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Journal of Electrical Systems and Information Technology xxx (2016) xxx-xxx

Optimal allocation of SVC and TCSC using quasi-oppositional chemical reaction optimization for solving multi-objective ORPD

problem

Susanta Duttaa, Sourav Paula, Provas Kumar Royb*

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, 735102, West Bengal, India

Received 22 January 2016; received in revised form 7 October 2016; accepted 10 December 2016

Abstract

This paper presents an efficient quasi-oppositional chemical reaction optimization (QOCRO) technique to find the feasible optimal solution of the multi objective optimal reactive power dispatch (RPD) problem with flexible AC transmission system (FACTS) device. The quasi-oppositional based learning (QOBL) is incorporated in conventional chemical reaction optimization (CRO), to improve the solution quality and the convergence speed. To check the superiority of the proposed method, it is applied on IEEE 14-bus and 30-bus systems and the simulation results of the proposed approach are compared to those reported in the literature. The computational results reveal that the proposed algorithm has excellent convergence characteristics and is superior to other multi objective optimization algorithms.

© 2017 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Quasi-oppositional chemical reaction optimization (QOCRO); Reactive power dispatch (RPD); TCSC; SVC; Multi-objective optimization

1. Introduction

In the last few years, voltage collapse problems in power systems have been of permanent concern for electric utilities: several major blackouts throughout the world have been directly associated to this phenomenon. In the present day scenario, due to increase in power demand, restriction on the construction of new lines, environment, unscheduled power flow in lines creates congestion in the transmission network and increases transmission loss. The RPD problem is an important issue in modern power system that control tap ratios of transformers, reactive compensation devices and generator voltages to minimize a certain object while satisfying large number of constraints and maintaining reliability.

* Corresponding author. E-mail address: roy_provas@yahoo.com (P.K. Roy). Peer review under the responsibility of Electronics Research Institute (ERI).

http://dx.doi.org/10.10167j.jesit.2016.12.007

2314-7172/© 2017 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

HT 1411-16

S. Dutta et al. /Journal of Electrical Systems and Information Technology xxx (2016) xxx—xxx

Effective control of reactive compensation on weak nodes improves voltage profile, reduces power loss and improves both steady state and dynamic performance of the system.

The development of flexible AC transmission system (FACTS) controllers has been initiated by Electric Power Research Institute (EPRI) in which power flow is dynamically controlled by various power electronic devices. FACTS controllers are emerging as an effective and promising alternative to enhance the power transfer capability and stability of the network by redistributing the line flows and regulating the bus voltages. In this paper two types of FACTS devices namely static var compensator (SVC) and thyristor controlled series compensator (TCSC) are studied. The main objective of this paper is to find the optimal location of FACTS devices in the transmission network to minimize the transmission loss, voltage deviation and the voltage stability index of the system.

ORPD is usually modeled as a nonlinear optimization problem. Many classic optimization techniques such as linear programming (LP) (Kirschen and Van Meeteren, 1988), nonlinear programming (NLP) (Lee et al., 1985), quadratic programming (QP) (Quintana and Santos-Nieto, 1989), Newton method (Liu et al., 1992) and interior point method (IPM) (Yan et al., 2006) were applied in last two decades for solving ORPD problems. The gradient and Newton methods cannot handle inequality constraints efficiently. LP method needs the objective function and the constraints to be linearized as it has severe limitations in handling nonlinear discontinuous functions and constraints. The linearization may lead to loss of accuracy. Moreover, conventional methods are sensitive to the initial guess of the search point when the functions have multiple local minima, and are not efficient in handling problems with non-linear characteristics. Thus, the conventional algorithms are fast but theoretically prone to converge to local minima when solving highly nonlinear problems, and they also face difficulties in handling discrete variables. Therefore, these approaches are not appropriate for solving ORPD based FACTs allocation problems. To overcome these limitations, the robust and flexible evolutionary optimization techniques such as, genetic algorithm (GA) (Iba, 1994), evolutionary strategies (ES) (Bhagwan Das and Patvardhan, 2003), evolutionary programming (EP) (Liang et al., 2006), particle swarm optimization (PSO) (Yoshida et al., 2000), differential evolution (DE) (Liang et al., 2007) and real coded genetic algorithms (RGA) (Subbaraj and Rajnaryanan, 2009) have efficiently been applied in power system optimization problems. These evolutionary algorithms have shown success in solving the ORPD problems since they do not need the objective and constraints as differentiable and continuous functions.

