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Ain Shams University Ain Shams Engineering Journal

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ELECTRICAL ENGINEERING

Optimal location of STATCOM using chemical reaction optimization for reactive power dispatch problem

Susanta Dutta c , Provas Kumar Roy * , Debashis Nandi

a Department of Electrical Engineering, Dr. B.C. Roy Engineering College, Durgapur, West Bengal, India

b Department of Electrical Engineering, Jalpaiguri Government Engineering College, Jalpaiguri, West Bengal, India

c Department of Information Technology, National Institute of Technology, Durgapur, West Bengal, India

Received 10 October 2014; revised 1 April 2015; accepted 26 April 2015 Available online 12 June 2015

KEYWORDS Abstract Optimal reactive power dispatch (ORPD) problem has a significant influence on optimal Flexible AC transmission

operation of power systems. However, getting optimal solution of ORPD problem is a strenuous system;

task for the researchers. The inclusion of flexible AC transmission system (FACTS) devices in Static synchronous

the power system network for solving ORPD problem adds to its complexity. This paper presents compensator (STATCOM);

the application of chemical reaction optimization (CRO) for optimal allocation of a static syn- Optimal reactive power

chronous compensator (STATCOM) to minimize the transmission loss, improve the voltage profile dispatch (ORPD);

and voltage stability in a power system. The proposed approach is carried out on IEEE 30-bus and Chemical reaction

IEEE 57-bus test systems and the simulation results are presented to validate the effectiveness of the optimization (CRO);

proposed method. The results show that the proposed approach can converge to the optimum solu- Transmission loss tion and obtains better solutions as compared to other methods reported in the literature.

2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).

1. Introduction transmission lines, switches and relays, active/reactive compo- nents, and loads. Power system networks are complex systems

The electric power grid is the largest man-made machine in the that are nonlinear, non-stationary, and prone to disturbances world. It consists of synchronous generators, transformers,

and faults. Reinforcement of a power system can be accom- plished by improving the voltage profile, increasing the trans- mission capacity and others. Nevertheless, some of these

* Corresponding author at: Jalpaiguri Government Engineering solutions may require considerable investment that could be College, Jalpaiguri, 735102, West Bengal, India. Tel.: +91 9474521395;

fax: +91 3561 256143. difficult to recover. FACTS devices are an alternate solution

E-mail address: roy_provas@yahoo.com (P.K. Roy). to address some of those problems [1,2] . Peer review under responsibility of Ain Shams University.

Optimal reactive power dispatch (ORPD) is an important tool for power system operators for both planning and reliable operation in the present day power systems. The important aspect of ORPD is to determine the optimal settings of control

Production and hosting by Elsevier

variables for minimizing transmission loss, improve the

234 S. Dutta et al. voltage profile and voltage stability, while satisfying various

2. Mathematical problem formulation equality and inequality constraints. The ORPD problem is in

general non-convex and non-linear and exists many local

2.1. Static model and mathematical analysis of static minima.

synchronous compensator

Over the last two decades, many researchers performed a lot of researches on ORPD. Various optimization techniques

Although, there are several FACTS devices for controlling are evolved to solve ORPD problem. These algorithms are power flow [22] and voltage profile in power system, for this generally divided into two categories, namely, classical mathe- study, only STATCOM device is considered to minimize the matical optimization algorithms and intelligent optimization transmission loss, improve the voltage profile and voltage sta- algorithms. The classical algorithms are starting from an initial bility of power system network. Static model of this FACTS point, continuously improve the current solution through a

device is as described below.

certain orbit, and ultimately converging to the optimal solu- Static synchronous compensator (STATCOM) is connected tion. These algorithms include linear programming (LP) [3] in parallel with the specific bus of a power system. The primary quadratic programming (QP) [4] , non-linear programming goal of STATCOM is to enhance the reactive power compen- (NLP) [5] and mixed integer linear programming (MILP) [6] , sation which adjusts the reactive power and voltage magnitude and benders decomposition [7] . Though, some of these tech- of power system network. It consists of three basic compo- niques, have a good convergence but most of them suffer from nents, namely, transformer, voltage source converter (VSC) local optimality. Since ORPD is multimodal and non-linear and capacitor. The STATCOM is modeled as a controllable optimization problem and severely depends on the initial voltage source (E ) in series with an impedance

. The real guess, the classical techniques are unable to produce global

[23] optimal solution. To overcome this deficiency, various intelli-

part of this impedance represents the cupper losses of the cou- gent optimization algorithms known as heuristic techniques

pling transformer and converter, while the imaginary part of are applied to solve ORPD problem. Some of the well popular

this impedance represents the leakage reactance of the cou- optimization techniques are evolutionary programming (EP)

pling transformer. STATCOM absorbs requisite amount of [8] , genetic algorithm (GA) [9,10] , simulated annealing (SA)

reactive power from the grid to keep the bus voltage within [11,12] , tabu search (TS) [13,14] , differential evolution (DE)

reasonable range for all power system loading. Fig. 1 shows [15,16] , particle swarm optimization (PSO) [17,18] and artifi-

the circuit model of a STATCOM connected to the ith bus cial bee colony (ABC) [19] , etc. Recently, a harmony search

of a power system. The injected active and reactive power flow equation of the ith bus are given below:

algorithm (HSA) was developed by Sirjani et al. [20] for simul- taneous minimization of total cost, the voltage stability index,

p Þ voltage profile and power loss of IEEE 57-bus test system

i ¼G p jV i j

i jjE p jjY p j cosðd i

using shunt capacitors, SVC and static synchronous compen-

ij Þ ð1Þ sators (STATCOM). Saravanan et al. presented PSO [21] to

jV i jjV j jjY ij j cosðd i

j ¼1

find optimal settings and location TCSC, SVC and UPFC devices for improving system load ability with minimum cost

p Þ of installation.

p jV i j

i jjE p jjY p j sinðd i

The literature survey shows that most of the population N X

ij Þ ð2Þ based techniques successfully solved optimal located FACTS

jV i jjV j jjY ij j sinðd i

j ¼1

based ORPD problem. However, the slow convergence toward the optimal solution is the main concern for most of these

The implementation of STATCOM in transmission system heuristics algorithms. Furthermore, these techniques often

introduces two state variables (|E p | and d p ); however, |V i | is produce the local optimal solution rather than global optimal

known for STATCOM connected bus. It may be assumed that solution.

