Small Signal Stability Improvement and Congestion Management Using PSO Based TCSC Controller


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In this paper an attempt has been made to study the
application of Thyristor Controlled Series Capacitor (TCSC)
to mitigate small signal stability problem in addition to
congestion management of a heavily loaded line in a
multimachine power system. The Flexible AC Transmission
System (FACTS) devices such as TCSC can be used to control
the power flows in the network and can help in improvement
of small signal stability aspect. It can also provide relief to
congestion in the heavily loaded line. However, the
performance of any FACTS device highly depends upon its
parameters and placement at suitable locations in the power
network. In this paper, Particle Swarm Optimization (PSO)
method has been used for determining the optimal locations
and parameters of the TCSC controller in order to damp small
signal oscillations. Transmission Line Flow (TLF) Sensitivity
method has been used for curtailment of non-firm load to
limit power flow congestion. The results of simulation reveals
that TCSC controllers, placed optimally, not only mitigate
small signal oscillations but they can also alleviate line flow
congestion effectively.

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Small Signal Stability Improvement and Congestion Management Using PSO Based TCSC Controller

  1. 1. ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 03, October 2011 Small Signal Stability Improvement and Congestion Management Using PSO Based TCSC Controller D. Mondal1, A. Chakrabarti2 and A. Sengupta3 1 Haldia Institute of Technology, Department of Electronics and Instrumentation Engineering, Purba Medinipur, Haldia-721657, India. (E-mail: 2, 3 Bengal Engineering and Science University, Department of Electrical Engineering, Howrah-711103, India (E-mail: and )Abstract— In this paper an attempt has been made to study the employed as the first choice to mitigate these problems.application of Thyristor Controlled Series Capacitor (TCSC) However, performance of PSS gets affected by networkto mitigate small signal stability problem in addition to configurations, load variations etc. Hence installations ofcongestion management of a heavily loaded line in a FACTS devices have been suggested in this paper to achievemultimachine power system. The Flexible AC TransmissionSystem (FACTS) devices such as TCSC can be used to control appreciable damping of system oscillations.the power flows in the network and can help in improvement But when TCSC has been installed at different locations,of small signal stability aspect. It can also provide relief to its performance and effect is different. It is important to locatecongestion in the heavily loaded line. However, the TCSC devices at suitable place in the transmission networkperformance of any FACTS device highly depends upon its to achieve desired objectives. The optimal allocation of TCSCparameters and placement at suitable locations in the power has been reported in literatures [5]-[7] based on many aspectsnetwork. In this paper, Particle Swarm Optimization (PSO) - optimal power flow (OPF) with lowest cost generation,method has been used for determining the optimal locations reactive power planning, etc. In this paper the TCSC hasand parameters of the TCSC controller in order to damp small been used for small signal stability improvement and a novelsignal oscillations. Transmission Line Flow (TLF) Sensitivitymethod has been used for curtailment of non-firm load to stochastic method, Particle Swarm Optimization [8] has beenlimit power flow congestion. The results of simulation reveals implemented for finding the optimal location and parametersthat TCSC controllers, placed optimally, not only mitigate of the TCSC controller. Though PSO has been employed insmall signal oscillations but they can also alleviate line flow several research papers [9]-[10] for the design of optimalcongestion effectively. FACTS controllers, the applications are mostly limited to the case of single machine infinite bus system.Keywords—Congestion management, Particle Swarm In this paper the application of TCSC controller has beenOptimization, Small Signal Stability, Thyristor Controlled extended to study the small signal oscillation problem in caseSeries Compensator, Transmission Line Flow Sensitivity. of a multimachine power system and a novel use of TCSC has been explored for transmission overload curtailment and I. INTRODUCTION congestion management. Transmission Line Flow (TLF) In deregulated power industry congestion occurs more sensitivity values for the most overloaded line have