Determining optimal location and size of capacitors in radial distribution networks using moth swarm algorithm

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 5, October 2020, pp. 4514~4521
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i5.pp4514-4521  4514
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Determining optimal location and size of capacitors in radial
distribution networks using moth swarm algorithm
Thanh Long Duong1
, Thuan Thanh Nguyen2
, Van-Duc Phan3
, Thang Trung Nguyen4
1,2
Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City, Vietnam
3
Faculty of Automobile Technology, Van Lang University, Vietnam
4
Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Vietnam
Article Info ABSTRACT
Article history:
Received Feb 14, 2020
Revised Mar 14, 2020
Accepted Mar 28, 2020
In this study, the problem of optimal capacitor location and size
determination (OCLSD) in radial distribution networks for reducing losses is
unraveled by moth swarm algorithm (MSA). MSA is one of the most
powerful meta-heuristic algorithm that is taken from the inspiration of
the food source finding behavior of moths. Four study cases of installing
different numbers of capacitors in the 15-bus radial distribution test system
including two, three, four and five capacitors areemployed to run the applied
MSA for an investigation of behavior and assessment of performances.
Power loss and the improvement of voltage profile obtained by MSA are
compared with those fromother methods. As a result, it can be concluded
that MSA can give a good truthful and effective solution method for
OCLSD problem.
Keywords:
Modified moth swarm
algorithm
Optimal location
Optimal size
Radial distribution network Copyright © 2020Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Thang Trung Nguyen,
Power System Optimization Research Group,
Faculty of Electrical and Electronics Engineering, Ton Duc Thang University,
19 Nguyen HuuTho street, Tan Phong ward, District 7, Ho Chi Minh City, Viet Nam.
Email: nguyentrungthang@tdtu.edu.vn
NOMENCLATURE
Cr The number of randomly selected control variables among Dim variables
CI, MI The current iteration and the maximum iteration
Dim The number of control variables of each solution
g The gth variable of each solution
GP Source power at bus 1
Gr1, Gr2, Gr3 The number of solutions in group 1, group 2 and group 3
Ic Current magnitude of the cth branch
Ic
max
The maximum current magnitude of each branch
LD Total load demand
Levy1, Levy2 Two Lévy flight distributions
Nb Number of branches
Nbus Number of buses
NC Number of capacitors
PL Total active power losses
Qmin, Qmax The minimum and maximum rated power of capacitor
R1,R2,R3,R4,R5 Random numbers distributed uniformly within the interval [0,1]
Rc Resistor of the cth branch
Vmin , Vmax The minimum and maximum rated voltage of bus
Xr1, Xr2, Xr3, Xr4, Xr5, Xr6 Randomly selected solutions from solutions
Xbest,XGbest The best solution in group 1, group 2 and all groups

Int J Elec & Comp Eng ISSN: 2088-8708 
Determining optimal location and size of capacitors in… (Thanh Long Duong)
4515
1. INTRODUCTION
In a power system, lines have one of the important elements in transmitting electric energy from
power plants to industrial zones and house holds. There are commonly two-line types such as transmission
lines and distribution lines. Here, transmission lines are managed by Transmission Company while other ones
are controlled by Electrical Company. However, current running on distribution linesis higher than that of
transmission lines because of its low voltage, leading to higher power lossesas well as voltage regulation.
Also, distribution lines are developing large and being extended. A solution to the mentioned difficulties can
be solved by installing distributed generators [1] or adding capacitors at proper locations [2]. In this paper,
we only focus on finding the best location and the most appropriate size of capacitors in radial distribution
networks. The strategic mission of the considered OCLSD problem is to determine the most suitable location
and sizing of capacitors at buses in a radial distribution system in order to decrease power losses, improve
the voltage profile, power factor and avoid overloadas presented in a highly efficient method (HEM) [2].
The OCLSD problem has received more attention from researchers and many methods have been proposed.
In solving OCLSD problem, a manner implemented in methods has been doneintwo ways. One is to
determine the optimal locations for capacitor placementat candidate busesfirstly and then the optimal sizing
of capacitors is calculated. Another is simultaneously done a determination both the optimal location and
sizing of capacitors. References [3-5] have used a fuzzy techniqueto find the most suitable positions for
capacitor placement while real coded genetic algorithm (RCGA) [3], particle swarm optimization (PSO) [4]
and differential evolution (DE) [5] and multi agent PSO (MAPSO) [5] have been applied for sizing of
capacitors. Similar to methods above, references [6-11] and [12] have also located the candidate buses by
using loss sensitivity factor (LSF) and then the optimal capacitor sizes have been done bytime-varying inertia
weighting PSO (TVIWPSO) [6], maximum load-ability index (MLI) [7], genetic algorithm (GA) [8],
inertia weighting PSO (IWPSO) [9], ant colony optimization (ACO) algorithm [10], modified harmony
algorithm (MHA) [11] and artificial bee colony algorithm (ABC) [12]. Dissimilar to the previous methods,
teaching learning based optimization (TLBO) [13], hybrid method of chaotic search, opposition-based
learning, DE and quantum mechanics (HCODEQ) [14], particle swarm optimization approaches (PSOs) [15]
and flower pollination algorithm (FPA) [16] have solved such OCLSD problem by considering locations and
size of capacitor as control variables of each solution. On the other hand, voltage enhancement can be
reached by using wind turbines and photovoltaic systems [17, 18], network reconfiguration [19-21],
and distributed generators [22]. In this paper, MSA is applied to OCLSD problem. The results obtained from
MSA are competed with the lately reported results. Moth swarm algorithm (MSA) was evolved by Al-Attar
Ali Mohamed in 2017 [23] and employed for solvingoptimization problems such as combined economic and
emission dispatch [24] and image segmentation [25, 26]. In summary, the novelty and contribution of
the paperare as follows:
 The first application of MSA for different case of installing capacitors in radial distribution network
 Demonstration of the effectiveness of the number of capacitors for voltage enhancement
 Show a detail of MSA procedure for updating new solutions
 Successfully apply MSA for solving OCLSD problem
 MSA can reach higher quality solutions than other ones.
2. MODEL OF THE OCLSD PROBLEM
2.1. Objective function
Connecting series capacitors or parallel capacitors to the buses of distribution system can
significantly reduce total active power losses as well as enhance to the operation stability of the power
system. So, minimizing total active power losses (PL) is a key duty in addressing OCLSD problem.
Its mathematical formula is given by
2
1
Minimize
Nb
c c
c
PL I R