In the literature, it is observed that the optimal location and setting of FACTS devices has retained the interest of worldwide researchers in power systems, where various methods and criteria are used in this field. A linear programming approach was presented by Sundar and Ravikumar (2012) to locate the optimal position of TCSC devices to solve OPF under normal and network contingency conditions. To test the superiority, this approach was implemented on standard 6-bus, IEEE 14-bus and IEEE 118-bus test systems. Lima et al. (2003) proposed mixed integer linear programming (MILP) to find optimal setting and location of thyristor control phase shifter (TCPST) for determining maximum loadability of transmission system. Sharma (2006) presented MINLP approach for the optimal placement of TCSC in power system. Mahdad et al. (2010) developed parallel GA to find the optimal position of static var compensator (SVC) to minimize fuel cost, voltage deviation and reactive power violation. The proposed method was implemented on IEEE 30-bus and IEEE 118-bus test systems and the results were compared with those of others optimization techniques. A harmony search algorithm (HSA) was developed by Sirjani et al. (2012) for simultaneous minimization of total cost, the voltage stability index, voltage profile and power loss of IEEE 57-bus test system using shunt capacitors, SVC and static synchronous compensators (STATCOM). Duong et al. (2013) introduced min cut algorithm to select the optimal position and sizing of TCSC devices in standard 6-bus, IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems to solve the OPF under normal and contingencies operating condition. Roy et al. (2011) proposed BBO to solve TCSC and TCPS based ORPD problem for minimizing voltage deviation and transmission loss of IEEE 30-bus test system. Saravanan et al. (2007) applied PSO to find best location of TCSC, SVC and unified power flow controller (UPFC) devices to improve system load ability. Palma-Behnke et al. (2004) proposed sequential quadratic programming (SQP) approach to solve SVC and UPFC based OPF problem. A graphical interface based GA was introduced by Ghahremani and Kamwa (2013) to enhance the system static loadability using different types of FACTS devices. Sebaa et al. (2014) proposed the cross-entropy (CE) approach for optimal location and tuning of TCPSTs and SVCs for optimal power flow. Sedighizadeh et al. (2014) proposed a multi-objective optimization approach to find the optimal location and setting of TCSC and SVC devices in order to simultaneously minimize power loss, increase of the stability margin and voltage profile improvement. Benabid et al. (2009) proposed non dominated sorting PSO (NSPSO) to determine optimal location and setting of SVC and TCSC devices for maximizing static voltage stability margin (SVSM), reduce real power losses (RPL), and load voltage deviation (LVD). Fuzzy based evolutionary algorithm to solve ORPD

S. Dutta et al. / Journal of Electrical Systems and Information Technology xxx (2016) xxx—xxx

Fig. 1. Circuit structure of TCSC device.

Fig. 2. Circuit model of TCSC connected between sth bus and ith bus.

incorporating FACTS was implemented by Bhattacharya and Gupta (2014). Ghasemi et al. (2014) proposed a chaotic parallel vector evaluated interactive honey bee mating optimization (CPVEIHBMO) approach to find the feasible solution of the multi objective ORPD problem with considering operational constraints of the generators. Belwin et al. (2013) proposed enhanced bacterial foraging algorithm (EBFA) to determine the optimal location and setting of SVC and TCSC devices for the dual objective of OPF.

In most of the above mentioned algorithms, the population stuck to the local optimum position and reluctant to move toward the best position to find the global optimal solutions. In this article, CRO algorithm is proposed to avoid this prematurity. However, although this algorithm has superior searching ability, it suffers from slow convergence rate. To overcome this drawback and improve solution quality, quasi-oppositional based learning (QOBL) is integrated with conventional CRO and the proposed quasi-oppositional chemical reaction optimization (QOCRO) approach is successfully applied to find optimal position of FACTS device in to reduce power losses, improve voltage profile and improve the voltage stability.

2. Series and shunt FACTS modeling

Numerous modeling methods for FACTS devices are presented in Gerbex et al. (2001) and Ambriz-Perez et al. (2000). Shunt compensation are used to provide reactive power compensation and series compensator is used to enhanced the power flow.

2.1. Static modeling of TCSC

Fig. 1 presents the general circuit structure of TCSC. It consists of a series capacitor in parallel with a thyristor controlled reactor (TCR). TCR is a variable reactor XL controlled by firing angle a (Hingorani and Gyugyi, 2000). The effective reactance of TCSC may be represented as follows:

fee (a) = X* L(X) = -jXc (1)

XL(a) - Xc

The static model of TCSC based network is shown in Fig. 2. The modified line reactance (Xnew) of the transmission line after incorporating TCSC is given as follows.

Xnew = Xst — XC (2)

Xnew = (1 — T )Xst (3)

where, T = §e is the degree of series compensation and Xst is the line reactance between the sth and the ith bus.

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105 The power flow equations of the TCSC incorporating line may be expressed as follows.

Pst = V2Gst - VsVtGst cos(5s - St) - VsVtBst sin(Ss - St) Qst = -VjBst - VsVtGst sin(5s - St) + VsVtBst cosft - St) Pts = Vf Gst - VsVtGst cos(Ss - St ) + VsVtBst sin(Ss - St ) Qts = -VfBst + VsVtGst sin(Ss - St) + VsVtBst cos(Ss - St)

Rst Rst

where Gst =

Rft + (Xst - Xc)2 Rft + [(1 - T)Xst]2

Xst Xc

(1 - T)Xst

Rft + (Xst - Xc)2

Rf + [(1 - T)Xst)2

(8) (9)

112 Here, Pst, Qst are the active and reactive power flows through the sth and the ith bus; Pts, Qts are the active and reactive

113 power flows through the tth and the sth bus; Vs, Vt are the voltage magnitude, respectively, at the sth and the tth bus;

114 Ss, St are the phase angle, respectively, at the sth and the tth bus; Gst, Bst are the conductance and susceptance of the

115 line connected between the sth and the tth bus; Rst, Xst are the resistance and reactance of the line connected between

116 the sth and the tth bus; Xc is the capacitive reactance of the fixed capacitor.

