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IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com

IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com


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  • 1. N.Srikanth, Atejasri / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1817-1824 ENHANCING POWER SYSTEM STABILITY BY USING Thyristor Controlled Series Compensator N.Srikanth (M.Tech)*, ATEJASRI-M.Tech** Dept of EEE, GIET, RAJAHMUNDRY, A.P-INDIA,Abstract Passivity- based controller is designed for can provide the benefits of increased system stability,the thyristor controlled series capacitor (TCSC) reduced system losses, and better voltage regulationaimed at enhancing power system stability. The Protective distance relays, which make use ofdesign problem formulated as optimization impedance measurements in order to determine theProblem and then particle swarm optimization presence and location of faults, are "fooled" by(PSO) technique was used to search for optimal installed series. Capacitance on the line when theparameters. The proposed control and technique presence or absence of the capacitor in the faultare employed on test system under different cases circuit is not known a priori. This is because theand location of TCSC. To validate the capacitance cancels or compensates some of theeffectiveness of the TCSC on enhancing system inductance of the line and therefore the relay maystability, Eigen values analysis and nonlinear perceive a fault to be in its first zone when the faulttime-domain simulation implemented on SMIB is actually in the second or third zone of protection.equipped with TCSC. The eigenvalue analysis and Similarly, first zone faults can be perceived to besimulation results show the effectiveness and reverse faults! Clearly this can cause some costlyrobustness of proposed controllers to improve the operating errors. The conventional protections likestability performance of power system by efficient distance, differential, and by using relays powerdamping of low frequency oscillations under controllers are very much in use nowadays.various disturbances. Recent trend to overcome those problems isKeywords: Power system stability; Thyristor the application of FACTS technology, is beingControlled Series Compensator; particle swarm promoted as a means to extend of FACTSoptimization; technology, is being promoted as a means to extend the capacity of existing power transmission networksI.INTRODUCTION to their limits without the necessity of adding new Modern interconnected power systems are transmission lines There have been significantlarge, complex and operated closer to security limits. activities and achievement research and applicationFurther more environmental Constraints restrict the of flexible AC transmission systems (FACTS).expansion of transmission network and the need for Thyristor controlled series compensation (TCSC) islong distance power transfers has increased as a an important device in the FACTS family. It canresult Stability has become a major concern in many have various roles in the operation and control ofpower systems and many blackouts have where the power systems, such as scheduling power flow;reason has been instability i.e. rotor angle instability, decreasing Unsymmetrical components andvoltage instability or frequency stability. Power enhancing transient stability.system stabilizers (PSS) are now routinely used inthe industry to damp out power system oscillations. This was a very simple control; theHow ever, during some operating conditions, this maximum amount compensation was inserted at thedevice may not produce adequate damping, observed same time that the faulted line was switched outwhich detract from the overall system performance advances in high-power electronics, high-efficiencyand become unstable, and power input stabilizers power electronics have led to development ofwere found to lead to large changes in the generator thyristor -controlled it can change its apparentother effective alternatives are needed in addition to reactance .PSS. These problems are well known [1-4]. TCSC is able to directly schedule the real In order to meet the high demand for power power flow control by selected line and allow thetransmission capacity, some power companies have system to operate closer to the line limits. Moreinstalled series capacitors on power transmission importantly because of its rapid and flexiblelines. This allows the impedance of the line to be regulation ability, it can imp rove transient stability tolowered, thus yielding increased transmission and dynamic performance of the power systems.capability. The series capacitor makes sense because [13].The objective of this paper is to study the impactits simple and could be installed for 15 to 30% of of TCSC on enhancing power system stability, whenthe cost of installing a new transmission line, and it subjected to small or severe disturbances, as well as 1817 | P a g e
