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Title: Comparison of modern heuristic algorithms for loss reduction in power distribution network equipped with renewable energy resources
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Ain Shams Engineering Journal xxx (xxxx) xxx

Contents lists available at ScienceDirect

Ain Shams Engineering Journal
journal homepage: www.sciencedirect.com

Comparison of modern heuristic algorithms for loss reduction in power
distribution network equipped with renewable energy resources
Amr M. Ibrahim ⇑, Rania A. Swief
Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt

a r t i c l e

i n f o

Article history:
Received 24 April 2017
Revised 1 November 2017
Accepted 6 November 2017
Available online xxxx
Keywords:
Heuristic algorithms
Power loss reduction
Probabilistic optimal power flow
Renewable energy resources

a b s t r a c t
This paper presents a comparison between four modern heuristic algorithms for optimal loss reduction of
power distribution network equipped with renewable energy resources. These algorithms are
Gravitational Search Algorithm (GSA), Bat Algorithm (BA), Imperialist Competitive Algorithm (ICA) and
Flower Pollination Algorithm (FPA). Placing Renewable Distributed Generators (RDGs) such as wind turbine (WT) and photovoltaic panels (PV) in the electrical grid might share in reducing the power loss. In
this research, the proposed heuristic algorithms are utilized to find the optimal location and size of RDGs
on the distribution network for the purpose of reducing power loss. A probabilistic optimal load flow
technique is implemented to model the behavior of RDGs based on different penetration levels. The proposed algorithms are applied to 69-bus system. The acquired results based on the heuristic algorithms
are listed to clarify the effectiveness of the proposed algorithms in reducing the power losses of the studied system.
Ó 2018 Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under
the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction
Optimal load flow is a significant optimization issue for operating the electrical power systems in an effective and economical
way. Many deterministic techniques are employed to find an
answer for optimal load flow problems [1,2].
With the tendency of integrating Renewable Distributed Generators (RDGs) [3–5], various uncertainties occur in the load flow
issue like load variations. Due to the indiscriminate manner of
renewable energy resources (wind speed and solar radiations),
the input data and the solutions of the optimization issue are subjected to a considerable influence. Thus, there is a need to take into
consideration the load changes and subsequently the electrical grid
process has to be investigated according to an accurate estimation
of the load demand. This can be accomplished by utilizing the optimal probabilistic load flow (OPLF).
The goal of replacing the deterministic load flow analysis with
the OPLF is to construct a probabilistic model based on the uncer⇑ Corresponding author.
E-mail address: amrmohamedhassan@yahoo.com (A.M. Ibrahim).
Peer review under responsibility of Ain Shams University.

Production and hosting by Elsevier

tainty parameters in the input data of the electrical grid such as
electrical load and generation [6].
In the last few years, a lot of articles are focused on solving
OPLF. Optimal probabilistic load flow can be diversified via modern
simulation methodologies and modern analytical probabilistic
mechanisms. A method based on Monte Carlo Simulation (MCS)
methodology is suggested, considering the normal manner of
energy reproduction for renewable energy systems [7]. Also this
methodology is appeared in other article to resolve OPFL for medium voltage distribution networks [8]. Cumulants mechanism
combined with ‘‘Gram-Charlier” extension is offered to solve OPLF
in many manuscripts [9–11]. To account for the uncertainties and
correlations of the system load, the First-Order Second Moment
Method (FOSMM) is investigated [12]. The unscented transformation (UT) mechanism is utilized for the aim of investigating the
OPLF for wind farms [13]. The modifications of Point Estimated
Method (PEM) are utilized to solve OPLF in power network
equipped with wind turbines (WTs) and photovoltaic (PV) systems
[14] also this method is employed for electric vehicles application
[15].
The problems of optimization confront major obstacles in the
electrical engineering area. These obstacles are altered according
to the different levels of complexity and nonlinearity of the problem constrains. Many of the optimization methodologies have been
used over the years in various scientific fields in the real world and
have proved their effective ability to solve many problems [16–21].

https://doi.org/10.1016/j.asej.2017.11.003
2090-4479/Ó 2018 Ain Shams University. Production and hosting by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