In this article, a recently developed heuristic algorithm named chemical reaction optimization (CRO) algorithm based on the different chemical reactions on the molecular structure of molecules, introduced by Lam et al. in 2010 is used to find the optimal location of STATCOM device for solving ORPD problem. The effectiveness of the proposed CRO algorithm is demonstrated by implementing it in two standard systems namely IEEE 30-bus and IEEE 57-bus systems and its perfor- mance is compared with PSO, DE and other optimization techniques recently published in the literature.

The remaining sections of this paper are organized as fol- lows: Section 2 describes the problem formulation of ORPD problem. Section 3 briefly describes the CRO technique and the different steps of the proposed CRO approach. Section 4 discusses the computational procedure and analyzes the DE, PSO and CRO results when applied to case studies of

FACTS based ORPD problem. Lastly, Section 5 outlines the

conclusions. Figure 1 Schematic static model of STATCOM.

Optimal location of STATCOM 235 the power consumed by the STATCOM source is zero in

2.2.2. Minimization of voltage deviation steady state.

Since bus voltage is one of the most important security and ser- P Ep ¼ realðE p I p Þ

vice quality indexes of the power system, the minimization of deviations of voltages from desired values is considered as another objective in this study. The objective function of volt-

P E P p jE p j 2 þ jE p jjV i jjY p j cosðd i

p þh p Þ¼0

age profile improvement, i.e. voltage deviation minimization at load buses, may be expressed as:

where V i is the voltage at the ith bus; Y p is the admittance of the STATCOM; G

p ,B p are the conductance and susceptance,

f 2 ðx; yÞ ¼ min

sp

respectively, of the STATCOM; h ij is the admittance angle of

V L f L f ð8Þ

f transmission line connected between the ith bus and jth bus, ¼1 respectively; d

is the voltage source angle of the where V L f is the voltage at the ith load bus; V L f is the desired STATCOM; E p is the voltage sources of STATCOM

sp p

voltage at the ith load bus, usually set to 1.0 p.u. converters.

2.2.3. Minimization of L-index

2.2. Objective function It is very important to maintain constantly acceptable bus volt- age at each bus under normal operating conditions. However,

The conventional formulation of ORPD problem determines when the system is subjected to a disturbance, the system con- the optimal setting of control variables such as generator ter-

figuration is changed. The non-optimized control variables minal voltages, transformers tap setting, reactive power of

may lead to progressive and uncontrollable drop in voltage shunt

resulting in an eventual widespread voltage collapse. In this STATCOM and its phase angle to minimize the transmission

compensators, controllable

voltage source of

work, voltage stability enhancement is achieved through min- loss while satisfying the operational constraints. However, in

imizing the voltage stability indicator L-index. The indicator order operate the power system in reliable and secure mode,

values vary in the range between 0 and 1. the voltage profile and voltage stability index of the power sys-

The L-index of a power system is briefly discussed below: tem are also considered as the objective functions in this study.

For a multi-node system, the relation among voltage and current of load and generator buses may be expressed as follows:

2.2.1. Minimization of total real power loss

The objective of transmission loss minimization may be

expressed by

I g y gl y gg V g

X NTL h 2 2 i

f 1 ðx; yÞ ¼ P loss ¼

G k V þV

i jjV j j cosðd i

By matrix inversion, the above equation may be rearranged as

k ¼1

follows:

where f #

1 ðx; yÞ is the transmission loss minimization objective

Z ll F lg

function; P loss is the total active power loss; G k is the conduc-

ð10Þ tance of the kth line connected between them ith and jth buses;

I g K gl Y gg V g

V i ,V j are the voltage of the ith and jth buses, respectively; d i ,d j The sub-matrix F lg may be expressed as under: are the phase angle of the ith and jth bus voltages. x is the vec-

tor of dependent variable consisting of load voltages

(V l 1 ;...V l NL ), generators’ reactive powers (Q g 1 ;...;Q g NG ),

The voltage stability index of the jth bus may be expressed by

transmission lines’ loadings (S l 1 ;...;S l NTL ), controllable volt-

age source of STATCOM (E N

p 1 ;...;E p

n ) and phase angle of

STATCOM (d ;...;d ); y is the vector of independent vari-

ji

where j ¼ 1; 2; . . . ; N l ð12Þ

ables consisting of generators’ voltages (V g 1 ;...;V g NG ), trans-

i ¼1

formers’ tap settings (T 1 ;...;T NT ), reactive power injections where V g ;V l are the vectors of the bus voltage of the generator (Q i 1 ;...;Q i NC ) and voltage of the buses where STATCOMs

and load buses, respectively; I g ;I l are the vectors of the bus are used (V STATCOM 1 ;...;V STATCOM n ).

currents of the generator and load buses, respectively. Z ll , Therefore, the independent and dependent vectors may be

F lg ,K gl ,Y gg are the sub-matrices obtained by partial inversion expressed as

of the admittance matrix, N g ;N l are the number of generator

and load buses, respectively.

h x i ¼V

l 1 ;...;V l NL ;Q g 1 ;...Q g NG ;S l 1 ;...;S l NTL ;E p 1 ;...;E p n ;d p 1 ;...;d p n

To move the system far away from the voltage collapse point, the voltage stability index needs to minimize. The global

L-index indicator of the power system is expressed as follows: y ¼V g ;...;V g ;T 1 ;...;T NT ;Q ;...;Q ;V STATCOM ;...;V STATCOM

L max ¼ maxðL 1 ;L 2 ;...;L N Þ

Therefore, to enhance the voltage stability and to move the system far from the voltage collapse margin, the objective

where NG; NL are the number of generator and load buses; function may be represented as follows: NTL; NT; NC are the number of transmission lines, regulating

transformers and shunt compensators, respectively.

f 3 ðx; yÞ ¼ min L max

236 S. Dutta et al.

2.2.4. Constraints Any change in the atom type makes the molecules different The ORPD incorporating STATCOM is subjected to the fol-

from others. Each molecule has two kinds of energies PE lowing constraints:

(potential energy) and KE (kinetic energy). PE represents the objective function of a molecule while the KE of a molecule