  • 2. N.Srikanth, Atejasri / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1817-1824location of TCSC. To optimize the TCSC parameters C dv c=is(t)-iT(t) u………..................... (1)particle swarm optimization (PSO) .Technique is dtused to find optimal parameters and then location of L di T = VC u……..………….................. (2)TCSC. The rotor speed deviation is used as objective dtfunction. is (t) =I m cos (wt)……………………… (3) Section (II) of this paper discusses modeling In equation (1) the switching variable u= 1 whenof TCSC while sections (III) derive dynamic the thyristor valves are conducting (S is closed), andmodeling of power system The rest of the sections are u= 0 when the thyristor are blocked(S is open) .organized as follows: in section (IV) an over view ofparticle swarm optimization is presented Section (V) VCF to IM:formulation problem and o objective function arederived. The simulation and results are presented in XTCSC=VCF = XC- X2C 2β+SIN2β+section VI). Finally conclusions are discussed in IM XC-XL ∏section (VII) 4X2C COS2β (K tan kβ –tan β)II. TCSC MODELLING XC-XL (K2-1) ∏………………….. (4) The basic TCSC configuration consists of a Orseries capacitor bank C in parallel with a thyristor-controlled reactor and bypass inductor L as shown in XTCSC=VCF = XC- X2C σ+SINσ +Figure.1. This simple model utilizes the concept of a IM XC-XL ∏variable series reactance. The series reactance isadjusted automatically within limits to keep the 4X2C COS2 (σ/2) (K tan (k σ/2) –tan (σ/2)specified amount of active power flow across the line. XC-XL (K2-1)There are certain values of inductive and capacitivereactance which cause steady-state resonance. Generally, in a TCSC, two main operational blocks can be clearly identified A) An External control: Control operates the controller Accomplish specified compensation objectives; this control directly relies on measured systems variables to define the Reference for the internal control, which is usually the value of the controller reactance. It may be comprised of different control loops depending on the control objectives. Typically the principal steady The TCSC can be continuously controlled state function of a TCSC is power flow control,either in capacitive or in inductive area, avoiding the which is usually accomplished either automaticallysteady- state resonant region considering the three With a “slow” PI to guarantee steady-steady error –basic operating modes of the TCSC: Thyristor free control Obeying specified limits concerningblocked, Thyristor bypassed and Vernier operation. reactance or the firing angle, or manually throughThe vernier mode is subdivided into two categories, direct operator intervention Additional functions fornamely: inductive vernier mode (900< α <αres) and stability improvement, such as damping controls maycapacitive vernier mode (αres <α < 1800) see Fig. 1. be included in the external control. For the purposes of mathematical analysis a The equivalent impedance X’e Of the device issimplified TCSC circuit is shown in fig.2. represented as a function of the firing angle based onTransmission-line current I assumed to be the the assumption of a sinusoidal steady-state controllerindependent-input variable and is modeled as an current. In this model, it is Possible to directlyexternal current source, is (t). It is further assumed represent some of the actual TCSC internal Controlthat the line current is sinusoidal. Then the current blocks associated with the firing angle control, asthrough the fixed series capacitor, thyristor valve i T Opposed to just modeling them with a first order lag(t), and the line current I S (t),are expressed as function. B)An Internal control: provide appropriate gate drive signals for the thyristor valve to produce the desired compensating reactance Fig .3 shown below illustrate block diagram of TCSC model used in this paper for both operation Fig .2 A simplified TCSC circuit modes 1818 | P a g e
