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International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN 2250-155X Vol. 3, Issue 4, Oct 2013, 237-246 Š TJPRC Pvt. Ltd.

IMPLEMENTATION OF PSO FOR MULTI OBJECTIVE OPTIMIZATION WITH STATIC VAR COMPENSATOR K. PADMA1, K. VAISAKH2 & P. RAMESH3 1

Assistant Professor, Department of Electrical Engineering, A.U.C.E (A), Andhra University, Andhra Pradesh, India 2

Professor, Department of Electrical Engineering, A.U.C.E (A), Andhra University, Andhra Pradesh, India

3

P. G. Scholar, Department of Electrical Engineering, A.U.C.E (A), Andhra University, Andhra Pradesh, India

ABSTRACT This paper presents an application of particle swarm optimization based algorithm is developed effectively to solve the multi objective optimal power flow problem i.e. minimization of cost of generation, minimization of voltage deviation, minimization voltage stability L-Index, minimization of total power loss and minimization of installation cost of SVC device by incorporating a set of constraints . Simulations for OPF are carried out on IEEE 30-bus test system without and with SVC FACTS device. It has been observed that proposed method provide acceptable solutions and found to be suitable for implementing in planning and operation of modern power systems.

KEYWORDS: Multi, Objective Optimization, Particle Swarm Optimization (PSO) Technique, SVC FACTS Device, Newton Raphson Method

INTRODUCTION The increased demand for electric power [1] requires increased transmission capabilities. The recently developed Flexible AC Transmission System (FACTS) technology [2] provides a way to relieve the stability problem imposed by increasing load demand. FACTS controllers provide fast and reliable control over three main parameters, i.e., voltage magnitude, real and reactive power. For this reason, control of FACTS devices has received greater attention in power system performance enhancement. Power flow is a function of transmission line impedance, the magnitude of sending and receiving end voltages and the phase angle between voltages. By controlling one or a combination of the power flow arrangements, it is possible to control the active as well as the reactive power flow in the transmission line. In this paper particle swarm optimization based algorithms are developed effectively to solve the multi objective optimal power flow problem i.e. minimization of cost of generation, minimization of voltage deviation, minimization voltage stability L-Index ,minimization of total power loss and minimization of installation cost of SVC device by incorporating a set of constraints including voltage stability and SVC FACTS device. Simulations for OPF are carried out on IEEE 30-bus test system without and with SVC FACTS device. From the optimal power flow solutions it has been observed that the FACTS devices significantly improve the performance of the power systems under a given operating conditions.

STATIC VAR COMPENSATOR A Static VAR Compensator [3] [4] is FACTS device for providing fast-acting reactive power compensation on high-voltage electricity transmission networks. The SVC is an automated impedance matching device The linearized equation for the SVC total susceptance model is given by (1), where the total susceptance BSVC is taken as the state variable,


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K. Padma K. Vaisakh & P. Ramesh

Figure 1: Variable Shunt Susceptance

 Pk  0 0  Q   0 Q  k  k  i

i

 k   B   SVC BSVC 

(1)

th

At the end of i iteration, the variable shunt susceptance BSVC is updated according to (2),

B

i 1 SVC

B

i SVC

 B   SVC  BSVC

i

 i  .BSVC 

(2)

This changing susceptance represents the total SVC susceptance necessary to maintain the nodal voltage magnitude at the specified value. The SVC is represented by the structure shown in Figure 1.

