.


UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1 11

1. INTRODUCTION

The power flow analysis is one of  the important and 
extensively used studies in electrical power system 
engineering. It is considered a fundamental tool for many 
other power system studies such as stability, reliability, fault, 
and contingency study. The main objective of  a power flow 
study is to find the bus voltages and the power flow in the 
transmission system for a particular loading condition. The 
steady-state performance of  an electrical power system is 
described by a system of  non-linear algebraic equations. 
These equations represent the active and reactive power 
balance. The inherent difficulty of  the power flow problem 
is the task of  obtaining analytical solutions to the power 
flow equations. An extensive research has been carried 
out since the latter half  of  the twentieth century [1], [2] to 

solve this problem. The solution of  power flow problem 
has been based on numerical technique methods such as 
Gauss-Seidel [3], Newton-Raphson method [4]-[14], and 
fast-decoupled method [15]-[18]. Although some of  these 
methods are widely used in power utilities, they are sensitive 
to the starting (guess) values. In some cases, especially in 
heavily loaded conditions, they fail to converge. It was 
found that the factors affecting the convergence of  the 
previous methods are the R/X ratio of  the transmission 
systems and the singularity of  the Jacobian matrix for a 
heavily loaded system. Different attempts have been done 
to improve the reliability of  these methods [19], [20]. 
Artificial intelligence techniques had been applied to 
power flow study [21]-[23]. Recently, the fields of  swarm 
intelligence have attracted many researches as a branch 
of  artificial intelligence that deals with the collective 
behavior of  swarms such as flocks of  bird, colonies of  
aunts, schools of  fish, and swarm of  bees [24], [25]. 
The important features of  swarm intelligence are self-
organization, scalability, adaptation, and speed. The swarm 
intelligence techniques have been applied in many power 
system studies [26]-[28]. In this paper, the load flow 
problem is approached as an optimization problem using 

Application of Artificial Bee Colony Algorithm in 
Power Flow Studies
Kassim Al-Anbarri and Husham Moaied Naief
Department of Electrical Engineering, Faculty of Engineering, Mustansiriyah University, Bab Al-Muadham Campus, 
46049 Baghdad, Iraq

A B S T R A C T
Artificial bee colony (ABC) algorithm is one of the important artificial techniques in solving general-purpose optimization 
problems. This paper presents the application of ABC in computing the power flow solution of an electric power system. 
The objective function to be minimized is the active and reactive power mismatch at each bus. The proposed algorithm 
has been applied on typical power systems. The results obtained are compared with those obtained by the conventional 
method. The results obtained reveal that the ABC algorithm is very effective for solving the power flow problem in the 
maximum loadability region.

Index Terms: Artificial Bee Colony, Maximum Loadability, Power Flow, Swarm Artificial Technique

Corresponding author’s e-mail: alanbarri@yahoo.com

Received: 10-03-2017 Accepted: 25-03-2017 Published: 12-04-2017

Access this article online

DOI: 10.21928/uhdjst.v1n1y2017.pp11-16 E-ISSN: 2521-4217
P-ISSN: 2521-4209

Copyright © 2017 Al-Anbarri and Naief. This is an open access article 
distributed under the Creative Commons Attribution Non-Commercial 
No Derivatives License 4.0 (CC BY-NC-ND 4.0)

O R I G I N A L  RE SE A RC H  A RT I C L E UHD JOURNAL OF SCIENCE AND TECHNOLOGY



Kassim Al-Anbarri and Husham Moaied Naief: Application of Artificial Bee Colony Algorithm in Power Flow Studies

12 UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1

swarm intelligence. The objective function is to minimize 
the power mismatch. This paper is organized as follows: 
Section 2 reviews the Newton-Raphson (NR) technique in 
solving load flow problem. The basics model of  artificial 
bee colony (ABC) is presented in section 3. Section 4 
discusses the results obtained by applying the proposed 
algorithms on a typical system. Finally, section 5 presents 
the conclusion.