  • 3. N.Srikanth, Atejasri / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1817-1824 WS dt2 d2δ = Ws (PM- PE)…….…………... (9) dt2 2GH From equation 6 δ value can be substituted d2(θc-Wst) = Ws (PM- PE)……………(10) dt2 2GH Ẃs = WB {PM- PE- D (∆w)} …………… (11)Fig .3 shown below illustrate block diagram of TCSC model used in this paper for both operation modes 2H The structure of the proposed stability control B.GENERATORELECTRICALDYNAMICSloop is depicted in Fig. 3. It consists of a washout The internal voltage, Eq; equation ifilter to avoid a Controller response to the dc offset ofthe input signal, a Dynamic compensator and alimiter. The dynamic compensate or Consists of two …….... (12)(or more) lead-lag blocks to provide the necessary In this work a simplified IEEE type –ST1Aphase-lead characteristics Finally, the limiter is used is used, which Can be representing by equation (15).to improve controller response to large deviations in The inputs are the terminal Voltage (V t ) andthe input signal. reference voltage Vref . KA and TA are the gain and time constant of the excitation systemIII. DYNAMIC MODELING OF POWERSYSTEM In this paper, a simple single machine infinite bus (SMIB) system is used as shown in fig .4. ……...…… (13)The generator is represented by the third-order model. Where Pe,The dynamics of the Machine in classical model, canbe represented by the following. ..................... (14) Pe= Vq Iq +Vd Id……………………..................... (15) ….…………………………. (16)Fig:4 single machine infinite bus Vd = Xd Id………………………………… (17)A.MECHANICAL EQUATIONS ………………………... (18) For Small-signal analysis, the lineraizedincremental δ =θ e –w s t…………………….……… (5) model around a nominal operating point is usually employed. The lineraized power system model can δ·= w B (∆w) …………………………. (6) bewrittenas:Here δ, w , H, D, PM and Pe are the angle, speed,moment Inertia , damping coefficient, inputmechanical Power and output electrical power,respectively, of the machine .To measure the angularposition of the rotor with respect to a synchronouslyrotating frame of reference.δ =θe -wst; rotor angular displacement fromsynchronously rotating frame called ( torqueangle/power angle). Where, M d2 δ = PM-PE…………………… (7) dt2 2GH d2 δ = PM-PE………………… (8) …………………………..(19) 1819 | P a g e
  • 4. N.Srikanth, Atejasri / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1817-1824 4) The above concept is explained using only XY axis (2dimensional space). However, the method can be easily applied to n dimensional problem. Each particle keeps track of its coordinates in the problem space , which are associated with the best solution (evaluating value) it has achieved so far. This value is called p best. …… (20) Another best value that is tracked by the global version of the particle swarm optimizer is the overall best value, and its location, obtained so far byIV. OVERVIEW OF PARTICLE SWARM any particle in the group, is called G best.In PSO, eachOPTIMIZATION [17–19] particle moves in the search space with a Velocity Particle swarm optimization (PSO) method. according to its own previous best solution and itsIt is one of the optimization techniques and a kind of Group’s previous best solution. The velocity updateevolutionary computation technique. The method has in a PSO Consists of three parts ; namelybeen found to be robust in solving problems featuring momentum, cognitive and social parts. The balancenonlinearity and non differentiability, multiple among these parts determines the performance of aoptima, and high dimensionality through adaptation, PSO algorithm.which is through adaptation, which is derived fromsocial- psychological theory. It is a population basedsearch algorithm*The method is developed from research on swarmsuch as fish schooling and bird flocking.*It can be easily implemented, and has stableconvergence Characteristic with good computationalefficiency. The PSO method is a member of widecategory of swarm intelligence methods for solvingthe optimization problems. It is population basedsearch algorithm where each individual is referred toas particle and represents a candidate solution. Each Fig:5 Position updates of particles in particle swarmparticle in PSO flies through the search space with an optimization Techniqueadaptable velocity that is dynamically modifiedaccording to its own flying experience and also the For example, the jth Particle is represented as xj= (xj.1,flying experience of the other Particle. xj.2 ….. xj.n) in the g-dimensional space. The best previous Position of the jth Particle is recorded andThe features of the searching procedure can be represented as best Pbest = (Pbestj.1, Pbestj.2 …….., Pbestj.1)summarized as follows .The index of best among all of the particles in the1) Initial positions of p best and g best are different. group is represented by particle G bestg The rate of theHowever, using the different direction of p best and position change (velocity) for particle is representedg best , all agents gradually get close to the global as Vj=( Vj.1,Vj.2,……………,V j.n). The modifiedoptimum. velocity and position of each particle can be2) The modified value of the agent position is calculated using the current Velocity and the distancecontinuous and the method can be applied to the from pbest j.g to g best gcontinuous problem. How ever, the method can beapplied to the discrete problem using grids for XY V j,g(t+1) = W .v j.g +C*1rand()*(pbest j.g-xtj.g)position and its velocity. C*2rand ()*(pbest j.g- xtj.g)3) There are no inconsistency in searching …………….