Use of FACTS Devices for Power Flow Control and Damping of Oscillations in Power Systems

Transcription

1 Diss. ETH No Use of FACTS Devices for Power Flow Control and Damping of Oscillations in Power Systems A dissertation submitted to the SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH for the degree of Doctor of Technical Sciences presented by RUSEJLA SADIKOVIĆ Master of Science, Faculty of Electrical Engineering, University of Tuzla born October 14 th, 1969 in Tuzla, Bosna and Hecegovina accepted on the recommendation of Prof. Dr. Göran Andersson, examiner Prof. Dr. Caludio A. Cañizares, co-examiner 2006

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3 Acknowledgments This dissertation presents the results of my research done at the Power system Laboratory of the Swiss Federal Institute of Technology (ETH) during the years First of all I would like to express my deep gratitude to my advisor Prof. Göran Andersson for giving me the opportunity to work on this project. His valuable suggestions and his encouragement and patience have been a big help for me over the last for years. I am very grateful to Dr. Petr Korba four his skilled guidance, valuable comments, stimulating discussions and support throughout this project. Special thanks go to Prof. Claudio A. Cañizares for accepting to coreferee this thesis. I also would like to thank my colleagues at the laboratory for the enjoyable discussions and friendly atmosphere. I particularly thank my office-mates Dr. Andrei Karpatchev and Mirjana Milosević for the relaxed work atmosphere in our office. I am very grateful as well to Maria Lourdes Steiner-Igcasenza for proofreading this thesis. Finally, I would like to extend my deepest gratitude and personal thanks to those closest to me. In particular, I would like to thank my husband Adnan, my son Berin and my parents for their support, encouragement and understanding. Rusejla Sadiković 3

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5 Abstract Due to the deregulation of the electrical market, difficulty in acquiring rights-of-way to build new transmission lines, and steady increase in power demand, maintaining power system stability becomes a difficult and very challenging problem. In large, interconnected power systems, power system damping is often reduced, leading to lightly damped electromechanical modes of oscillations. Implementation of new equipment consisting high power electronics based technologies such as Flexible Alternating Current Transmission Systems (FACTS) and proper controller design become essential for improvement of operation and control of power systems. The aim of this dissertation is to examine the ability of FACTS devices, such as Thyristor Controlled Series Capacitor (TCSC), Unified Power Flow Controller (UPFC) and Static VAr Compensator (SVC) for power flow control and damping of electromechanical oscillations in a power system. A power flow control strategy is based on linearization of active and reactive power flows around an operating point. A control strategy for damping of oscillations, including several FACTS devices and PSSs, is based on different approaches, both off-line and on-line, e.g. residue based method, pole shifting method and genetic algorithms. The robustness of each approach is discussed. One part of this dissertation deals with location of FACTS devices considering multiple tasks, power flow control and damping of oscillations. The results of the case studies demonstrate advantages and disadvantages of the considered control approaches. 5

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7 Kurzfassung Als Folge der Liberalisierung vieler Elektrizitätsmärkte ergeben sich für den Netzbetrieb zusätzliche anspruchsvolle Aufgaben. Die Erschwernis des Baus zusätzlicher Übertragungsleitungen aufgrund langwieriger Bewilligungsverfahren sowie ein starkes Wachstum der Nachfrage nach elektrischer Energie stellen an die Netzbetreiber hohe Ansprüche bezüglich der Gewährleistung der Systemstabilität. In grossen, stark vermaschten Netzstrukturen werden Leistungspendelungen nur bedingt gedämpft und können zu erheblichen elektromechanischen Schwingungen führen. Aus diesem Grund ist die Anwendung neuer Kontrollmechanismen basierend auf leistungselektronischen Technologien wie Flexible Alternating Current Transmission Systems (FACTS) hinsichtlich eines sicheren Netzbetriebs notwendig. Das Ziel dieser Dissertation ist die Untersuchung der Eignung von FACTS Geräten, wie Thyristor Controlled Series Capacitor (TCSC), Unified Power Flow Controller (UPFC) sowie Static VAr Compensator (SVC) in Bezug auf Lastfluss-Steuerung sowie Dämpfung von Leistungspendelungen. Es wird ein auf der Linearisierung des Wirk- und Blindleistungsflusses basierendes Verfahren zur Lastfluss-Regelung vorgestellt, welches die Dämpfung von Leistungspendelungen mittels FACTS Geräten und PSS s beinhaltet. Dabei setzt sich dieses Verfahren aus den folgenden off- und on-line Methoden zusammen: Der Residuen basierten Methode, der Pol-Verschiebungsmethode und den genetischen Algorithmen. Erläuterungen bezüglich der Robustheit dieser Methoden werden ebenfalls diskutiert. Ein weiterer Bestandteil dieser Dissertation setzt sich mit der Bestimmung des Einsatzortes von FACTS-Geräten auseinander. Als Resultat der untersuchten Fallstudien werden sowohl Vor- als auch 7

8 8 Kurzfassung Nachteile der betrachteten Methoden zur Lastfluss-Steuerung aufgezeigt.