PARTICLE SWARM OPTIMIZATION Particle Swarm Optimization [5] is one of the optimization techniques belongs to evolutionary computation techniques and is developed through simulation of bird flocking in two-dimension space. The position of each individual (agent) is represented by XY axis position. Modification of the agent position is realized by the position and velocity information. Moreover, each agent knows the best value so far in the group (gbest) among pbests. Each agent tries to modify its position. This modification can be represented by the concept of velocity. Velocity of each agent can be modified by the equation (3): (3) Using the above equation, a certain velocity which gradually gets close to pbest and gbest can be calculated. The current position (searching point in the solution space) can be modified by the equation (4): (4)

MULTI OBJECTIVE OPTIMIZATION POWER FLOW PROBLEM Multi objective optimization [7] with such objective functions gives a set of optimal solutions instead of giving one optimal solution. The problem consists of number of objectives to be optimized simultaneously and it is associated with a number of equality and inequality constraints. The minimization function implemented in PSO is defined as eq. (5) (5) Where equation (5) can be written as (6)


Implementation of PSO for Multi Objective Optimization with Static VAR Compensator

Where

239

are the weight factors and represents the importance of the objective functions. It also has to

satisfy

The objective of OPF has to be changed to the maximization of fitness to be used as follows (7) Fuel Cost Minimization This objective function will minimize the total generation cost and the function is given as in equation (8) Minimize

=

Where ,

,

)

(8)

the amount of generations in MW at generator i are the cost coefficients

ng = number of generators Minimization of Voltage Stability Index (L-Index) Computation The voltage stability L-index [8] is a good voltage stability indicator with its value change between zero (no load) and one (voltage collapse). The voltage stability g

L j = 1   F ji i 1

L -index is computed as given in equation (9),

Vi Vj

(9)

j  g  1,...,n

The objective function considering the minimization of voltage stability index can be represented as = min (

(10)

Power Loss Minimization The objective of real power loss minimization is given as in equation (11) (11) Where = total number of transmission lines = The conductance of line i-j =The voltage magnitude at bus i = The voltage magnitude at bus


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K. Padma K. Vaisakh & P. Ramesh

Voltage Deviation Minimization The Voltage Deviation (VD) to be minimized is given as the following equation (12) (12) Where = The voltage magnitude at bus i Minimization of Cost of SVC FACTS Device The minimization of the cost of the SVC can be represented as Eq. (13) (13) Where: = Cost of SVC in US$/var = Operating range of SVC in MVAR

= MVAR flow before placing FACTS device. = MVAR flow after placing SVC FACTS device. Equality Constraints These are the sets of nonlinear power flow equations that govern the power system, i.e, Load Flow Constraints n

PGi  PDi   Vi V j Yij cos( ij   i   j )  0

(14)

j 1

n

QGi  Q Di   Vi V j Yij sin( ij   i   j )  0

(15)

j 1

where PGi and QGi are the real and reactive power outputs injected at bus i respectively, the load demand at the same bus is represented by PDi and Q Di , and elements of the bus admittance matrix are represented by Yij and

 ij .

In Equality Constraints These are the set of constraints that represent the system operational and security limits like the bounds on the following: 

Generators Real and Reactive Power Outputs

PGim in  PGi  PGim ax , i  1,  , ng

(16)

m in m ax QGi  QGi  QGi , i  1,  , ng

(17)


Implementation of PSO for Multi Objective Optimization with Static VAR Compensator

241

Voltage Magnitudes at Each Bus in the Network

Vi m in  Vi  Vi m ax , i  1, , NL

(18)

where NL is the number of load buses. 

Transformer Tap Settings

Ti m in  Ti  Ti m ax , i  1,  , nt 

(19)

Reactive Power Injections Due to Capacitor Banks

QCim in  QCi  QCim ax , i  1,  , cs 

(20)

Transmission Lines Loading

S i  S im ax , i  1, , nl 

Voltage Stability Index

L j  Lmax j , 

(21

j  1,, NL

(22)

FACTS Device Constraint: SVC Settings m in m ax B svc  Bsvc  Bsvc

SVC susceptance

(23)

The equality constraints are satisfied by running the power flow program. The generator bus real power generations ( Pgi ), generator terminal voltages ( V gi ), transformer tap settings ( T i ), the reactive power compensation ( QCi ), SVC target node voltage ( V k ) are the control variables and they are self-restricted by the representation itself. The active power generation at the slack bus ( Pgs ), load bus voltages ( V Li ) and reactive power generation ( Q gi ), line flows ( S i ), and voltage stability ( L j )-index are state variables which are restricted through penalty function approach. The installation of shunt reactive power sources involves the investment cost. The location of FACTS device and its size also involves the investment cost.