117 2.2. Static modeling of SVC

118 The schematic diagram of SVC device is illustrated in Fig. 3. It consists of fixed capacitor and thyristor-controlled

119 reactor. The equivalent susceptance Beq, which neglects harmonic current, can be expressed as

Beq = BL(a) + Be

whereBL(a) =--(1--), Bc = ю x e

The reactive power provided by SVC in power flow framework can be expressed as

Qsvc = - Vk ■bsvc The constraint on the reactive power at bus k is

< Bsvc < B

126 3. Problem formulation of ORPD

127 The mathematical problem formulations of different single and multi-objective functions of ORPD used in this

128 article are as follows:

129 3.1. Single objective optimization

130 3.1.1. Minimization of total real power loss

131 This fitness function of power loss minimization may be described as under:

Fi = min(Pioss ) = min

J2gp(v2 + Vf -2VsVt cos dst)

133 where Pioss is the total active power loss; Gp is the conductance of the pth branch connected between the sth and tth

134 bus; 0st is the admittance angle of the transmission line connected between the sth and the tth bus; Ntl is the number

135 of transmission lines; Vs, Vt are the voltage magnitudes of the sth and the tth bus, respectively.

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Fig. 3. Schematic diagram of SVC.

136 3.1.2. Minimization of voltage deviation

137 The objective function of voltage deviation minimization at load buses, maybe expressed as:

F2 = min \VLf - VLf |

139 where, VLf is the voltage at the 5th load bus; Vs/ is the desired voltage at the 5th load bus, usually set to 1.0 p.u.

140 3.1.3. Minimization ofL-index

141 When a system is being subjected to a disturbance, it is desirable to maintain constant bus voltage when the system

142 returns to normal operating conditions. The undesirable voltage may cause widespread voltage collapse. In this work,

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143 voltage stability is enhanced by minimizing voltage stability index (L-index) (Lam and Li, 2010) and is represented

144 byEq. (16).

145 F3 = min Lmax (16)

146 where Lmax = max(Lj), j = 1,2,..., Npq (17)

Lj = n -£ FßV i

Fji = -—1^1] 1 [Y2]

and <( Lj 1 Z/jiVjh j = 1, 2,...,Npq (18)

148 3.1.4. Constraints

149 The various constraints of the ORPD problem are as follows:

150 Pof -PDf -VfJ2Vh[Gfh cos (0f -0h) + Bfh sin (0f -eh)} =0, f = I,..., Nb (19)

151 QGf - QDf - Vf^Vh [Gfh sin (6f - 0h) - Bfh cos (f - 0h)} =0,f =1,..., Nb (20)

152 Vf <VGf ^V^f, f =!,..., Ng (21)

153 Qmfn <Qcf <Qf, f = 1,..., Nc (22)

154 Tf™ <Tf < fX f =1,..., NT (23)

155 Vf <VLf f =!,..., Nl (24)

156 QGf <QGf <QGfi, f =1,...,Ng (25)

157 SLf < S/f*, f =1,...,Ntl (26)

158 where Gfh, Bfh are the real and imaginary part of the bus admittance matrix of the transmission line connected between

159 the f th and the hth bus; PG, QGf are the active and reactive power generation of the f th bus; PDft QDf are the active

160 and reactive load demands of the f th bus; Vg^, Vg3^ are the minimum and maximum generator voltage of the f th bus

161 respectively; Qc™, Qm^ are the reactive power injection limits of the f th shunt compensator; Tmin, Tmax are the tap

162 setting limits of the f th transmission line; NG, Nc and NT are the number of generators, shunt compensators and tap

163 changing transformers, respectively; V™n, Vf are load voltage limits of the fth load bus; Qgf, Qgf are reactive

164 power generation limits, of the fth generator bus; Sf is the maximum apparent power flow in the fth line; NL is the

165 number of load buses.

166 3.2. Multi-objective optimization

167 In this paper, penalty factors approach is used to solve multi-objective ORPD by converting three conflicting

168 objective functions to a single objective function as follows:

169 Minimize X = F1 + pf 1 x F2 + pf2 x F3 (27)

170 where, pf1 and pf2 are the penalty factor of load-bus voltage violation and voltage stability index respectively.