9 Contents 1 Introduction Thesis outline Contributions List of Publications Modeling of FACTS devices Thyristor Controlled Series Capacitor Unified Power Flow Controller Static VAr Compensator Use of FACTS Devices for Damping of Power System Oscillations Introduction Modal Analysis FACTS POD Controller Design Case Studies Design of TCSC POD Controller Design of UPFC POD Controller Design of SVC POD Controller Summary

10 10 Contents 4 On the Location of the TSCS Dynamic Criterion Static Criterion Case Study Summary Self-Tuning Controllers Adaptive Model Identification Residue Based Adaptive Control Pole Shifting Adaptive Control Summary Coordinated Tuning of PSS and FACTS POD Controllers Genetic Algorithms Selection Crossover Mutation PSS and FACTS POD Controller design Case study Case Study with the TCSC - Case Study I Case Study with the SVC - Case Study II Case Study with the TCSC and the SVC - Case Study III Summary

11 Contents 11 7 Concluding Remarks 111 A IEEE 39 Bus Test System Data 115 B IEEE 68 Bus Test System Data 121 C IEEE Sensitivity Analysis 129 Bibliography 133

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13 Chapter 1 Introduction Modern bulk power systems cover large geographic areas, e.g. the European UCTE system and the North American systems, and have a large number of load buses and generators. Additionally, available generating plants are often not situated near load centers and power must consequently be transmitted over long distances. To meet the load and electric market demands, new lines should be added to the system, but due to environmental reasons, the installation of electric power transmission lines must often be restricted. Hence, the utilities are forced to rely on already existing infra-structure instead of building new transmission lines. In order to maximize the efficiency of generation, transmission and distribution of electric power, the transmission networks are very often pushed to their physical limits, where outage of lines or other equipment could result in the rapid failure of the entire system. With such increasing stress on the existing transmission lines the use of Flexible AC Transmission Systems (FACTS) devices becomes an important and effective option. FACTS technologies offer competitive solutions to today s power systems in terms of increased power flow transfer capability, enhancing continuous control over the voltage profile, improving system damping, minimizing losses, etc. FACTS technology consists of high power electronics based equipment with its real-time operating control [1, 2, 6]. There are two groups of FACTS controllers based on different technical approaches, both resulting in controllers able to solve transmission 13

14 14 Chapter 1. Introduction problems. The first group employs reactive impedances or tap-changing transformers with thyristor switches as controlled elements; the second group employ self-commutated voltage-sourced switching converters. The sophisticate control and fast response are common for both groups. The Static VAr Compensator (SVC), Thyristor Controlled Series Capacitor (TCSC) and Phase Shifter, belong to the first group of controllers while Static Synchronous Compensators (STATCOM), Static Synchronous Series Compensators (SSSC), Unified Power Flow Controllers (UPFC) and Interline Power Flow Controllers (IPFC) belong to the other group. The power system may be thought of as a large, interconnected nonlinear system with many lightly damped electromechanical modes of oscillation. If the damping of these modes become too small, or even positive, it can impose severe constraints on the system s operation. It is thus important to be able to determine the nature of those modes, find stability limits and in many cases use controls to prevent instability. The poorly damped low frequency electromechanical oscillations occur due to inadequate damping torque in some generators, causing both local-mode oscillations (1 Hz to 2 Hz) and inter-area oscillations (0.1 Hz to 1 Hz) [19]. The traditional approach employs power system stabilizers (PSS) on generator excitation control systems in order to damp those oscillations. PSSs are effective but they are usually designed for damping local modes and in large power systems they may not provide enough damping for inter-area modes. Hence, in order to improve damping of these modes, it is of interest to study FACTS power oscillation damping (POD) controllers [17]. In large power systems the number of inter-area modes is usually larger than the number of control devices available [3]. Generally, damping of power system oscillations is not the primary reason of placing FACTS devices in the power system, but rather power flow control [6, 7]. However, when installed, supplementary control lows can be applied to existing devices in order to improve damping, as well as satisfy the primary requirements of the device. One of the very important questions in the practical application of controller installation is whether to use local or remote input signals (often referred to as global signals) as feedback signals. There are different approaches, [3, 13, 15, 17]. The advantages of the local signals are their

15 15 simplicity and reliability. On the other hand, they might not give adequate observability of some of the significant inter-area modes [4]. The advantage of the global signals is that they contain information about the overall network dynamics in contrast to the local signals. But from an economic viewpoint, the implementation of a control scheme using global signals may be more cost effective than installing new control devices [3]. Since remote signals are often transmitted by the existing communication channels, time delay is involved, which could be an impediment. In this thesis, the local signal is used as the controller s feedback signal. A conventional damping control design considers a single operating condition of the system. In this kind of controller the feedback is fixed and amplifies the control error, which in turn determines the value of the input signal u (controller output) to the system. The way in which the error is processed is the same for all operating conditions. In Chapter 3, a conventional lead-lag controller designed for nominal operating point is presented and applied on three different types of FACTS devices. This controller is simple, but works often only within a limited operating range. In case of contingencies, changed operating conditions can cause poorly damped or even unstable oscillations since the controller parameters yielding satisfactory damping for one operating condition may no longer provide sufficient damping for another one. In order to address this issue, researchers, over the years, have proposed different approaches for adaptive control structures for PSSs as well as for FACTS devices. Some of them are reviewed in Chapter 5. The primary idea is to overcome the problems that might be encountered by conventionally tuned controllers with the changing of operating conditions. Dealing with an adaptive on-line tuning, the identification of the static and dynamic characteristics of the system plays an important role together with the control strategy itself. In Chapter 5, on-line identification based on the automatic detection of oscillations in power systems using dynamic data such as currents, voltages and angle differences measured across transmission lines, provided on-line by phasor measurement units, is presented [5]. The on-line collected measured data are subjected to a further evaluation with the objective to estimate dominant modes (frequencies and damping) during any operation of the power system or to give reduced transfer function of the unknown power system.