2

A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx

The majority of heuristic algorithms have been advanced to deal
with the optimization obstacles. Power loss reduction in distribution systems problem has attracted the attention of many
researchers in recent years [22–24]. Using modern heuristic algorithms in conjunction with a probabilistic load flow analysis is
one of the main contributions of this work when compared with
other previous studies.
Many heuristic optimization algorithms have detonated
through the past few years with novel methodologies being suggested continuously. Heuristic optimization methods proved a
great effectiveness in finding solutions for electrical power network problems [25–29]. In this article, four powerful heuristic
algorithms are used for optimal loss reduction of power distribution network equipped with wind turbines and photovoltaic panels. These novel algorithms are Gravitational Search Algorithm
(GSA), Bat Algorithm (BA), Imperialist Competitive Algorithm
(ICA) and Flower Pollination Algorithm (FPA).
The proposed heuristic algorithms are considered as powerful
tools in solving considerable number of optimization problems.
Each algorithm that applied in this work is formerly approved its
effectiveness in solving many complex optimization problems;
Gravitational Search Algorithm [30–34], Bat Algorithm [35–38],
Imperialist Competitive Algorithm [39–42] and Flower Pollination
Algorithm [43–46]. These algorithms are implemented in this article using MATLAB toolbox.
This research introduces an optimal probabilistic load flow
(OPLF) method for finding out the optimal power loss reduction
for a distributed network equipped with RDGs (WT or PV units).
The location and the sizing of RDGs sources, to reduce the energy
losses of the distribution system, are investigated utilizing four
modern heuristic optimization algorithms; GSA, BA, ICA and FPA.
Load flow has been executed utilizing forward–backward sweep
methodology. This optimization problem is solved on the basis of
a Probabilistic Load Flow (PLF) analysis which is used to model
the behavior of the wind speed, solar radiation and load level variations at each bus. These models are combined to participate in the
optimization problem for determination of the optimum location
and for sizing the RDGs modules that minimize the system power
losses on the feeders. The optimization algorithms are applied for
IEEE 69-bus standard system with several penetration levels
(12.5 kW, 25 kW and 50 kW), different RDGs sources (WT units
and PV panels) and different power injections (active power only,
reactive power only and, active and reactive power).
The rest of the paper is constructed as follows: Section 2 presents a clarification of the optimal probabilistic load flow (OPLF)
in power system studies. Section 3 formulates the OPLF. Section 4
describes in details the proposed heuristic algorithms. Section 5
evaluates the results of the proposed heuristic algorithms when
applied on 69-bus IEEE standard systems. Eventually, Section 6
introduces the extracted conclusion.

Wind speed and solar irradiation uncertainties are commanding
the execution of OPLF. To realize the probabilistic behavior of the
RDGs, a simulation for the Probability Distribution Function
(PDF) for wind energy and solar energy is illustrated through the
following sections:
A. Wind data
To imitate the attitude of wind speed, the following formula,
based on Weibull Probability Density Function (WPDF) [14,47], is
used:

K v
C C

uðv Þ ¼ ð Þ

K 1

v K
expð
Þ
C

ð1Þ

where v is the wind speed,uðvÞ is the Weibull PDF, K is the shape
coefficient and C is the scale parameter [48]. In this research, the
Weibull coefficients of the wind speed are assumed to be C = 8.78,
K = 1.75 [14], the typical WPDF of wind speed is illustrated in Fig. 1.
To find the output power of the WTs in the OPLF analysis, a separation of Weibull PDF to different levels is established. For every
level, wind speed is ruled by specified boundaries. The probability
for every level of wind speed is determined as follows:

ProbWT ðLÞ ¼

Z v L2
v L1

uðv Þdv

ð2Þ

where v L1 and v L2 are the wind speed boundaries of level L.
Wind farms are operated between minimum and maximum
speed boundaries. Below the minimum speed level or above the
maximum speed level, problems occur and the farm can’t produce
energy. In this paper, the step of wind speed is set to be 1 m/s. The
total number of levels is reduced by gathering some levels with
each other as illustrated in Fig. 2. (i.e. levels up to 4 m/s produces
the same output power that is equal to zero [no level], same for
levels above 25 m/s, also with levels from 14 m/s to 25 m/s the output power is constant and equal to P rated ) [49]. The produced wind
speed samples can be transformed to wind turbine output power
using wind speed-power criteria that illustrated as follows:

