Artificial bee colony algorithm applied to optimal power flow solution incorporating stochastic wind power

International Journal of Power Electronics and Drive Systems (IJPEDS)
Vol. 12, No. 3, September 2021, pp. 1890~1899
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v12.i3.pp1890-1899  1890
Journal homepage: http://ijpeds.iaescore.com
Artificial bee colony algorithm applied to optimal power flow
solution incorporating stochastic wind power
Vian H. Ahgajan1
, Yasir G. Rashid2
, Firas M. Tuaimah3
1,2
Department of Electronic Engineering, College of Engineering, University of Diyala, 32001 Diyala, Iraq
3
Department of Electrical Engineering, College of Engineering, University of Baghdad, Baghdad, Iraq
Article Info ABSTRACT
Article history:
Received Oct 28, 2020
Revised Jun 27, 2021
Accepted Jul 7, 2021
This paper focuses on the artificial bee colony (ABC) algorithm, which is a
nonlinear optimization problem. is proposed to find the optimal power flow
(OPF). To solve this problem, we will apply the ABC algorithm to a power
system incorporating wind power. The proposed approach is applied on a
standard IEEE-30 system with wind farms located on different buses and
with different penetration levels to show the impact of wind farms on the
system in order to obtain the optimal settings of control variables of the OPF
problem. Based on technical results obtained, the ABC algorithm is shown to
achieve a lower cost and losses than the other methods applied, while
incorporating wind power into the system, high performance would be
gained.
Keywords:
Artificial bee colony
Optimal power flow
Production cost
Voltage profile
Wind power This is an open access article under the CC BY-SA license.
Corresponding Author:
Yasir G. Rashid
Department of Electronic Engineering
College of Engineering, University of Diyala
Baqubah, Diyala, Iraq
Email: yasserghazee_enge@uodiyala.edu.iq
1. INTRODUCTION
The majority of the world's fossil-fuel power generation operations use coal and natural gas to
generate electricity, which is one of the most expensive commodities used to generate electric power.
Polluting emissions from electricity generation based on the combustion of fossil fuels account for a sizable
portion of global greenhouse gas emissions [1], [2]. As a result of economic and environmental reasons,
workers in the field of electric energy were encouraged to increase and develop renewable energy. The
electrical power control are experiencing noteworthy changes due to an increase in wind energy penetration
level, causing unused challenges to system operation and planning [3], [4]. Therefore, the operators of power
systems both in the planning and operating stage are very interested in optimal power flow (OPF) [5]. The
main objective of an optimal power flow methodology is to find the ideal working of a power system by
optimizing a specific objective whereas fulfilling certain indicated physical and security limitations [6], [7].
In recent years, the rapid development of computational intelligence have motivated researchers in
the field of optimization algorithms to resolve various complex optimization cases such as particle swarm
optimization algorithm (PSO) [8], [9], improved colliding bodies optimization method [10], imperialist
competitive method [11], black-hole-based optimization technique [12], differential evolutionary technique
[13], hybrid algorithm of PSO and GSA algorithms [14], gravitational search method (GSM) [15], [16],
improved PSO algorithm [17], biogeography-based optimization technique [18], chaotic self-adaptive
differential harmony search method [19], grey wolf optimizer [20], fuzzy-based hybrid PSO algorithm [21],
differential search technique [22], multiphase search optimization technique [23], harmony search technique