(1) Equality constraints represents its ability of escaping from a local minimum. During the CRO [24–26] process, the following four types

of elementary reactions are likely to happen. These are on-

li Þ¼

V i V j ½g ij cos h ij þb ij sin h ij

wall ineffective collision, decomposition, inter-molecular inef-

i ¼1 i ¼1 j ¼1

ð15Þ fective collision and synthesis. These reactions can be catego-

X NB

X NB X NB rized into single molecular reactions and multiple molecular ðq gi

reactions. The on-wall ineffective collision and decomposition

reactions are single molecular reactions, while the inter- where p gi ;p li are the active power generation and demand,

i ¼1 i ¼1 j ¼1

molecular ineffective collision and synthesis reactions are of respectively, of the ith bus; q gi ;q li are the reactive power gener-

the latter category.

ation and demand, respectively, of the ith bus; g ij ;b ij are the conductance and susceptance, respectively, of the line con-

(1) On-wall ineffective collision

nected between them ith bus and jth bus and NB is number of buses.

In this reaction process each molecule hits the wall of the container and generates a new molecule whose molecular

(2) Inequality constraints structure is closed to the original one. Since, the On-wall inef- fective collision is not so severe, the resultant molecular struc- ture is not too different from the original one. A molecule ‘ms’

v min 6 v gi 6 v gi max gi collides into the wall is allowed to change to another molecule p min 6 p 6 p gi max gi gi ; i ¼ 1; 2; . . . ; NG

‘ms 1 ’, if the constraint described below is satisfied.

A single compound breaks down into two or more mole- li 6 s max

cules in the decomposition process. In this reaction, the newly s

formed molecules are far away from the original molecule. As compared with on-wall ineffective collision, the generated

t min i 6 t i 6 t max i ; i ¼ 1; 2; . . . ; NT

molecules have greater change in the potential energy than the original ones. The molecule m, hits a wall of the container

q min ci 6 q ci 6 q max ci ; i ¼ 1; 2; . . . ; NC

and participate in decomposition reaction, to generate two molecules ms 1 and ms 2 if the inequality constraint (24) holds,

KE ms þ PE ms P PE ms 1 þ PE ms 2 ð24Þ @ min pi 6 @ pi 6 @ max pi ; i ¼ 1; 2; . . . ; N STATCOM

E min Pi 6 E Pi 6 E max Pi ; i ¼ 1; 2; . . . ; N STATCOM

(3) Intermolecular ineffective collision

This chemical reaction takes place when two different mole- where v gi ;v max gi are the voltage operating limits of the ith gen-

cules react among themselves, forming two different molecules. erator bus; p min gi ;p max gi are the active power generation limits of

min

However, in this reaction, the molecular structures of the the ith bus; q min max gi ;q gi are the reactive power generation limits

newly generated molecules are closed to the original molecules. of the ith bus; v min ;v max li are the voltage limits of the ith load

Therefore in this collision, the molecules react much less vigor-

bus; s 1 li ;s max li are the apparent power flow and maximum appar- ously than decomposition collusion. When two molecules, ‘m ’

li

and ‘m ent power flow limit of the ith branch; t 2 min ’, collide with each other, they may form to two new

;t i

max

are the tap set-

molecules, m 1 ting limits of the ith regulating transformer; q 2

1 and ‘m 1 ’, if the following inequality holds: reactive power injection limits of the ith shunt compensator;

KE ms 1 1 þ PE 0 2 þ KE 0 þ PE ms 2 P PE ms 1 þ PE ms 2 ð25Þ

max min

d p i ;d p i are the phase angle limits of the ith STATCOM;

are the voltage limits of the ith STATCOM; NG; NL; NTL; NT; NC are the number of generator bus, load

E max ;E min

(4) Synthesis

The synthesis reaction is opposite to the decomposition bus, transmission line, regulating transformer and shunt com-

reaction. In this reaction two or more reactants combine pensator; respectively.

together to form an entirely different new molecule. Synthesis collision allows the molecular structure to change

3. Chemical reaction optimization in a larger extent. The two molecules m 1 and ‘m 2 1 ’ collide with

each other and form a new molecule m if the following condi- tion is satisfied.

Chemical reaction optimization (CRO) was introduced by Lam and Li in the year 2010. It is a new optimization tech-

KE ms 1 þ PE ms 1 þ KE ms 2 þ PE ms 2 P PE ms 1 0 ð26Þ nique based on the various chemical reactions occur among the molecules. A molecule consists of several atoms and is

The kinetic energy for the newly formed molecule ‘m’ is mod- characterized by the atom type, bond length and torsion.

ified as follows:

Optimal location of STATCOM 237

ms 1 The various steps for implementing the CRO algorithm can 0 þ PE ð31Þ

be summarized as follows: KE ms 0 1 ms þ PE ms Step 1: The various input parameters of the CRO algo-

rithm are initialized. The molecular structures of þ PE ms 1 ð32Þ

ms 1 0

the molecules are generated randomly. The molecu- Step 6: To enhance the search space, the inter-molecular lar structures of the molecules represent various

ineffective collision is applied on each molecule to feasible solution vectors.

update its molecular structure. The inter- Step 2: The value of the objective function of the individual

molecular ineffective collision occurs when two feasible solution set represents the potential energy

molecules collide and then produce two new mole- (PE) of the individual molecule. An initial kinetic

cules. To perform this reaction, two molecules ms 1 energy (KE) is assigned to all the molecules.

and ms 2 from the population are selected and two Step 3: Depending upon the PE values, sort the population

new molecules ms 1 0 and ms 0 2 are generated by per- and in order to retain the best solutions intact, few

forming the crossover operation of DE. The origi- best molecules are kept as elite molecules.

nal molecules ms 1 and ms 2 are replaced by the Step 4: To allow the algorithm to escape from a local min-

new molecules ms 1 0 and ms 2 0 if the newly generated imum, the on-wall ineffective collision operations

molecules have better fitness value (PE). The KE are performed on non-elite molecules. In this pro-

of the molecules ms 1 and ms 2 are modified using cess, one molecule ms is selected randomly from

(33) and (34)

the population and one molecule ms 1 is generated

using mutation operation as described below

ms KE 0 1 ½

ms 1 þ KE ms 1 þ PE ms 2

þKE ms 2 ms i;j 0 k;j n;j 1 þ PE ms 0 2 ð33Þ ms

1 1 1 are the jth components of three different þ KE 2 ms 1 þ PE ms 2 ð34Þ molecules chosen randomly from the current population.

