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

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

Arshi Ansari (Project Scholar) Department of Electrical Engineering

G. H. Raisoni college of Engineering Nagpur, India.

K. D. Joshi (Associate Professor) Department of Electrical Engineering

1. 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)

   1. 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

      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 non- linear programming problem is used which include binary decisions for actual placement of SVC. In [10], optimal location of three SVCs 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.

   2. 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

      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

   3. 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).

      Pi = Individual best position (Pbest)

      Pg = Global best position

      rnd1& rnd2 = 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.

      1. 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	0.37
         8	0.38
         9	0.19
         10	0.125

         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.

         (1)

         (2)

         (3)

         Where ,
         	Xi (t)	=	New particle position
         	Xi (t-1)	=	Previous position
         	Vi (t)	=	New particle Velocity
         	Vi (t-1)	=	Previous Velocity
         	w	=	Inertia Weight
         	1 & 2	=	Two positive numbers

         The PSO algorithm is explained using following steps:

         Start

         Size of swarm, N=10

         Insert initial 10 SVC Size i.e j=10

         Set iteration number, i=1

         Find Pbest with highest value of objective function for jth particle

         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,

         F = F1+F2 = VD + Ploss (4)

         Where,

         VD = Voltage deviation

         Ploss = Network real power loss

         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

         Vdev = Voltage Deviation

         Find Velocity of j in ith iteration using equation (2)

         Vref = load bus reference voltage value =1 Vi = load bus voltage

         Find position of particle j in ith iteration using equation (1)

         Npq = load bus number

         Subject to 0.95 < Vm (per unit) <1.1.

         No

         If f(x1) —f(x10) are same .i.e converges to one value

         Yes

         Stop

         Fig 2: PSO Algorithm flowchart

      2. 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. 1 and 2 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.

         Table 2: PSO parameters

         Parameters	PSO
         Population Size	10
         Inertia weight	0.9-0.4
         Constant 1	1.4
         Constant 2	1.4
         No. of Iterations	20

         F2 = Ploss = gk [Vi2 + Vj2 2 Vi V j cos ij ] (6) Where,

         i = i + 1

         gk = Conductance

         Vi = Sending end voltage Vj = Receiving end voltage

         ij = Angle between Viand Vj

   4. SIMULATION RESULT

      1. Particle Swarm Optimization

         IEEE – 5 bus system shown in Fig 3.

         North

         Lake

         Main

         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

         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 .

         IEEE-14 bus test system (shown in Fig-5).

         Table 3: Results with SVC and PSO

         Bus no	SVC size in p.u	Min VD (p.u)	Ploss (p.u)	Min VD+Ploss (p.u)
         2	0.6540	0.4843	0.069	0.5533
         3	1.6594	0.1032	0.063	0.1662
         4	1.5021	0.0598	0.061	0.1208
         5	3.0116	0.2491	0.067	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 4: Bus no. Vs SVC Size, Minimum Voltage Deviation (p.u) and Ploss (p.u), VD+Ploss (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	0.0091	1	0.1891	0.1982
         5	0.0103	1	0.1884	0.1988
         6	0.0099	0.16	0.1894	0.1992
         9	0.018	1	0.1985	0.2165
         10	0.0291	1	0.227	0.2561
         11	0.0232	1	0.2508	0.274
         12	0.0256	0.88	0.2991	0.3247
         13	0.0109	0.86	0.235	0.2459
         14	0.0445	0.92	0.2894	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

         1

         0.8

         0.6

         0.4

         VD(p.u)

         Svc size

         Ploss

         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 IEE 14 bus System

      2. 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.

      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

      Average of Voltage sensitivity for IEEE 14 bus system is highest at bus number 6 shows optimal place for SVC.

      C.Power World Simulator

      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.7 :Power world IEEE 5 bus system without SVC

         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	0.0053
         5	0.0105

      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.

      Fig. 9: Power world IEEE 14 bus system without SVC

      VI. REFERENCES:

      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

   5. CONCLUSION:

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.

1. 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.

2. 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) 648657.

3. N.Yorino, E.E.El-Araby,H Sasaki,and Sh. Harada,A new formulation for FACTS allocation for security enhancement against voltage collapse.

4. L.Gyugi ,Power electronics in electric utilities: Static Var Compensators, proc. of the IEEE, vol. 76,no 4,pp 483-494,Apr1988.

5. N. G. Hingorani and L. Gyugyi ,Understanding FACTS Concepts and Technology of Flexible AC transmission Systems, Piscataway: IEEE Press 1999.

6. Shishir Dixit, Laxmi Srivastava, Ganga Agnihotri,Optimal placement of SVC for minimize of Power loss and improving voltage profile using GA.978-1-4799-2900-9/14/$31.00 ,2014 IEEE.

7. Singh J.G, Singh S.N, Srivastava S.C,An Approach for optimal placement of static Var compensators based on reactive Power Spot price.IEEE Trans.Power Syst.vol 22,No. 4,pp 2021-2029,2007.

8. Hsio.Y,T,Liu C.C,Chiang H.D,A new approach for optimal VAR sources planning in large scale Electric Power Systems.IEEE Trans.Power Syst,vol 8,pp988-996,1993.

9. 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.

10. K.Sundareswaran, Hariharan.B, Fawas Palasseri , Daniel Sanju Antony,and Binyamin Subair ,Optimal Placement of Static VAr Compensators (SVCs) Using Particle Swarm Optimization 978-1- 4244-8542-0/10/$26.00 ©2010 IEEE

11. J.Kennedy, and R.Eberhart, Particle Swarm Optimization. in Proc. 1995 IEEE International Conf. on Neural Network,vol 4,pp.1942_1948.

12. 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.

13. R.Eberhart, Y.Shi , Particle Swarm Optimization: Development, application and resources, .in IEEE Proc. Int. Conf, Evolutionary Computation ,Volume 1,2001.

14. Yamille del Valle, Ganesh Kumar Venayagamoorthy, Salman Mohagheghi, Jean-Randy L Haupt,Sue Ellent Haupt,Practical Genetic AlgorithmSecond Edition.

15. 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

16. H. Saadat, Power System Analysis.-2002McGraw Hill, Higher Education (ISBN 0-07-284-869-3)

17. Enrique Acha FACTS-Modeling and Simulation in power Networks

    ,Willey Publication.(ISBN 0-470-85271-2)

18. Y.Shuyuan, M.Wnag, and L. Jiao ,A Quantum Particle Swarm Optimization ,Proc. of the conf. on Evolutionary Computation 2004,pp.320-324.