SIMULATION RESULTS The proposed PSO algorithm is implemented on IEEE 30-bus test system to solve the multi objective optimal power flow problem incorporating SVC FACTS device. The optimal parameters used for the simulation are summarized in Table 1 Table 1: Optimal Parameter Settings for PSO Parameter Population size Number of iterations Cognitive constant, c1 Social constant, c2 Inertia weight, W

IEEE 30-Bus System 20 150 2 2 0.3-0.95


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K. Padma K. Vaisakh & P. Ramesh

IEEE 30-Bus System Results This section presents the details of the study carried out on IEEE-30 bus test system for security enhancement. For simulation studies, four different cases have been considered: Case (a): Single objective optimization without SVC device installation. Case (b): Single objective optimization with SVC device installation. Case (c): Multi objective optimization without SVC device installation. Case (d): Multi objective optimization with SVC device installation. SVC device is placed in optimal location obtained from trial and error method. The optimal settings of control variables during minimization of objective function are given in Table 2. From Table 2, it is noted that PSO algorithm for multi objective optimization with SVC exhibits best performance and is very effective for optimising the problem and in improving the system performance while maintaining all control variables within their limits under the given network operating conditions. Table 2: Optimal Settings of Control Variables for IEEE 30-Bus System Control Variables

Limits(p.u) Min

Max

PG1 0.50 2.000 PG2 0.20 0.800 PG3 0.10 0.350 PG4 0.10 0.300 PG5 0.15 0.500 PG6 0.12 0.400 VG1 0.95 1.10 VG2 0.95 1.10 VG3 0.95 1.10 VG4 0.95 1.10 VG5 0.95 1.10 VG6 0.95 1.10 Tap - 1 0.9 1.1 Tap - 2 0.9 1.1 Tap - 3 0.9 1.1 Tap - 4 0.9 1.1 QC10 0.0 0.10 QC12 0.0 0.10 QC15 0.0 0.10 QC17 0.0 0.10 QC20 0.0 0.10 QC21 0.0 0.10 QC23 0.0 0.10 QC24 0.0 0.10 QC29 0.0 0.10 Cost ($/h) Ploss (p.u.) Ljmax Cost of SVC(US$/Kvar) Voltage Deviation CPU time(sec)

Individual Optimization without with FACTS SVC 1.7718 1.7721 0.4867 0.4864 0.2109 0.2114 0.1215 0.1190 0.2144 0.2156 0.1200 0.1203 1.0868 1.0769 1.0667 1.0542 1.0405 1.0326 1.0645 1.1000 1.0348 1.0254 1.0425 1.0742 1.0464 1.0696 0.9000 0.9312 0.9568 0.9905 0.9623 0.9668 0.0783 0.0335 0.0000 0.0370 0.0629 0.0000 0.0518 0.1000 0.0785 0.0287 0.0386 0.0816 0.0429 0.0709 0.0260 0.0027 0.0260 0.0344 800.8705 800.6439 0.0912 0.0905 0.1381 0.1332 0 127.3839 0.0382 0.0371 45.5510 52.32

Multi Objective Optimization without with FACTS SVC 1.7649 1.7677 0.4991 0.4878 0.2185 0.2127 0.1185 0.1206 0.2119 0.2140 0.1210 0.1200 1.0816 1.0838 1.0616 1.0658 1.0373 1.0406 1.0931 1.0818 1.0314 1.0364 1.0635 1.0346 0.9744 1.01 1.0554 1.0646 1.0229 1.0462 0.9742 1.0094 0.0778 0.0200 0.0243 0.0000 0.0361 0.0379 0.0248 0.0429 0.0399 0.0713 0.0621 0.0682 0.0001 0.1000 0.0001 0.0280 0.0000 0.0514 800.4794 800.1432 0.0898 0.0883 0.1484 0.1320 0 127.382 0.0360 0.0353 53.57 54.135