Step 7: Lastly, the molecules participate in synthesis colli- If there is enough energy for the new molecule to be gener- sion operation to update their molecular structure. ated, i.e. if criterion (29) is satisfied, replace the original mole- Two molecules ms and ms are selected randomly cule with the new one, and update the relevant KE using (30) .

1 is KE þ PE P PE

from the population set and one molecule ms 0

ms ms ms 1

generated by performing the crossover operation. If the newly generated molecule gives better func-

tion value (PE), the new molecule is included and the original molecules are excluded. The new mole-

Step 5: For each decomposition operation, two molecules cule ms 0 1 updates its KE using (35) are selected from the population and two molecules are generated by performing the crossover opera-

KE ms 0 1 ms 1 þ PE ms 1 þ KE ms 2 tion of DE. Afterward, they are tested against the

synthesis criterion: KE

If this criterion is satisfied by the selected mole- Step 8: The feasibility of each solution is checked by satis- cules, replace the original molecules by the newly

fying its operational constraints. generated molecules and update the KE of the

Step 9: Sort the solutions from best to worst and replace new molecules using (31) and (32) .

the worst solution by the best elite solutions.

Table 1 Transmission loss for different input parameters of IEEE 30-bus system with STATCOM. Input parameter

Input parameter KE loss_rate

Input parameter

KE initial

KE initial TL 0.05 5000

TL

KE loss_rate

KE initial

TL

KE loss_rate

238 S. Dutta et al.

Table 2 Comparison of simulation results obtained by different algorithms without STATCOM. Control variables

Real power loss minimization

Voltage stability index minimization PSO

Voltage deviation minimization

DE CRO V 1 (p.u.)

1.0867 1.0916 V 2 (p.u.)

1.0811 1.0901 V 5 (p.u.)

1.0919 1.0846 V 8 (p.u.)

1.0568 1.0697 V 11 (p.u.)

1.0991 1.0992 V 13 (p.u.)

0.9001 0.9067 Q i 10 (p.u.)

0.0468 0.0440 Q i 12 (p.u.)

0.0466 0.0246 Q i 15 (p.u.)

0.0499 0.0496 Q i 17 (p.u.)

0.0492 0.0464 Q i 20 (p.u.)

0.0499 0.0453 Q i 21 (p.u.)

0.0485 0.0434 Q i 23 (p.u.)

0.0499 0.0489 Q i 24 (p.u.)

0.0498 0.0451 Q i 29 (p.u.)

0.0498 0.0484 SVD (p.u.)

2.6716 2.6503 TL (MW)

5.5 adaptive inertia weight (PSO-w) [27] , PSO with a constriction DE factor (PSO-cf) [27] , the comprehensive learning particle

PSO

swarm optimizer (CLPSO) [27] , the standard version of PSO

CRO

(SPSO) [27] , local search DE with self-adapting control param- eters (L-SACP-DE) [27] , seeker optimization algorithm (SOA) [27] , gravitational search algorithm (GSA) [28] , teaching learn-

5 ing based optimization (TLBO) [29] , quasi-oppositional TLBO

(QOTLBO) [29] , strength pareto evolutionary algorithm (SPEA) [30] , GA-1 [31] and GA-2 [32] , multi-objective PSO (MOPSO-1) [33] , DE-1 [34] , oppositional GSA (OGSA) [35] , multi-objective PSO

(MOPSO-2) [36] , multi-objective Transmission Loss (MW)

improved PSO (MOIPSO) [36] , multi-objective chaotic improved PSO (MOCIPSO) [36] available in the literature.

4.5 Since the performance of any algorithm depends on its input

parameters, they should be carefully chosen. After several Generation Cycles

runs, the following input parameters are found to be the best for the optimal performance of the DE and PSO algorithms.

Figure 2 Convergence characteristics of different algorithms for DE: Scaling factor (F) = 0.7; crossover probability transmission loss without STATCOM (IEEE 30-bus system).

(CR) = 0.2.

PSO: C 1 =C 2 = 2.05; x max = 0.9; x min = 0.4. Step 10: The CRO algorithm is terminated when the termi-

For CRO, the average value of the transmission loss over nation criterion is met. Otherwise go to Step 3.

25 different trials of IEEE 30-bus system with STATCOM for different values of KE loss_rate and KE initial is listed in Table 1 . It is clearly observed from Table 1 that the optimal

4. Simulation results and discussions settings of these input parameters for the optimal performance of the proposed CRO algorithm are as follows:

In this paper, to assess the efficiency of the proposed CRO KE loss_rate = 0.2; KE initial for each molecule = 10,000. approach, two case studies (IEEE 30 bus and IEEE 57-bus sys-

tems) of ORPD problems are used in the simulation study. All

4.1. IEEE 30-bus system

the programs are written in Matlab 7.0 and run on a PC with core i3 processor, 2.50 GHz, 4 GB RAM. The results of the

Firstly, the standard IEEE 30-bus system is used to evaluate ORPD problem obtained by CRO are compared with those

the correctness and the relative performance of the proposed obtained by DE, PSO and other techniques such as canonical

CRO method. This system consists of 6 generators, 4 regulat- GA (CGA) [27] , the adaptive GA (AGA) [27] , PSO with

ing transformers, 9 shunt compensators and 41 transmission

Optimal location of STATCOM 239

Table 3 Statistical comparison (50 trials) among various algorithms for IEEE 30-bus without STATCOM. Real power loss minimization Techniques fi

PSO DE CRO Best loss (MW)

4.6096 4.5749 4.5322 Mean loss (MW)

4.6503 4.6414 4.5413 Worst loss (MW)

4.7831 4.7328 4.5476 Voltage deviation minimization

DE CRO Best VD

Techniques fi TLBO [29]

0.1029 0.0849 Mean VD

0.1083 0.0863 Worst VD

Voltage stability index minimization Techniques fi

DE CRO Best L index

0.1198 0.1156 Mean L index

0.1221 0.1163 Worst L index

Table 4 Comparison of simulation results obtained by different algorithms with STATCOM. Control variables

Power loss minimization

Voltage stability index minimization PSO

Voltage deviation minimization

DE CRO V 1 (p.u.)

