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Optimal power system operation using parallel processing system

and PSO algorithm

Jong-Yul Kim a,, Kyeong-Jun Mun b, Hyung-Su Kim c, June Ho Park a

a Pusan National University, Geumjeong-gu, Busan, South Koreab Korea Atomic Energy Research Institute, Daejeon, South Koreac Namhae College, Gyeongnam, South Korea

a r t i c l e i n f o

Article history:

Received 2 December 2008

Received in revised form 15 February 2011

Accepted 1 June 2011

Available online 2 July 2011

Keywords:

Particle swarm optimization

Heuristic

Optimal power flow

PC cluster system

Parallel processing

a b s t r a c t

In recent studies, PSO algorithm is applied to solve OPF problem. However, population based optimiza-

tion method requires higher computing time to find optimal point. This shortcoming is overcome by a

straightforward parallelization of PSO algorithm. The developed parallel PSO algorithm is implemented

on a PC-cluster system with 8 Intel Pentium IV 2 GHz processors. The proposed approach has been tested

on the test systems. The results showed that computing time of parallelized PSO algorithm can be

reduced by parallel processing without losing the quality of solution.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

Optimal Power Flow (OPF) is a useful tool in planning and oper-

ation of a power system. The OPF problem can be described as the

optimal allocation of power system controls to satisfy the specific

objective function such as fuel cost, power loss, and bus voltage

deviation. The control variables include the generator real powers,

the generator bus voltages, the tap ratios of transformer and the

reactive power generations of VAR sources. Therefore, the OPF

problem is a large-scale highly constrained nonlinear non-convex

optimization problem [1]. Recently, many heuristic optimization

methods in[24]to overcome the limitations of the mathematical

programming approaches have been investigated. Particle Swarm

Optimization (PSO) is a newly proposed population based heuristic

optimization algorithm [5]. Compared with other heuristic optimi-zation methods, PSO has comparable or even superior search per-

formance for some hard optimization problems in real power

systems[68]. However, population based optimal research meth-

ods such as GA, EP and PSO require relatively higher computing

time than conventional optimization techniques. In parallel pro-

cessing, problems are divided into several sub problems, and allo-

cated to each processor. This can reduce computing time and

enhance computation efficiency [9]. In this paper, parallel PSO

algorithm is proposed to improve the computing time and also

PC-cluster system is developed to implement parallel PSO algo-rithm. To verify the usefulness of the proposed algorithm, parallel

PSO algorithm has been tested and compared with standard PSO

algorithm having with single processor. The standard IEEE 30 and

118-bus power systems have been employed to carry out the sim-

ulation study.

2. Optimal power flow problem formulation

The OPF problem can be formulated as a constrained optimiza-

tion problem as follows:

Minimize fx; u 1

subject to gx; u 0 2

hx; u 6 0 3

where x is a set of state variables, and u is a set of controllable

variables.

In this paper, the objective function of OPF is minimization of

fuel cost for all generators which can be formulated as follows:

Min fPgi XNg

i1

ai biPgi ciP2

gi

4

where f(Pgi) is the total fuel cost ($/h) of all generators; Pgi is the

active power output generated by theith generator;ai,bi,ciare fuel

cost coefficients; and Ng is the total number of generators. The

0142-0615/$ - see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijepes.2011.06.026

Corresponding author. Tel.: +82 55 280 1336; fax: +82 55 280 1339.

E-mail address: jykim@keri.re.kr(J.-Y. Kim).

Electrical Power and Energy Systems 33 (2011) 14571461

Contents lists available at ScienceDirect

Electrical Power and Energy Systems

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j e p e s

http://dx.doi.org/10.1016/j.ijepes.2011.06.026mailto:jykim@keri.re.krhttp://dx.doi.org/10.1016/j.ijepes.2011.06.026http://www.sciencedirect.com/science/journal/01420615http://www.elsevier.com/locate/ijepeshttp://www.elsevier.com/locate/ijepeshttp://www.sciencedirect.com/science/journal/01420615http://dx.doi.org/10.1016/j.ijepes.2011.06.026mailto:jykim@keri.re.krhttp://dx.doi.org/10.1016/j.ijepes.2011.06.026

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equality constraintsg(x, u) are the nonlinear power flow equations

which are formulated as follows:

Pgi Pdi ViXNbj1

VjYij coshi hj uij 0 i 1;. . .;Ng 5

Qgi Qdi ViX

Nb

j1 VjYij

sinhi hj uij

0 i

1;. . .