2. POWER FLOW FORMULATION

For N bus electrical power system, the bus power Si can be 
expressed by the following equation:

Si=SGi−SDi

Si=PGi−PDi+j(QGi−QDi) (1)

Where PGi is the active power generation at bus i

PDi is the active power demand at bus i

QGi is the reactive power generation at bus i

QDi is the reactive power demand at bus i

The current balance equation at bus i
*

*
1

N
i

i ik k
i k

S
I Y V

V =
= =∑

 
(2)

Where Yik is the i, k
th element of  bus admittance matrix

Vk is the bus voltage at bus k.

By substituting (1) into the (2) and resolved the resulting 
equation into the following two real equations:

( )k i k
1

cos
N

k i ki
i

P V V Y
=

γ= + −∑ ki δ δ
 

(3)

( )k i k
1

sin
N

k i ki
i

Q V V Y
=

γ= + −∑ ki δ δ
 

(4)

For N bus power system, there are 2N real non-linear 
algebraic equations similar to (3) and (4). These equations 
are non-linear function of  the state variables (|V|,δ). The 
conventional technique to solve these equations is using a 
numerical technique. The most widely used method is NR 
method. This method is based on expanding the above 
equations by Taylor series. The compact linearized form of  
the above equations is as follows:

i

i|V|
P P|V|i

Q Q|V|i

J JP
J JQ

∆ ∆δ    
=     ∆ ∆    

δ

δ  
(5)

Where the left-hand side of  (5) is the vector of  power 
mismatch, which can be calculated as:

sp cal
i i i

sp cal
i i i

P P P
Q Q Q

 ∆ − 
=   ∆ −      

(6)

The traditional algorithm for obtaining power flow solution 
is as follows:
1. Assume a guess values for the state variables (flat start 

|V|=1.0 pu; δ=0)
2. Evaluate the vector of  power mismatch and the elements 

of  the Jacobian matrix
3. Calculate the vector of  state variable disturbance
4. Update the state variables at the end of  iteration
5. Check the absolute value of  the elements of  the 

vector of  power mismatch, if  it is less than a specified 
tolerance; calculate the line flow in each transmission 
line. Otherwise, go to step 2.

The previous algorithm works reliably in ordinary loading 
conditions. Unfortunately, it is found in some cases 
(e.g., heavily loaded conditions and high R/X ratio system) 
that the above algorithm fails to converge. This is because of  
singularity of  the Jacobian matrix. For this purposes, a swarm 
intelligence technique is presented to avoid the singularity of  
the Jacobian matrix.

3. POWER FLOW ALGORITHM USING ABC METHOD

The honey bees foraging behavior, learning, and memorizing 
characteristics have been attracted many researcher in the area 
of  swarm intelligence. The pioneer work of  Karaboga [24] 
which describes an ABC algorithm based on the behavior 
of  honey bee is first attempt model in this aspect. One of  
the main features of  ABC algorithm is its ability to conduct 
both global search and local search in each iteration.

According to the ABC algorithm, there are three categories 
of  artificial bees in the colony. These are employed bees, 
onlookers bees, and scouts bees. The bee colony is divided 
into two halves, the first half  of  colony includes employed 
bees, and the second half  includes the onlookers. The 
onlooker’s bees are those waiting on the dance area in hive 
as a decision-maker for choosing the suitable food source. 
The employed bees are those collecting the nectar from food 



Kassim Al-Anbarri and Husham Moaied Naief: Application of Artificial Bee Colony Algorithm in Power Flow Studies

UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1 13

source. While the scout bees are those searching the food 
sources. The searching cycle in the ABC algorithm consists 
of  the following steps [29]:
• At the initialization step, the bees select a set of  food 

source positions randomly. After determining the 
nectar amount, the bees come to the hive to share the 
information with those waiting on the dance area.

• At the second step, the employed bees use the gained 
information to choose new food sources in neighborhood 
area after going to the old position, which is visited by 
themselves previously.