1.0997 1.0829 V 2 (p.u.)

1.0869 1.0675 V 5 (p.u.)

1.0817 1.0333 V 8 (p.u.)

1.0370 1.0378 V 11 (p.u.)

1.0996 1.0967 V 13 (p.u.)

0.9007 0.9010 Q i 10 (p.u.)

0.0493 0.0230 Q i 12 (p.u.)

0.0475 0.0487 Q i 15 (p.u.)

0.0497 0.0447 Q i 17 (p.u.)

0.0352 0.0479 Q i 20 (p.u.)

0.0339 0.0497 Q i 21 (p.u.)

0.0377 0.0489 Q i 23 (p.u.)

0.0497 0.0471 Q i 24 (p.u.)

0.0500 0.0481 Q i 29 (p.u.)

0.0495 0.0499 Optimal location

29 23 30 21 23 22 26 26 3 E P (p.u.)

1.0775 1.0943 d P (deg.) V STATCOM (p.u.)

1.0689 1.0692 SVD (p.u.)

2.5639 2.3004 TL (MW)

lines. The generator and transmission-line data adopted from STATCOM are taken as 1.10 p.u. and 0.9 p.u., respectively. [37] are illustrated in Tables A1–A3 . The maximum and mini-

The limits of phase angle of STATCOM are taken as mum voltage limits at all the buses are taken as 1.10 p.u. and

0 6d p 6 0 0 . The resistance and reactance of equivalent

0.95 p.u., respectively. The upper and lower tap settings limits STATCOM converter is 0.01 p.u. and 0.1 p.u., respectively. of regulating transformers are taken as 1.10 p.u. and 0.9 p.u.,

The performance of the proposed CRO method is demon- respectively. The upper and lower voltage limits of

strated by applying it in conventional ORPD problem (Case

240 S. Dutta et al.

1) and ORPD with STATCOM (Case 2) and its results are

5.6 DE compared with those of other methods. PSO

5.4 CRO

Case A: Transmission loss minimization (i) ORPD without STATCOM device

5.2 The effectiveness of the proposed CRO method along with

5 PSO and DE is initially verified by applying it to minimize

transmission loss of IEEE 30-bus system without any 4.8

STATCOM. The transmission loss and the optimal settings Transmission Loss (MW)

of control variables obtained by PSO, DE and CRO algo- rithms are reported in Table 2 . The results show that the trans-

4.6 mission loss found by the proposed CRO method is lower than

PSO, and DE. Fig. 2 shows the variation of real power loss Generation Cycles

against the number of iterations for the CRO, DE and PSO algorithms. Moreover, 50 trials with different initial popula-

Figure 3 Convergence characteristics of different algorithms for tions are carried out to test the robustness of the CRO algo- transmission loss with STATCOM (IEEE 30-bus system).

rithm and its statistical results are compared with those of

Table 5 Statistical comparison (50 trials) among various algorithms for IEEE 30-bus with STATCOM. Techniques fi

Voltage stability index PSO

Real power loss

Voltage deviation

DE CRO Best

Table 6 Comparison of simulation results obtained by different algorithms without STATCOM. Control variables

Real power loss minimization

Voltage stability index minimization PSO

Voltage deviation minimization

DE CRO V 1 (p.u.)

1.0586 1.0594 V 2 (p.u.)

1.0448 1.0491 V 3 (p.u.)

1.0350 1.0527 V 6 (p.u.)

1.0349 1.0416 V 8 (p.u.)

1.0578 1.0597 V 9 (p.u.)

1.0599 1.0592 V 12 (p.u.)

0.9040 0.9017 Q i 18 (p.u.)

0.0995 0.0989 QC i 25 (p.u.)

0.0578 0.0585 QC i 53 (p.u.)

0.0629 0.0629 SVD (p.u.)

5.0365 5.3439 TL (MW)

25.1395 24.8609 L-index

Optimal location of STATCOM 241

Table 7 Statistical comparison (50 trials) among various algorithms for IEEE 57-bus without STATCOM. Real power loss minimization Techniques fi

SOA GSA CRO Best loss p.u.)

DE L-SACP-DE

0.2462 0.2444 0.2438 Mean loss (p.u.)

0.2574 0.2483 0.2443 Worst loss (p.u.)

0.2875 0.2816 0.2451 Voltage deviation minimization

DE CRO Best VD

0.6724 Mean VD

0.6793 Worst VD

Voltage stability index minimization Techniques

DE CRO Best L index

0.2316 0.2286 Mean L index

0.2388 0.2293 Worst L index

Table 8 Comparison of simulation results obtained by different algorithms with STATCOM. Control variables

Real power loss minimization

Voltage stability index minimization PSO

Voltage deviation minimization

DE CRO V 1 (p.u.)

1.0247 1.0304 V 2 (p.u.)

1.0092 1.0099 V 3 (p.u.)

1.0007 1.0025 V 6 (p.u.)

1.0128 1.0108 V 8 (p.u.)

1.0494 1.0494 V 9 (p.u.)

1.0592 1.0588 V 12 (p.u.)

0.9144 0.9007 Q i 18 (p.u.)

0.0834 0.0983 QC i 25 (p.u.)

0.0572 0.0583 QC i 53 (p.u.)

0.0629 0.0627 Optimal location

31 33 45 38 37 37 42 27 29 E p (p.u.)

1.0695 1.0738 d p (deg) V STATCOM (p.u.)

1.0611 1.0685 SVD (p.u.)

4.0867 4.1256 TL (MW)

TLBO [29] , QOTLBO [29] , SPEA [30] , GA-1 [31] and GA-2 about the same and the variation is negligible. These facts [32] . The statistical results reported in Table 3 show that the

strongly demonstrate the robustness of the proposed CRO best, worst and the average results obtained by CRO are near

for the conventional ORPD problem. The worst and mean loss

242 S. Dutta et al.

Table 9 Statistical comparison (50 trials) among various methods for IEEE 57-bus with STATCOM. Techniques fi

Real power loss minimization

Voltage stability index minimization PSO

Voltage deviation minimization

DE CRO Best

of SPEA, GA-I and GA-2 are not available (NA) in the

literature.