16 16 Chapter 1. Introduction Based on two approaches of on-line identification of the power system, a control strategy for on-line tuning of the POD controllers is developed. The first approach is based on modal analysis, i.e. residue method, and the second employs self-tuning controllers (STC) based on the pole shifting method. The self-tuning controller is based on the idea of separating the estimation of unknown parameters from the design of the optimal controller, [29]. Although controllers tuned by the conventional design approach are simple, lack of robustness of that kind of controllers is not the only problem encountered. Conventional procedures become time consuming and difficult to implement for cases in which: there is a significant number of PSSs and FACTS POD controllers to be coordinated, coordination must be conducted for a variety of operating conditions and certain performance specifications have to be satisfied. As a consequence of the presence of different types of the stabilizers in the system, e.g. the PSSs and FACTS POD controllers, the undesired and detrimental interactions between them may occur [34]. To avoid this a simultaneous optimization and coordination of the parameter settings of both stabilizers is required in order to enhance overall system stability and minimizing possible adverse interactions. A solution to this problem is the use of Genetic Algorithms (GA) methodology, and this has been investigated in Chapter 6. In [38] and [39], PSS tuning by means of GA is presented. These papers investigate the use of genetic algorithms to design robust PSS, in which several operating conditions and system configurations are simultaneously considered in the design process. In [38], simultaneous tuning of nine PSSs in 14 operating conditions for the New England power system was performed. The objective function used for GA optimization was the sum of the damping ratios for all eigenvalues in all operating conditions. Two additional objective functions that allowed some eigenvalues to be shifted to the left-hand side of the complex plane or to a

17 1.1. Thesis outline 17 wedge-shape sector in the complex plane were further investigated in [39]. In [40], the authors propose the use of advanced techniques in GA for the optimal tuning of PSSs again for different operating conditions. The results obtained in these papers proved that GA could be a powerful tool for robust PSS damping controller design. Considering FACTS POD tuning, the GA approach is used in [36] in order to design SVC and TCSC damping controllers to enhance damping of inter-area modes in a three-area six-machine system. In Chapter 6 of this thesis, the GA approach is used as well, as a tool for design of multiple POD controllers in a large, realistic system. 1.1 Thesis outline Following the Introduction, Chapter 2 describes the injection models of the FACTS devices, and their use in power flow control. Chapter 3 gives an overview of the conventional POD controller design and their application on the TCSC, UPFC and SVC. In Chapter 4, an approach for the optimal location of FACTS devices combining the static (for optimal location of the power flow controller) and the dynamic criteria (for optimal location of the damping controller) is presented. The concept of one-line tuning of the FACTS POD controllers is presented in Chapter 5. In Chapter 6 a method for simultaneous coordinated tuning of the FACTS POD controller and the PSS controllers is presented. Chapter 7 summarizes the findings in this work with some suggestions for future research directions. 1.2 Contributions The main contributions of this dissertation can be summarized as:

18 18 Chapter 1. Introduction Application of POD controller to Unified Power Flow Controllers (UPFC) based on residue approach, considering different local signals as feedback signals. Proposal of an approach for location of FACTS devices for multiple control objectives, considering static and dynamic criteria. Application of self-tuning controllers based on residue method and on pole shifting method. Application of genetic algorithm methodology to coordination of power system controllers for robust damping of electromechanical oscillations. 1.3 List of publications The work presented in this dissertation has been reported by the following publications: 1. R. Sadikovic and G. Andersson, Power Flow Control by Sensitivity Based Facts Controllers, IPEC 2003, Singapore, November R. Sadikovic, G. Andersson and P. Korba, A Power Flow Control Strategy for FACTS Devices, WAC 2004, Spain, June R. Sadikovic, P. Korba and G. Andersson, Application of FACTS Devices for Damping of Power System Oscillations, IEEE PowerTech 2005, Russia, June R. Sadikovic, G. Andersson and P. Korba, Method for Location of FACTS for Multiple Control Objectives, X SEPOPE, Brasil, May R. Sadikovic, P. Korba and G. Andersson, Self-tuning Controller for Damping of Power System Oscillations with FACTS Devices, IEEE PES General Meeting, Canada, June R. Sadikovic, G. Andersson and P. Korba, Damping Controller Design for Power System Oscillations, Intelligent Automation & Soft Computing Journal, Vol. 12, No. 1, pp: 51-62, 2006.