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Artificial bee colony algorithm applied to optimal power flow solution … (Vian H. Ahgajan)
1891
[24], Jaya optimization technique [25], artificial bee colony (ABC) algorithm [26], differential evolution
(DE) [27], biogeography-based optimization (BBO) [28], teaching-learning-optimization algorithm [29], and
the firefly algorithm (FA) [30]. This paper was motivated by two factors. First, the application of the artificial
bee colony algorithm to solve the optimum power flow problem has been studied. Second, solving OPF
considering wind power penetration of different sites (single & multiple) and studying the impact of the wind
power penetration on the slack bus generation, the total production cost, active power losses and voltage
deviation.
2. OPF PROBLEM FORMULATION
The solution to the OPF problem involves the optimization of objective function and obtaining the
optimal settings of the power system control variables. The formal OPF problem can be written as [31]:
(1)
Subject to
(2)
(3)
Where F refers to the target (objective) function to be minimized, x and u are state and control variables
respectively. The state vector x including; i) PG1, generating power at swing (slack) bus, ii) QG, reactive
generating power outputs, and iii) VL, load bus voltage. x can be written as:
(4)
Where NG, NL, NTL and SL are the number of generator buses, number of load buses, transmission lines
and number of transmission line loading, respectively. The control vector u including; i) PG, generator active
power outputs, ii) VG, generator voltages, iii) QC, shunt VAR compensations, and iv) T transformer tap
settings. u can be written as:
(5)
Where NC and NT are the shunt VAR compensators output and the transformers regulated number,
respectively [31].
2.1. OPF objective functions
Two different objective functions are chosen in the current paper. The 1st
is the economic objective
whereas the 2nd
is the technical objective.
2.1.1. Economic objective
The main objective of the optimization problem is minimizing the operating costs in the wind-thermal
power system.
a. Cost model of thermal power generators
Consider as a generator fuel cost, given as in (6) [25], [32]:
∑ (6)
Where , , cost coefficients of fuel generators , N number of generation units, active power
generation of generators .
b. Cost model of wind power turbines
The goal of the current paper's optimization problem is to minimize the overestimated and
underestimated costs of wind energy caused by wind speed uncertainty. According to:
∑ (7)

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 12, No. 3, September 2021 : 1890 – 1899
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Where is underestimation scaled average cost for wind power in $/MW h, is
directly cost output wind power and is overestimation scaled average cost for wind power in
MW. be written as:
∑ (8)
Where wj is active power generated by jth wind turbine and qj is direct cost coefficient.
∑ (9)
E(Y_(oe.j)) can be written as:
= + + ( + wj )
+ ( ) ( 1 + , ( ) ( 1 + , ( )
(10)
and
∑ (11)
E(Y_(ue.j)) can be written as:
= ( + wj )
+ ( ) ( 1 + , ( ) ( 1 + , ( )
(12)
Where Cpwj and Crwj are the overestimation and underestimation cost coefficient of jth wind
generator in $/MW h respectively. ( ) and are the overestimation and underestimation
anticipated value of wind power for jth wind turbine. kj and cj are a shape factor and a scale of the jth wind
generator respectively estimating of wind speed in the Weibull probability density function (pdf). vinj, vout,I,
vr,j are cut-in, cut-out and rated wind speed respectively. v1 = vin + (vr − vin) w1/wr is an intermediary
parameter in [6]. Minimize the total production cost in wind-thermal power system can be expressed as [33]:
(13)
2.1.2. Technical objective
In this paper, two objective functions are considered for the technical category. First, minimize the
total active power losses which can be expressed as:
∑ ( ) (14)
Where m is the total number of lines in the system, Gk is the conductance of the kth line, Vj and Vi are the
voltage magnitude at bus j and bus i respectively, δj and δi are the voltage phase angle at bus j and i
respectively [34]. Second, minimize the voltage deviation (VD) of all load buses to improve the voltage
profile on load buses. The voltage deviation given by (15) [35]:
∑ (15)
3. OVERVIEW ON ARTIFICIAL BEE COLONY ALGORITHM
In 2005, Dervis Karaboga proposed a new optimization technique that is the artificial bee colony
(ABC) algorithm. The ABC algorithm has been shaped by closely watching the exercises and actions of
genuine bees while they were looking for nectar assets and sharing the sum of the assets with other colony

