Available via license: CC BY-NC 4.0
Content may be subject to copyright.
Indonesian Journal of Electrical Engineering and Computer Science
Vol. 22, No. 3, June 2021, pp. 1739~1747
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v22.i3.pp1739-1747 1739
Journal homepage: http://ijeecs.iaescore.com
Chaotic theory incorporated with PSO algorithm for solving
optimal reactive power dispatch problem of power system
Shaima Hamdan Shri, Ayad Fadhil Mijbas
Department of Electrical Techniques, Technical Institute-Suwaira, Middle Technical University, Iraq
Article Info
ABSTRACT
Article history:
Received Oct 25, 2020
Revised May 3, 2021
Accepted May 19, 2021
In this paper, the chaotic particle swarm optimization (CPSO) algorithm is
combined with MATPOWER toolbox and used as an optimization tool for
attaining solving the optimal reactive power dispatch (RPD) problem, by
finding the optimal adjustment of reactive power control variables like a
voltage of generator buses (VG), capacitor banks (QC) and transformer taps
(Tap) while satisfying some of equality and inequality constraints at the same
time. CPSO and Simple PSO algorithms will be checked in a large system
such as IEEE node -118. CPSO and Simple PSO algorithms have been
implemented and simulated in the MATLAB program, version (R2013b/m-
file). Then compassion these results with the results obtained in the other
algorithms in the literature like the comprehensive learning particle swarm
optimization (CLPSO) algorithm. The simulation results confirm that the
CPSO algorithm has high efficiency and ability in terms of decrease real
power losses (), and improve voltage profile compared with the
obtained by using the simple (PSO) algorithm and (CLPSO) at light load.
Keywords:
CPSO
Optimal reactive power
dispatch
PSO
This is an open access article under the CC BY-SA license.
Corresponding Author:
Shaima Hamdan Shri
Department of Electrical Techniques
Technical Institute-Suwaira
Middle Technical University, Iraq
Email: shaima123@mtu.edu.iq
1. INTRODUCTION
Optimal reactive power dispatch (RPD) problem is considered as a complex, non-continous
problem. The power system involves of generation, transmission and distribution system to provide the
electric power to the consumers. It is an essential modern problem in the power system operating and control.
The objective of (RPD) problem is to find the best value of reactive power independent (control) variables so
as to minimize a certain objective function such as power loss and voltage deviation. The main goals in this
work are to get minimum power loss, and enhance voltage profile for the system and this goals can be
achieved through an optimal alteration of the reactive power control variables like, generator voltages value
(VG), the amount of (VAR) that injected from the capacitor banks (QC) and transformer taps (Tap) settings
while dealing with equality and inequality constrains at the same time [1]. The electrical loads are not
constant and vary from hour to hour. Any varying in power demands can lead to higher or lower voltages in
the system, so it must keep the reactive power devices like (viz. VG, Tap and QC) varying simultaneously
with the changing in the electric load and voltage [2]. Undeniably, over the last decades, RPD problem plays
a vital role in the power system operation and control and has recorded an ever-intense interest of the authors
because of remarkable and great effect on the economic, safe and security operation problem.
This problem is considered as a branch problem of the optimal power flow (OPF) calculation.
Carpentier was the first to introduce the model and concept of (OPF) in the early 1960s [3]. Then, many
ISSN: 2502-4752
Indonesian J Elec Eng & Comp Sci, Vol. 22, No. 3, June 2021 : 1739 - 1747
1740
researchers has been working on solving OPF problem by utilizing multi methods and like ant lion optimizer
(ALO) and integration of the invasive weed optimization (IWO) and Powell’s pattern search (PPS)
method [4], [5]. Ariantara et al. Using differential evolution (DE) Algorithm for the solution of OPF [6].
In the past, researchers were presented a lot of researches on (RPD) problem, and presented a
number of optimization algorithms. These algorithms are classified into two types: conventional optimization
algorithms and computational optimization algorithms. The concept of conventional algorithm is beginning
from an initial point. These algorithms contain interior point methods (IPM) [7], linear programing (LP) [8],
non-linear programming [9] and dynamic programming (DP) [10]. These algorithms have several
disadvantages such as unable to dealing with complex optimization problem, unable to dealing with problem
that include very large number of variables, huge calculations, big implementation time and convergence to
the nearby local optima. So, it becomes essential for finding and developing methods able to avoid these
disadvantages.