(21)procedures even if continuous and discrete statevariables are utilized with continuous axes and grids X (t+1) j,g = X(t)j,g+ V(t+1)j,g ………………(22)for XY positions and velocities. Namely, the method j = 1, 2... ncan be applied to mixed integer nonlinear g = 1, 2... moptimization problems with continuous and discretestate variables naturally and easily. Where n number of particles in a group m number of member in a particles 1820 | P a g e
  • 5. N.Srikanth, Atejasri / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1817-1824t pointer of iteration (generations) washout block serves as a high-pass filter, with theVt j.g velocity of particle j at iteration t time constant TW, high enough to allow signalsVG MIN ≤ VJ..Gt ≤ VGMAX; associated with oscillations in input signal to passW inertia weight factor unchanged. Without it steady changes in input wouldC1,C2 acceleration constant modify the output. The damping torque contributedRand () , rand() random number between 0 and 1 by the TCSC can be considered to be in to two parts.Xt j.g current position of particle j at iteration t ; The first part KP, which is referred as the directPbest j Pbest o f particle j ; damping torque, is directly applied to thegbest gbest of the group electromechanical oscillation loop of the generator. The second part KQ and KV, named as the indirect In the above procedures, the parameter Vmax damping torque, applies through the field channel ofdetermined the resolution, or fitness, with which the generatorregions be searched between the present position andthe target position. If Vmax is too high particles might In the above figure the parameters Kw, T1fly past good solutions. If Vmax is too small particles and T2 are to be determined, Tw is summed to 20,may not explore sufficiently beyond local solutions In T1=T3 and T2=T4.The input signal to the controller ismany experiences with PSO Vmax was often set at 10- the speed deviation and the output is the change in20% of the dynamic range of the variable on each conduction angle. In steady state ∆σ=0, and Xe =Xeq–dimension. XTCSC0 while during dynamic period the series compensation is modulated for damping system The constants c1 and c2 represent the oscillations , in this case Xe =Xeq –XTCSC .weighting of the stochastic acceleration terms thatpull each particle Pbest and gbest positions. Low Where σ = σ+ ∆σ and ( σ =2( ∏-σ )), wherevalues allow particles to roam far from the target σ0 is the initial value of firing angle, and Xeq is totalregions before being tugged back. On the other hand, reactance of the system.high values result in abrupt movement toward, orpast, target regions. Hence, the acceleration constants A.Objective functionc1 and c2 were often set to be 2.0 according to past TCSC controller is designed to minimize theexperiences Suitable selection of inertia weigh tin power System oscillations after a small or lager(19) provides a balance between global and local disturbance so as to improve the stability. Theseexplorations, thus requiring less iteration on average oscillations are reflected in the deviation in theto find a sufficiently optimal solution .As originally generator rotor speed (∆w). An integral time absolutedeveloped, often decreases linearly from about0.9 to error of the speed deviations is taken as the objective0.4 during a run. In general, the inertia weight is set Function J, expressed asaccording to the following equation: tsim J= ∫(t, x) dt……….………… (24) w=wmax- wmax - wmin ×iter t itermax………............... (23) Where │∆w (t, x) │ is the absolute value of Where itermax is the maximum number of the speed deviation for a set of controller parametersiterations (generations), and iter is the current number x (K w ,T1, T2) and t is the time range of theof iterations. simulation. With the variation of K w ,T 1,T2 , the TCSC based controller parameters, J will also beV. PROBLEM FORMULATION changed. For objective function calculation, the time- The structure of TCSC controller domain simulation of the power system model isimplemented in stability control loop was discussed carried out for the simulation period. It is aimed toearlier, fig. 5 show TCSC with stability control loop. minimize this objective function in order to improve the system stability. The problem constraints are TCSC controller parameter bounds; there the optimization problem can be written as Minimize J ……………...