;Ng 6

wherePgi and Qgi are the active and reactive power generations at

bus i; Pdi and Qdi are the active and reactive power demands at

bus i; Viand Vjare the voltage magnitude at bus iandjrespectively;

hiand hjare the voltage angles at buses i andjrespectively; uijis theadmittance angle; Yijis the admittance magnitude; and Nbis the to-

tal number of buses.

The OPF inequality constraints, h(x, u), represent limits of con-

trol variables and state variables. The system operation constraints

consist of the transmission line loadings, load bus voltages, reac-

tive power generations of generator, and active power generation

of slack generator. These variables should be within the set lower

and upper limits.

Si 6 Si 6 Smaxi i 1;2;. . .;Nl 7

Vmini 6 Vi 6 Vmaxi i 1;2;. . .;Nb 8

Qmingi 6 Qgi 6 Qmaxgi i 1;2;. . .;Ng 9

Pmings 6 Pgs 6 Pmaxgs 10

Concerning control variables, active power output and voltage

of generators, transformers tap ratio, and shunt capacitors are re-

stricted by lower and upper limits as follows:

Pmingi 6 Pgi 6 Pmaxgi i 1;2;. . .; Ng 1 11

Vmingi 6 Vgi 6 Vmaxgi i 1;2;. . .;Ng 12

tmini 6 ti 6 tmaxi i 1;2;. . .;Nt 13

shmini 6 shi 6 sh

maxi i 1;2;. . .; Nsh 14

3. Parallel computation of PSO algorithm using PC clustering

3.1. PC cluster system

After mid 1980, high performance computers have been needed

according to the development of large scale science and engineer-

ing. Since supercomputers are expensive, cluster systems replacedsupercomputers because it has the availability of inexpensive high

performance PCs, and high speed networks, and development of

integrated circuits. PC cluster system provides higher availability

as well as greater performance by lower cost with interconnecting

several PCs or workstations. PC cluster system is very competitive

with parallel machine in terms of a ratio of cost to performance be-

cause clustering is one of the types of parallel or distributed pro-

cessing system, which is composed of a collection of

interconnected low cost PCs working together as single and inte-

grated computing resources. Also, it is easy to add nodes that con-

struct the PC cluster. A basic construction diagram for PC cluster is

shown inFig. 1.

The performance of the PC cluster system depends on the qual-

ity of message passing system, libraries, and compilers for parallelprogramming and performance of individual nodes. Therefore, it is

important to select each component described above properly to

obtain better performance. The PC cluster system implemented

in this paper is composed of eight nodes based on fast Ethernet

with Ethernet switch. For operating system, master node uses

Windows 2000 server, and slave nodes use Windows 2000 pro.

To connect each node, fast Ethernet card and switching hub were

used. In data communication, MPI library was used, which is effec-

tive for parallel application by using message-passing method

through TCP/IP over Internet. Symantec PC anywhere was used

for remote control of each node, and MS visual C++ 6.0 was used

for compilers of parallel programming. Table 1shows the picture

and the specification of the PC cluster system developed in this

paper.

3.2. Parallel computing of PSO algorithm

The PSO is basically developed through the simulation of bird

flocking in two-dimensional space. In PSO, each particle i

(i= 1, . . .,N) in the population is characterized by three vectors

(xi, vi,pi) which represent their temporal position, velocity, and

the best position. The fitness of each particle is given by the func-

tion valuef(xi). Each particle stores its best position pi called per-sonal best, p-best, which gives the best fitness in memory. They

can also consult their neighbors best position. Most simply, the

neighbor is the whole population (fully connected topology), and

therefore, the neighbors best is the best position among personal

bests of the whole population. Hence, the position pgis called glo-

bal best. Now each particlei moves around the search space, and

renews its velocity using its past experience (personal best) and

the populations experience (global best) as follows:

vi xvi c1r1pi xi c2r2pg xi 15

The parameterc1andc2are the acceleration constant, r1 andr2are the uniform random numbers within the range [0, 1]. Ifviis lar-

ger than a predefined velocity vmax called maximum velocity, it is

set to vmax. Similarly, if it is smaller than vmax, it is fixed to vmax.The parameterx is called inertia weight [10], which controls theexploration (global search)exploitation (local search) tradeoff.

x xini xfin MAXiteration Iteration=MAXiteration

xfin 16

Then the particle changes its position by the equation of

motion:

xi xi vi 17

The population size is one of the key factors that will affect the

search performance of the PSO algorithm for seeking the optimal

solution. The larger population size can guarantee the higher

chance of obtaining the optimal solution. However, it is obviousthat more computing time is needed. To reduce the computing

time with same quality of solution, parallel PSO algorithm is pro-

posed and paralleled by the PC cluster system. The most important

issue of parallelizing PSO algorithm is exchange model of evolution

information. Different ways will result in different performances.