19 Chapter 2 Modelling of FACTS Devices Flexible AC transmission systems (FACTS) devices are installed in power systems to increase the power flow transfer capability of the transmission systems, to enhance continuous control over the voltage profile and/or to damp power system oscillations [6, 7]. The ability to control power rapidly can increase stability margins as well as the damping of the power system, to minimize losses, to work within the thermal limits range, etc. In this chapter, injection models of the Thyristor Controlled Series Capacitor (TCSC), Unified Power Flow Controller (UPFC) and Static Var Condensator (SVC), used in this dissertation, with appropriate controls, are presented. 2.1 Thyristor Controlled Series Capacitor Model A Thyristor Controlled Series Capacitor (TCSC) configuration consists of a series capacitor bank, C, in parallel with a thyristor-controlled reactor, L, as shown in Figure 2.1. This simple model utilizes the concept 19

20 20 Chapter 2. Modelling of FACTS Devices of a variable series reactance. The series reactance is adjusted automatically, within limits, to keep the specified amount of active power flow across the line. There are the certain values of inductive and capacitive reactance which cause steady-state resonance. The TCSC can be continuously controlled either in capacitive or in inductive area, avoiding the steady-state resonant region. The details about the modelling of the TCSC can be found in [6, 7]. The control action of the TCSC is usually expressed in terms of its percentage of the compensation, k c, defined as: k c = x c x l 100% (2.1) where, x l is the line reactance and x c is the effective capacitive reactance provided by TCSC. C L Figure 2.1: Basic TCSC topology The TCSC is assumed to be connected between buses i and j in a transmission line as shown in Figure 2.2, where the TCSC is presented simplified like a continuously controllable reactance (capacitive) [11]. V i -jx c r l + jx l V j I se - + V s Figure 2.2: TCSC located in a transmission line

21 2.1. Thyristor Controlled Series Capacitor Model 21 From Figure 2.2 the line current I se is given by : I se = V i V j r l + j(x l x c ) (2.2) The influence of the capacitor is equivalent to a voltage source which depends on voltages V i and V j. The current injection model of the TCSC is obtained by replacing the voltage across the TCSC by an equivalent current source I s as seen in Figure 2.3. In Figure 2.2, V S = jx c I se, and from Figure 2.3 follows I S = Current injections into nodes i and j are V S r l + jx l = jx ci se r l + jx l (2.3) V i I ij r l + jx l V j I s Figure 2.3: Replacement of a voltage source by a current source V i r l +jx l V j I si I sj Figure 2.4: Current injection model for a TCSC I Sj = jx c V i V j r l + jx l r l + j(x l x c ) (2.4) I Si = I Sj (2.5)

22 22 Chapter 2. Modelling of FACTS Devices and therefore the appropriate current injection model of the TCSC can be presented as shown in Figure 2.4. I si I sj TCSC k max c C damp + + Ts+1 cd + st cd Power network k min c P - + P Control Strategy k c P ref Figure 2.5: General form of the TCSC control system The general form of the TCSC control system used in this thesis is shown in Figure 2.5, where the Control Strategy block represents the design method for power flow controller based on linearization of power flow equations around an operating point. The output of the block is the change of the compensation degree given by: k c = P(r 2 l + (x l x c ) 2 )/{2(V 2 i V i V j cos θ ij )(1 k c )... r 2 l (V i V j cos θ ij ) 1 x l + V i V j sinθ ij (1 k c )} (2.6) where P = P ref P is the input in the block. K cd is the proportional part and T cd is the integral time constant of the TCSC PI controller. The time constant T approximates delay due to the main circuit characteristics and control systems. C damp is the signal from TCSC damping controller, explained in next chapter. P is the TCSC line active power and P ref is the line active power to be maintained by TCSC. k min and k max are the limits on the compensation degree changes.

23 2.2. Unified Power Flow Controller Unified Power Flow Controller The UPFC can provide simultaneous control of all basic power system parameters (transmission voltage, impedance and phase angle). The controller can fulfill functions of reactive shunt compensation, series compensation and phase shifting, meeting multiple control objectives. From a functional perspective, the objectives are met by applying a DC capacitor, shunt connected transformer and voltage source converter in parallel branch and dc capacitor, voltage source convertor and series injected transformer in the series branch. The two voltage source converters are a so called back to back AC to DC voltage source converters operated from a common DC link capacitor, Figure 2.6. The shunt converter is primarily used to provide active power demand of the series converter through the common DC link. Converter 1 can also generate or absorb reactive power, if it is desired, and thereby provides independent shunt reactive compensation for the line. Converter 2 provides the main function of the UPFC by injecting a voltage with controllable magnitude and phase angle in series with the line, Figure 2.7. The reactance x s describes the reactance seen from terminals of the series transformer and is equal to (in p.u. base on system voltage and base power) x S = x k r 2 max(s B /S S ) (2.7) where x k denotes the series transformer reactance, r max the maximum per unit value of injected voltage magnitude, S B the system base power, and S S the nominal rating power of the series converter. The UPFC injection model is derived enabling three parameters to be simultaneously controlled [8]. They are namely the shunt reactive power, Q conv1, and the magnitude, r, and the angle, γ, of injected series voltage V se. Figure 2.7 shows the circuit representation of a UPFC, where the series connected voltage source is modelled by an ideal series voltage which is controllable in magnitude and phase, and the shunt converter is modelled as an ideal shunt current source. In Figure 2.7, I sh = I t + I q = (I t + ji q )e jθi (2.8) where I t is the current in phase with V i and I q is the current in quadrature with V i. In Figure 2.8 the voltage source V se is replaced by the

24 24 Chapter 2. Modelling of FACTS Devices shunt side i shunt transformer series transformer Converter 1 Converter 2 series side j Figure 2.6: Implementation of the UPFC by back-to-back voltage source converters V i I se V se V i jx s V j I sh P sh Q sh P se, Q se Figure 2.7: The UPFC electric circuit arrangement current source I inj = jb s V se in parallel with x s. The active power V i jx s V j I sh I inj Figure 2.8: Transformed series voltage source supplied by the shunt current source can be calculated from