So, several optimization techniques have been presented in order to avoid these disadvantages of the
conventional optimization algorithms and these algorithms called computational optimization algorithms and
the basic concept of these algorithms are beginning from an initial solution swarm like, genetic algorithm
(GA) [11], gentoo penguin algorithm (GPA) [12], hybrid GA-IPM [13], meleagris gallopavo algorithm
(MGA) [14], chaotic predator-prey brain storm optimization (CPB) algorithm [15], Gravitational search
algorithm (GSA) and sine cosine algorithm (SCA) [16], enhanced fruit fly optimization algorithm (EFF) and
status of material algorithm (SMA) [17] and polar wolf optimization (PWO) algorithm [18] and particle
swarm optimization (PSO) [19], have been presented for the solution of RPD problem in the literature. From
all these algorithms, PSO shown great reliability to overcome the drawbacks of the conventional algorithms
and can easily be applied to multi problems, but it doesn't mean that PSO algorithm doesn't involve any
disadvantages. Therefore, in solving the non-continuous and complex problems this algorithm is declining to
the local minima at the premature convergence, on the other hand, also it depends on its parameter settings.
So, many researchers working for enhance PSO algorithm and prevent that disadvantages by using sundry
methods and techniques compact with PSO algorithm. Zhang et al. have proposed a two-phase HPSO
technique to solved the RPD problem [20]. Vlachogiannis et al. have applied (PSO, GPAC-PSO, and LPAC-
PSO) algorithms for reactive power and voltage control [21].
In the presented work, simple PSO has been developed to solve the RPD problem for minimizing
power losses and voltage profile enhancement. So as to enhance the searching quality of the simple PSO
algorithm and to avoid falling into the local minima and to decrease the calculation time, Chaotic PSO
(CPSO) is utilized so as to overcome these disadvantages. The chaos greatly helps the CPSO algorithm for
slip more easily from the local minima because of the special behavior, and strong ability for the chaotic
theory. Simple PSO and CPSO are applied for solving the RPD problem on IEEE Node-118 system, then the
simulation results were compared with other algorithm in the literature, like comprehensive learning particle
swarm optimization (CLPSO).
2. PROBLEM FORMULATION
In this section, the main goal in this study is to find the best combinations of reactive power
independent variables so as to decrease the power losses ( for the system while dealing with numbers of
equality and inequality constrains at the same time. So, the objective function in this work can be expressed
as shown in (1) [22], [23].
(1)
where, is the active power loss function. depict the number of branches. is the conductance of
branch. are the voltage magnitudes at node. , are the difference angles voltage at node
and. (i and j) are the sending and receiving nodes of branch K.
2.1. System constrains
Equality constrains are the load flow equation and defined [24]:
(2)
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752
Chaotic theory incorporated with PSO algorithm for solving optimal reactive … (Shaima Hamdan Shri)
1741
where are the real (MW) and reactive power (VAR) output from the generators at node. are
the real (MW) and reactive power (VAR) load demand at node. are the mutual and susceptance
conductance among node and node. depict the voltage angle magnitude in node and. Inequality
constrains involves independent (control) variables like, generator voltages (, injected reactive power
from capacitor ( and transformer positions ( [25]:
(3)
where depict the number of generator nodes. are the Minimum limit and maximum limit of
generator voltage magnitude at i-node. depict the total number of transformers. are the
Minimum limit and Maximum limit of transformer ratio at branch . depict the total number of injected
VAR source. , : are the Minimum limit and Maximum limit of injected VAR source from
shunt capacitor at node . And also involves dependent (state) variables such as voltage at load bus ( and
reactive power output from the generators ( [25]:
(4)
where, depict the number of generator nodes. are the minimum (lower) limit and maximum
(upper) limit of reactive power output of generator at node. depict the number of load nodes.
: are the Minimum (lower) limit and Maximum (upper) limit of voltage magnitude at i-node.
2.2. The generalized objective function
In this problem, the dependent variables can be added to (1) by utilizing penalty factors to constrain,
so (1) can be written as shown in (5) [25]:
(5)
where and are penalty terms; is the limit value of inequality constrains; is the total number of
load nodes; is the numbers of generation station and is given in (1).