………….. (25) Subject toFig:6 TCSC with stability control loop K min w≤ K w≤ K max w It consists of a gain block with gain KT, a T min 1 ≤ T 1 ≤ T max 1… …………...(26)signal washout block and two-stage phase T min 2 ≤ T2 ≤ T max 2compensation block as shown in figure .The phasecompensation block provides the appropriate phase- A particle swarm optimization is used tolead characteristics to compensate for the phase lag solve the Optimization problem and then search forbetween input and the output signals. The signal optimal parameters 1821 | P a g e
  • 6. N.Srikanth, Atejasri / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1817-1824 tripped off. At t=0.5 secVI. SIMULATION AND RESULTS 2. Severe disturbance assuming three phase short The objective function described by circuit Occur at bus 2 in all case TCSC is connectedequation (21) is evaluated using PSO toolbox given in first between bus(2-3) .and then between bus(3-4).[21], for each individual by simulating SMIB shownin fig. 4. a three phase short at bus bar 2 is A. small disturbanceconsidered and TCSC first is assumed to be Table (III) shows Eigen values of the testedconnected between bus (2-3), and then between system with and with out TCSC as well as thebus(3-4) to find the best location n. Fig .6 shows the different locations of TCSCflow chart o f PSO algorithm used in this work and Table (III): Eigen values analysistable (I) illustrates the parameters used for thisalgorithm. Table (II) shows the bounds for unknown stat Without TCSC TCSCparameters of gain and time constants as well as the es TCSC Between Betweenoptimal parameter obtained from PSO algorithm. bus(2-3) bus(3-4) δ -0.087+5.618 -2.4+4.1713 -0.4276+5.596 ,w Eq́ -0.167+0.393 -0.1737+0.373 -0.1682+0.396 It is clear from above table the system is stable in both cases, in other words the proposed TCSC controllers shift the,electro mechanical mode eigenvalue to the left of the line (s=-2.4,-0.42766).in S-plane which in turn enhances the system Stability . B. severe disturbance Case (I): Now TCSC is supposed to be connected between bus (2-3).The value of x L and x C was chosen as 0.068 and 0.034 pu respectively. A three phase short circuit occur at t= 0.5 sec figures (8,9,10) shows rotor angle and speed deviation and active power respectivelyFig: 7 flow chart of PSO algorithms with and without TCSC. Table (I): PSO parameters parameter Value Swarm size 30 Max.gen 100 C 1C2 2.0,2.0 Wstrat ,wend 0.9,0.4 Table (II):Bounds &optimized parameters Rotor angle (rad) Vs Time(sec) parameter Kw T1=T3 T2=T4 Fig .8 Rotor angle min 20 0.1 0.2 max 100 1 1 TCSC 66.5 0.1832 0.4018 connected between bus(2-3) TCSC 80.67 0.1124 0.2523 connected between bus(3-4)To assess the effectiveness of the proposed controller Rotor speed (rad) Vs Time(sec)and best location the following cases are considered Fig .9 Rotor speed deviation1. Small disturbance assuming that line 2(L2) is 1822 | P a g e
  • 7. N.Srikanth, Atejasri / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1817-1824 Active power Pe (PU) Vs Time (sec) Active power Pe (PU) Vs Time(sec) Fig 10. Active power Fig 13. Active power No TCSC with TCSC No TCSC with TCSC It is clear from above figures the proposed It is obvious from above figures dampingTCSC controller damp and suppresses the oscillations and suppressing .The oscillation in between whenand provides good damping characteristics by TCSC is connected between Bus (3-4).stabilizing system much faster, which in turnenhances system stability. VII. CONCLUSION In this paper the impact of TCSC onCase (II): enhancing power system stability was investigated for Now TCSC is supposed to be connected small and severe disturbances. Optimal parametersbetween bus (3-4),the value of x Land x C was chosen and different locations of TCSC were evaluated. Theas 0.068 and 0.034 pu respectively . A three phase problem is formulated as optimization problem toshort circuit occur at t= 0.5 sec figures (11, 12,13) minimize the rotor angle deviation and PSO (shows rotor angle and speed deviation , and power particle swarm optimization) techniques employed torespectively with and without TCSC. find out the optimal parameters and allocation of TCSC, under different test cases. The proposed controller and design approach testes on SIMB using MATLAB environment. The non-linear