1 s2.0 S2090447915000696 main
Ain Shams University Ain Shams Engineering Journal
www.elsevier.com/locate/asej www.sciencedirect.com
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)
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