beenfrequently on many individual transmission systems when considered for calculating the necessary load curtailment forcontingency or load increase happens in power system and the alleviation of the transmission may even cause some physical violations such as The paper has been organized as follows: section II de-transmission line overload or low/high bus voltage profile in scribes the definition and method of (TLF sensitivity based)the system. In these cases, it may be needed to shed some congestion managements. The small signal modeling of theload to ensure that transmission overload security limits are multimachine system working with TCSC controllers has beensatisfied. The development of FACTS has potential represented in section III. In section IV the general theory ofcontribution on load curtailment issues [1]. Thyristor PSO and the proposed optimization problem has been dis-Controlled Series Compensator (TCSC) is a series controlled cussed. The impact of TCSC on load curtailment has beendevice in the FACTS family that are increasingly applied for examined in section V. The PSO algorithm has been imple-this purpose in long transmission lines in modern power mented in the section V to determine optimal location andsystems [2]. In [3] TCSC and SVC were used as re-dispatch parameters of the TCSC controller. The validity of the pro-tools for congestion management with Total Transfer posed methods have been tested in a 3-machine, 9-bus sys-Capability (TTC) improvement. tem. Another challenging problem to the researcher in modernpower industry is the low frequency power oscillations. II. CONGESTION MANAGEMENTTraditionally [4], Power System Stabilizers (PSS) have been A. Definition of Congestion ManagementCorresponding author: D. Monal, Haldia Institute of Technology, When the producer and consumer of electric energy desireDept. Electronics and Instr. Engg., (E-mail:© 2011 ACEEE 12DOI: 01.IJCSI.02.03.86
  2. 2. ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 03, October 2011to produce and consume an amount of electric energy, the S ijtransmission system may operate at or beyond one or more Tijk  (2) Pktransfer limits and the system is said to be congested. Inheavily congested conditions, transmission congestion can The load curtailment at bus k can be obtained asbe relieved by curtailing a portion of non-firm transactions.An example of two-bus system has been shown in Fig. 1 to Tijk Pkcut  ΔS ijexplain transmission congestion.  Tijk (3) In Fig. 1(a), the maximum real power output of the machine Nis 60 MW, the transmission line flow limit is 55 MW and theload is 58 MW. Therefore, there is a transmission overload in where S ij  S ij  S ijthe transmission line to serve the load. Congestion can bealleviated by curtailing some portion of the load. In Fig. 1(b), S ij : Actual power flow through transmission line i-jthe load has been curtailed from 58 MW to 54 MW and thecongestion has been alleviated. S ij : Flow limit of transmission line i-jB. Methods of Congestion Management N : Total numbers of branches between load buses. The higher the TLF sensitivity the more is the effect of a The power flow Pij through the transmission line i-j is a single MW power transfer at any bus. Hence, based on the TLF sensitivity values the loads are curtailed in requiredfunction of the line reactance X ij , the voltage magnitudes amounts at the load buses in order to eliminate theVi , V j and the phase angle ( δ i  δ j ) between the sending transmission congestion on the congested line i-j.and receiving end voltages (,) as shown in equation (1). III. SMALL SIGNAL MODELING ViV j A. Modeling of TCSC Pij  sin (δi  δ j ) (1) X ij The basic TCSC module and the transfer function modelFrom equation (1), it has been seen that the power flow can of a TCSC controller [11] have been shown in Fig. 2(a) andbe affected with the change of voltage magnitudes, the 2(b) respectively. This simple model utilizes the concept of areactance of the transmission lines or the power angle (). It variable series reactance which can be adjusted throughhas been well established that voltage magnitudes can be appropriate variation of the firing angle (  ). The controllercontrolled through VAR support. The reactance of the line comprises of a gain block, a signal washout block and a phasecan be reduced through series compensation and the power compensator block. The input signal is the normalized speedangle can be varied via power injection changes at either deviation ( ν ), and output signal is the stabilizing signalbus, e.g. generation or load changes. In this paper, series (i.e. deviation in conduction angle, Δσ ).compensation of line reactance has been considered for