DE 32 PSO CRO

(ii) ORPD with STATCOM

In order to check the feasibility of the proposed method for complicated network, it is applied to solve ORPD with

STATCOM of the same test system. The simulation results of transmission loss, the controlled variables, optimal position

of STATCOM and its voltage rating obtained by PSO, DE 26 and CRO are shown in Table 4 . The simulation results show

Transmission Loss (MW)

that using STATCOM the transmission loss has substantially 24 reduced for all the algorithms. Moreover, the results indicate

0 20 40 60 80 100 that the proposed CRO algorithm gives more reduction in loss

Generation Cycles (4.5297 MW) compared to PSO (4.5802 MW) and DE (4.5493 MW). The convergence of minimal transmission loss

Figure 4 Convergence characteristics of different algorithms for with evolution generations shown in Fig. 3 certifies the results

transmission loss with STATCOM (IEEE 57-bus system). of Table 4 vividly. Especially, CRO algorithm can not only

maintain the diversity of the objective function solutions at

the beginning of searching but also converge in the best solu-

DE tion at the later searching. The statistical results of CRO, 0.34

PSO DE and PSO are reported in Table 5 . From Table 5 it is very

0.32 CRO evident that CRO not only has found the highest quality results among the all algorithms compared, but also possesses

the highest probability of finding the better solution for the problem under consideration. 0.28

Case B: Voltage deviation minimization

Voltage Stability Index 0.24

The results obtained for this objective function by PSO, DE and CRO without and with STATCOM devices are reported

in 5th, 6th and 7th columns of Tables 2 and 4 , respectively. 0 20 40 60 80 100 It is observed from the simulation results that voltage devia-

Generation Cycles tion is improved by incorporating STATCOM from

0.1086 p.u. to 0.1013 p.u. by PSO, from 0.1029 p.u. to Figure 5 Convergence characteristics of different algorithms for 0.0928 p.u. by DE and from 0.0849 p.u. to 0.0803 p.u. by

voltage stability index with STATCOM (IEEE 57-bus system). CRO method. Moreover, it is observed that voltage deviation using proposed CRO is better as compared to that obtained by PSO and DE algorithms. The statistical results for voltage

index minimization objective, before using FACTS devices in deviation minimization objective illustrated in Tables 3 and

the transmission network, the L-index obtained using PSO,

5 , show the superiority of the proposed CRO method over DE and CRO was 0.1210 p.u., 0.1198 p.u. and 0.1156 p.u., other approaches.

respectively. However, after installing STATCOM with opti- mal settings in the optimized location using PSO, DE and

Case C: Minimization of L-index voltage stability CRO, the voltage stability index in the different buses is signif- icantly reduced. However, the best L-index is obtained using

To further investigate the efficiency of the proposed CRO CRO method for both the cases (i.e. without and with method, it is applied on the same IEEE 30-bus system to min-

STATCOM).

imize voltage stability index. The 8th–10th columns of Tables 2 and 4 show the optimal settings of control variables, optimal

4.2. IEEE 57-bus system

locations and optimal parameter setting of STATCOM obtained by applying PSO, DE and CRO techniques for nor-

In order to assess the effectiveness and robustness of the pro- mal and FACTs based ORPD problem. For voltage stability

posed CRO method, a larger test system consisting of 57 buses

Optimal location of STATCOM 243 with and without STATCOM is considered to solve ORPD

algorithm, simulations are carried out for conventional problem. This system (IEEE 57-bus) consists of seven genera-

ORPF problem and STATCOM based ORPD problems. tor buses (the bus 1 is the slack bus and buses 2, 3, 6, 8, 9 and

12 are PV buses), fifty load buses and 80 branches, in which Case A: Transmission loss minimization branches (4–12, 20–21, 24–26, 7–29, 32–34, 11–41, 15–45,

(i) ORPD without STATCOM device 14–46, 10–51, 13–49, 11–43, 40–56, 39–57, and 9–55) are tap changing transformers. In addition, buses 8, 25 and 53 are

The optimal settings of control variables obtained by CRO, selected as shunt compensation buses. The base load of the sys-

PSO and DE for this case are illustrated in Table 6 . It is noted tem is 1272 MW and 298 MVAR. The full system data

that all the state variables and control variables are in their adopted from [38] are listed in Tables A4–A6 . The voltage

specified limits. To assess the potential of the proposed magnitude limits of all buses are set to 0.94 p.u. for lower

approach, a comparison among the results obtained by the bound and to 1.06 p.u. for upper bound. In this study, the

CRO, DE, PSO approaches and those reported in the litera- allowed steps for tap changers are between 0.9 and 1.1 p.u.,

ture are carried out. The results of this comparison are given the allowed voltage changes are between 0.95 and 1.05. In

in Table 7 . It is worth mentioning that the comparison is car- order to test and validate the robustness of the proposed

ried out with the same control variable limits, and other system

Table A1 Transmission line data of IEEE 30 bus system. Bus no.

X (p.u.) B /2 (p.u.) From

R (p.u.)

X (p.u.)

B /2 (p.u.)

Bus no.

R (p.u.)

Table A2 Load data of IEEE 30 bus system. Bus

Load (p.u.) no.

Load (p.u.)

Bus

Load (p.u.)

Bus

Active load

Active load Reactive load (p.u.)

Reactive load

no.

Active load

Reactive load

no.

(p.u.)

(p.u.)

(p.u.)

(p.u.)

(p.u.)

244 S. Dutta et al. to minimize transmission loss STATCOM based power system

Table A3 Generators’ input data of IEEE 30 bus system. network. The detailed simulation results of CRO, PSO and DE Bus no.

P int (MW)

are illustrated in Table 8 . It is found that the active power 1 Slack power

Q min (Mvar)

Q max (Mvar)

0.00 10.0 losses achieved by the proposed CRO algorithm is equal

2 80.0 50.0 23.8378 MW while it is equal to 24.2316 MW and

5 50.0 40.0 24.4341 MW for DE and PSO methods, respectively. As can

8 20.0 40.0 be derived from the results, the proposed algorithm gives the

11 20.0 24.0 best performance in comparison with the PSO and DE meth-

13 20.0 24.0 ods. Moreover, to verify the robustness, the CRO, DE and PSO algorithms are executed for 50 trials with different start-

data. Table 7 clearly shows that the CRO technique outper- ing points. Table 9 presents the minimum, maximum and aver- forms PSO, PSO-w, PSO-cf, CLPSO, SPSO, CGA, AGA,

age transmission loss produced by the proposed algorithm DE, L-SACP-DE, SOA and GSA.

comparing with the other reported results. It is worth mention- ing that the best, mean and the worst loss obtained by the pro-

(ii) ORPD with STATCOM device posed CRO method are better than those obtained by the DE and PSO methods, which clearly suggest the robustness of the

The effectiveness of the CRO method is further evaluated proposed CRO method. The convergence of optimal solution by implementing the proposed method on IEEE 57-bus system

using DE, PSO and CRO is shown in Fig. 4 . It is found from

Table A4 Transmission line data of IEEE 57 bus system. Bus no.

