IJERT-Improvement of Voltage Stability by Optimal Placement and Sizing of Static Var Compensator using Particle Swarm Optimization

International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 05, May-2015 Improvement of Voltage Stability by Optimal Placement and Sizing of Static Var Compensator using Particle Swarm Optimization K. D. Joshi (Associate Professor) Department of Electrical Engineering G. H. Raisoni college of Engineering Nagpur, India. Arshi Ansari (Project Scholar) Department of Electrical Engineering G. H. Raisoni college of Engineering Nagpur, India. Abstract— In this paper, Particle Swarm optimization (PSO) algorithm is used to determine the optimal placement and size of Static Var Compensator in transmission network. The objective function is defined to minimize voltage deviation and power loss and combination of voltage deviation and Power loss. The results are tested on IEEE 5 bus and 14 bus system with the help of MATLAB. Optimal placement of SVC is verified by voltage sensitivity method. Optimal sizing of SVC is verified by Power World Simulator. Keywords— Static Var compensator, Voltage Deviation, Power loss, Particle swarm optimization algorithm (PSO) I. INTRODUCTION Today, Electricity demand is increased as number of industries is increasing day by day. Electricity consumption is becoming high in commercial and residential areas also. The electric utilities are suffering from different government policies, electricity theft and loss of generation. High consumption of electricity causes increase in number of transmission line in power network, which results in complex power system. Hence, utilization of electrical power is more as compare to generation. Result is, Power systems are running closer to stability. Voltage stability is defined as ability of power system to maintain acceptable voltages at all buses in normal as well as after being subjected to disturbance [1]. The voltage instability may occur when a power system is heavily loaded in transmission line and lacks in local reactive power sources [2]. The reactive power sources are power electronic devices known as Flexible alternative current transmission system (FACTS) which helps in preventing voltage instability [3].Facts devices include Static var Compensator (SVC), Thyristor controlled series compensator (TCSC), unified power flow controller (UPFC) etc [4][5]. Several methods like genetic algorithm (GA), reactive power spot price index (QSPI), simulated annealing (SA), artificial immune system (AIS) are used for optimal placement of Static Var compensator. In [6], considering more critical contingencies, GA is applied for minimizing real power loss, voltage deviation and rating of SVC for optimal placement of IJERTV4IS050280 SVC. In [7], Optimal placement of SVC is done using QSPI technique which explains optimal placement of SVC reduces real and reactive power spot prices, real power loss, generation cost etc. In [8], simulated annealing technique is used for optimal location to install VAR Sources. It also finds the type and sizes of VAR sources as well as setting of VAR sources at different loading condition. In [9], optimal placement of SVC is done by maximizing loading where nonlinear programming problem is used which include binary decisions for actual placement of SVC. In [10], optimal location of three SVC’s were identified through Particle Swarm Optimization (PSO) where Voltage Stability Index (VSI) is used as the main objective function. Minimum value of VSI at particular bus shows optimal bus for SVC placement. After reviewing above papers, it clears the idea that there are many modern methods which are used for optimal placement of SVC. In this paper, optimal placement of SVC is done with the help of one of the modern method like PSO. This paper also include optimal sizing of SVC.As SVC is costly, its size is also important. Hence this paper determines optimal placement and sizing of SVC. Second part of this paper shows information related to SVC. Third part of this paper shows basics of PSO and its algorithm. Fourth part of this paper comprises of problem formulation where voltage deviation (VD) and power (real and reactive both power) loss are used as two main objective function. Minimized value of VD, Power loss and VD+Ploss with different sizes of SVC are found out. Fifth part of this paper shows simulation results. At particular bus minimum