25 2.2. Unified Power Flow Controller 25 With the UPFC losses neglected, P CONV 1 = Re[V i ( I sh)] = V i I t (2.9) P CONV 1 = P CONV 2 (2.10) The apparent power supplied by the series voltage source converter is calculated from S CONV 2 = V se I se ( = re jγ V i V j V i jx s ) (2.11) Active and reactive power supplied by Converter 2 are distinguished as P CONV 2 = rb s V i V j sin(θ i θ j + γ) rb s V 2 i sin γ (2.12) Q CONV 2 = rb s V i V j cos(θ i θ j + γ) + rb s V 2 i cos γ (2.13) Substitution of (2.9) and (2.12) into (2.10) gives I t = rb s V i V j sin(θ i θ j + γ) + rb s V i sin γ (2.14) The current of the shunt source is then given by I sh = (I t + ji q )e jθi = ( rb s V j sin(θ ij + γ) + rb s V i sin γ + ji q )e jθi (2.15) From Figure 2.8 the bus current injections can be defined as where I i = I sh I inj (2.16) I j = I inj (2.17) I inj = jb s V se = jb s rv i e jγ (2.18) Substituting (2.15) and (2.18) into (2.16) and (2.17) gives I i = ( eb s V j sin(θ ij + γ) + rb s V i sinγ + ji q )e jθi + +jrb s V i e j(θi+γ) (2.19)

26 26 Chapter 2. Modelling of FACTS Devices I j = jb s V i e j(θi+γ) (2.20) where I q is an independently controlled variable, representing a shunt reactive source. Based on (2.19) and (2.19), the current injection model can be presented as in Figure 2.9. Besides the expressions for current V i jx s V j I si I sj Figure 2.9: UPFC current injection model bus injection, due to the control purposes, it is very useful to have expressions for power flows from both sides of the UPFC injection model defined. At the UPFC shunt side, the active and reactive power flows are given as P i1 = rb s V i V j sin(θ ij + γ) b s V i V j sin(θ ij ) (2.21) Q i1 = rb s Vi 2 cos γ + Q conv1 b s Vi 2 + b s V i V j cos θ ij (2.22) whereas at the series side they are P j2 = rb s V i V j sin(θ ij + γ) + b s V i V j sin θ ij (2.23) Q j2 = rb s V i V j cos(θ ij + γ) b s Vj 2 + b s V i V j cos θ ij (2.24) As can be seen from previous equations, the UPFC current injection model is defined by the constant series branch susceptance, b s, which is included in the system bus admittance matrix, and the bus current injections, I i and I j. If there is a control objective to be achieved, the bus current injection are modified through changes of the UPFC control parameters r, γ and I q. In the case of power flow control, i.e. the third control variable, I q, is inactive, so the UPFC performs the function of the series compensation, the control objective is to maintain the power of controlled line at the expected value. That means the UPFC should operate in the automatic power flow control mode keeping the active and reactive line power flow at the specified values P ref and Q ref.

27 2.2. Unified Power Flow Controller 27 The control objective can be achieved by linearizing the line power flow equations, (2.23) and (2.24), around an operating point [10]. Figure 2.10 shows the general form of the UPFC control system used in this dissertation. The linearization results with the Control Strategy block in Figure The outputs of the block are the changes of the control variables r and γ, given by r = P sin(θ ij + γ) + Qcos(θ ij + γ) b s V i V j (2.25) γ = P cos(θ ij + γ) Qsin(θ ij + γ) rb s V i V j (2.26) where P = P ref P and Q = Q ref Q are the inputs in the block. In this thesis it is assumed that the third control variable I q is inactive, so the UPFC performs the function of the series compensation. K γ and K r are the proportional parts and T γ and T r are the integral time constants of the UPFC PI controllers. C dampγ and C dampr are the signals from the UPFC damping controllers, explained in the next chapter. I si C damp st I sj Power network UPFC limiter + C dampr + r + st r P Q P - Control Q strategy + r P ref Qref Figure 2.10: General form of the UPFC control system Operation of the UPFC demands proper power rating of the series and shunt branches. The rating should enable the UPFC to archive predefined power flow objective. The flow chart of Figure 2.11 shows an algorithm for UPFC rating [8].

28 28 Chapter 2. Modelling of FACTS Devices The algorithm starts with definition of the series transformer short circuit reactance, x k, and the system base power, S B. Then, the initial estimation is given for the series converter rating power, S S, and the maximum magnitude of the injected series voltage, r max. In the next step can be determined the effective reactance of the UPFC seen from the terminals of the series transformer, (x S ). Load flows are computed by changing the angle γ between 0 0 and in steps of 10 0, with the magnitude r kept at its maximum value r max. Such rotational change of the UPFC parameter influences active and reactive power flows in the system. The largest impact is given to the power flowing though the line with UPFC installed. The control objective is to maintain the active and reactive power flow whose prescribed values should be achieved within the UPFC steady state operation. Then, the power flow procedure is performed to check whether the predefined objective is achieved satisfactory with estimated parameters. If the load flow requirements are not satisfied at any operating points, it is necessary to go one step back, estimate again S S and r max, and perform new rotational change of the UPFC within the power flow procedure. This loop is performed until the load flow requirements are completely fulfilled. In addition, the active, reactive and apparent power of the series converter are calculated for each step change in the angle γ. With the power flow requirements fulfilled and the series converter powers calculated, it has to be checked whether the maximum value of the series converter apparent power max S conv2, is larger than the initially estimated power S s. If max S conv2 is not larger than the power S S, it is necessary to check whether the power S S is at an acceptable minimum level. If not, the value of S S is reduced and the loop starts again. The acceptable minimum is achieved when two consecutive iterations do not differ more than the pre-established tolerance. When the power S S is minimized, the load flow procedure is performed with smaller step of rotational change of the angle γ(1 0 ), in order to get maximum absolute value of the series/shunt converter active power, max P conv1. The value given by max P conv1 is considered to be minimum criterion for dimensioning shunt converter rating power, whereas the power S S represents series converter rating power as a function of the maximum magnitude r max.