S. Dutta et al. /Journal of Electrical Systems and Information Technology xxx (2016) xxx-xxx 7

71 4. Algorithms

72 4.1. Chemical reaction optimization

73q5 Chemical reaction optimization (CRO) is a relatively new meta-heuristics technique introduced by Tizhoosh (2005)

74 in 2010. It is based on four different types of chemical reactions namely (i) on-wall ineffective collision, (ii) decompo-

75 sition, (iii) inter-molecular ineffective collision and (iv) synthesis. Among these reactions, on-wall ineffective collision

76 and decomposition reactions are of single molecular reactions, where as inter-molecular ineffective collision and 7^6 synthesis reaction are of the later category.

4.1.1. On-wall ineffective collision 79 This reaction occurs when a molecule hits the surface and bounces back. After collision, a molecule p is permitted to convert to another molecule p if the condition shown in Eq. (28) satisfies.

81 Ekf + E/ > E/ (28)

82 where Ek, Ep are the kinetic and potential energy, respectively. The different steps of this reaction are as follows:

83 Step 1: A new molecule, f' is generated using mutation operation of DE (Liang et al., 2007). The jth component

84 ff j of the molecule f is updated using Eq. (29)

f'ij = fkj + F X (fmj - (29)

where fm,j, fn,j are the components of three different molecules chosen randomly from the current population.

Step 2: The potential energy Ef of the molecule f is evaluated and if Ef + Ef > Ef is satisfied, f is replaced by f and the KE of the new molecule f is modified using Eq. (30):

E% = rand (0, 1) x E% + E% - E % (30)

4.1.2. Decomposition

This reaction is also an uni-molecular reaction. A molecule f can decompose into two new molecules, f and f2, if inequality Eq. (31) holds

Ek% + Ep% > E/1 + E/2

The various steps of decomposition process may be described as follows:

Step 1: One molecule f is selected randomly from the current population and crossover operation (Liang et al., 2007) of DE is applied on f and f to generate two new molecules f and f2.

Step 2: Potential energy of the newly generated molecules f and f 2 are evaluated using the objective function of the specified problem and if the condition Ekff + Epff > Epfi + Epf is satisfied, the newly formed molecules f and f 2 are pushed into the population while the original molecule f is removed from the population. The KE of the molecules f and f 2 as modified using Eqs. ((32)-(33)):

E^1 = rand (0, 1) x

k +E% -(E% + E?)

E%2 = [1 - rand (0, 1)] x

E% + E% - (E% 1 + E%2)

4.1.3. Inter-molecular ineffective collision

In this reaction, two molecules ¡i,p2 collide with each other and create two new molecules p 1, p2. As the impact is not severe, the molecular structures of the newly generated molecules are nearer to the original molecules. This collision occurs if

EX1 + Ep 1 + EX2 + Ep? > EX + EX1 (34)

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The algorithm steps of inter-molecular ineffective collision are as described below:

Step 1: Two molecules p1 and p 2 are selected from the population and two new molecules p 1 and p2 are generated by performing crossover operation of DE (Liang et al., 2007).

Step 2: The potential energy of Ep1 and Ep2 of the molecules p[ and p'2 are evaluated and if the condition

Ep 1 + Ep1 + Ep2 + Ep2 > Ep1 + Ep2 holds, replace molecules p1, p2 by molecules p'vp'2 respectively, and update the KE of the molecules p\ and p'2 as under:

E^1 = rand (0, 1) x

E P + EP1 + Ef + EP2 - E1 + E'^

e'I2 = [1 - rand (0, 1)] x

EP1 + EP1 + EP2 + EP2 - I EP1 + E'P2

4.1.4. Synthesis collision

In this process, two molecules p1, p2 collide with each other and generate a new molecule p!v The newly formed molecule is entirely different from the original molecules. The condition of this collision is as under

Ep1 + Ep 1 + Ep2 + Ep2 > Ep' (37)

The different algorithm steps of this process are as follows:

Step 1: Select two molecules p1 and p2 from the population set to consider them as parents chromosomes and crossover operation of GA (Iba, 1994) is implemented on these molecules to produce a child chromosome p!v

Step 2: The potential energy Ep of the newly generated molecule p 1 is calculated. If the conditions described in Eq. (38) is satisfied, omit molecules p1 and p2 from the population and push the molecule p 1 into the population. The

kinetic energy Ep of the new molecule is updated using Eq. (38)

Ep' = rand (0, 1) x (Ep 1 + Ep 1 + Ep2 + Ep2 - Epp ) (38)

In this proposed method, among the above mentioned four reactions, the processes used in each iteration are probabilistically decided. After a specified number of iterations, the reaction processes are stopped and the molecule having the lowest PE is considered as the optimal solution.