2.3. Concept of average voltage
In this study, the new average voltage index is suggested to deal with all voltage nodes as well as
satisfy most of the electrical utility limits. The equation of this concept can be written as shown in (6):
(6)
where depict the average voltage of all system; depict the voltage in node i. depict the total number
of nodes.
3. OPTIMIZATION PROCESS
3.1. Simple PSO algorithm
PSO algorithm is a best type for artificial intelligence, which mimics the social behavior of the
animals which does not have any leader when searching for food like, bird flocking and fish schooling. It has
several advantages such as simple, fast, can applied for solving optimization problem and guarantees best
solution within lesser calculation time and the convergence characteristic have very stable than other
stochastic algorithms and capable of dealing with continuous and discrete variables and does not have
mutation and crossover operation like genetic algorithm. An individual represents the probable solution and
every group of individuals represents a swarm. This theory was first put forward in 1995 [26]. Each
individual has best position discover by the individual it self and it is stored in a memory called local best
position , and the best position discovered among all individuals in the swarm also stored in a
memory called global best position (, at every step the location of and are changing. Then,
ISSN: 2502-4752
Indonesian J Elec Eng & Comp Sci, Vol. 22, No. 3, June 2021 : 1739 - 1747
1742
the velocity and position of every individual in the swarm are changed by employing the calculation of the
present individual velocity and the location from position and position. The velocity and distance
from location and location of the agents will be changed by utilizing (7) and (8) [27].
=*[**(*()] (7)
(8)
where, is the inertia coefficient of PSO technique. represents the velocity of individual. are
the two learning factors that utilized to pull each agent to location and location within range
[]. , are the two random numbers within limit [0 to 1]. depicts the local best position.
represents the global best position. represents the position of the individual and is the
constriction factor and it is utilize to improve the performance of the simple PSO algorithm and it was
introduced by Shi indicate that using of this factor may be necessary and can be expressed [28].
(9)
A proper choice of the inertia weight () can achieve a balance between global location and local
location. So, in this work, was reduced linearly from (0.4-0.9) for each iteration (step) to search in a big
area at the start of the simulation and to attains balance between global position ( and local position
[28]:
(10)
where is the max (upper) value of weight. is the min (lower) value ofweight. is the current
iteration and is the max (upper) iteration.
3.2. CPSO algorithm
Despite the advantages of the simple PSO algorithm, but it has several limitations such as highly
depend on its parameter and decline to the local optimal at the premature convergence especially when the
problem is very complex.In this work, so as to prevent these limitations and to boost the quality and
performance, and the searching ability of the simple PSO algorithm, chaotic theory with Simple PSO are
merged to form a hybrid algorithm called the CPSO algorithm. and undeniably, this merge is a very helpful to
slip from the local optimal because of the special behavior and great ability of the chaotic CPSO algorithm [29].
In this work, the logistic map equation of the hybrid CPSO algorithm was described by the (11) [30].
(11)
Where, k is the number of the iteration (steps), and the control parameter µ was set within a range (0.0 to
4.0). The magnitude of µ decides whether β stabilizes at a constant area, oscillates within restricted limits, or
behaves chaotically in an unpredictable form. And (11) was shows chaotic dynamics when µ = 4.0 and β^1
{0,0.25,0.5,0.75,1}, it shows the sensitive depend on its initial conditions, which is the basic features of
chaotic. The new inertia weight factor (WCPSO) was calculated by multiplying the (WPSO) for (10) and logistic
map for (11) to form (12).