Implementation of PSO for Multi Objective Optimization with Static VAR Compensator

243

Figure 2 shows the convergence characteristics of the cost of generation for multi objective optimization and single objective optimization without and with SVC FACTS device

Figure 2: Convergence Characteristics for Cost of Generation of IEEE 30-Bus System Figure 3 shows the convergence characteristics of the Installation cost of SVC for multi objective optimization and single objective optimization with SVC FACTS located at all the selected bus.

Figure 3: Convergence Characteristics for Cost of SVC of IEEE 30-Bus System The Figures 4-8 shows the voltage deviations of SVC, voltage profiles, voltage angles, voltage stability L-index and percentage MVA loading of the lines for multi objective optimization and single objective optimization without and with SVC FACTS device located at selected bus.

Figure 4: Voltage Deviations of SVC for IEEE 30-Bus System


244

K. Padma K. Vaisakh & P. Ramesh

Figure 5: Voltage Profiles of IEEE 30-Bus System after Optimization without and with SVC

Figure 6: Voltage Angles of IEEE 30-Bus System after Optimization without and with SVC

Figure 7: Voltage Stability Indices of IEEE 30-Bus System after Optimization without and with SVC

Figure 8: Percentage MVA Line Loadings of IEEE 30-Bus System after Optimization without and with SVC


Implementation of PSO for Multi Objective Optimization with Static VAR Compensator

245

CONCLUSIONS The feasibility, effectiveness and generic nature of heuristic optimization approaches has been investigated and is exemplarily demonstrated on the IEEE 30-bus test system. Comparisons were made between single objective optimization and multi objective optimization without FACTS device and with SVC FACTS device for IEEE 30-bus system in terms of the solution quality and convergence characteristics. The result obtained by proposed algorithm has been compared with other recent methods reported in the references. It has been observed that proposed method provide an acceptable solutions and found to be suitable for implementing in planning and operation of modern power systems.

REFERENCES 1.

N.Li, Y.Xu, and H.Chen (2000), “FACTS Based Power Flow Control in Interconnected Power Systems”, IEEE Trans .on Power Systems, Vol.15, No.1, pp. 257-262, Feb.

2.

N.G. Hingorani, L. Gyugyi, “Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems”, IEEE Press, New- York, 2000.

3.

Mathur RM, Varma RK (2002) Thyristor Based FACTS Controllers for Electrical Transmission Systems. IEEE Computer Society Press.

4.

H.Ambriz-Perez, E.Acha, and C.R. Fuerte-Esquivel, “Advanced SVC models for Newton-Raphson Load Flow and Newton Optimal Power Flow studies”, IEEE Trans. on Power Systems 15(1) 129-136.

5.

Kennedy, J. and Eberhart, R.: Particle Swarm Optimization. In Proceedings of the Fourth IEEE International Conference on Neural Networks, Perth, Australia. IEEE Service Center (1995) 1942-1948.

6.

C. A. C. Coello, G. T. Pulido, and M. S. Lechuga MS, “Handling multiple objectives with particle swarm optimization,” IEEE Trans. Evol. Comput., vol. 8, no. 3, pp. 256–279, Jun. 2004.

7.

Hsiao-Dong Chiang and Rene Jean Jumeau, “Toward a practical performance index for detecting voltage collapse in electric power systems”, IEEE Transactions on power systems, Vol.10, No.21, 1992, pp.584-592.


27 implementation of pso full  

This paper presents an application of particle swarm optimization based algorithm is developed effectively to solve the multi objective op...

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