4.2. Opposition based learning

Opposition-based learning (OBL), originally introduced by Rahnamayan et al. (2007) is one of the most successful concepts in computational intelligence, which enhances the search abilities of the conventional population based optimization techniques in solving nonlinear optimization problem. The main concept behind OBL is to consider the opposite of a guess and comparing it with the original assumption, thereby improving the chances to find a solution faster. By simultaneously checking the opposite solution, the possibility of starting with a better solution is possible. The OBL is based on the opposite point and opposite number those are defined as under: Opposite number: Let x e [m, n] be a real number. Its opposite number xo is defined by:

xo = m + n -x (39)

Opposite point: Let P = (x1, x2,..., xn) be a point in n-dimensional space, where

xr e [mr,nr], r e {1, 2,...., n}. The opposite point Po = (x1o, x2o,..., xno) is defined by its components:

xro = mr + nr — xr (40)

However, it is observed in the literature (Gitizadeh, 2010) that a quasi-opposite solution is usually better than the opposite one. Quasi-opposite point (Pqo = xf, xq2 ,..., xqo,..., xT) may be defined as the point between the center of the search space and the opposite point. Mathematically, Pqo may be defined as follows:

Pqo = rand(c, Po); c = a+b (41)

S. Dutta et al. / Journal of Electrical Systems and Information Technology xxx (2016) xxx—xxx 9

246 4.2.1. Quasi-oppositional based optimization

247 The concept of quasi-oppositional based optimization is applied to speed up the convergence speed of conventional

248 meta-heuristic approaches. It is based on quasi-oppositional based initialization and quasi-oppositional based generation

249 jumping which are briefly discussed below:

4.2.1.1. Quasi-oppositional based initialization. Quasi-oppositional learning can be utilized to obtain a fitter starting candidate solution without any prior knowledge about the solutions.

Initialization of each element x% of quasi-opposite population (Pqo) may be described as follows:

for r = 1: np (np = population size)

fors = 1 :nd(nd =no of control variables)

-randiß ,a +bs —x ); cs =-

4.2.1.2. Quasi-oppositional based generation jumping. A similar approach can be applied to the current population by which the current population may be forced to jump to a better solution. After generating a new population by using CRO, the quasi-opposite population is generated based on a jumping rate jr. Quasi-opposite population jumping based on jr may be described as below:

for r = \:np (np = population size)

for s = i:nd(nd =no of control variables)

if rand{0,1) < jr (jr =jumping rate)

x?°=rand(c„as+bs-xrsy, cs =

257 5. Simulation results and discussions

In order to test the effectiveness, BBO, CRO and the proposed QOCRO methods are tested on IEEE14-bus and IEEE 30-bus systems. To check the feasibility of the proposed QOCRO method and to validate the performance of the proposed method, it is compared with BBO and CRO and other optimization techniques available in the literature. The program is written in MATLAB-7 software and executed on a 2.5 GHz core i3 processor with 4-GB RAM. For implementing the BBO, CRO and QOCRO, population size of 50 and the maximum number of generation (iterations) of 100 are taken in the simulation study.

264 5.1. Input parameters

A complete evaluation on all possible combinations of the input parameters is impractical. Our goal is to assign parameter values of CRO and QOCRO algorithms with relatively good performance for the two test instances. After a number of careful experimentation, following optimum values of CRO and OCRO parameters have finally been settled for all cases: KElossRate = 0.8; InitialKE= 100; MoleColl = 0.2 and jumping rate = 0.3.

In this simulation study, the reactance limit of TCSC in p.u. is taken as 0 < XTCsc < 0.20 and susceptance limits of SVC in p.u. is assumed to be 0 < BSVC <0.15.

271 5.2. System 1

272 Initially, the performance of BBO, CRO and proposed QOCRO algorithms are verified by applying them on IEEE

273 14-bus system which consists of five generators, fourteen buses, twenty transmission lines and eleven loads. Bus

274 9 is taken as the possible reactive power compensation bus. The three branches 5-6, 4-7, 4-9 are under load tap

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Table 1

Q11 Simulation results for both single and multi-objective ORPD without FACTS devices (IEEE 14-bus system). Techniques ^ Single objective

Multi-objective

Power loss minimization

VD minimization

L-index minimization

CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO

TL (pMW.) 12.4892 12.4509 12.4257 14.7841 14.4550 16.5831

VD (p.u.) 0.3999 0.5706 0.7105 0.0299 0.0290 0.0279

L-index 0.0832 0.0795 0.0768 0.0908 0.0905 0.0903

CT (Sec.) 12.2891 5.0312 4.9756 12.2906 5.0213 5.0003

13.6718 13.5226 13.5059

0.8529 0.9439 0.9483

0.0750 0.0744 0.0737

12.2298 5.0541 5.0112

13.1020 13.0845 12.9679

0.1023 0.0988 0.0982

0.0758 0.0757 0.0752

12.2098 5.0348 4.9917

Table 2

Simulation results for both single and multi-objective ORPD with SVC device (IEEE 14-bus system). Techniques ^ Single objective

Power loss minimization

VD minimization

L-index minimization

Multi-objective

CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO

TL (MW) 12.2539 12.2122 12.2014

VD (p.u.) 0.5625 0.6007 0.4230

L-index 0.0859 0.0813 0.0877

CT (Sec.) 12.3365 5.0781 5.0397

15.1738 14.9917 15.3846

0.0256 0.0251 0.0236

0.0886 0.0917 0.0893

12.3544 5.0692 5.0481

13.4327 13.9864 13.3317

0.9153 0.8865 0.9106

0.0742 0.0734 0.0728

12.3216 5.0893 5.0664

12.9306 12.8246 12.7843

0.0982 0.0931 0.0858

0.0749 0.0741 0.0743

12.2837 5.0973 5.0341

Table 3

Simulation results for both single and multi-objective ORPD with TCSC device (IEEE 14-bus system).