The proposed configuration is a kind of parallel algorithm based

on coarse grain model, in which the population is divided into

some sub-populations evolving independently.

Each sub-population exchanges require information only be-

tween two neighboring sub-populations connected by arrowed

lines as shown inFig. 2. Each sub-population is allocated in each

processor that involves in parallel computing. With each processor

that can communicate with the neighboring sub-populations, the

best solution of each processor is transferred to the neighboringprocessors by migration operation every generation. The flowchart

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for searching optimal solution using the proposed parallel PSO ispresented inFig. 3.

3.3. PSO algorithm for the optimal power flow problem

In optimal power flow problem to allocate power system con-

trols optimally, we should determine the unit active power out-

puts, generator-bus voltage magnitudes, transformer tap ratios,

shunt capacitor capacities. To get the effective solution of optimal

power flow by the proposed parallel PSO, we should design PSO

appropriately for the optimal power flow problem. To solve the

OPF problem by PSO, we select unit active power outputs, genera-

tor-bus voltage magnitudes, transformer tap ratios, and shuntcapacitors as control variables in PSO position vector as follows:

S1 Pg1;. . .;Pgn; Vg1;. . .; Vgn; t1;. . .; tn; sh1;. . .; shn

S2 Pg1;. . .;Pgn; Vg1;. . .; Vgn; t1;. . .; tn; sh1;. . .; shn

.

.

.

Sp Pg1;. . .; Pgn; Vg1;. . .;Vgn; t1;. . .; tn; sh1;. . .; shn

where Pgi is the active power output of the ith generator, Vgi the

voltage magnitude of the ith generator bus, ti the transformer tap

ratios of the ith transformer, shi the no. of bank of the ith shunt

capacitor andp is the no. of position vector.

In the evaluation procedures of PSO, fitness value can be ob-

tained by the following equations. As shown in Eq.(18), fitness is

composed of fuel cost of the generator and several constraints forthe power system operations.

Fig. 1. Configuration of parallel PSO algorithm with the ring structure.

Table 1

Specification of PC cluster system.

Item Specification

CPU Intel 2.0 GHz

Mother board LeoTech P4XFA

Chipset VIA P4X266A

RAM DDR SD RAM 256 MB

HDD Samsung 40 GB 5600 rpm

NIC 3Com 3CSOHO 100-TX

Network switch 3Com 3C16465C Switch

Operating system Window 2000 Server/Window 2000 Pro

MPI library MPICH 1.2.5

Compiler Visual C++ 6.0

Fig. 2. Structure of population in parallel PSO algorithm.

Fig. 3. Flow chart of parallel PSO algorithm.

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Fitness aPNg

i1FiPgi

PNcj1xj Penj

18

where Fi(Pgi) is the fuel cost function of the ith generator, xj thecoefficient of the jth constraint, Penj the penalty function of the

jth constraint, Ng the no. of generators, Ncthe no. of constraints

anda is the constant value.

4. Test results

Two test systems, IEEE 30 and 118-bus systems are used to ver-

ify the proposed algorithm with emphasis on the validity of the

calculation results and the effectiveness of the proposed algorithm.

The simulation parameters of PSO algorithm are listed in Table 2.

4.1. IEEE 30-bus system

The IEEE 30-bus systemhas a total of 24 control variables as fol-

lows: five unit active power outputs, six generator-bus voltage

magnitudes, four transformer-tap settings, and nine shunt capaci-

tors. Transformers are in-phase transformers with assumed tap-

ping range of 0.91.1 pu and shunt capacitors are in the range of00.05 pu. The lower voltage magnitude limits at all buses are

0.95 pu, and the upper limits are 1.1 pu for generator buses and

1.05 pu for the remaining buses including the reference bus.

The best cost of PSO algorithm with single processor gives

800.68 $/h, and proposed parallel PSO algorithm with eight proces-

sors gives 800.64 $/h. Both of algorithms show almost same quality

solution which is less than the 804.8 $/h reported in [11]. OPF solu-

tion found by parallel PSO and corresponding control variables set-

ting are described in Table 3. More detail searching performance of

parallel PSO is presented inTable 4. The computing times for stan-

dard and parallel PSO algorithm with eight processors are 8.03 s

and 1.73 s respectively.

