s good for voltage stablty. Thrd column of Table 1.1 shows that all FACTS devces are good enough for the case of transent stablty. A combnaton of shunt and seres can better perform load flow control, voltage stablty and transent stablty. From the above analyss t s clear that UPFC s one of the most promsng devces n FACTS concept. Fgure 1.2: Statstcs for FACTS applcatons to power system stablty Table 1.1: Performance Analyss of FACTS devces [20] 12

34 Many approaches have been acheved to the modelng and control of the UPFC. The foremost recurrent approach contnues to model the UPFC as a power njecton model [51], [52]. The power njecton model gnores the dynamcs of the UPFC and employs the UPFC actve and reactve power njecton as the control nputs nto the power system. In the case where UPFC dynamcs are nvolved, the superor approach to controllng the UPFC s to use PI control [53], [54], [55]. However PI control s less productve n dampng oscllatons that nclude multple modes. For multple mode dampng, many lead-lag blocks are necessary that demand extra coordnated tunng. Another drawback s PI control shows poor performance as the system condtons shft from the operatng pont at whch the controller was tuned. FACTS devces have been examned n [56],[57] usng energy functons to formulate the controllers and compute the crtcal clearng tme. Ths method s not sutable for controller formaton snce t constrans the assessment of the dervatves of power system bus voltages and angles as well as needs numercal dfferentators or approxmatons. A feedback lnearzaton based UPFC s explaned n [10]. The nonlnear dynamc model s transformed nto a lnear one by coordnate transformaton. From thence, the lnear control technque s used n the transformed lnear model. However, the detals of the dynamc models must be known exactly when the exact feedback lnearzaton technques are used. It s very dffcult to perform ths task because errors and external dsturbances are nherent n power systems. To overcome the above-mentoned challenges, the followng contrbutons are made n ths thess. 1.2 Research objectve Though technologcal barrers exst, as n most technology areas, t s mportant to overcome them by developng proper understandng of the process wth related attrbutes. The next chapters explan the varous efforts drected for mprovng the nterarea oscllaton dampng appled to mult-machne power system. Exhaustve lterature revew reveals that the nonlnear controllers are least explored out of dfferent methods. 13

35 Smlarly, current work emphaszes the nonlnear control technque appled to multmachne power system. Based on these gudng prncples, the objectves of the current research are as follows: Explore the exstng methods and models for power system stablty study. Develop an advanced nonlnear controller for transent stablty mprovement usng UPFC as a stablzng devce. Derve an adaptve law for uncertan parameters whch are otherwse dffculty to be measured precsely. Develop the software program to smulate small scale and transent phenomena. 1.3 Thess outlne The other chapters of ths thess are organzed as follows: Chapter 2 gves an overvew of basc operaton, modelng and nterfacng of power system components. In order to mplement computer control of a power system, t s mperatve to gan a clear understandng of the representaton of the power system components. Ths chapter explans the mathematcal models for synchronous generators, assocated exctaton systems, nterconnectng transmsson network ncludng statc loads and other devces such as UPFC. The chapter explans the basc operaton and characterstcs of dfferent power system components. The basc knowledge of these devces s essental for controller development n the subsequent chapters Chapter 3 deals wth the Lead-Lag control desgn for mult-machne power system wth UPFC. Ths chapter explores the conventonal methods avalable for oscllaton dampng. A procedure for lnearzng power system equatons ncludng UPFC s explaned n ths chapter. Phllps-Heffron model explaned n ths secton helps to study the mpact of control functons of the UPFC up on system oscllaton stablty. The egen-values correspondng to electromechancal mode of oscllaton are dentfed usng partcpaton 14

36 factor method. The procedure for calculatng the controllablty ndex s explaned n ths chapter. The most relevant control sgnal s used for the development of dampng controller. Along wth smulaton results the advantages and dsadvantages of the tradtonal methods are also outlned. Chapter 4 ntroduces the dynamc modelng and adaptve control of sngle machne-nfnte bus (SMIB) system wth UPFC. A new method to generate a nonlnear dynamc representaton of the power network s ntroduced to enable more sophstcated control desgn. The dynamc model s developed usng generator termnal currents. The developed dynamc representaton helps to convert nonlnear power system equatons nto standard parametrc feedback form. Once the new representaton s obtaned, sutable adaptve laws for control sgnal and uncertan parameters are derved. Smulaton results are gven to valdate the theoretcal conjectures. The man dsadvantage of ths method s the assumpton of nfnte bus. The nfnte bus assumpton requred for ths approach s not vald for large mult-machne systems when the fault affects the power system. The adaptve law derved n ths secton s used n the sxth chapter to mprove the effcency of the controller. Chapter 5 provdes the dynamc modelng and nonlnear control of mult-machne power system wth UPFC. Frst part of ths chapter deals wth a new nonlnear dynamc modelng for power system wth UPFC to enable more sophstcated control desgn. Once the new modelng s obtaned, an advanced nonlnear control desgn usng back steppng methodology s explaned n the second part of the chapter. The effectveness of ths approach s presented n a case study on a two-machne power system. Chapter 6 ntroduces an ntegrated lnear-nonlnear control of mult-machne power system wth UPFC. Ths chapter begns wth the dsadvantages of the method developed n the prevous chapter. Desgn of an ntegrated lnear-nonlnear controller s explaned to fully utlze the mult-functonal UPFC. An adaptve law for uncertan parameters s derved n the second part of the chapter whch s otherwse very dffcult to be measured precsely. In the case studes, we explore all the three degrees of freedom for UPFC, 15