Techniques ^ Single objective Multi-objective

Power loss minimization VD minimization L-index minimization

BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO

TL(MW.) 12.3346 12.3041 12.2863 15.0445 14.8218 15.0052 13.5812 13.6148 13.4882 12.9342 12.8835 12.8100

VD (p.u.) 0.7213 0.5947 0.6806 0.0265 0.0262 0.0253 0.8308 0.8541 0.9446 0.01023 0.0996 0.0918

L-index 0.0887 0.0856 0.0824 0.0898 0.0855 0.0882 0.0738 0.0726 0.0717 0.0743 0.0738 0.0731

CT (Sec.) 12.3822 5.0962 5.0182 12.3912 5.1165 5.0434 12.1232 5.1427 5.0218 12.0869 5.1322 5.0098

275 changing transformers and their upper and lower limiting values are taken within the interval [0.9, 1.1]. The bus

276 voltages are considered within the range of [0.95, 1.05]. The system line, load and bus data used in this study, is the

277 same as in Subburaj et al. (2007). To assess the efficiency of the BBO, CRO and QOCRO methods, different single

278 and multi-objective functions are considered.

279 5.2.1. Single objective optimization

280 Initially three different objectives namely, transmission loss minimization, voltage deviation minimization and 281q7 voltage stability index minimization are considered individually. In order to verify the superiority, the simulation

282 results of the proposed QOCRO algorithm is compared to those obtained by CRO, BBO, GA-1 (Devaraj and Roselyn,

283 2010), GA-2 (Mandal and Roy, 2013), TLBO (Abido, 2006), QOTLBO (Abido, 2006), SPEA (Abou El Ela et al.,

284 2011) and DE [40].

285 5.2.1.1. Case I: loss minimization. Firstly, the IEEE 14 bus system without any FACTS devices is considered for

286 investigation. Later, individually, SVC and TCSC devices are optimally placed in the transmission system using

287 different algorithms. The optimal results are listed in Tables 1-4. It is observed that the transmission loss obtained by

288 BBO, CRO and QOCRO methods are 12.4892 MW, 12.4509 MW and 12.4257 MW, respectively, for normal ORPD.

289 However, it is also found that after incorporating the SVC and TCSC individually, the power loss is significantly

290 reduced. It is also noticed that after incorporating the SVC and TCSC simultaneously, loss value obtained by BBO,

Techniques ^ Single objective Multi-objective

Power loss minimization VD minimization L-index minimization

BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO

TL (MW.) VD (p.u.) L-index CT (Sec.) 12.2216 0.6132 0.0824 12.4312 12.1835 0.5897 0.0807 5.1282 12.1543 0.5649 0.0792 5.0718 15.3792 0.0243 0.0873 12.4862 15.0062 0.0235 0.0889 5.2007 15.4917 0.0228 0.0854 5.1213 14.8711 0.8756 0.0731 12.4128 14.3642 0.8389 0.0729 5.1990 13.9864 0.8934 0.0722 5.0641 12.8875 0.0952 0.0744 12.1328 12.7931 0.0883 0.0736 5.1882 12.7247 0.0842 0.0731 5.0713

% DD o J

•a □ a

0 20 40 60 80 D 00

Iteration Cycles

Fig. 4. Convergence characteristics of transmission loss obtained by QOCRO, CRO and DE for IEEE 14-bus system without FACTS device.

291 CRO and QOCRO methods are further reduced. The convergence graph of BBO, CRO and QOCRO illustrated in Fig. 4

292 shows that QOCRO has better convergence speed and requires less time to produce a better power loss than the other

293 methods.

294 5.2.1.2. Case II: voltage deviation minimization. Here BBO, CRO and QOCRO approaches are applied on the same

295 test system with the objective of voltage deviation minimization without and with SVC and TCSC devices. The

296 corresponding results obtained by the different methods are listed in the 5th-7th columns of Tables 1-4. The results

297 clearly suggest that voltage deviation is significantly reduced by incorporating SVC in optimal location. Furthermore,

298 it is observed from the simulation results that by simultaneously placing the SVC and TCSC in optimal location with

299 optimal size, voltage deviation can further be reduced. However, the simulation results indicate that reduction of voltage

300 deviation obtained by QOCRO is best among all the discussed algorithms for both normal ORPD and FACTS based

301 ORPD problems. This fact clearly suggests that QOCRO outperforms CRO and BBO in terms of solution quality. The

302 convergence graph of BBO, CRO and QOCRO for voltage deviation in the IEEE 14 bus system with SVC and TCSC

303 devices is illustrated in Fig. 5.

