Reactive power optimization with artificial bee colony algorithm
INTRODUCTION
Reactive power optimization (RPO) is an important
optimizaton process in terms of voltage stability, voltage
quality and active power loss. The main object function in
RPO is the total active power loss function, but in later
years, systems were analyzed in terms of reactive supply
costs and voltage profile.
Since voltage profile minimizes the deviations between
the nominal and bus voltages, the reactive power
transferred from the bus will decrease and the lines
current will also decrease. As such, these provide
supplements for the decrement of active power loss. The
effects of the reactive power supplies connected to buses
are quite important on reduction of active power loss.
However, due to the installation, some extra equipment
and devices costs like disjoncteur needs to be be
addressed from a different perspective. Based on this,
*Corresponding author. E-mail: salihtosun[at]duzce.edu.tr. Tel:
+905364159613. Fax: +903805421134.
cost functions are used in RPO, leading to a multiobjective
function. This function is a non linear function
having a lot of variables and constraints. Firstly, this
problem was solved with classical methods such as
linear, non-linear, quadratic and dynamic programming.
Since the problems have a lot of variables, constraints,
different local minimiums and the possibility of getting
trapped in the local minimum, the metaheuristic methods
are preferred as the solution to these problems.
In previous years, metaheuristic methods such as
simulated annealing, ant colony optimization, genetic
algorithm, plant growth simulation algorithm, particle
swarm optimization, sequential quadratic programming
algorithm, as well as artificial immune system, give more
satisfied results in finding global optimum points. So
nonlinear problems having multi variables and constraints
like RPO have been solved generally with heuristic
methods.
Deep and Shahidehpour used decomposition approach
in considering RPO linearly. As such, they divided the
bus systems into 16 and 30 bus systems for
decomposition approach.
However, they divided the 16 bus system into two
different systems having 7 and 9 buses. By this way, they
decreased the complexity and used the classical method
(Deep and Shahidehpour, 1990). Jwo et al. (1995) solved
RPO with simulated annealing by combining the
compensator and the active power loss of the system,
and as such, they controlled the system in terms of
voltage deviations, while Putman et al. (1999) solved the
problem with a simplex method. Zhu et al. (1998) solved
RPO with neural network using analytical hierarchical
process. They analysed the RPO in terms of voltage
quality and active power loss. Grudinin (1998) used
successive quadratic programming method and bi-level
programming method (a method that traces object
function and controls variable value continuously). They
applied their study on IEEE-30 bus system and other 278
bus system. Yoshida and Fukuyama (1999) analysed
voltage security with particle swarm optimization (PSO).
In the direction of this object, they used RPO at 14 and
112 bus systems. However, Liu et al. (2000) realized a
hybrit study with genetic algorithm (GA), simulated
annealing (SA) and tabu search (TS). Deng et al. (2002)
minimized the active power demanded in 24 h with
algorithmic combined approach, wherein the data
belonging to the previous day represents the next day’s
variable values. Khiat et al. (2003) analysed West
Algerian transmission system in terms of RPO. In their
study, they used a hybrid system for both heuristic and
numerical methods. Mantawy and Al-Ghamdi (2003)
used particle swarm optimization as their new RPO
method introduced by them. As such, they applied their
methods on IEEE-6 bus system. Lin et al. (2003)
analysed RGO considering voltage stability and they
applied 14 bus system. They used non-linear
programming in their studies. Wei et al. (2003) expressed
that GA could get trapped by local minimums, so this can
be solved with big crossover and mutation rates, but they
stated that this method may slow the steps of the
solution. So they solved RPO using a method called
immune genetic algorithm. Chuanwen and Bompardb
(2005) represented a hybrid method using chaotic
particle swarm optimization and linear interior methods.
They stated that particle swarm optimization started the
search process in a big solution space so it is a drawback
for the solution time. So they used a method that
narrowed the initial solution space. They applied their
algorithm to IEEE-30 bus system and compared their
results with PSO both graphically and numerically.
Durairaj and Kannan (2005) made RPO with improved
genetic algorithm. They tried to minimize voltage stability,
voltage quality, active power loss and total cost in the
objective function. As such, they applied their algorithm
IEEE-30 and 57 bus systems. Abido and Bakhashwain
(2006) analysed RPO using a multiobjective evolutionary
Ozturk et al. 2849
algorithm. They used the best active power loss and the
best voltage deviation, and tried to minimize these two
different objectives. Li et al. (2006) used adaptive particle
swarm optimization algorithm for RPO. They applied their
algorithm IEEE-30 bus system and compared the results
with genetic algorithm and particle swarm algorithm.
Lenin and Mohan (2006) used ant colony algorithm for
RPO. They applied ACO IEEE-30, 57 and 191 bus
systems and compared the results with GA and adaptive
GA. Abbasy et al. (2007) used differential evolution
algorithm for the multiobjective optimization. They,
especially, focused on cost function and used the
reactive power production cost functions of the generator
and compensator. Chettih et al. (2008) applied the
particle swarm method to the West Algerian network.
They compared the results before and after using the
method. Xiangzheng (2007) solved IEEE-6 bus system
with immune algorithms and compared the results with
GA. Lu and Ma (2008) used direct neural dynamic
programming. They applied their algorithm IEEE-6 bus
system and compared the results with GA. Zhang et al.
(2008) analysed the system for active power loss and
voltage profile and used the application of oriented
search algorithm. Lirui et al. (2008) optimized the reactive