37 namely AC voltage control, DC voltage control and oscllaton dampng usng newly developed hybrd controller. Chapter 7 provdes concluson and suggestons for future work. It s a summary of the work done and concluded the present study. It explans the mportance of the proposed dynamc representaton for the development of nonlnear controller. Moreover, some suggestons on the extensons to potental topcs for future research are proposed. 1.4 Conclusons Ths chapter hghlghts the reasons for nter-connectons and the dffcultes that occur whle constructng a new transmsson lne. The full utlzaton of the transmsson lnes wthout proper controllers could result n the rapd falure of the entre system. The chapter also explans the consequences of the low frequency nter-area mode of oscllatons. Secton 1.1 provdes the nsght nto varous past developments n the area of power system stablty. For the sake of smplcty, t s dvded nto two man sectons. Secton A focuses on the bref hstory of conventonal methods. Secton B descrbes FACTS devces. Ths secton s dvded nto two sub-sectons. The frst sub-secton explans the exstng technques and the second sub-secton explans the emergng ones. The nterest measure of FACTS shows the mportance of UPFC. It s the most promsng devce n the FACTS concept. It has the ablty to adjust the three control parameters,.e., the bus voltage, transmsson lne reactance and phase angle between two buses, ether smultaneously or ndependently, and how a UPFC performs these functons are explaned n the next chapter. 16

38 Chapter 2 Basc Operaton, Modelng and Interfacng of Power System Components 17

39 Chapter 2 Basc Operaton, Modelng and Interfacng of Power System Components 2.1 Introducton In order to mplement computer control of a power system, t s mperatve to gan a clear understandng of the basc operaton and representaton of the power system components. In the frst part of ths chapter, we brefly revew the basc operaton of UPFC and PWM technques used for VSCs. Voltage-source converter s the buldng block of UPFC. The UPFC conssts of two voltage-source converters. These back-to-back converters are operated from a common DC lnk provded by a DC storage capactor. The bascs of the VSCs are brefly dscussed n the begnnng of the chapter. In the second part, development of the mathematcal models of power system components s explaned. Before the power systems network can be solved, t must frst be modeled. Sngle phase representaton s used for balanced system. In ths secton, we present smple models for generators, loads, transmsson lnes, UPFC, etc. The nterface of the UPFC wth the power network s explaned at the end of ths chapter. 2.2 Basc operaton of UPFC UPFC s a devce placed between two buses referred to as the UPFC sendng bus and the UPFC recevng bus. It conssts of two voltage-source converters, as llustrated n Fgure 2.1. The back-to-back converters, labeled shunt converter and seres converter n the fgure, are operated from a common DC lnk provded by a DC storage capactor. The shunt converter s prmarly used to provde actve power demand of the seres converter through the common DC lnk. Shunt converter can also generate or absorb reactve power, f t s desred, and thereby t provdes ndependent shunt reactve compensaton for the lne. 18

40 Seres converter provdes the man functon of the UPFC by njectng a voltage wth controllable magntude and phase angle n seres wth the lne. For the fundamental frequency model, the VSCs are replaced by two controlled voltage sources [60]. The UPFC s placed on the hgh-voltage transmsson lnes. Ths arrangement requres stepdown transformers n order to allow the use of power electroncs devces for the UPFC. Fgure 2.1: Basc Crcut Confguraton of the UPFC Applyng the Pulse Wdth Modulaton (PWM) technque to the two VSCs the followng equatons for magntudes of shunt and seres njected voltages are obtaned V V SH mshv 2 2V mv 2 2V dc dc B B (2.1) The phase angles of V SH and V are SH ( S SH ) ( S ) (2.2) 19