  (1)
2.2. Constraints
2.2.1. Constraints of balancing power system
In distribution system, sum of total load demandand active power lossesin lines must be equal to
generation power as follows:
 GP LD PL (2)

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 10, No. 5, October 2020 : 4514 - 4521
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2.2.2. The voltage restriction
The voltage at buses is limited by its lower bound and upper bound below:
min max ; 1,...,  i busV V V i N (3)
2.2.3. Capacitor size restriction
Selecting size of capacitors for connecting to distribution systemcan reduce power loss or lead to
over compensation. Such over compensation not only make power loss extra but also partly impacts on
the stability of the system. In this paper, capacitors’ size and location are selected to be control variables
mean while size is a continuous variable but location is a discrete variable. Size of capacitor must be
restricted by the minimum and maximum rated power of capacitor as the following in equality:
min max ; 1,...,  k cQ Q Q k N (4)
2.2.4. Restriction of branch current
The current running on branchesis equal or smaller than the maximum current of conductor that can
be subjected. It is presented as in (5),
max
; 1,..., c cI I c Nb (5)
3. METHOD
3.1. Moth swarm algorithm
In MSA [23], the optimal solution of the considered problem related to a light source of the moon is
considered as thebest moth swarm position and its fitness is the luminescence intensity of the moon.
From aninitial moths in population Gr, theyare assigned three groups with Gr1, Gr2 and Gr3 by basing on
their calculated fitness. In which, moths in Gr1 are called Path finders that take on finding the light sources to
direct the swarm, those from Gr2 are named Prospectors that find the food according to the positions
determined by Pathfinders and those from the last group are called on lookers that exploit the food
source found by Prospectors. The whole operation of these groups has been respectively implemented in three
phases below:
3.1.1. Reconnaissance phase:
In the first phase, three popular techniques such as the mutation, adaptive crossover and selection
techniques are used for updating new positions of Pathfinders to avoid falling into local search zones.
The formulas of these techniques are formed as shown in (6), (7) and (8) respectively.
     1 2 3 4 5 11. 2. ; 1, ,     s r r r r rS X Levy X X Levy X X s Gr (6)
,
,
,
if
; 1,...,
if
 
 

s g
s g
s g
X g Cr
Z g Dim
S g Cr
(7)
( ) ( )
( ) ( )
 
 

s s s
s
s s s
X if Fitness Z Fitness X
X
Z if Fitness Z Fitness X
(8)
For implementing the work in the transverse orientation phase, XLight with Gr solutions
areestablished. Each solutionin XLight is randomly selected from the kept solutions of Gr dependent on
the probability value of solutions Ps. This probability value is given by,
1


s
s Gr
s
s
Fit
P
Fit
(9)
where Fits is the luminescence intensity factor of each solution s it is calculated from the objective function
value Fitnesss as presented in (10).