power using dual population ant colony optimization.
They stated that one population ant colony could get
trapped by the local minimal, so they started to attain
more optimum solution using dual population. In order to
present the efficiency of their algo-rithm which is more
than one population algorithm, they used RPO problem.
Zhang et al. (2008) minimized the active power loss of a
30-bus system using self-adaptive differential evolution
algorithm. Lin et al. (2008) made voltage and active
power loss control using improved tabu search algorithm.
Firstly, they optimized active power loss in their algorithm
and saved the best ten solutions, therby giving the
maximum voltage range. They gathered these results
using fuzzy set and obtained a single objective function
and searched for optimal values with this function. Wei et
al. (2008) searched optimal solutions for IEEE-30, 57 and
118 bus systems using bacterial chemotaxis method,
whereas Wang et al. (2008) used plant growth simulation
algorithm for RPO. Jikeng et al. (2008) applied adaptive
immune algorithm for the solution of RPO and they
applied their algorithm, IEEE 14 and 118 bus systems,
and compared the results with GA. Varadarajan and
Swarup (2008) used differential evolutionary algorithm for
the minimization of the active power loss at IEEE 14, 30,
57 and 118 bus system. Li et al. (2009) made dynamic
optimal reactive power dispatch based on parallel particle
swarm optimization algorithm.
They gathered the active power loss with transformator
and compensator cost functions as a single object
function. They applied their algorithms 5 different IEEE
bus systems and compared the results with PSO. Aribia
2850 Sci. Res. Essays
and Abdallah (2007) studied multiobjective optimization
for reactive dispatch and they minimized the active power
loss, voltage deviation and VAR source cost separately.
In this study, ABC, being a new heuristic method is
used for the multiobjective reactive power optimization.
Karaboga introduced this algorithm as artificial bee
colony into the literature in 2005. This algorithm runs
based on some behaviour of bees, while bees collect
nectar from the nectar sources. Generally, nonlinear
function optimization is realized with ABC.
MULTIOBJECTIVE REACTIVE POWER OPTIMIZATION
The importance of reactive power management increases
gradually, in the direction of increasing reactive power
demand. Voltage is very important in power management;
as it must be high enough to support loads and
must be low enough not to cause any fault of equipment.
Hence, voltage must be controlled from each point and
must be supported. This can be realized to a large extent
by controlling reactive power consumption and sources.
The controllable devices such as generator, sencron
capacitor, reactor and FACTS devices are used for
decreasing the loss and increasing the voltage control
(capacity) in RPO. At the same time, these devices
consist of constraints for the optimization problem.
In this study, there are three object function
optimization called multiobjective RPO. These functions
are: active power loss, voltage profile of load buses and
cost function of reactive power sources.
Active power loss
Among the most important issues of power system,
system loss is the most important. Active power loss (Ploss
) is a serious economic loss among these losses, so it is
needed to minimize the active power loss. Active power
loss object function is given in Equation 1 (Deep and
Shahidehpour, 1990; Li et al., 2009).
Î Î
= = + -
k NE k NE
Q loss k i j i j ij minf P g (V V 2VV cos ) 2 2 q (1)
is the number of transmission lines, is the
conductance of the line connecting i and j bus, is the
voltage value of i th bus, is the voltage value of jth bus,
is phase angle of the voltage value between i and j
bus and is total active power loss in Equation 1.
Voltage profile
The other object function is related to the minimization of
the voltage oscilations between bus voltage and nominal
voltage. The first usage of the object for this object
function is the relation of reactive power transmission to
the bus voltage level, in that the load bus voltage values,
close to the nominal values, provide the diminution of the
reactive power value transmitted to the load bus. The
dimunition of the reactive power value causes the
dimunition of the line current. Active power loss is
presented with I2R. So the dimunition of the line current
causes the dimunition of active power loss in the voltage
profile. The second usage of the object for this object
function is to stabilize the load bus voltage to a nominal
value at the event of the unforeseen sudden voltage
unstability scenarios. The average voltage deviation of
the load bus can be minimized using Equation 2 (Abido
and Bakhaswain, 2006; Zhang et al., 2008).


| |
PQ
PQ
i N
i ref
dev N
V V
V


Î
-
=






































































where is voltage deviation, is load bus number,
is load bus voltage and is load bus reference
(nominal) voltage value.
Reactive power source cost
Another object function to be minimized in RPO is the
cost function of reactive power sources connected to the
system. The cost of reactive power sources consist of the
installation and purchasing costs. The cost of installation
and extra equipment cost includes switching and
disjoncteur costs. The object function is presented in
Equation 3 with the combination of reactive power
sources costs (Durairaj and Kannan, 2005; Li et al.,
2009).
where is the cost of the establishment and the
equipment added to ith bus, is the cost of MVAr
produced by Var sources connected to ith and is the
per-unit value of reactive power transferred from the Var
source connected to the ith bus. However, is the
absolute value because FACTS devices can be run






inductively or capacitively, considering the needs of the
system.
Constraints of the problem
In order to attain practical variable values, there must be
working conditions constraints in RPO. If the constraints
are not used in RPO, the variables take the values that
are harmful to the system. Both generator voltages and
reactive power sources have value ranges. As such,
active and reactive power equations are used for the
equality constraint at the minimization of active power
loss.