VD and minimum power loss and minimum size of SVC, Minimum VD +Ploss these four criterions helps in finding optimal placement of SVC. II. STATIC VAR COMPENSATOR Static Var Compensator is shunt connected FACTS device. Means it is installed in parallel with a bus. This device is able to generate or absorb reactive power at location where it is placed .SVC is made up of mechanically switched reactor, Thyristor controlled reactor (TCR), Thyristor Switched Capacitor (TSC), Harmonic Filter and mechanically switched capacitor. If load is capacitive, TCR consume VARs and lower system voltage. If load is inductive, capacitor www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 183 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 05, May-2015 banks are switched on to supply VARs and higher system voltage. Hence, SVC consumes or supply reactive power to compensate voltage. The equivalent diagram of SVC having fixed capacitor FC with TCR is shown in Fig.1.This combination provides a fast variable source of reactive power. Fig 1: Equivalent Circuit of SVC III. BASIC CONCEPT OF PARTICLE SWARM OPTIMIZATION The PSO is based on the behavior of colony of living things like colony or swarm of insects such as ants, bees, termites, wasps. PSO is inspired by a flock of birds and fish schooling [11], [12]. PSO is population based algorithm. The word “Particle” denotes a bird in a flock or bee in a colony.” Swarm” means moving particles which have certain velocity. ”Optimization” means obtaining best results from given circumstances. The PSO algorithm was originally proposed by Kennedy and Eberhart in 1995.They proposed an algorithm where each particle is located randomly in space. Particle is assumed to have two characteristics a) Position b) Velocity. Each particle wonders around in the space and remembers its best position .This individual best position (obtained by using its own knowledge) is called “Pbest”. Particle achieve best position in a group (obtained by sharing knowledge among a group) is called “Gbest”. Individuals or particles in swarm, approach the optimum through its current velocity, earlier experience and the knowledge of its neighbors [13].The formulae used to find modified position and velocity are shown in equation (1) and (2). Xi (t )  Xi (t  1)  Vi (t ) Vi (t )  w *Vi (t  1)  1* rnd1* ( Pi  Xi (t  1))   2 * rnd 2 * ( Pg  Xi (t  1)) Vi (t )  Inertia  Cognitive  Social . Pi = Pg = rnd1& rnd2 = Individual best position (Pbest) Global best position Two random numbers in the range of (0,1) Equation (3) shows three components. First component shows the term inertia which develop the tendency of the particle to carry on in the similar direction in which it was moving.[14]shows, inertia weight is used in original version of PSO to equilibrium the local and global search during the optimization process. Second component shows the linear pull towards the best position found by the given particle. This component is known as “self-knowledge”. Third component shows linear pull towards the position found by any particle .This component is known as “group knowledge. A. PSO Algorithm: Consider an objective function which has to maximize or minimize. Suppose Minimize Take minimize function to be F(X). With Xl ≤ X ≤ Xu Where , Xl Lower limits of X Xu Upper limits of X Here F(X) is given in equation 5 and 6. Initial SVC size used in PSO algorithm is given in table below. Table 1: Initial SVC Size Sr.No.(j) SVC Size (p.u) 1 0.16 2 0.22 3 0.33 4 0.25 5 0.4 6 0.028 7 8 0.37 0.38 9 0.19 10 0.125 (1) (2) (3) Where , Xi (t) Xi (t-1) Vi (t) Vi (t-1) w Ф1 & Ф2 IJERTV4IS050280 = = = = = = New particle position Previous position New particle Velocity Previous Velocity Inertia Weight Two positive numbers www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 184 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 05, May-2015 The PSO algorithm is explained using following steps: Start C. Problem Formulation: The aim of optimization problem is to minimize voltage deviation and power loss. In particle swarm optimization, objective function is given as follows, Size of swarm, N=10 Insert initial 10 SVC Size i.e j=10 (4) F = F1+F2 = VD + Ploss Where, Set iteration number, i=1 VD = Voltage deviation Ploss = Network real power loss Find Pbest with highest value of objective function for jth particle F1= VD = ( | Vi –Vref | / Npq ) (5) Where, Find Gbest with highest value