4517
1
for 0
1
1 for < 0


 
 
s
ss
s s
Fitness
FitnessFit
Fitness Fitness
(10)
3.1.2. Transverse orientation phase:
From information about the luminescence intensityshared by Pathfinders, Prospectors fly according to
a logarithmic spiral pathto update their position. The process for updating Prospector’sposition is shown as (11),
, 1 1 2. .cos2 ; 1, ,
     i i Light i iX X X e X i Gr Gr Gr (11)
where  is a randomlyselected number in range of (-1-(CI/MI),1) [17]; Gr2iscalculated by:
2 1( ) 1
  
     
  
CI
Gr round Gr Gr
MI
(12)
3.1.3. Celestial navigation phase:
In the last phase, Onlookers are divided in two smallgroups. Moths in two small groups are updated
their new positions by using the following (13) and (14),
6 1 2 2 1. . ; 1,...,        k k r best kX X X R X R X k Gr Gr Gr (13)
   3 6 4 , 5
2 1
2
. 1 ;
w 1,...,
   
             
   
  
k k r ligth k k best k
CI CI
X X R X R X X R X X
MI MI
ith k Gr Gr Gr
(14)
3.2. The implementation of MSA toOCLSD problem
Two parameters of OCSA problem such as the location and sizing of capacitors are considered as
the control variables of MSA. These variables are a solution corresponding to a moth. The process for
executing MSA to OCSA problem is described as Figure 1 (see in appendix). Such figure displays
the flowchart of MSA.
4. NUMERICAL RESULTS
The method applying MSA has been tested on distribution system of 15 buses for solving
the optimal capacitor placement problem. The single line diagram of such system and its dataare taken
from [5]. The process for calculating MSA method is implemented on a PC with processor Core i5 – 2.2 GHz
and 4GB of RAM. In addition, after determining location and size of capacitors, power flow method is
applied to calculate branch currents and then power loss is obtained by using (1). Population size and
the number of maximum iterationsare set to 30 and 100. Fifty trial runs are implemented for MSA.
Total active power loss objective function isemployed to assess the ability of MSA with four differentcases
regarding the placementof different location of capacitors. The four cases are described as follows:
 Case 1: Considers aconnection of two capacitorsat two different buses
 Case 2: Investigates an installation of three capacitors at three different buses
 Case 3: Studies the installationof four capacitors at four different buses
 Case 4: Inspects five capacitorsat five different buses.
4.1. Power loss optimization
The active power loss of the investigated system is 61.8kW [2]. This value can reduce by connecting
capacitors. In power loss reduction, the determination of accurate location and suitable size of capacitors has
played a very important role. If this process is incorrect, it leads to over compensation. For this reason, MSA
has been applied in determining the optimal location and sizing of capacitors. Results obtained by MSA
along with other methods for all investigated cases are shown in Tables 1-8. Tables 1-4 show the optimal
position and size of capacitors of MSA and other methods. For case 1, the optimal locations found by MSA
are bus 4 and bus 6, those for case 2 are buses 4, 6 and 11. Those for case 3 are buses 4, 6, 9 and 11, and
those from case 4 represent buses 4, 6, 7, 9 and 11. The optimal capacitor sizes given by MSA for case 1 are