29 2.2. Unified Power Flow Controller 29 DEFINE x k, S B r max, Initial S S CALCULATE 2 SB xs = xkrmax SS PERFORM LOAD FLOW = [0 :10 : 360 ] IS LOAD FLOW REQUIREMENTS FULFILLED? NO (INCREASE S s ) YES CALCULATE P conv2, Q conv2, S conv2 IF max S conv2 > S S? YES (INCREASE S s ) NO IS DECREASE S s S S minimum? YES PERFORM LOAD FLOW = [0 :10 : 360 ] CALCULATE max P conv1 OUTPUT S S, S conv1, r max Figure 2.11: Algorithm for optimal rating of the UPFC, [8]

30 30 Chapter 2. Modelling of FACTS Devices 2.3 Static VAr Compensator The Static VAr Compensator (SVC) is a shunt connected device whose main functionality is to regulate the voltage at a chosen bus by suitable control of its equivalent reactance. A basic topology consists of a series capacitor bank, C, in parallel with a thyristor-controlled reactor, L, as shown in Figure In practice the SVC can be seen as an adjustable reactance [1], that can perform both inductive and capacitive compensation. The details about the modelling of the SVC can be found in [6, 7]. The SVC connected at node j is shown in Figure C L Figure 2.12: Basic SVC topology Figure 2.14 shows the injection model of the SVC, where I jsvc is the complex SVC injected current at node j, V i and V j are the complex voltages at nodes i and j. The reactive power injection in node j is given by: Q j = Vj 2 B SV C (2.27) where, B SV C = B C B L, B C and B L are the susceptance of the fixed capacitor and thyristor controlled reactor, respectively. The reactive power can be transferred into injected current at bus j given by I jsvc = jv j B SV C (2.28) Figure 2.15 shows the SVC control block diagram where V t is the voltage magnitude at the SVC terminal, V ref is the voltage to be maintained by SVC, K is the gain of the controller, T is the time constant associated

31 2.3. Static VAr Compensator 31 with the SVC control action, B min and B max denote the limits to the change of the SVC susceptance and C damp is the signal from the damping controller. V i r l + jx l V j jb SVC Figure 2.13: Representation of a SVC V i r l + jx l V j I j Figure 2.14: Current injection model of a SVC

32 32 Chapter 2. Modelling of FACTS Devices B max C damp j SVC + + Power network B min V t - + V K 1+sT B V ref Figure 2.15: General form of the SVC control system

33 Chapter 3 Use of FACTS Devices for Damping of Power System Oscillations 3.1 Introduction The power system may be thought of as a large, interconnected nonlinear system with many lightly damped electromechanical modes of oscillation. If the damping of these modes become too small or negative, it can impose severe constraints on the system s operation. It is thus important to be able to determine their nature, find stability limits and in many cases use controls to prevent their instability. Electromechanical oscillations can be broadly classified into two main groups: Inter area oscillations Local oscillations Inter-area oscillations are observed when a group of machines in one area swings against another group in another area normally with a frequency below 1 Hz. The study the inter-area modes is quite complicated since it requires detailed representation of the entire interconnected sys- 33

34 34 Chapter 3. Use of FACTS Devices for Damping... tem and inter-area modes are influenced by several states of larger areas of the power network. Local oscillations are observed when one particular plant swings against the rest of the system or several generators at frequencies of typically 1 Hz to 2 Hz [12]. With the power industry moving toward deregulation, long-distance power transfers are steadily increasing, outpacing the addition of new transmission facilities and causing the inter-area oscillations to become more lightly damped [11]. During the last decade, FACTS devices have been employed to damp power system oscillations [13, 14, 15, 16]. Sometimes, these controllers are placed in the power system for some other reasons (to improve the voltage stability or to control power flow) [6, 7], then to damp power oscillations. However, when installed, supplementary control can be applied to existing controllers in order to improve damping, as well as satisfy the primary requirements of the device. POD control can be applied as well through power system stabilizer (PSS) on generator excitation control systems. PSSs are effective but they are usually designed for damping local electromechanical oscillations and in large power systems tuning all of them might be very difficult. In this chapter, POD control has been applied to three FACTS devices, TCSC, UPFC and SVC in order to damp inter-area oscillations. The main focus is on the TCSC, UPFC and SVC influence on power oscillation damping when a large disturbance is applied. The controller design method utilizes the residue approach [15, 16, 17]. The presented approach solves the optimal location of the FACTS devices, as well as the selection of the proper feedback signals. 3.2 Modal Analysis In order to identify oscillatory modes of a multi-machine system, the linearized system model including PSS and FACTS devices system can be used by where x ẋ = A x + B u y = C x + D u (3.1) is the state vector of length equal to the numbers of states n