(12)
To enhance the behavior of the simple PSO, this work presents a novel velocity update by blending
inertia weight factor WPSO with the logistic map equation (β). Finally, by blending (12) with (7), the
following velocity changed equation to the proposed CPSO algorithm was obtained:
= **( **() (13)
In the CPSO algorithm, WCPSO was oscillates and decrease simultaneously from (0.9-0.4) for total iteration,
but in traditional PSO was decrease linearly. Table 1 shows a final choice of the control parameters CPSO
and simple PSO algorithms that is considered the optimal choice in this study.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752
Chaotic theory incorporated with PSO algorithm for solving optimal reactive … (Shaima Hamdan Shri)
1743
Table 1. Parameters used for CPSO and PSO algorithms
Parameters of CPSO and PSO algorithms
CPSO
PSO
n
100
100
c1
2
2
c2
2
2
r1
1
1
r2
1
1
wmax
0.9
0.9
wmin
0.4
0.4
µ
4
-
B1
0.75
-
maxiter
300
300
numbers of particles
100
100
4. CASE STUDY AND SIMULATION RESULTS
To verify and test the performance and ability for the proposed methods (i.e. simple PSO and
CPSO) for solving RPD problem in a complex power system, IEEE node-118 systems is employed. This
system is involve, 12 injected reactive power sources () from shunt capacitors, 186 branches, 54 generator
voltages ( and 9 transformer tap ratios () at branches 8, 32, 36, 51, 93, 95, 102, 107 and 127, the
limits of these variables are illustrated in Table 2. Branch, bus, generator, the upper and lower limits of the
reactive power in Mvar for the generators and other operating data are given in [31]. So, this system has 75
control (independent) variables as displayed given in Table 3 (see appendix), and at base case the initial
active and reactive power generations are =4374.86 Mw and =795.68 Mvar, the initial active and
reactive power loads are =4242.00 Mw and =1438.00 Mvar, the initial active and reactive power
losses are =132.86 Mw and =783.69 Mvar and they are 3 voltages outside the limits in the base
placed at bus 53, 76 and 118 and the value of these voltages in p.u are =0.946, =0.943 and
= 0.949. The simulation results are given in Table 3 (see appendix) for the goal of minimization of
for the system and according to these results, found the results that yielded from the CPSO algorithm are the
best for solving large power system compared to the results that obtained in the simple PSO and other
algorithms in the literature like comprehensive learning particle swarm optimization CLPSO [32] algorithms.
Figure 1 shows the comparison among the percentage reduction of power losses for the used algorithms, and
Figure 2 shows the comparison among the real power loss value () for the used algorithms. The
convergence characteristics of in MW for the simple PSO and CPSO algorithms are expose in Figures 3
and 4, and from these figures, it can be seen that CPSO algorithm performs best and reaching to the global
solution in less time than simple PSO for the solution of RPD problem. The voltage profile are given in
Figure 5 and from this figure it is clear that the voltage average at initial is about 0.986, at PSO is about
1.024, and at CPSO is about 1.045 and also all buses voltages are inside the limits after CPSO algorithm but
in the simple PSO algorithm and are still outside the limits. The power loss reduction () is
15.1% (from 132.8 Mw to 112.65 Mw) achieved by utilizing CPSO algorithm, which is consider the largest
reduction in than that accomplished in the simple PSO, CLPSO [32] algorithms.
Figure 1. Real power loss reduction in percentage
Figure 2. Comparison of real power loss ()
Table 2. Control variables limits
System Type
Variables
Min
Max
118 Bus
Generator voltage (
Transformer position ()
VAR source compensation ()
ISSN: 2502-4752
Indonesian J Elec Eng & Comp Sci, Vol. 22, No. 3, June 2021 : 1739 - 1747
1744
Figure 3. Convergence for 118 node power
system with simple PSO algorithm
Figure 4. Convergence for 118 node power
system with CPSO algorithm
Figure 5. Voltage profile of 118-node system
5. CONCLUSIONS
In this study, two types of algorithms are utilized they simple PSO and CPSO. The chaotic particle
swarm optimization algorithm is combined with MATPOWER toolbox and used as an optimization tool for
attaining solving the optimal reactive power dispatch problem. The objective function has been utilized to
decrease power loss in the power system branches and improve voltage profile. The efficiency and high
quality of CPSO algorithm have been proved by examining on IEEE Node-118 system. CPSO provided the
best technique to search for an optimal solution that decreased the calculation time and has high speed
convergence in both power loss minimization and voltage profile improvement compared with the results
obtained from using simple PSO and other results reported in the literature like comprehensive learning
particle swarm optimization algorithm. Where, a percentage reduction in power loss be (15.1%) for CPSO,
(10.1%) for PSO, and (1.3%) for CLPSO.