simulation and eigenvalue analysis results show effectiveness of the proposed controller to enhance power system stability and best allocation n of TCSC. REFERENCES [1] W.Watson and M.E. Coultes, “ Static Exciter Stabilizing Signals on Large Generators - Mechanical Problems”, IEEE Rotor angle (rad) Vs Time (sec) Trans. on Power Apparatus and Systems, Fig .11 Rotor angle Vol PAS-92, Vol PAS-92, 1973. [2] D.C. Lee, R.E. Beaulieau and J.R. Service, “A Power System StabilizeUsing Speed and Electrical Power Inputs- Design and Experien ce”,IEEE Trans. on Power Apparatus and Systems,. Vol PAS-100, 1981, pp.4151-4167. [3] E.V.Larsen and D.A. Swann, “Applying Power System Stabilizers”, Parts 1-111IEEE Trans. on Power Apparatus and Systems, PAS-100, 1981pp. 3017-3046. [4] P. Kundur, M. Klein, G.J. Rogers and M.S. Rotor speed (rad) Vs Time(sec) Zwyno, "Application of power system Fig .12 Rotor speed deviation stabilizers for enhancement of overall stability IEEE Trans Vol PS-4, May 1989, pp. 6 14-626. [5] N.G. Hingorani, L. Gyugyi, “Understanding FACTS: Concepts and and Technology of 1823 | P a g e
  • 8. N.Srikanth, Atejasri / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1817-1824 Flexible ac Transmission Systems”, IEEE [18] Y. Shi and R. Eberhart, “ A modified Press, Newyork, 1999. particle swarm optimizer,” in proc. IEEE[6] A.Edris, “FACTS technology development: Int. Conf. Evol. Comput. Anchorage, AK, an update”,IEEE Eng. Rev.20 (3) pp .4 -9. May 1998, pp. 69–73. 2000. [19] Y. Shi and R. C. Eberhart, “Empirical stud y [7] Canizares CA. et al. “Using FACTS of particle swarm Optimization,” inProc. controllers to maximize available transfer IEEE Int . Conf. Evol. Comput. capability”. Bulk power systems and Washington, DC, disturbances. Optimal July dynamics, part IV, restructing; 1998 1999 , pp . 1945– 195 0.[8] 1. D.N. Ewart, R.J. Koessler, J.D. Mou [20] R. C. Eberhart and Y. Shi, “Comparison ntford, D. Maratukulam "Investigation of between genetic algorithms and Particle FACTS Options to Utilize the Full Thermal swarm optimization,” inPro c. IEEE Int. Capacity of AC Transmission", a paper Conf . Evol. Comput .Anchorage, AK, May presented at an EPRI Workshop, The Future 1998, pp. 611 – 616. in High- Voltage Transmission: Flexible [21] B. Birge, Particle swarm optimization AC Transmission System (FACTS), toolbox, Available at November 14-16, Cincinnati, Ohio.1990. http://www.mathworks.com/matlabcentral/fe[9] Hague, M. H , “Improvement of First Swing le exchange/. Stability Limit by Utilizing full Benefit of [22] P. Mattavelli, G. C. Verghese and A. M. Shunt FACTS devices”, IEEE Trans. on Stankovitctt, “Phasor dynamics of Power Systems vol. 19, No. 4, November Thyristor-Controlled series capacitor 2004. systems,” IEEE Trans. PowerSystsem., vol-[10] Rouco L.,”Coordinated design of multiple 12, pp. 1259–1267, 1997. controllers for dampingpower system oscillations”. Electr Power Energy System, Appendix vol.23, pp.517-30; 2001 Single-machine infinite bus system data; [11] Larsen EV, Juan J, Chow JH. “Concepts for (On a 100 MVA base- 400 KV base) design of FACTS controllers to damp power Pe=0.6; VT=1.03; V∞ =1.0 (slack) swings”. IEEE Trans on Power Systems; Generator: vol.10 (2), pp-948-956,1995 r a=0.00327; Xd=1.7572; Xq=1.5845; Xd́=0.4245;[12] Pourbeik, P. and Gibbard, M. J.,” Damping T́ do=6.66;H=3.542; f=50 and synchronizing torque induced on Transformer: generators by FACTS”, Power Systems, rt =0.0; Xt=0.1364 IEEE Transactions on, Volume 11( 4 ),pp- Transmission line:(per circuit) 1920 – 1925,1996. rL2=rL3=0.0;XL2= XL3= 0.40625; Bc=0.059;[13] C. Gama and R. Tenorio, “Improvements for XL4=0.13636 power system performance: Modeling, Excitation system (Exc): analysis and benefits of TCSC’s,” in Proc. Efd= ± 6.0; Ka= 400; Ta= 0.025; Kf =0.45; IEEE/Power Eng .Soc . Winter Meeting, Tf=1.0; Td= 1.0; Tr=0.001; Singapore, January 2000. TCSC: [14] Enrique Acha , Claudio R. Fu erte-Esquivel, Tr= 0.5; Kp= 5; Ki=1.0;αmax= pi; Hugo Ambriz-Pérez, César Angeles- αmin=pi/2; Camacho,” FACTS: Modeling and Simulation in Power Networks”, Wiley; 2004.[15] R. Mohan Marthur, Rajiv, K. Varma,” Thyristor Based-FACTS controllers for electrical transmission systems”, Wiley; 2002.[16] K.R. Padiyar” Power System Dynamics: Stability and Control”. Institute of Tech, Bangalore. DEEE, BS Publication. 2002. [17] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in IEEE Int. Conf. Neural Networks, vol. IV, Perth, Australia, 1995, pp.1942 –1948.[17] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in IEEE Int. Conf. Neural Networks, vol. IV, Perth, Australia, 1995, pp.1942 –1948. 1824 | P a g e