of F(x) for any svc size among N=10, number of SVC using equation 5 and 6 Find Velocity of j in ith iteration using equation (2) Vdev = Voltage Deviation Vref = load bus reference voltage value =1 Vi = load bus voltage Npq = load bus number Find position of particle j in ith iteration using equation (1) Subject to 0.95 < Vm (per unit) <1.1. No If f(x1) ---f(x10) are same .i.e converges to one value i=i+1 F2 = Ploss = Σ gk [Vi2 + Vj2 – 2 Vi V j cos θij ] (6) Where, gk = Conductance Yes Vi = Sending end voltage Vj = Receiving end voltage θij = Angle between Viand Vj Stop Fig 2: PSO Algorithm flowchart IV.SIMULATION RESULT B. PSO Parameters: Studies on PSO shows that, the particles diverge from its required position i.e go to infinity called explosion. Hence to control this explosion inertia weight ‘w’ is used. Value of ’w’ gradually reduces over time. Ф1 and Ф2 are called acceleration constant .They controls the travelling of each particle towards its individual best and global best position. Small value of them limits movement of particle while large value may cause particles to diverge [15]. Hence it is necessary to define the values of these particles accurately. Table 1 Shows, PSO parameters used in this paper. A. Particle Swarm Optimization IEEE - 5 bus system shown in Fig 3. North Lake Main Table 2: PSO parameters Parameters PSO Population Size 10 Inertia weight 0.9-0.4 Constant Ф1 1.4 Constant Ф2 1.4 No. of Iterations 20 IJERTV4IS050280 South Elm Fig 3: IEEE 5 bus system IEEE 5 bus data is taken from [16]. Matlab programming with SVC and without SVC are taken from [17]. Matlab programming for www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 185 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 05, May-2015 IEEE-14 bus test system (shown in Fig-5). PSO is taken from [18].Results are tested not including SVC, including SVC and with PSO. Table No 3 shows, load buses where SVC is connected. For load buses SVC size , total Voltage deviation , power loss and combination of total voltage deviation and power loss is given . Table 3: Results with SVC and PSO Bus no SVC size in p.u Min VD (p.u) Ploss (p.u) 2 0.6540 0.4843 0.069 Min VD+Ploss (p.u) 0.5533 3 1.6594 0.1032 0.063 0.1662 4 5 1.5021 3.0116 0.0598 0.2491 0.061 0.067 0.1208 0.3161 As shown in table no.3,VD , Ploss and VD + Ploss are minimum at bus number 4.SVC size is minimum at bus number 2 but VD, Ploss, VD + Ploss values are more as compare to bus number 4.Another minimum size is 1.5021 at bus number 4. This also explained in Fig.3, where ‘bus number’ is scale on X-axis. On Y-axis SVC size (p.u), Min VD (p.u), Ploss (p.u) and VD + Ploss (p.u) are shown Which shows, optimal placement of SVC is at bus number 4 and optimal size of SVC is 1.5021(p.u) for IEEE 5 bus system. Fig 5: IEEE 14 Bus System The program is run for different load buses of the IEEE 14 bus and results are shown in table 4 given below. Table 4:Results with SVC and PSO for IEEE 14 bus system. Bus no VD(p.u) Svc size Ploss VD+Poss 4 5 6 9 10 11 12 13 14 0.0091 0.0103 0.0099 0.018 0.0291 0.0232 0.0256 0.0109 0.0445 1 1 0.16 1 1 1 0.88 0.86 0.92 0.1891 0.1884 0.1894 0.1985 0.227 0.2508 0.2991 0.235 0.2894 0.1982 0.1988 0.1992 0.2165 0.2561 0.274 0.3247 0.2459 0.3339 As shown in table no. 4, VD, Ploss and VD + Ploss are minimum at bus number 5. Svc size is minimum at bus number 6 but other values are high as compare to bus number 5.The same idea is explained by fig 6.On X axis ‘bus number’ is scaled . On Y-axis SVC size(p.u), Min VD(p.u), Ploss(p.u) and VD+Ploss (p.u) are shown Which shows, optimal placement and size of SVC is at bus number 9 and optimal size of SVC is 0.16 (p.u). 1.2 Fig 4: ‘Bus no.’ Vs ‘SVC Size, Minimum Voltage Deviation (p.u) and Ploss (p.u), VD+Ploss (p.u)’for IEEE 5 bus System 1 0.8 VD(p.u) Svc size 0.6 Ploss 0.4 VD+Poss 0.2 0 0 5 10 15 Fig 6: ‘Bus no.’ Vs ‘SVC Size, Minimum Voltage Deviation (p.u) and Ploss (p.u), VD+Ploss(p.u)’for IEEE 14 bus System IJERTV4IS050280 www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 186 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 05, May-2015 B. Voltage Sensitivity: Optimal placement of SVC is done by another approach i.e using Voltage sensitivity method. Voltage sensitivity is given by formula, (6) Where VSF = Voltage sensitivity factor VM = Voltage magnitude of bus The bus where voltage sensitivity factor is highest that bus is best for placement of SVC. Fig.7 :Power world IEEE 5 bus system without SVC Table 5: .Average of Voltage sensitivity for IEEE 5 bus system Bus Number Average of voltage sensitivity 3 -0.0093 4 0.02845 5 0.02664 Average of Voltage sensitivity for IEEE 5 bus system is highest at bus number 4 shows optimal place for SVC. Table: 6: Average of Voltage sensitivity for IEEE 14 bus system Bus Number Average of voltage sensitivity 4 -0.00974 5 -0.00804 6 0.000309 9 -0.02939 10 -0.03097 11 -0.02279 12 -0.017 13 -0.01648 14 -0.0323 Fig.8:Power world IEEE 5 bus system with SVC at bus 4 Table7: IEEE 5 bus result with 1.5 sizes of SVC with Power World Simulator Bus number VD (p.u) 3 0.0062 4 5 0.0053 0.0105 C.2 IEEE 14 bus diagram without SVC and with SVC IEEE 14 bus system is shown in fig. Without SVC p.u voltages at the buses are less as compared to With SVC of size p.u connected at bus number 6. Average of Voltage sensitivity for IEEE 14 bus system is highest at bus number 6 shows optimal place for SVC. C.Power World Simulator C.1 IEEE 5 bus diagram without SVC and with SVC: Optimal size of SVC is verified by Power World Simulator. IEEE 5 bus system is shown in fig.7 & 8.Where, Without SVC p.u voltages at the buses are less as compared to With SVC of size 1.p.u connected at bus number 4. Fig. 9: Power world IEEE 14 bus system without SVC IJERTV4IS050280 www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 187 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 05, May-2015 VI. REFERENCES: [1] [2] [3] [4] [5] [6] [7] Fig.10 Power world IEEE 14 bus system with SVC at bus number 6 Table 7: IEEE 14 bus result with 0.16 (p.u) sizes of SVC with Power World Simulator Bus number VD(p.u) 4 0.000303 5 0.000303 6 0.000288 9 0.00159 10 0.004562 11 0.00256 12 0.006456 13 0.0052 14 0.002872 [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] V. CONCLUSION: A. Chakraborti, D.P. Kothari, A.K. Mukhopadhyay, A. De,“ An introduction to Reactive Power Control and Voltage Stability in Power Transmission Systems”, 1st edition, Prentice Hall India, 2010. J.R. Shin, B.S. Kim, J.B. Park, K.Y. Lee, A new optimal routing algorithm for loss minimization and voltage stability improvement in radial power systems, IEEE Transactions on Power Systems 22 (May (2)) (2007) 648–657. N.Yorino, E.E.El-Araby,H Sasaki,and Sh. 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Minguez R,Milano F,Zaratc-Minamo R,Conejo A,”Optimal Network Placement of SVC Devices.”IEEE Trans.Power System,vol 22,No.4,pp 1851-1861,2007. K.Sundareswaran, Hariharan.B, Fawas Palasseri , Daniel Sanju Antony,and Binyamin Subair ,”Optimal Placement of Static VAr Compensators (SVC’s) Using Particle Swarm Optimization” 978-14244-8542-0/10/$26.00 ©2010 IEEE J.Kennedy, and R.Eberhart, ”Particle Swarm Optimization.” in Proc. 1995 IEEE International Conf. on Neural Network,vol 4,pp.1942_1948. J.Kennedy, and R.Eberhart ,”A New Optimization using Particle Swarm Theory,”in proc. 6th Int. symp. Micro Machine and Human Science 1995, pp39-43. R.Eberhart, Y.Shi ,” Particle Swarm Optimization: Development, application and resources,” .in IEEE Proc. Int. Conf, Evolutionary Computation ,Volume 1,2001. Yamille del Valle, Ganesh Kumar Venayagamoorthy, Salman Mohagheghi, Jean-Randy L Haupt,Sue Ellent Haupt,”Practical Genetic Algorithm”Second Edition. Carlos Hernandez and Ronald G. Harley, “Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems ”,IEEE Transactions on evolutionary computations, Vol. l2, No 2.,April 2008 H. Saadat, ”Power System Analysis.-2002”McGraw Hill, Higher Education (ISBN 0-07-284-869-3) Enrique Acha ”FACTS-Modeling and Simulation in power Networks” ,Willey Publication.(ISBN 0-470-85271-2) Y.Shuyuan, M.Wnag, and L. Jiao ,”A Quantum Particle Swarm Optimization ,”Proc. of the conf. on Evolutionary Computation 2004,pp.320-324. The result obtained from the IEEE 5 bus and 14 bus system test shows that the PSO algorithm is very efficient in finding minimum SVC size, voltage deviation and power loss ,Voltage deviation +Ploss (p.u).Hence optimal placement of SVC in IEEE 5 bus system is at bus number 4. And optimal size of SVC is1.5021 p.u. Similarly in IEEE 14 bus system, optimal placement of SVC is bus number 6 and optimal size of SVC is 0.16 p.u. optimal placement is justified by voltage sensitivity method and optimal sizing is justified by Power world simulator. IJERTV4IS050280 www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.) 188