6. SUGGESTIONS FOR FUTURE WORK
In the future, the research can be developed by optimizing total voltage deviation (TVD) and voltage
stability index (VSI) separately as a single objective function or as multi-objective functions in order to
achieve more improvement in the RPC problem.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752
Chaotic theory incorporated with PSO algorithm for solving optimal reactive … (Shaima Hamdan Shri)
1745
APPENDIX Table 3. Simulation result of IEEE- 118 node systems
Control Variables
Base Case
CPSO
PSO
CLPSO [32]
1
0.955
1.028
1.019
1.033
4
0.998
1.048
1.038
1.055
6
0.990
1.036
1.044
0.975
8
1.015
1.047
1.039
0.966
10
1.050
1.099
1.040
0.981
12
0.990
1.033
1.029
1.009
15
0.970
1.026
1.020
0.978
18
0.973
1.034
1.016
1.079
19
0.962
1.028
1.015
1.080
24
0.992
1.047
1.033
1.028
25
1.050
1.075
1.059
1.030
26
1.015
1.091
1.049
0.987
27
0.968
1.027
1.021
1.015
31
0.967
1.012
1.012
0.961
32
0.963
1.021
1.018
0.985
34
0.984
1.047
1.023
1.015
36
0.980
1.046
1.014
1.084
40
0.970
1.024
1.015
0.983
42
0.985
1.029
1.015
1.051
46
1.005
1.054
1.017
0.975
49
1.025
1.069
1.030
0.983
54
0.955
1.033
1.020
0.963
55
0.952
1.030
1.017
0.971
56
0.954
1.032
1.018
1.025
59
0.985
1.062
1.042
1.000
61
0.995
1.077
1.029
1.077
62
0.998
1.072
1.029
1.048
65
1.005
1.096
1.042
0.968
66
1.050
1.051
1.054
0.964
69
1.035
1.078
1.058
0.957
70
0.984
1.043
1.031
0.976
72
0.980
1.040
1.039
1.024
73
0.991
1.039
1.015
0.965
74
0.958
1.028
1.029
1.073
76
0.943
1.026
1.021
1.030
77
1.006
1.053
1.026
1.027
80
1.040
1.067
1.038
0.985
85
0.985
1.062
1.024
0.983
87
1.015
1.025
1.022
1.088
89
1.000
1.083
1.061
0.989
107
0.952
1.024
1.008
0.976
110
0.973
1.041
1.028
1.041
111
0.980
1.049
1.039
0.979
112
0.975
1.023
1.019
0.976
113
0.993
1.039
1.027
0.972
116
1.005
1.080
1.031
1.033
48
0.150
0.047
0.056
0.028
74
0.120
0.112
0.120
0.005
79
0.200
0.150
0.140
0. 148
82
0.200
0.190
0.180
0.194
83
0.100
0.163
0.166
0.069
105
0.200
0.026
0.190
0.090
107
0.060
0.077
0.129
0.049
110
0.060
0.137
0.014
0.022
(MW)
4374.8
4354.7
4361.4
NR*
(Mvar)
795.68
535.56
653.58
NR*
Reduction in (%)
0
15.1
10.1
1.3
(Mw) Total
132.8
112.65
119.34
130.96
NR*: means that the value was not reported.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the Electrical Techniques Department, Al Suwaira
Technical Institute, Middle Technical University for their encouragement and support.
ISSN: 2502-4752
Indonesian J Elec Eng & Comp Sci, Vol. 22, No. 3, June 2021 : 1739 - 1747
1746
REFERENCES
[1] H. Khazali, et al., "Optimal reactive power dispatch based on harmony search algorithm," International Journal of
Electrical Power & Energy Systems, vol. 33, pp. 684-692, 2011, doi: 10.1016/j.ijepes.2010.11.018.
[2] K. R. C. Mamandur, et al., “Optimal control of reactive power flow for improvements in voltage profilesand for
real power loss minimization," IEEE Trans Power Apparat Syst, vol. PAS-100, pp. 3185-3194, 1981, doi:
10.1109/TPAS.1981.316646.
[3] X. He, et al., "Fuzzy Multiobjective Optimal Power Flow Based on Modified Artificial Bee Colony Algorithm,"
Mathematical Problems in Engineering, vol. 2014, pp. 1-12, 2014, doi: 10.1155/2014/961069.
[4] R. Kouadri, et al., "Optimal Power Flow Solution for Wind Integrated Power in presence of VSC-HVDC Using
Ant Lion Optimization," Indonesian Journal of Electrical Engineering and Computer Science (IJEECS), vol .12,
no. 2, pp. 625-633, 2018, doi: 10.11591/ijeecs.v12.i2.pp625-633.