• At the third stage, the onlooker bee chooses a particular 
area for the food sources depending on the information 
given by the employed bees on the dance area.

To utilize the ABC algorithm, there are some control 
parameters that should be set [30]; they are number of  
variables, lower bound of  variables (LB), upper bound of  
variables (UB), population size (colony size) (nPop), number 
of  onlooker bees (nn Onlooker), maximum number of  
iterations (MaxIt) (the stopping criteria), abandonment 
limit parameter (Limit), and acceleration coefficient upper 
bound (A).

A. Steps of ABC Implementation
The steps of  ABC can be outlined as follows [31]:
1. Generate a randomly distributed initial population 

solutions (food source positions).
2. Evaluate the population which represents the nectar 

quantity. The population of  the positions (solutions) 
is subjected to iterated cycles, C =1, 2,…, C

max
, of  the 

search processes of  the employed bees, the onlooker 
bees and scout bees. Based on a probabilistic approach, 
the artificial employed or onlooker bee makes a change 
on the position (solution) in her memory for finding a 
new food source and tests the nectar amount (fitness 
value) of  the new source (new solution).

3. Apply the roulette wheel selection (choose the best fit 
individuals).

4. Calculate the probability rate (Pi) related with solutions;

 1

i
i npop

ii

fit
P

fit
=

=
∑  

(7)

 The fitness values (fit) are computed by the following 
expression:

 

1
if 0

1
1 abs( ) if 0

i
ii

i i

f
ffit

f f

 ≥ +=  
 + <   

(8)

 Usually, the value of  Pi is between {0,1}.
5. Find the new solutions for the onlookers depending on 

the probability Pi related with the solutions.
6. Reapply roulette wheel selection.
7. Find the abandoned solution if  exists, change it with 

new randomly generated solution.
8. Register the best solution achieved so far.
9. C=C+1 (until maximum cycle number is reached).

B. ABC Implementation for Power Flow Study
ABC optimization is applied to obtain the bus voltage 
magnitude (|Vi|) and voltage phase angle (δi) by minimize 
the following objective function:

minf(δ,|V|) (9)

Where,

δ=(δ1,……………, δn)

|V|=(|V
1
|,……………, |Vn|)

This objective function is constrained by the inequalities 
LB and UB.

LB<|V|<UB

LB<δ<UB

The optimization process starts with setting the number of  
solutions (food sources) in ABC algorithm, which represents 
the number of  flowers, the bees will reach to food sources, 
and then computes the nectar’s quantity, the food sources 
are initialized using a random number generator.

The voltage magnitude and voltage phase angle are limited 
to the following range:

0.5<|Vi|<1.05

−5<δi<5

The objective function (f) that designed to determine the load 
flow problem using ABC algorithm is as follows:

2 2
i if P Q= ∆ + ∆∑ ∑  

(10)

Where i = 1, 2, 3,… number of  buses

In ABC algorithm, the objective function (fitness value) 
describes the quality of  food source (solution). The food 



Kassim Al-Anbarri and Husham Moaied Naief: Application of Artificial Bee Colony Algorithm in Power Flow Studies

14 UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1

source that has the best quality will be registered in a 
memory as the best food source (solution) ever found. 
The neighborhood search process uses to obtain the best 
fitness value will continue by employed bees and onlookers. 
The fitness value will be computed for each new solution 
(food source), and the new solution (food source) that 
having the best fitness value will be the new reference in 
memory. The optimization process will continue to looking 
for the food source near to hive, which depending on the 
probability that computed previously from fitness value. 
The new solution (food source) after neighborhood search 
will be registered if  its fitness is better. The optimization 
process will continue until reach to the best fitness value or 
reach to the maximum cycle number afterward the solution 
converges and the mismatch power is close to zero. The 
flow chart of  ABC approach in load flow computation is 
shown in Fig. 1.