Neglecting washout stage, the TCSC controller model cancongestion management and TLF sensitivity (sensitivities be represented by the following state equations;of the line flows to load change) value for the most overloadedline has been considered for calculating the necessary load 1 K  1  K T        tcsc  T ω  tcsc  1   ω (4)curtailment. T2 ωs  2  ω s  T2     1 1 X tcsc     X tcsc (5) Ttcsc Ttcsc Fig. 1(a) Two-bus system with congestion Fig. 2(a) TCSC module Fig. 1(b) Two-bus system with congestion alleviatedThe TLF sensitivity at a bus k due to change load powerPk for a congested line i-j is Tijk and has been calculatedusing the relation shown in equation (2) Fig. 2(b) Structure of a TCSC based controller© 2011 ACEEE 13DOI: 01.IJCSI.02.03.86
  3. 3. ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 03, October 2011The steady-state relationship between the firing angle  Eliminating ΔI g from the respective equations (8)-(11), theand the equivalent TCSC reactance, X tcsc is given by [12] overall system matrix with TCSC controller can be obtained asX tcsc   X C  C1(2(π  α)  sin (2(π  α)))  C 2 cos 2 (π  α)( ω tan ( ω (π  α))  tan (π  α)) (6) Atcsc ( 7m  2 )  ( 7 m  2 )  A  B D 1 C  (16) XC X L X C  X LCwhere X LC  X  X , C1  C L π 4X 2 LCand C 2  . The linearized TCSC equivalent reactance πX Lcan be obtained from (6) is Fig. 3 Block-diagram: Power System with TCSC controller The block-diagram of the power system with TCSC as aΔXTCSC   2C1(1 cos(2α)) C2 sin(2α)( tan((π  α)) tanα) feedback controller has been depicted in Fig. 3.  cos  (  )  IV. FORMULATION OF OPTIMIZATION PROBLEM C     (7)    cos  ( (  ))   A.Particle Swarm Optimization (PSO) Particle Swarm Optimization was first developed in 1995B. Multimachine model with TCSC by Eberhart and Kennedy [8]. The PSO algorithm begins by initializing a random swarm of M particles, each having R The general theory of the small signal stability problem in unknown parameters to be optimized. At each iteration, thecase of a multimachine system and its linearized model has fitness of each particle has been evaluated according to thebeen described in [13] and is given by selected fitness function. The algorithm stores and  ΔX  A1ΔX  B1ΔI g  B 2 ΔV g  E1ΔU (8) progressively replaces the best fit parameters of each particle ( pbesti, i=1, 2, 3, . . . , M) as well as a single most fit particle 0  C 1 Δ X  D 1 Δ I g  D 2 Δ Vg (9) (gbest) among all the particles in the group. The parameters of each particle (pi) in the swarm are updated in each iteration 0  C 2 ΔX  D3ΔI g  D4 ΔV g  D5 ΔVl (10) (n) according to the following equations: 0  D6 ΔV g  D7 ΔVl (11) veli (n)  w veli (n  1)  acc1  rand1  (gbest  pi (n  1)) The multimachine linearized model with TCSC controller  acc2  rand2  (pbesti  pi (n  1))can be formulated separately by adding the state variables (17)Δxtcsc  Δ ΔX tcsc T corresponding to the TCSC (18) pi (n)  p i (n  1)  veli (n)controller in equations (8)-(10) and the TCSC power flowequation in the network equation (11). where, vel i (n) is the velocity vector of particle i and is a vector The TCSC linearized real power flow equation between of random values  (0,1) . acc1, acc2 are the accelerationbus s and t can be obtained from the following equation coefficients that pull each particle towards gbest and pbesti Pst Pst Pst Pst Pst positions respectively and are often set to be 2.0. w is theΔPst  Δθ s  ΔV s  Δθt  ΔVt  Δα (12) θ s V s θt Vt α inertia weight of values  (0,1) . rand1 and rand2 are two uniformly distributed random numbers in the ranges [0, 1].where, Pst  V s2 g st  V s Vt (g st cos δ st  b st sin δ st ) (13) B. Objective Function and Optimization Problem 1 R st  j(X st  X tcsc ) The problem is to search the optimal location and the Y  and st R  j(X  X tcsc ) st st R st  (X st  X tcsc ) 2 2 parameter set of the TCSC controller using PSO algorithm. The objective is to maximize the damping ratio ( ) as much g st  jbst (14) as possible. This results in minimization of the critical damping index (CDI) given by Ps Pstwith  CDI  J  (1   i ) (19) α α Here,  i is the damping ratio of the i-th critical swing mode.    V s2 g  V sVt ( cos δ st g  sin δ st b ) There are four unknown parameters: the TCSC controllers α st α st α st (15) gain (Ktcsc), lead time (T1), the lag time (T2) constants and© 2011 ACEEE 14DOI: 01.IJCSI.02.03.86