X (p.u.) B /2 (p.u.) From

R (p.u.)

X (p.u.)

B /2 (p.u.)

Bus no.

R (p.u.)

To

From

To

Optimal location of STATCOM 245 the convergence graphs that for CRO only about 45 iterations

demonstrate that the L-index reduction accomplished using are needed to find the optimal solution. However, for both DE

the CRO approach is better than that obtained by the other and PSO, almost 85 iterations are required to achieve optimal

approaches. Hence, the conclusion can be drawn that CRO results.

is better than all the other listed algorithms in terms of global search capacity and local search precision. Furthermore, it can

Case B: Voltage deviation minimization

be seen that all the control variables optimized by the various discussed methods are acceptably kept within the limits. Fig. 5 Here, PSO, DE and CRO approaches are applied on the

shows the convergence performance of algorithms with the same test system with the objective of voltage deviation mini-

evolution process. It shows that, compared with PSO, and mization without and with STATCOM devices. The corre-

DE, CRO has faster convergence speed and needs lesser itera- sponding results obtained by the different methods are listed

tion cycles to achieve the optimal L-index level. The statistical in the 5th–7th columns of Tables 6 and 8 . The voltage devia-

results of L-index minimization objective for normal and tion value obtained by PSO, DE and CRO methods is

STATCOM based ORPD problem are illustrated in the last 0.7135 p.u., 0.6919 p.u. and 0.6724 p.u., respectively, for

three columns of Tables 7 and 9 , respectively. The statistical ORPD

results clearly suggest the robustness of the proposed methods STATCOM, voltage deviation value obtained by PSO, DE

without FACTS.

over other discussed methods.

and CRO methods is 0.7008 p.u., 0.6803 p.u. and 0.6533 p.u., respectively. This clearly suggests that voltage deviation

5. Conclusion

has been significantly reduced by incorporating STATCOM in optimal location. However, the simulation results indicate

Chemical reaction optimization (CRO) has proven to be an that reduction of voltage deviation obtained by CRO is best

efficient nonlinear optimization technique for solving different among all the discussed algorithms for both normal ORPD

types of real world problems of various field of engineering. In and FACTS based ORPD problems. This fact clearly suggests

this article CRO is used to find the optimal location of that CRO outperforms PSO and DE in terms of solution

STATCOM for solving optimal reactive power dispatch quality.

(ORPD) problem. Minimization of the transmission loss, improvement of the voltage profile and voltage stability are

Case C: Minimization of L-index voltage stability considered as the objective function to evaluate the system per- formance. It is observed that the STATCOM can reduce the

Finally, PSO, DE and CRO techniques are applied for L- transmission loss, voltage deviation and voltage stability index index minimization on IEEE 57-bus system to test the superi-

of a power system network effectively. Moreover, for all the ority of the proposed CRO approach. The optimal control

three different objectives, CRO produces better solutions than variables, TL, VD, and L-index values obtained using PSO,

so far best known results by any other method. Furthermore, DE and CRO approaches in the IEEE 57-bus power system

from the statistical comparative results, it is found that the for L-index minimization objective of normal ORPD and

proposed CRO algorithm is robust and suitable for sizing STATCOM based ORPD are elaborated in the columns 8th–

and locating STATCOM devices in power system transmission 10th of Tables 6 and 8 , respectively. The results clearly

system. Considering all these results of the study for ORPD

Table A5 Load data of IEEE 57 bus system. Bus

Load (p.u.) no.

Load (p.u.)

Bus

Load (p.u.)

Bus

Active load Reactive load (p.u.)

Active load

Reactive load

no.

Active load

Active load

no.

(p.u.)

(p.u.)

(p.u.)

(p.u.)

(p.u.)

246 S. Dutta et al. simulated annealing algorithm. In: International conference on

Table A6 Generators’ input data of IEEE 57 bus system. information science and management engineering (ISME), vol. 2; Bus no.

P int (MW)

Q min (Mvar)

Q max (Mvar)

[13] Wennan L, Yihua L, Xingtao X, Maojun I. Reactive power 2 0 50 optimization in area power grid based on improved Tabu search

3 40 60 algorithm. In: Third international conference on electric utility 6 0 25 deregulation and restructuring and power technologies, DRPT; 8 45 20 2008. p. 1472–77.

9 0 9 [14] Zou Y. Optimal reactive power planning based on improved Tabu

search algorithm. In: International Conference on Electrical and Control Engineering (ICECE); 2010. p. 3945–8.

[15] Shaheen HI, Rashed GI, Cheng SJ. Application of differential problems with different characteristics, dimensions, and con- evolution algorithm for optimal location and parameters setting of UPFC considering power system security. Eur Trans Electr

straints it can be concluded that CRO performs better, at least

Power 2009;19(7):911–32 .

matching many of the previously reported methods. [16] Chao-Ming H, Shin-Ju C, Yann-Chang H, Sung-Pei Y. Optimal active-reactive power dispatch using an enhanced differential Appendix A

evolution algorithm. In: 6th IEEE Conference on Industrial Electronics and Applications (ICIEA); 2011. p. 1869–74.

See Tables A1–A6 . [17] Zhao B, Guo CX, Cao YJ. A multiagent-based particle swarm optimization approach for optimal reactive power dispatch. IEEE Trans Power Syst 2005;20(2):1070–8 .