4. RESULTS AND DISCUSSION

The ABC algorithm is being applied to the 6-bus system as 
follows:

A. Six Bus Test Power System with Normal Load
The ABC method is applied to the 6-bus system with a 
particular normal loading condition [32]. The test system 
is shown in Fig. 2 consists of  three generating stations and 
three load stations. After initialize the control parameters of  
ABC algorithm, each variable was initialized with random 
number using random number generator. The elements of  
power mismatch vectors ΔP and ΔQ are computed using 
Equation 6. The best food source (load flow solution) will 
be selected by applying roulette wheel selection.

A comparison between the results that obtained from 
conventional (NR) with that found from ABC algorithm 
is given in Table I. As shown from these tables, the results 

Fig. 1. Flow chart of application of artificial bee colony technique in 
power flow study

TABLE I 
The Bus Voltages using NR Method and ABC 

Technique
Bus No. NR-method ABC algorithm

Vi δi Vi δi
1 1.05 0 1.05 0.0
2 1.05 −3.635 1.05 −3.635016
3 1.07 −4.117 1.07 −4.117675
4 0.989 −4.18 0.989013 −4.180701
5 0.9813 −5.306 0.981364 −5.306448
6 1.004 −5.856 1.004079 −5.856946

ABC: Artificial bee colony, NR: Newton‑Raphson

obtained are identical. The final objective function value 
in ABC optimization process after 15000 iterations is 
1.5902×10−11. The performance of  ABC algorithm to obtain 
the best solution is clarified by graph that was shown in Fig. 3.

B. Six Bus Test Power System with Heavy Load
To simulate the heavy load condition, the load at bus 4, 5, 
and 6 is increased as shown in Appendix A. It is found that 
the conventional NR method is failed to converge. However, 
when the ABC algorithm is applied, the solution converges as 
shown in Table II. The final objective function value in ABC 
optimization process after 5000 iteration is 8.99 × 10−4. The 



Kassim Al-Anbarri and Husham Moaied Naief: Application of Artificial Bee Colony Algorithm in Power Flow Studies

UHD Journal of Science and Technology | April 2017 | Vol 1 | Issue 1 15

Fig. 2. Six bus test power system

TABLE II 
The Bus Voltages for the Heavily Loaded Case 

using ABC Technique where the NR Method Fails 
to Solve

Bus No. Vi δi
1 1.0500 0
2 1.0500 −52.3630
3 1.0700 −63.0819
4 0.7575 −46.0854
5 0.6721 −58.3285
6 0.8341 −68.0498

ABC: Artificial bee colony, NR: Newton‑Raphson

Fig. 3. The performance of artificial bee colony algorithm, best solution 
versus iteration

Fig. 4. The performance of artificial bee colony algorithm, best solution 
versus iteration

performance of  ABC method to obtain the best solution is 
clarified by graph that was shown in Fig. 4.

5. CONCLUSION

A meta-heuristic approach to solve power flow problem has 
been presented. The proposed algorithm is based on ABC 
technique which is considered to be one of  the type of  swarm 
intelligence techniques. The proposed algorithm is applied 
to the six bus system with different loading conditions, and 
the results obtained have been compared with the results of  
(NR) method. The main advantages of  ABC algorithm are 
the flexibility of  modeling, accuracy, strong convergence, 
and reliability, which considered reasonable and acceptable 
optimization process. In addition, the presented algorithm 
shows promising results regarding heavily loaded system.

6. ACKNOWLEDGMENT

The author would like to thank the Department of  Electrical 
Engineering, Faculty of  Engineering, Mustansiriyah 
University (www.uomustansiriyah.edu.iq), Baghdad, Iraq, for 
its support in the present work.

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APPENDIX A 
Buses Data of 6-Bus Case with Heavily Loaded Condition

Bus No. |V|pu δ (°) PG (MW) QG (MVAR) PD (MW) QD (MVAR)
1 1.05 0 0 0 0 0
2 1.05 0 80 0 0 0
3 1.07 0 90 0 0 0
4 1.0 0 0 0 255 130
5 1.0 0 0 0 255 130
6 1.0 0 0 0 255 152