41 The seres converter njects an AC voltage V V ( ) n seres wth the 20 S transmsson lne. Seres voltage magntude V and ts phase angle wth respect to the sendng bus are controllable n the range of 0 V V max and respectvely. The shunt converter njects controllable shunt voltage such that the real component of the current n the shunt branch balance the real power demanded by the seres converter. The real power can flow freely n ether drecton between the AC termnals. On the other hand, the reactve power cannot flow through the DC lnk. It s absorbed or generated locally by each converter. The shunt converter operated to exchange the reactve power wth the AC system provdes the possblty of ndependent shunt compensaton for the lne. If the shunt njected voltage s regulated to produce a shunt reactve current component that wll keep the sendng bus voltage at ts prespecfed value, then the shunt converter s operated n the Automatc Voltage Control Mode. Shunt converter can also be operated n the VAR control mode. In ths case shunt reactve current s produced to meet the desred nductve or capactve VAR request. The bascs of VSCs and PWM technques are brefly dscussed n the next secton. A. Basc concepts of voltage source converters and PWM technque The typcal three-phase VSC s shown n Fgure 2.2 [5]. It s made of sx valves, (1-1 ) to (6-6 ) each consstng of a gate turn off devce (GTO) paralleled wth a reverse dode, and a DC capactor. The desgnated order 1 to 6 represents the sequence of valve operaton n tme. It conssts of three-phase legs, whch operates n concert, 120 degrees apart. An AC voltage s generated from a DC voltage through sequental swtchng of the GTOs. Beng an AC voltage source wth low nternal mpedance, a seres transformer s essental to ensure that the DC capactor s not short-crcuted and dscharged rapdly nto a capactve load such as transmsson lne. The DC voltage always has one polarty and the DC current can flow n ether drecton. Controllng the angle of the converter output voltage wth respect to the AC system voltage controls the real power exchange between the converter and the AC system. 0

42 Fgure 2.2: Three Phase Voltage Source-Converter The real power flows from the DC sde to AC sde (nverter operaton) f the converter output voltage s controlled to lead the AC system voltage. If the converter output voltage s made to lag the AC system voltage, the real power wll flow from the AC sde to DC sde (rectfer operaton). Inverter acton s carred out by the GTOs whle the rectfer acton s carred out by the dodes. Controllng the magntude of the converter output voltage controls the reactve power exchange between the converter and the AC system. The converter generates reactve power for the AC system f the magntude of the converter output voltage s greater than the magntude of the AC system voltage. If the magntude of the converter output voltage s less than that of the AC system, the converter wll absorb reactve power. The converter output voltage can be controlled usng varous control technques. Pulse Wdth Modulaton (PWM) technques can be desgned for the lowest harmonc content. It should be mentoned that these technques requre large number of swtchng per cycle leadng to hgher converter losses. Therefore, PWM technques are currently consdered unpractcal for hgh voltage applcatons. However, t s expected that recent developments on power electronc swtches wll allow practcal use of PWM controls on such applcatons n the near future. Due to ther smplcty many authors, vz., [58], [59], [60], have used PWM control technques n ther UPFC studes. Hence, the same approach s used n ths thess. 21

43 When snusodal PWM technque s appled, turn on and turn off sgnals for GTOs are generated comparng a snusodal reference sgnal V R of ampltude A R wth a saw tooth carrer waveform V C of ampltude A C as shown n Fgure 2.4 [5]. The frequency of the saw tooth waveform establshes the frequency at whch GTOs are swtched. Consder a phase-leg as shown n Fgure 2.3. In Fgure 2.4, VR V results n a turn on C sgnal for the devce 1 and gate turn off sgnal for the devce 4 and VR VC results n a turn off sgnal for the devce 1 and gate turn on sgnal for the devce 4. The fundamental frequency of the converter output voltage s determned by the frequency of the reference sgnal. Controllng the ampltude of the reference sgnal controls the wdth of the pulses. In two-level or multlevel converters, there s only one turn-on, turn-off per devce per cycle. Wth these converters, the AC output voltage can be controlled, by varyng the wdth of the voltage pulses, and / or the ampltude of the DC bus voltage. It goes wthout sayng that more pulses means more swtchng losses, so that the gans from the use of PWM have to be suffcent to justfy an ncrease n swtchng losses. For FACTS technology wth hgh power n the tens of megawatts and converter voltage n KVs and tens of KVs, low frequences n the few hundred Hertz or may be the low klohertz range may seem feasble and worth consderng. The least cost and smplest controllable three-phase converter would seem to be a sx-valve converter wth one turnoff devce / dode per valve. In FACTS applcatons, there wll usually be a need for a transformer between the converter valves and the AC system; there s therefore a certan flexblty provded by the transformer turn rato to match the avalable devce current and voltage ratng. 22