  4. 4. ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 03, October 2011TCSC location number (Nloc). These parameters have to be V. APPLICATION AND RESULTSoptimized by minimizing the objective function J given bythe equation (19). With a change of location and the A. Application of TLF sensitivity on Load Curtailmentparameters of the TCSC controller, the damping ratio ( ) as This section describes first the transaction curtailmentwell as J varies. result using TLF sensitivity procedures, and then the resultsThe optimization problem can then be formulated as: obtained along with the application of TCSC in the proposedMinimize J [Equation (19)] system. Suppose maximum output of all the generators areS. T. : 250 MW. The real load increased at bus 5 is 50 % more thanEquality Constraints the base load. n PGi  PLi  V V Y k 1 i k ik ( X tcsc ) cos(θi θ k   ik )  0 (20) n QGi  QLi  V V Y k 1 i k ik ( X tcsc ) sin(θi θ k   ik )  0 (21)Inequality constraints Vi  1  0.05 min max min max PGi  PG  PGi ; QGi  QG  QGi min max K tcsc  K tcsc  K tcsc ; T1min  T1  T1maxT2min  T2  T2max ; min max N loc  N loc  N locC. Particle configuration The particle can be defined as a vector which containsthe TCSC controller parameters and the location number: Ktcsc,T1, T2 and Nloc as shown in equation (22) Particle: [Ktcsc T1 T2 Nloc ] (22)The particle configurations corresponding to the TCSCcontroller has been shown in Fig 4. The initial population hasbeen generated randomly for each particle and are kept within Fig. 5 3-machine, 9-bus system with the application of TCSCa typical range. It is assumed that the flow limits of lines # 4, 5 and 9 as 70 To optimize equation (19), routines from PSO toolbox [14] MW and for the lines # 6, #7 and 8 as 100 MW, execution ofhave been used. The objective function corresponding to power flow calculation (Table I) revealed that the line # 4 iseach particle has been evaluated by small signal analysis congested as the real power flow through this line is 85.44program of the proposed test system (Fig. 5). This system MW which has exceeded its proposed flow limit of 70MW.has been widely used in literature [13] for small signal stability Therefore, some transaction must be curtailed to avoidanalysis in power systems. The network branches (line # 4, 5, congestion in order to maintain the safety of the system.6, 7, 8 and 9) between two load buses are selected here for Applying TLF sensitivity procedure, the required amount oflocating the TCSC module and therefore, line #4 and line #9 load curtailment is obtained as 17.12 MW (Appendix A.2). min max After installation of TCSC it has been found that theare given as N loc and N loc respectively. . amount of load curtailment is significantly reduced and the effect is different for different locations of the TCSC module (Table II). In this stage therefore, it may be essential to choose a suitable installing location of the TCSC controller. The optimal location of TCSC can be determined based on different factors such as the stability of the system, the load pattern of the system, the type of contingencies etc. In the following section the issue of small signal stability problem has been considered to identify the optimal location of the TCSC Fig. 4 Particle configuration for TCSC controller controller.© 2011 ACEEE 15DOI: 01.IJCSI.02.03.86
  5. 5. ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 03, October 2011 TABLE I. POWER FLOW AFTER LOAD INCREASE WITHOUT TCSC TABLE III. EIGENVALUES WITHOUT AND WITH TCSC TABLE II. POWER FLOW AFTER INSTALLATION OF TCSC TABLE IV. PSO BASED TCSC PARAMETERS AND LOCATIONThe results obtained in Table II indicate that when TCSC hasbeen installed in line # 6 power flow through the congestedline # 4 is well below its flow limit (70 MW) and the requiredamount of load curtailment in the over loaded bus 5 is zero.This implies that installation of TCSC in line # 6 alleviatedpower flow congestion 100 % in the congested line # 4 withoutcurtailment of any load.B. Application of PSO and Small Signal Stability Analysis In this section the validity of the proposed PSO algorithmhas been tested on a 3-machine 9-bus system (Fig. 5). Thecomplex eigenvalues of the system with and without TCSCdynamics are listed in Table III. It has been observed thatwithout TCSC dynamics the electromechanical mode #1 isthe critical one as the damping ratio of this mode is smallestcompared to other modes. Therefore, stabilization of this modeis essential in order to improve small signal stability. ThePSO algorithm (Fig. 6) generates the optimal location and theoptimal values of the TCSC controller parameterssimultaneously by minimizing the desired objective functionJ and the results are represented in Table IV. The convergencerate of objective function J for gbest with the number ofgenerations for 200 has been shown in Fig. 7. Fig. 6 Algorithm of the implemented PSO It is evident form Table IV that the application of PSObased TCSC controller in its optimal location (line # 6)improved the damping ratio of the critical swing mode # 1about 33% over the damping ratio without TCSC controller.In view of the results obtained in Table II and Table IV it maybe reasonable to conclude that the line #6 is the best locationof the TCSC controller. Fig. 7 Convergence of the objective function for gbest© 2011 ACEEE 16DOI: 01.IJCSI.02.03.86