304 5.2.1.3. Case III: minimization of L-index voltage stability. The 8th-10th columns of Tables 1-4 show the optimal

305 results for normal and FACTS based ORPD problem. It is observed that after installing SVC and TCSC, the voltage

306 deviation in the different buses are significantly reduced. However, the best voltage deviation is obtained using QOCRO

307 method for all the cases (i.e. without FACTS, with SVC, with TCSC and with both TCSC and SVC).

308 5.2.2. Multi-objective optimization

309 In order to validate the impacts of FACTS devices, simultaneous minimization of power loss, voltage deviation and

310 L-index is made for the same test system. The best compromising solutions with optimal settings of control variables

12 S. Dutta et al. /Journal of Electrical Systems and Information Technology xxx (2016) xxx-xxx

Iteration C ycles

Fig. 5. Convergence characteristics of voltage deviation obtained by QOCRO, CRO and DE for IEEE 14-bus system with SVC and TCSC.

Table 5

Simulation results for both single and multi-objective ORPD without FACTS devices (IEEE 30-bus system). Techniques ^ Single objective

Power loss minimization

VD minimization

L-index minimization

CRO QOCRO BBO CRO QOCRO BBO

Multi-objective

CRO QOCRO BBO

CRO QOCRO

TL (MW) VD (p.u.) L-index CT (Sec.)

4.5674 4.5521 2.0546 2.0304 0.1253 0.1265

4.5303 2.0995 0.1251

5.5691 0.0929 0.1493

5.5585 0.0923 0.1487

5.6486 0.0899 0.1491

5.5503 2.2793 0.1202

4.9329 2.4761 0.1184

4.9452 2.9113 0.1123

5.2652 0.1348 0.1223

5.2433 5.2584 0.1245 0.1197 0.1212 0.1198

16.0545 7.8311 7.4734

15.8916 7.7842 7.3925 16.1323 7.8346 7.7003

16.1107 7.7642 7.6838

311 obtained by BBO, CRO and QOCRO algorithms, without and with FACTS devices are listed in 11th-13th columns of

312 Tables 1-4. It is evident from the simulation results that the voltage profiles, transmission loss and L-index minimization

313 are greatly improved after incorporating FACTS in optimal position. It is also observed that the QOCRO approach

314 outperforms the CRO and BBO algorithm for all the cases.

315 5.3. System 2

316 In order to further judge the performance of the proposed methods, they are finally applied on IEEE 30-bus system

317 for both single and multi-objective optimization problem.

318 5.3.1. Single objective optimization

319 5.3.1.1. Case I: loss minimization. The results obtained for transmission loss minimization objective function for

320 various cases are reported in 2nd-4th columns of Tables 5, 8-10 respectively. It may be seen from simulation results

321 that QOCRO gives significantly better transmission loss compared to BBO and CRO approaches. For normal ORPD

322 without FACTS for transmission loss minimization objective, the results obtained by adopting the BBO, CRO and

323 QOCRO algorithms are compared to those appeared in a recent literature by adopting QOTLBO (Abido, 2006), TLBO

324 (Abido, 2006), SPEA (Abou El Ela et al., 2011), GA-1 (Devaraj and Roselyn, 2010), GA-2 (Mandal and Roy, 2013)

325 and DE [40] and this comparative results are listed in 2nd column of Table 6. It is evident that the QOCRO approach

326 outperforms all other approaches. Moreover, it is noticed that the proposed QOCRO method with SVC and TCSC

327 gives best results among the results of all the discussed cases of different algorithms.

328 5.3.1.2. Case II: voltage deviation minimization. In this case study, QOCRO based approach is applied for improve-

329 ment of voltage profile. The optimal results are listed in the 5th-7th columns of Tables 5, 8-10, respectively. For all

330 these four cases, it is found from the simulation results that the voltage deviation obtained by QOCRO formulation

Techniques Power loss minimization VD minimization L-index minimization

CRO 4.5521 0.0899 0.1184

QOCRO 4.5303 0.0923 0.1123

BBO 4.5674 0.0929 0.1202

QOTLBO (Abido, 2006) 4.5594 0.0856 0.1242

TLBO (Abido, 2006) 4.5629 0.0913 0.1252

SPEA (Abou El Ela et al., 2011) 5.1170 NA 0.1397

GA-1 (Devaraj and Roselyn, 2010) 4.5800 NA NA

GA-2 (Mandal and Roy, 2013) 4.6501 NA NA

DE [40] 4.5550 0.0911 0.1246

Table 7

Simulation results for multi-objective ORPD without FACTS devices (IEEE 30-bus system).

Techniques Power loss minimization VD minimization L-index minimization

CRO 5.1503 0.1245 0.1212

QOCRO 5.0744 0.1197 0.1198

BBO 5.1842 0.1348 0.1227

QOTLBO 5.2594 0.1210 0.1254

TLBO 5.2779 0.1297 0.1261

Table 8

Simulation results for both single and multi-objective ORPD with SVC device (IEEE 30-bus system).