35 3.2. Modal Analysis 35 y is the output vector of length m u is the input vector of length r A is the n by n state matrix B is the control or input matrix of size n by r C is the output matrix of size m by n D is the feed forward matrix of dimensions m by r. The equation det(λi A) = 0 (3.2) is referred to as the characteristic equation of matrix A and the values of λ, which satisfy the characteristic equation, are the eigenvalues of matrix A. Because the matrix A is a n by n matrix, it has n solutions of eigenvalues λ = λ 1,λ 2,...λ n (3.3) with assumption that λ i λ j,i j. For every eigenvalue λ i, there is an eigenvector φ i which satisfies Equation Aφ i = λ i φ i (3.4) φ i is called the right eigenvector of the state matrix A associated with the eigenvalue λ i. Each right eigenvector is a column vector with the length equal to the number of the states. Left eigenvector associated with the eigenvalue λ i is the n-row vector which satisfies ψ i A = λ i ψ i (3.5) The right eigenvector describes how each mode of oscillation is distributed among the system states. In other words, it indicates on which system variables the mode is more observable. The right eigenvector is called mode shape. The left eigenvector, together with the system s initial state, determines the amplitude of the mode. A left eigenvector carries mode controllability information. Numerous indices, such as participation factors, transfer function residues and mode sensitivities can be calculated from eigenvectors. Those indices are very useful in system analysis and controller design.

36 36 Chapter 3. Use of FACTS Devices for Damping... For a particular eigenvalue λ i = σ i + jω i, the real part of the eigenvalue gives the damping, and the imaginary part gives the frequency of oscillation. The relative damping ratio is given by ξ = σ i σ 2 i + ω 2 i (3.6) The oscillatory modes having damping ratio less than 3% are said to be critical [18]. When designing damping controls one has to take care about margin due to uncertainties or disturbances. Hence the damping ratio of at least 5% should be the objective of the control design [19]. Participation factors The sensitivity of a particular eigenvalue λ i to the changes in the diagonal elements of the state matrix A is given, [18], by p ki = λ i a kk = ψ ki φ ki (3.7) where ψ ki is the k th element in the i th row of the the left eigenvector ψ i, and φ ki is the k th element in the i th column of the right eigenvector φ i. The participation factor p ki is a measure of the relative participation of the kth state variable in the ith mode, and vice versa. The participation factor is used in this thesis for purpose of conventional tuning of PSSs, in Chapter 6. Controllability and observability In order to modify a selected oscillatory mode by a feedback controller, the chosen input of the controller must influence the behavior of that mode and the mode must also be visible in the chosen feedback signal i.e. the behavior of that mode should be reflected in the feedback signal. The measures for those two properties are the modal controllability and observability, respectively. The modal controllability and modal observability matrices are defined, [18], by B = Φ 1 B C = CΦ (3.8) The mode is not controllable if the corresponding row of the matrix B is a zero vector, and the mode is not observable if the corresponding

37 3.2. Modal Analysis 37 column of the matrix C is a zero vector. If a mode is either not controllable or not observable, feedback between the output and the input will have no effect on the mode. Residues Considering (3.1) with single input and single output (SISO) and assuming D = 0, the open loop transfer function of the system can be obtained by G(s) = y(s) u(s) = C(sI A) 1 B (3.9) The transfer function G(s) can be expanded in partial fractions of the Laplace transform of y in terms of C and B matrices and the right and left eigenvectors as G(s) = = N i=1 N i=1 Cφ i ψ i B (s λ i ) R i (s λ i ) (3.10) Each term in the denominator, R i, of the summation is a scalar called residue. The residue R i of a particular mode i gives the measure of that mode s sensitivity to a feedback between the output y and the input u; it is the product of the mode s observability and controllability. Figure 3.1 shows a system G(s) equipped with a feedback control H(s). When applying the feedback control, eigenvalues of the initial system G(s) are changed. It can be proven, [17], that when the feedback control is applied, the shift of an eigenvalue can be calculated by λ i = R i H(λ i ) (3.11) It can be observed from (3.11) that the shift of the eigenvalue caused by the controller is proportional to the magnitude of the corresponding residue. For a certain mode, the same type of feedback control H(s), regardless of its structure and parameters, can be tested at different locations. For the mode of the interest, residues at all locations have to be calculated. The largest residue then indicates the most effective location to apply the feedback control.

38 38 Chapter 3. Use of FACTS Devices for Damping FACTS POD Controller Design Supplementary control action applied to FACTS devices to increase the system damping is called Power Oscillation Damping (POD). Since FACTS controllers are located in transmission systems, local input signals are always preferred, usually the active or reactive power flow through FACTS device or FACTS terminal voltages. Figure 3.1 shows the considered closed-loop system where G(s) represents the power system including FACTS devices and H(s) FACTS POD controller. y ref + - e H(s) u G(s) y(s) Figure 3.1: Closed-loop system with POD control Input K p 1 1+sT m st w 1+sT lead 1+sT lead 1+sT w 1+sT lag 1+sT lag Output m c stages Figure 3.2: POD controller structure The POD controller consists of an amplification block, a wash-out and low-pass filters and m c stages of lead-lag blocks as depicted in Figure 3.2 (usually m c = 2). The transfer function, H(s), of the POD controller is given by ( ) ( )( ) mc 1 stw 1 + stlead H(s) = K 1 + st m 1 + st w 1 + st lag = KH 1 (s) (3.12) where K is a positive constant gain and H 1 (s) is the transfer function of the wash-out filter, low pass filter and lead-lag blocks. T m is a measurement time constant and T w is the washout time constant. T lead and T lag are the lead and lag time constant, respectively. Changes of an eigenvalue λ i can be described by (3.11). The objective of the FACTS damping controller is to improve the damping ratio of the selected oscillation mode i. Therefore, λ i must be a real negative value in order to