[5] M. Kaur, et al., "An integrated optimization technique for optimal power flow solution," Soft Computing, vol. 24,
pp. 10865-10882, 2020, doi: 10.1007/s00500-019-04590-3.
[6] H. Ariantara, et al., "The Solution for optimal power flow (OPF) Method Using Differential Evolution Algorithm,"
IJITEE (International Journal of Information Technology and Electrical Engineering), vol .1, no. 1, pp. 19-24,
2017, doi: 10.22146/ijitee.25141.
[7] S. Granville, et al., "Optimal reactive dispatch through interior point methods,” IEEE Trans. Power Syst., vol. 9,
no. 1, pp. 136-146, Feb. 1994, doi: 10.1109/59.317548.
[8] R. Hooshmand, et al., "Application of artificial neural networks in controlling voltage and reactive power,” Scientia
Iranica, vol. 12, no. 1, pp. 99-108, 2005.
[9] D. Pudjianto, et al., "Allocation of VAR support using LP and NLP based optimal power flows,” IEE Proc. Gen.
Trans. Dist., vol. 149, no. 4, 2002, pp. 377-383, doi: 10.1049/ip-gtd:20020200.
[10] F.C. Lu, et al., “Reactive power/voltage control in a distribution substation using dynamic programming,” IEEE
Proc. Gen. Trans. Distrib. vol. 142, 1995, pp. 639-645, doi: 10.1049/ip-gtd:19952210.
[11] Ghasempour, et al., “A new genetic based algorithm for channel assignment problem,” Computational Intelligence,
Theory and Applications, Ed. B. Reusch, Berlin: Springer, pp. 85-91, 2006, doi: 10.1007/3-540-34783-6_10.
[12] K. Lenin, “Diminution of real power loss by novel gentoo penguin algorithm," International Journal of Informatics
and Communication Technology (IJ-ICT), vol. 9, no. 3, pp. 150-156, 2020, doi: 10.11591/ijict.v9i3.pp151-156.
[13] W. Yan, et al., "A hybrid genetic algorithm-interior point method for optimal reactive power flow," IEEE Trans.
Power Syst., vol. 21, pp. 1163-1168, 2006, doi: 10.1109/TPWRS.2006.879262.
[14] K. Lenin, "Meleagris Gallopavo Algorithm for Solving Optimal Reactive Power Problem," International Journal of
Applied Power Engineering (IJAPE), vol. 7, no. 2, pp. 99-110, 2018, doi: 10.11591/ijape.v7.i2.pp99-110.
[15] K. Lenin, “Power loss reduction by chaotic based predator-prey brain storm optimization algorithm," International
Journal of Applied Power Engineering (IJAPE), vol. 9, no. 3, pp. 218-222, 2020, doi: 10.11591/ijape.v9.i3.pp218-
222.
[16] M. S. Ghayad, et al., "Reactive power control to enhance the VSC-HVDC system performance under faulty and
normal conditions," International Journal of Applied Power Engineering (IJAPE), vol. 8, no. 2, pp. 145-158, 2019,
doi: 10.11591/ijape.v8.i2.pp145-158.
[17] K. Lenin, "Solving optimal reactive power problem by enhanced fruit fly optimization algorithm and status of
material algorithm," International Journal of Applied Power Engineering (IJAPE), vol. 9, no. 2, pp. 100-106, 2020,
doi: 10.11591/ijape.v9.i2.pp100-106.
[18] K. Lenin, "Polar wolf optimization algorithm for solving optimal reactive power problem," International Journal of
Applied Power Engineering (IJAPE), vol. 9, no. 2, pp. 107-112, 2020, doi: 10.11591/ijape.v9.i2.pp107-112.
[19] H. Yoshida, et al., “A particle swarm optimization for reactive power and voltage control considering voltage
security assessment," IEEE Trans. Power Syst., vol. 15, pp. 1232-1239, 2000, doi: 10.1109/59.898095.
[20] J. Zhang, et al., “JADE: adaptive differential evolution with optionalexternal archive,” IEEE Trans. Evolut.
Comput., “vol. 13, pp. 945-958, 2009, doi: 10.1109/TEVC.2009.2014613.
[21] J. G. Vlachogiannis, et al., “A comparative study on particle swarm optimization for optimal steady-state
performance of power systems," IEEE Trans. Power Syst., vol. 21 pp. 1718-1728, 2006,
doi: 10.1109/TPWRS.2006.883687.