References [18] Niknam T, Narimani MR, Jabbari M. Dynamic optimal power flow using hybrid particle swarm optimization and simulated [1] Hingorani NG, Gyugyi L. Understanding FACTS: concepts and

annealing. Int Trans Electr Energy Syst 2013;23(7):975–1001 . technology of flexible AC transmission systems. New York: IEEE

[19] Karaboga D, Basturk B. A powerful and efficient algorithm for Press; 2001.

numerical function optimization: artificial bee colony (ABC) [2] Galiana FD, Almeida K, Toussaint M, Griffin J, Atanackovic D,

algorithm. J Global Optim 2007;39(3):459–71 . Ooi BT, McGillis DT. Assessment and control of the impact of

[20] Sirjani R, Mohamed A, Shareef H. Optimal allocation of shunt FACTS devices on power system performance. IEEE Trans Power

Var compensators in power systems using a novel global harmony Syst 1996;11(4):1931–6 .

search algorithm. Int J Electr Power Energy Syst 2012; [3] Urdaneta AJ, Gomez JF, Sorrentino E, Flores L, Diaz R. A

hybrid genetic algorithm for optimal reactive power planning [21] Saravanan M, Raja M, Slochanal SMR, Venkatesh P, Abraham based upon successive linear programming. IEEE Trans Power

JPS. Application of particle swarm optimization technique for Syst 1999;14(4):1292–8 .

optimal location of FACTS devices considering cost of installa- [4] Grudinin N. Reactive power optimization using successive

tion and system loadability. Electr Pow Syst Res 2007; quadratic programming method. IEEE Trans Power Syst

1998;13(4):1219–25 . [22] Xiao Y, Song YH. Power flow studies of a large practical power [5] Lai LL, Ma JT. Application of evolutionary programming to

network with embedded facts devices using improved optimal reactive power planning-comparison with nonlinear programming

multiplier Newton–Raphson method. Eur Trans Electr Power approach. IEEE Trans Power Syst 1997;12(1):198–206 .

[6] Kim DH, Lee JH, Hong SH, Kim SR. A mixed-integer [23] Ghadir R, Reshma SR. Power flow model/calculation for power programming approach for the linearized reactive power and

systems with multiple FACTS controllers. Electr Power Syst Res voltage control-comparison with gradient projection approach.

In: International conference on energy management and power [24] Lam AYS, Li VOK. Chemical-reaction-inspired metaheuristic for delivery, proceed of EMPD, vol. 1; 1998. p. 67–72.

optimization. IEEE Trans Evol Comput 2010;14(3):381–99 . [7] Amjady N, Ansari MR. Non-convex security constrained optimal

[25] Li JQ, Pan QK. Chemical-reaction optimization for flexible job- power flow by a new solution method composed of Benders

shop scheduling problems with maintenance activity. Appl Soft decomposition and special ordered sets. Int Trans Electr Energy

Comput 2012;12(9):2896–912 .

Syst 2014;24(6):842–57 . [26] Szeto WY, Wang Y, Wong SC. The chemical reaction optimiza- [8] Venkatesh P, Gnanadas R, Padhy NP. Comparison and applica-

tion approach to solving the environmentally sustainable network tion of evolutionary programming techniques to combined

design problem. Comput-Aided Civil Inf Eng; 2013. economic emission dispatch with line flow constrained. IEEE

[27] Dai C, Chen W, Zhu Y, Zhang X. Reactive power dispatch Trans Power Syst 2003;18:688–97 .

considering voltage stability with seeker optimization algorithm. [9] Wei Y, Fang L, Chung CY, Wong KP. A hybrid genetic

Electric Power Syst Res 2009;79:1462–71 . algorithm-interior point method for optimal reactive power flow.

[28] Roy PK, Mandal B, Bhattacharya K. Gravitational search IEEE Trans Power Syst 2006;21(3):1163–9 .

algorithm based optimal reactive power dispatch for voltage

stability enhancement. Electr Power Compon Syst 2012;40: sorting genetic algorithm-II for robust multi-objective opti-

[10] Zhihuan L, Yinhong L, Xianzhong D. Non-dominated

mal reactive power dispatch. IET Gener Transm Distrib [29] Mandal B, Roy PK. Optimal reactive power dispatch using quasi- 2010;4(9):1000–8 .

oppositional teaching learning based optimization. Int J Electr [11] Keyan L, Wanxing S, Yunhua L. Research on reactive power

Power Energy Syst 2013;53:123–34 .

optimization based on adaptive genetic simulated annealing [30] Abido MA. Multiobjective optimal VAR dispatch using strength algorithm. In: International conference on power system tech,

pareto evolutionary algorithm. Vancouver, BC, Canada: IEEE Power Con; 2006. p. 1–6.

Congress on Evolutionary Computation; 2006 . [12] Guo L, Ding X, Chen G, Song J, Cui Q, Liu W. A combination

[31] Subburaj P, Sudha N, Rajeswari K, Ramar K, Ganesan L. strategy for reactive power optimization based on model of soft

Optimum reactive power dispatch using genetic algorithm. Acad constrain considered interior point method and genetic

Open Internet J 2007:21 .

Optimal location of STATCOM 247 [32] Devaraj D, Roselyn JP. Genetic algorithm based reactive power

Dr. Provas Kumar Roy was born in 1973 at dispatch for voltage stability improvement. Int J Electr Power

Mejia, Bankura, West Bengal, India. He Energy Syst 2010;32(10):1151–6 .

received the BE degree in Electrical [33] Duraira S, Kannan PS, Devaraj D. Multi-objective VAR dispatch

Engineering from R.E. College, Durgapur, using particle swarm optimization. Emerg Electr Power Syst

Burdwan, India in 1997; ME degree in 2005;4(1) .

Electrical Machine from Jadavpur University, [34] Abou El Ela AA, Abido MA, Spea SR. Differential evolution

Kolkata, India in 2001 and PhD from NIT algorithm for optimal reactive power dispatch. Electr Power Syst

Durgapur in 2011. Presently he is working as Res 2011;81(2):458–64 .

Professor in the department of Electrical [35] Shaw B, Mukherjee V, Ghoshal SP. Solution of reactive power

Engineering, Dr. B.C. Roy Engineering dispatch of power systems by an opposition-based gravitational

College, Durgapur, India. He has published search algorithm. Int J Electr Power Energy Syst 2014;55:29–40 .

more than 15 research papers in international journals. His field of [36] Chen G, Liu L, Song P, Du Y. Chaotic improved PSO-based