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members. The colony of artificial bees consists of three main groups, which are the employed bees, onlooker
bees and scout bees. This breed of bee features a distinctive part within the optimization preparation. The
employed bee can remember the location of the extra nectar as well as it chooses the best of the others to
drink from, while the onlooker bees use what the employed bees have collected to come up with a solution
for what nectar they can't remember. For an optimization problem, an algorithm consists of three steps is as
follows: In the first step, the employed bees are dispatched to find all the resources needed, and then the
nectar amount is calculated. Step two, the onlooker bees choose an asset that matches the information from
the already-discovered honeydew assets. The employed bumblebee was sent out to the fields to select new
locations in order to identify potential food sources. "Looking" bees would be further broken into two
categories: the "used" bees and the "observing" bees. The algorithm works on the basis that the number of
employable bees equals the number of available sources of nectar. When we understand where the issues
likely lie, we'll be better equipped to deal with them [36].
ABC algorithm:
a) Initialization phase
In the first step, variables ( = 1, 2, 3, … ) that have not been measured yet are selected at random,
using some sort of random methodology.
b) Employed bee phase
The new sources are identified by each employed bee whose amounts are equal to the half of the total
sources. a new source can be found by:
(16)
Where j is a randomly selected parameter index, is a random number between [0, 1] and it has to be
different from , is a random number within the range [-1, 1], is the current position of food source
which comparing two food postion visually by bee from this parameter the production of the neighbor
food source can be controlled. The new food source postion is produced and evaluated by the artificial
bee,by comparing the current food source with previous source taking its performance in the consider.
From the information that obtained if the new source has equal or better amount of food or nectar than the
old source,it used to replace the old source in the memory. Otherwise, the old source would be retained in
memory.
c) Onlooker bee phase
In this phase ,the onlooker bees are work on the principle of probability by selecting the food source with
probability can be written as:
=
∑
(17)
Where and are the fitness value and probability associated with solution respectively. In each
colony, great responsibility for random research is scout bees’ bear.
d) Scout bee phase
In this stage, the scout bee randomly investigates food sources without direction from the queen. Every
scout in the swarm thinks that he or she is an explorer. If the supply of food decreases below the gainful
level or as a result of applying a given level of the food application of the nectar, the bees associated with
it cease feeding. When you have new information, a new understanding, or a new insight, the limit on the
number of bees tells you how many from the source and how many to the destination.
(18)
Where and are the maximum and minimum limits for optimization parameter, rand (0, 1) is
a random number within the range [0, 1]. The number of iterations in ABC algorithm considered as the
important criterion for stopping an ABC algorithm.
An optimization algorithm might therefore determine that the stopping criteria to be:
1. Number of maximum iterations
2. Maximum error between two consecutive iterations
Figure 1 shown the flowchart of the ABC algorithm based OPF problem.

 ISSN: 2088-8694
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Figure 1. The flowchart of ABC based on OPF problem [37]
4. CASE STUDY
In this paper, two wind farms connecting to bus 10 and bus 24 are suggested. Figure 2 shown the
standard IEEE 30 system with two wind farms. The wind power penetration level is defined as the ratio of
the installed wind power capacity to the total-installed system generation capacity of 10%. The total power
generation of six thermal generating in system are around 400MW, therefore the installed wind power
capacity is 40 MW. Two wind farms included 10 wind turbines each one has rating 2 MW (Vestas V90, 2
MW) and connected at bus 10 and bus 24 (20 MW in each bus) is used to analyse the impact of incorporating
wind farm on different performance analysis of system. Several scenarios with dispersed wind penetration
levels from 0% to 100% have been investigated.
Figure 2. Single-line diagram of the IEEE 30-bus system including two wind farms at bus10 & bus 24