 ISSN: 2088-8708
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701.65 kVAR and 438.36 kVAR, those for case 2 are 488.25 kVAR, 408.08 kVAR and 300.10 kVAR, those
for case 3 are 457.09 kVAR, 377.03 kVAR,139.05 kVAR and 284.76 kVAR and those for case 4 are
460.75 kVAR, 156.03 kVAR, 209.75 kVAR, 152.14 kVAR and 284.19 kVAR.
Table 1. The optimum sizing and location of capacitors of methods for case 1
Bus no 3 4 6
Qc
(kVAR)
HEM [2] 805 0 388
TVIWPSO [6] 871 0 321
ACO [10] 0 630 410
MSA 0 701.65 438.36
Bus no 2 4 5 6 11 15
Qc
(kVAR)
GA [8] 750 0 300 0 150 0
MHA [11] 0 0 0 350 300 300
MSA 0 488.25 0 408.08 300.1 0
Bus no 4 6 9 11 13 15
Qc
(kVAR)
IWPSO [9] 450 450 0 0 150 150
MSA 457.09 377.03 139.05 284.76 0 0
Bus no 4 6 7 9 11 15
Qc
(kVAR)
PSO [4] 274 193 143 0 267 143
DE [5] 345 264 143 0 300 143
MSA 460.75 156.03 209.75 152.14 284.19 0
Tables 5-8 showa comparison between results obtained from MSA and other methods in term of
a power loss, a reduction of power loss (RPL) in kW and in (%). Column 3 of these tables shows that
the power losses value gotten by MSA is always better than other methods for all cases. That of MSA is
32.31kW for case 1, 30.34kW for case 2, 29.90 kW for case 3 and 29.75 kW for case 4 whilst that of others is
from 32.6 kW to 36.81 kW for case 1, from 31.12 kW to 31.67 kW for case 2, 30.3 kW for case 3 and from
30.55 kW to 30.96 kW for case 4. As valuing the reduction of power loss, MSA can reach less power loss
than other methods by from 0.29 kW to 4.5 kW for case 1, from 0.78 kW to 1.33 kW for case 2, 0.4 kW for
case 3 and from 0.8 kW to 1.21 kW for case 4. The reduction of power loss corresponding to
the improvement percentage of MSA over other ones is presented in column 5 of Tables 5-8. From these
comparisons, it can be seen that MSA can reach better optimal result than other methods for all cases.
In addition, the voltage at buses is also presented in Figure 2. Such figure shows the improvement of voltages
in cases with or without installing capacitors.
Table 5. Comparisonbetween results obtained from MSA and other methods for case 1
Method Total KVAR added Power loss kW RPL In kW RPL In %
HEM [2] 1193 32.6 0.29 0.89
TVIWPSO [6] 1192 32.7 0.39 1.19
ACO [10] 1040 36.81 4.5 12.22
MSA 1140 32.31 - -
Table 6. Comparison between results obtained from MSA and other methods for case 2
Method Total KVAR added Power loss kW RPL In kW RPL In %
GA [8] 1200 31.67 1.33 4.20
MHA [11] 950 31.12 0.78 2.51
MSA 1196.431 30.34 - -
Method Total KVAR added Power loss kW RPLIn kW RPLIn %
IWPSO [9] 1200 30.3 0.4 1.32
MSA 1258 29.90 - -

4519
Method Total KVAR added Power loss (kW) RPL InkW RPL In %
PSO [4] 1020 30.55 0.8 2.62
DE [5] 1195 30.96 1.21 3.91
MSA 1263 29.75 - -
Figure 2. The voltage improvement with and without installing capacitors
4.2. Discussion
The number of capacitors installed onto radial distribution system has asignificant impact on
reducing the power loss as well as improving the quality of voltages at busesin the radial distribution
systems. The selection of capacitor number needs to be calculated and analyzed carefully. For this view,
Figures 3 and 4 have been plotted to show analteration of power loss values and improvement of voltages
with different numbers of installed capacitors. As shown in Figure 3, the value of power loss decreases from
32.31 kW to 29.75 kW corresponding to from case of added two capacitors to case of added four capacitors.
On the other hand, Figure sees voltage is also highly improved, namely from 0.965 corresponding to
two-capacitor installation to 0.9699 pu corresponding to five-capacitor installation.
Figure 3. The change of power loss value by adding
number of added capacitors
Figure 4. The improvement of voltage by number of
added capacitors
5. CONCLUSION
In this research, MSA is recommended for determining the position and sizing of capacitors in
the standard distribution system with 15 buses. Results from using MSA show that the power losses are
downed up 29.49 kW by adding capacitors at 2 buses, 31.46 kW by adding capacitors at 3 buses, 31.9 by
adding capacitors at 4 buses and 32.05 kW by adding capacitors at 5 buses. In addition, the voltage at buses
compared between uncompensated system and compensated system are also improved. Namely, the voltage
improvement is 0.0205 pu for case 1, 0.0252pu for case 2, 0.0253 pu for case 3 and 0.0254pu for case 4.
In result comparison with other methods, itindicates that MSA can reach better optimal solutions with less

 ISSN: 2088-8708
4520
power loss for all cases. From here, it is possible to infer that the method is an effective method for solving
OCLSD problem. In addition, MSA can be applied in future work for determining optimal parameters of
STATCOM with the purpose of voltage profile enhancement.
APPENDIX
Produce initial solution Xs
Set value to , , 1MI Gr Gr
Determine fitness function
for each solution
Fitness
Set 1CI
Sort solutions calculate 2, etermine 3Gr d Gr
Updating new solution 1 using Eq. (6)-(7)Gr
Select best solution in group 1 using Eq. (8)
Determind using Eq. (9)-(10)lightX
Updating new solution using Eq. (11)-(12)Gr
Determine bestX
Updating new solution 3 using Eq. (13)-(14)Gr
Determine fitness function for
new solutions in group 3
CI MI
Stop
1 CI CI
Yes
No
Figure 1. The flowchart of MSA
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