Techniques ^ Single objective Multi-objective

Power loss minimization VD minimization L-index minimization

BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO

TL (MW) 4.4921 4.4815 4.4437 5.5318 5.5461 5.5392 5.5496 5.1347 4.9904 5.1121 5.0836 5.0238

VD (p.u.) 2.0012 1.9967 2.0128 0.0892 0.0882 0.0876 2.0608 2.1143 2.4215 0.1267 0.1183 0.1116

L-index 0.1249 0.1247 0.1253 0.1458 0.1413 0.1488 0.1113 0.1096 0.1083 0.1211 0.1198 0.1187

CT (Sec.) 16.3427 7.9923 7.8137 16.5010 7.9815 7.6937 16.5506 8.0641 7.9870 16.4862 7.9995 7.9361

Table 9

Comparative results for both single and multi-objective ORPD with TCSC device (IEEE 30-bus system).

Techniques ^ Single objective Multi-objective

Power loss minimization VD minimization L-index minimization

BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO BBO CRO QOCRO

TL (MW) 4.5031 4.4942 4.4727 5.5543 5.5317 5.5280 5.5782 5.4631 5.1673 5.1198 5.1037 5.0685

VD (p.u.) 2.1362 2.0935 2.2040 0.0907 0.0898 0.0891 2.1144 2.1603 2.2192 0.1311 0.1216 0.1149

L-index 0.1246 0.1248 0.1252 0.1433 0.1427 0.1446 0.1098 0.1086 0.1075 0.1204 0.1184 0.1179

CT (Sec.) 16.4121 7.9772 7.8246 16.4413 7.9204 7.7132 16.7112 7.9864 7.9213 16.5523 7.9756 7.9012

331 is the smallest among the three formulations, while that of BBO is the largest. The convergence curves for voltage

332 deviation vs. iteration cycles are depicted for all the algorithms in Fig. 6.

333 5.3.1.3. Case III: minimization of L-index voltage stability. The optimal results for various cases for L-index mini-

334 mization are elaborated in the columns 8th-10th of Tables 5, 8-10, respectively. The results clearly demonstrate that

335 the L-index reduction accomplished using the QOCRO approach is better than that obtained by the other approaches.

336 Hence, it may say that QOCRO is a better alternative than all the other listed approaches in terms of global search

S. Dutta et al. /Journal of Electrical Systems and Information Technology xxx (2016) xxx-xxx

Table 10

Comparative results for both single and multi-objective ORPD with SVC and TCSC device (IEEE 30-bus system).

Techniques ^ Single objective

Power loss minimization

VD minimization

L-index minimization

CRO QOCRO BBO CRO QOCRO BBO

Multi-objective

CRO QOCRO BBO

CRO QOCRO

TL (MW) VD (p.u.) L-index CT (Sec.)

4.4783 4.4518

2.3824 2.0645

0.1241 0.1238

16.5837 8.1231

4.4237 2.1902 0.1245 7.9882

5.5723 0.0884 0.1402 16.6944

5.5006 0.0873 0.1428 8.0642

5.4837 0.0869 0.1450 7.8912

5.5712 2.1048 0.1078 16.7322

5.5008 1.9976 0.1071 8.2114

5.2937 2.1362 0.1063 8.1134

5.1004 0.1178 0.1197 16.6932

5.0245 4.9937

0.1074 0.1039

0.1186 0.1173

8.1346 7.9

Iteration Cycles

Fig. 6. Convergence characteristics of voltage deviation obtained by QOCRO, CRO and DE for IEEE 30-bus system with SVC.

33£8 capacity and local search precision. Fig. 7 shows the convergence performance of algorithms with the evolution process.

338 It shows that, compared with BBO and CRO, QOCRO has faster convergence speed and needs lesser iteration cycles

339 to achieve the optimal L-index level.

5.3.2. Multi-objective optimization

Finally, to verify the feasibility, effectiveness and performance of the proposed QOCRO method for solving multi-objective problem, simultaneous minimization of power loss, voltage deviation and L-index is considered for both normal and FACTS based ORPD problems. The comparative results obtained by BBO, CRO and QOCRO are given in 11th-13th columns of Table 5,8-10. It is quite evident from the results that the incorporating FACTS devices in optimal location with optimal settings using various discussed algorithms gives better transmission loss, voltage deviation and L-index than the without FACTS device. The results presented in Table 7 shows that QOCRO is superior to CRO, BBO, TLBO and QOTLBO.

348 6. Conclusion

349 In this article, the optimal reactive power dispatch (ORPD) problem is formulated as single and multi-objective

350 optimization frameworks. BBO, CRO and QOCRO approaches for the location choice and the coordinated control

351 of SVC and TCSC are presented. It is found that the proposed QOCRO method is easy to be implemented on the

352 large-scale power systems. It is clear from the results that the QOCRO method can avoid the shortcoming such as the

353 premature convergence of CRO and BBO methods and can discover higher quality solution in reasonable computational

354 time for the problems studied in this paper.

S. Dutta et al. /Journal of Electrical Systems and Information Technology xxx (2016) xxx-xxx 15

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