39 3.3. FACTS POD Controller Design 39 move the real part of the eigenvalue to the left half complex plane. Figure 3.3 shows the displacement of the eigenvalue after FACTS damping control action. j Direction of R i Direction of i = K H 1 ( i ) R i i (1) i ( K= K) comp arg(r i ) (0) i ( K=0) Figure 3.3: Shift of eigenvalues with the POD controller From (3.11), it can be clearly seen that with the same gain of the feedback loop, a larger residue will result in a larger change of the corresponding oscillatory mode. Therefore, the best feedback signal for the FACTS damping controller is the one with the largest residue for the considered mode of oscillation. The same is true for the optimal location of the POD controller, which also automatically means the best location for the FACTS device in order to damp oscillations. In Figure 3.3, the phase angle shows the compensation angle, which is needed to move the eigenvalue direct to the left parallel with the real axis. This angle will be achieved by the lead-lag function and the parameters T lead and T lag, [17], determined by ϕ comp = arg(r i ) α c = T 1 sin( ϕ comp ) lead m = c T lag 1 + sin( ϕ comp ) m c T lag = 1 w i αc T lead = α c T lag (3.13)

40 40 Chapter 3. Use of FACTS Devices for Damping... where arg(r i ) denotes the phase angle of the residue R i, w i is the frequency of the mode of oscillation in rad/sec. The controller gain K is computed as a function of the desired eigenvalue location according to (3.11): K = λ i,des λ i R i H 1 (λ i ) (3.14) 3.4 Case Studies The FACTS POD controller location and the feedback signal should be selected in a such a way that the residues corresponding to each of the critical modes are as high as possible [20]. Anyhow, it might not be cost effective to place the FACTS device at a particular location just to damp oscillations. In order to satisfy the primarily requirements of the FACTS device as well as the damping of oscillations, a compromise has to be made for each individual case. In this chapter, only damping is considered, i.e. the primary aim is to damp oscillations. Since the FACTS devices are located in transmission lines, local input signals like power deviation, bus voltages or bus currents, are preferably used. To find the best location and the most appropriate feedback signal for FACTS POD controller, different lines in the system are tested. A 10 machine, 39 bus test system, known as New England system, shown in Figure 3.4, [21], is considered here for the case studies. The static and dynamic data are given in Appendix A Design of TCSC POD Controller The uncontrolled system has one critical oscillatory interarea mode characterized with eigenvalue λ = j2.35, and with low damping ratio, ξ = 0.022, i.e. less than 3%. Table 3.1 shows the numerical results of the residue values associated with critical mode calculated using the transfer functions P/ k c. P is active power deviation, chosen as a feedback signal, k c represent TCSC input, characterized by the compensation degree, i.e. the compensation in p.u. of the line reactance. According to Table 3.1, the line has the largest residue for the transfer function, having k c as the TCSC control variable and,

41 3.4. Case Studies 41 G 8 10 G G G 6 G G G 5 4 G G 7 G Figure 3.4: System configuration for the case study therefore, the most effective location to apply the feedback control. Using the method presented above, the POD controller parameters are calculated in order to shift the real part of the oscillatory mode, to the left half complex plane. The gain K is calculated in order to reach the relative damping ratio of the oscillatory mode at least 5%. The root-locus, when the gain of TCSC controller K varies from 0 to 10, is shown in Figure 3.5. It is clear that TCSC POD controller has minor influence on local modes, like on mode #4. The local modes can be successfully damped by PSSs, which are not used in this test system. It is also obvious that POD controller affects the oscillatory mode the most (mode #1), but another inter-area mode, mode #2, might become critical, if the POD gain K is too high. Some other modes are affected as well. In order to have good damping of inter-area modes, and as less as possible negative influence on the other modes, compromise for the POD gain has to be found for each individual application. With the chosen gain in this case, all modes affected remains well damped, see

42 42 Chapter 3. Use of FACTS Devices for Damping... Mode residues of the transfer function P/ k c TCSC location R i line line line line line line line line line line line line Table 3.1: Location indices of TCSC Figure 3.6. The obtained transfer function for the TCSC POD controller is: H(s) = P ( )( )( ) s s + 1 = (3.15) k c 0.1s s s + 1 In order to check controller ability to stabilize the system, a threephase fault is applied in the line closed to the bus 33. The fault is cleared after 50 ms by opening the faulted line. In Figure 3.7, a direct comparison between the power flow response of the system with the fault with and without damping control is given. The reference value for the active power flow is calculated from the steady state calculation for the faulted line out of service.

43 3.4. Case Studies jω Damping ratio 0.05 Mode 4 Mode 3 Mode Mode σ Figure 3.5: Root-locus of the TCSC POD controller when K varies from 0( ) to 10( ) jω Damping ratio σ Figure 3.6: Displacement of eigenvalues without ( ) and with ( ) the proposed POD control