To show the effects of the parallel operation by the PC cluster-

ing, speedup is evaluated. Speedup is described below:

speedup (Sp)

Sp T

Tp19

where T is run time on one processor and Tp is run time on p

processors.

Fig. 4 shows the speedup as the number of processors increases.

FromFig. 4, it is found that speedup increased as the number of

processors increased almost linearly, but somewhat lowered

because there exists overhead when communication executed

between processors.

4.2. IEEE 118-bus system

The IEEE 118-bus system has 118-bus, 14-generator,

9-transformer, 179-branch. It also has a total of 27 control

variables. The lower voltage magnitude limits at all buses are same

with IEEE 30-bus system. The best cost of standard PSO algorithm

using single processor is 17560.4 $/h, and proposed parallel PSO

algorithm with 8 processors also gives the similar result of

17554.0 $/h. These results are less than the 17860.09 $/h reported

in[12]. Minimum solution found by PSO algorithm in 118 bus sys-

tem and summary of searching performance are presented in Ta-

bles 5 and 6. The computing time is obviously reduced from

1362.26 s to 169.0 s by the parallel PSO algorithm with 8 proces-

sors. Fig. 5 shows the speed up as the number of processors

increases. FromFig. 5, it is found that speedup increased as the

number of processors increased almost linearly, but somewhat

Table 2

Simulation parameters.

Parameter Value

Max iteration 50

Population 60

C1 2.0

C2 2.0

w 0.90.4

Table 3

Minimum solution found by Parallel PSO-OPF in IEEE 30-bus system.

Parallel PSO-OPF solution

P1 177.13 V1 1.08

P2 48.82 V2 1.06

P5 21.40 V5 1.03

P8 21.30 V8 1.03

P11 11.82 V11 1.07

P13 12.00 V13 1.05t412 1.096 t610 0.984

t69 0.908 t2827 0.982

sh10 0.034 sh21 0.0484

sh12 0.0302 sh23 0.0370

sh15 0.0293 sh24 0.05

sh20 0.0455

Table 4

Summary of searching performance in IEEE 30-bus system.

Method Processor number Cost ($/h) Computation time (s)

Ref.[10] 1 804.8

PSO 1 800.68 8.03

Parallel PSO 8 800.64 1.73

0

1

2

3

4

5

1 4 6 8

No. of processors

Speed

up

Fig. 4. Speed up according to the processor number in IEEE 30-bus system.

Table 5

Minimum solution found by PSO-OPF in IEEE 118-bus system.

Parallel PSO-OPF solution

P1 290.00 V1 1.09

P10 328.88 V10 1.09

P12 210.00 V12 1.07

P25 241.60 V25 1.10

P26 241.61 V26 1.10

P49 237.97 V49 1.07

P59 195.00 V59 1.06

P61 210.01 V61 1.08

P65 345.77 V65 1.01

P66 315.00 V66 1.10

P80 336.16 V80 1.08

P89 315.00 V89 1.10

P100 230.34 V100 1.10

P103 265.00 V103 1.09

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lowered because there exists overhead when communication exe-

cuted between processors.

5. Conclusions

In these days, many heuristic optimization methods such as GA,

EP and PSO are developed and applied to OPF problem. However,

heuristic optimization methods require relatively higher comput-

ing time which is one of the major obstacles on dealing with the

on-line OPF. In this paper, parallel PSO algorithm based on PC-

cluster system is proposed and applied to the OPF problem. For

parallel computing, a PC cluster system consisting of 8 PCs is also

developed. To verify the performance of the proposed method, par-

allel PSO algorithm is tested on an IEEE 30 and 118-bus systems.

For repeated evaluating fitness function during evolution process,

it needs lots of computing cost by calculating load flow. Therefore,

proposed parallel PSO algorithm can divide the population into

several sub populations to share the burden of calculating the load

flow. As a result, computing time of parallel PSO algorithm can be

further improved.

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Table 6

Summary of searching performance in IEEE 118-bus system.

Method Processor number Cost ($/h) Computation time (s)

Ref.[11] 1 17860.09

PSO 1 17560.4 1362.26

Parallel PSO 8 17554.0 169.0

0

2

4

6

8

10

1 4 6 8

No. of processors

Speed

up

Fig. 5. Speed up according to the processor number in IEEE 118-bus system.

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