[22] M. Ghasemi, et al., “A new hybrid algorithm for optimal reactive power dispatch problem with discrete and
continuous control variables," Appl Soft Comput., vol. 22, pp. 126-140, 2014, doi: 10.1016/j.asoc.2014.05.006.
[23] K. Lenin, “Power loss reduction by gryllidae optimization algorithm," International Journal of Informatics and
Communication Technology (IJ-ICT), vol. 9, no. 3, pp. 179-184, 2020, doi: 10.11591/ijict.v9i3.pp179-184.
[24] M. Abdillah, et al., "Improvement of voltage profile for large scale power system using soft computing approach,"
TELKOMNIKA Telecommunication Computing Electronics and Control, vol. 18, no. 1, pp. 376-384, 2020,
doi: 10.12928/telkomnika.v18i1.13379.
[25] Rajan, et al., "Optimal reactive power dispatch using hybrid Nelder–Mead simplex based firefly algorithm," Int J
Elec Pwr Energy Syst, vol. 66, pp. 9-24, 2015, doi: 10.1016/j.ijepes.2014.10.041.
[26] R. Syahputra, I. Robandi, M. Ashari, "Reconfiguration of Distribution Network with Distributed Energy Resources
Integration Using PSO Algorithm," TELKOMNIKA (Telecommunication, Computing, Electronics and Control),
vol. 13, no. 3, pp. 759-766, 2015, doi: 10.12928/telkomnika.v13i3.1790.
[27] M. Damdar, et al., “Capacitor Placement Using Fuzzy And Particle Swarm Optimization Method For Maximum
Annual Savings,” ARPN Journal of Engineering and Applied Sciences, vol. 3, no. 3, pp. 25-30, June 2008.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752
Chaotic theory incorporated with PSO algorithm for solving optimal reactive … (Shaima Hamdan Shri)
1747
[28] R. C. Eberhart, et al., “Comparing inertia weights and constriction factors in particle swarm optimization,” In
Proceedings of the Congress on Evolutionary Computation, (CEC00), July 16-19, 2000, La Jolla, CA, USA, 2000,
pp. 84-88, doi: 10.1109/CEC.2000.870279.
[29] F. Mijbas, et al., "Optimal Stabilizer PID Parameters Tuned by Chaotic Particle Swarm Optimization for Damping
low frequency oscillations (LFO) for Single Machine Infinite Bus system (SMIB)," Journal of Electrical
Engineering & Technology, vol. 15, pp. 1577-1584,2020, doi: 10.1007/s42835-020-00442-5.
[30] D. Yang, et al., “On the efficiency of chaos optimization algorithms for global optimization,” Chaos, Solitons &
Fractals., vol. 34, no. 4, pp. 1366-75, 2007, doi: 10.1016/j.chaos.2006.04.057.
[31] The IEEE 118-Bus Test System [online]. Available at:
http://www.ee.washington.edu/research/pstca/pf118/pg_tca118bus.htm
[32] K. Mahadevan, et al., "Comprehensive learning particle swarm optimization for reactive power dispatch," Appl.
Soft Comput, vol. 10, pp. 641-652, 2010, doi: 10.1016/j.asoc.2009.08.038.
BIOGRAPHIES OF AUTHORS
Shaima Hamdan Shri, received the four-year B.Sc. degreein Electrical Power Engineering
Technics in 2013 from Electrical Engineering Technical College, Middle Technical University,
Iraq. In 2018, she concluded a Master in Electrical Power Engineering Technics from
Electrical Engineering Technical College, Middle Technical University, Iraq. Now an
Assistant Lecturer at Department of Electrical Techniques, Technical Institute-Suwaira,
Middle Technical University. Her main research interests include: Power System Stability and
Optimization, Optimal Power Flow, Control of Renewable Energy Systems.
Ayad Fadhil Mijbas, received the five-year B.Sc. degree in Electrical Engineering Science in
1993 from Al-Technology University, Iraq. In 2004, he concluded a Master in Electrical
Engineering Science/Control from Al-Technology University, Iraq. From 2006-2010 he has
been as a head of Electrical debarment and lecturer in Foundation of Technical
Education/Middle Technical University, Iraq. His main research interests include Electrical
control system.