1895
4.1. OPF without incorporating wind power
In this case, they used the artificial bee colony (ABC) algorithm to find a solution for OPF that did
not include a wind farm. The power generation in thermal generator, active power loss and total production
cost obtained by ABC algorithm is compared with other methods obtained in the [34]. Table 1 shows the
results of this comparison. An 800.638 $/hr total production cost has been obtained by ABC, which is better
than linear programming (LP) in [34].
Table 1. Comparison of ABC with LP for IEEE 30-bus system
Variable ABC LP [33]
Pg1(MW) 177.05 195.6439
Pg2(MW) 49.76 43.8668
Pg5(MW) 21.38 21.4574
Pg8(MW) 20.76 10.5771
Pg11(MW) 11.63 10.0866
Pg13(MW) 12 12.0000
Power Loss (MW) 8.9246 10.31
Production cost ($/hr) 800.6380 803.26
4.2. OPF incorporating single wind farm site
In this case, the wind farm is incorporated on bus 10 and bus 24 separately (20 MW in each bus), for
penetration levels from 25% to 100% with an interval of 25. The comparison results between ABC and the
results obtained in the [34] for slack bus generation, total production cost, active power losses and voltage
deviation are shown in Table 2. Figure 3 shows the load bus voltage profiles and Figure 4 shows the
convergence characteristic of total production cost for this case when the wind farm is incorporated at bus 10.
Table 2. Comparison of ABC with LP when wind farm with different wind power penetration levels
connected to system
Wind
penetration
Bus no. ABC LP [33]
slack bus Cost($hr) Losses
(MW)
VD
(p.u.)
(MW)
VD
(p.u.)
0% 10 177.05 800.638 8.9246 0.8977 176 802.46 10.31 0.8513
25% 171.38 783.142 9.152 0.604 175 791.03 9.12 0.594
50% 166.01 765.221 8.246 0.920 171 776.83 9.05 0.900
75% 160.65 747.941 7.888 0.931 166 764.63 8.79 0.912
100% 155.31 730.943 7.550 0.941 160 753.42 8.27 0.930
0% 24 177.05 800.638 8.9246 0.8977 176 802.46 10.31 0.8513
25% 171.28 782.447 8.522 0.924 177 790.89 9.03 0.900
50% 165.83 764.657 8.072 0.948 172 776 8.85 0.915
75% 160.43 746.814 7.674 0.972 168 764.63 8.34 0.960
100% 155.09 730.234 7.326 0.993 163 753.42 7.96 0.984
Figure 3. Load bus voltage profile 30-bus IEEE system
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
2 3 4 6 7 9 10 12 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Bus No.
without WF bus 10

 ISSN: 2088-8694
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Figure 4. Convergence characteristics of the ABC for penetration levels of wind power at bus 10 only
4.3. OPF incorporating multiple wind farm
This case shows the impact of incorporating a wind farm connected to bus 10 and bus 24 together
(20 MW in each bus). For penetration levels from 25% to 100% with an interval of 25%. Table 3 shows the
slack bus generation, the total production cost, active power losses and voltage deviation. Figure 5 shows the
load bus voltage profiles and Figure 6 shows the convergence characteristic of total production cost for this case.
Table 3. Comparison of ABC with LP when wind farm with different wind power penetration levels
connected to system
Wind
penetration
Bus no. ABC LP [ 33]
slack
bus
Cost($hr) Losses
(MW)
VD
(p.u.)
(MW)
VD
(p.u.)
0% 10
&
24
177.05 800.6380 8.9246 0.8977 176 802.46 10.31 0.8513
25% 165.90 764.670 8.614 0.639 170 758.89 9.03 0.602
50% 155.12 730.526 8.502 0.643 159 736.91 8.85 0.609
75% 144.44 694.795 7.599 0.905 148 701.78 8.34 0.885
100% 133.86 661.621 7.565 0.813 138 680.59 7.96 0.803
Total
production
cost
($/h)
Iterations
Total
production
cost
($/h)
Total
production
cost
($/h)
Total
production
cost
($/h)
Iterations
Iterations Iterations

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Figure 5. Load bus voltage profile 30-bus IEEE test system
Figure 6. Convergence characteristics of the ABC for penetration levels of wind power on bus 10 &
24 together
5. CONCLUSION
This paper proposes the application of artificial bee colony (ABC) algorithm optimal power flow for
a system that incorporates thermal units and wind farms during normal operation. The performance of the
ABC was applied to standard IEEE-30 bus system with and without incorporating wind farm to show its
impact on the the slack bus generation, the total production cost, active power losses and voltage deviation,
and compared its simulation results with another method. Based on technical results obtained are it can be
noticed that the ABC high performance than the rest methods, and concluded that an optimal integration and
location of wind farms give significant to system, such as reducing in the total production cost, active power
losses and improvement in the load bus voltage profile, while high performance can be noticed when a wind
farm site on bus 24 rather than its site on bus 10. Finally, the results are exceptionally much promising.
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
2 3 4 6 7 9 10121415161718192021222324252627282930
Bus No.
without WF bus 10& 24
Total
production
cost
($/h)
Total
production
cost
($/h)
Total
production
cost
($/h)
Iterations
Total
production
cost
($/h)
Iterations
Iterations Iterations

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