  6. 6. ACEEE Int. J. on Control System and Instrumentation, Vol. 02, No. 03, October 2011 VI. CONCLUSIONS 45.76 Tijk  = 0.7321; The investigation in this paper illustrated two novel uses 62.5of TCSC in a multimachine power system. The TCSC has S ij  (78.11 -70.0)=8.11 MWbeen installed for both dynamic and steady state secureoperation of the power system. The optimal location of the The amount of load curtailment at bus 5 is nowTCSC has been determined based on small signal stability 0.7321improvement in order to achieve dynamic stability. TLF Pkcut   8.11 =12.73 MW 0.4662sensitivity based load curtailment method has been usedalso to constrain line flow congestion. A new stochastic Improvement of load curtailmentoptimization technique, PSO algorithm, has been implemented 17.12  12.73 =  25.64%for optimal parameter setting and identification of the optimal 17.12site of TCSC controller by minimizing the desired objectivefunction. It has been revealed that the proposed approach REFERENCEScan provide both economic and secure operating conditionsto the power system. [1] G. Huang, P. Yan, “The impacts of TCSC and SVC on power system load curtailments”, IEEE Power Engineering Society Summer Meeting, Vancouver, BC, vol. 1, pp. 33-37, July, 2001. APPENDIX A [2] G. M. Huang and S. C. Hsich, “An optimal power deliveryA.1 Power flow result at base load problem in deregulated open access environments,” Proceedings of the 1996 IEEE International Conference on Control Applications, TABLEA.I. B ASE CASE POWER FLOW pp.450-455, 1996. [3] G. Huang, and P. Yan, “TCSC and SVC as Re-dispatch Tools for Congestion Management and TTC Improvement”, IEEE Power Engineering Society Winter Meeting, vol. 1, pp. 660-665, Aug. 2002. [4] P. Kundur, Power System Stability and Control. New York: McGraw- Hill; 1994. [5] M. M. El Metwally, A. A. El Emary, F. M. El Bendary, and M. I. Mosaad, “Optimal allocation of facts devices in power system uses genetic algorithms,” IEEE power system conference, MEPCON 2008, pp. 1-4, Mar. 2008.A.2 Transmission Line Flow (TLF) Sensitivity and load [6] M. Santiago-Luna and J. R. Cedeño-maldonado, “Optimalcurtailment placement of FACTS controllers in power systems via evolution1) Without TCSC: TLF sensitivity for a congested line #4 (4- strategies” IEEE PES Trans and distr conference and Exposition,5) due to change load power at bus 5 Latin America, Venezula, pp. 6-1, 2006. [7] N. P. Padhy, M. A. Abdel-Moamen and B. J. Praveen Kumar, S ij  (85.44-32.35) = 53.09 MW “Optimal location and initial parameter settings of multiple TCSCs Pk  (187.5-125.0) = 62.5 MW for reactive power planning using genetic algorithms,” IEEE power Engineering Society General Meeting, vol. 1, pp. 1110-1114, Jun. 53.09 2004. Tijk  = 0.8494; [8] J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” 62.5 IEEE International Conference on Neural Networks, vol. 4, pp. k 5 5 5 1942-1948, Nov.1995. T N ij  T45  T46    T89 = 0.7659 [9] S. Panda and N. P. Padhy, “A PSO-based SSSC controller for improvement of transient stability performance,” International Journal of Intelligent Systems and Technologies, vol. 2, no.1, pp.28- S ij = 85.44 MW and S ij =70 MW 35, winter 2007. [10] M. A. Abido, A. T. Al-Awami and Y. L. Abdel-Magid, “Analysis S ij  (85.44-70.0)=15.44 MW and design of UPFC damping stabilizers for power system stabilityThe amount of load curtailment at bus 5 is thus obtained enhancement,” IEEE Inter Symposium on Industrial Electronics, vol.3, pp. 2040-2045, 2006. 0.8494 [11] S. Panda, N. P. Padhy and R. N. Patel, “Modelling, simulationas Pkcut  15.44 =17.12 MW 0.7659 and optimal tuning of TCSC controller,” International journal simulation model, vol. 6, no. 1, pp. 37-48, 2007.2) With TCSC installed in line # 7(6-9): TLF sensitivity of the [12] C. R. Fuerte-Esquivel, E. Acha, and H. Ambriz-Pe’rez, “Acongested line #4 (4-5) due to change load power at bus 5 thyristor controlled series compensator model for the power Flow S ij  (78.11-32.35) = 45.76 MW solution of practical power networks,” IEEE Trans. on power systems, vol. 15, no. 1, pp. 58-64, Feb. 2000. Pk  (187.5-125.0) = 62.5 MW [13] P. W. Sauer and M. A. Pai, Power system dynamics and stability. Singapore: Pearson Education Pte. Ltd., 1998. k 5 5 5 T N ij  T45  T46    T89 = 0.4662. [14] B. Birge “Particle Swarm Optimization Toolbox”. http://© 2011 ACEEE 17DOI: 01.IJCSI.02.03.86