8
>
>
>
<

0;

PratedW T ððvvr vvci ÞÞ ;
ci
PWT¼
>
P ratedW T ;
>
>
:
0;

0 6 v 6 v ci
v ci 6 v 6 v r
v r 6 v 6 v co
v co 6 v

ð3Þ

2. Probabilistic models
Renewable distributed energy resources are vital for merging
any energy network. The presumption of having constant loads is
no more valid due to the great effect of uncertainty that appears
when using the renewable energy resources. A rise in the feeder’s
losses as well as in cables heating may occur by installing the RDGs
in wrong positions. OPLF discovers an optimum strategy to confront the variety of the entire load flow measurable factors. Thus,
an optimal probabilistic load flow is strongly advised in designing
electrical energy networks. In this work, the aim of OPLF is to
determine the optimum distribution of RDGs for reducing the
losses of the electrical network.

Fig. 1. Weibull PDF of wind speed.

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx

3

Fig. 2. Wind probability distribution.

where, PWT is the power generated from wind turbine in KW,
PratedW T is the rated power of the wind turbine in KW, v ci ,v r and v co are
the cut-in speed, rated speed and cut-off speed of the wind turbine,
respectively. The wind turbine applied in this research has the following data:
Rated power (P ratedW T ) = 600 KW, cut-in speed (v ci ) = 4 m/s, rated
speed (v r ) =14 m/s and cut-off speed (v co ) = 25 m/s [49]. In this
article, a real wind data based on the wind speed is employed
[49]. This data is illustrated in Fig. 2.
The output active and reactive power capability corresponding
to a power factor of 0.92 at the terminals of the machine is utilized
in this work [49]. From Eq. (3) based on Weibull PDF of wind speed,
the output active and reactive power are extracted into a form of
12 levels of wind speed as illustrated Fig. 3.
B. Photovoltaic data
PVs output power is influenced by solar irradiation that is why
solar radiation modeling is needed to model the PVs output power.
The solar radiation real-data is collected everyday hour per hour
through the year [48], PV’s output power is multilevel variable factor in the problem formulation. The irradiance data is divided into
levels, in every level, the solar irradiance is within specified boundaries. For estimating the uncertainty of PVs, Weibull Probability
Density Function is applied. The probability (ProbPV ) of every level
is determined through dividing the number of hours per year for
each level of irradiance by total number of hours per year as illustrated in Fig. 4.

Fig. 4 illustrates the PDF of the solar irradiance against the solar
irradiance levels that described in Table 3. The PV output power as
a function of solar irradiance is obtained as follows:

PPV

8
R2
>
R < RC
>
< PratedP V ðRSTD RC Þ
R
¼
P

R
6
R < RSTD
C
rated
V
P
RSTD
>
>
:
P ratedP V
R P RSTD

ð4Þ

where PPV is the PV output power in MW, RSTD is the solar irradiance
in the standard conditions usually set to 1000 W/m2, RC is a certain
radiation point, usually assumed to be 150 W/m2, P ratedP V is the PV
rated power in MW set to be 50 MW and R is the solar irradiance
in W/m [50].
The output active and reactive power capability corresponding
to a power factor of 0.92 at the terminals of the machine is used
in this article [49]. From Eq. (4) based on WPDF of solar irradiance,
the output active and reactive power are extracted into a form of
12 levels of solar irradiance as illustrated Fig. 5.
C. Load variations
In the last decade, most of the assumptions that are employed
in the load flow models could not give a precise indication about
the real system flows or about the load variations. In this work,
the load changes are simulated according to a method that split
the year into twelve intervals [51]. Table 1 presents the twelve
intervals of load changes, the load probability (ProbLoading ) of
appearance and the loading percentage relative to the peak load.

Fig. 3. Active and reactive power distribution for wind farms.

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

4

A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx

Fig. 4. Solar irradiance yearly distribution probability.

Fig. 5. solar irradiance active and reactive power generation distributions.

Table 1
Percentage of loading over one year.
Level No.

12 periods of load variation

Probability

% of peak load

1
2
3
4
5
6
7
8
9
10
11
12

Winter, weekday, high-load
Winter, weekday, low-load
Winter, weekend, high-load
Winter, weekend, low-load
Fall/Spring, weekday, high-load
Fall/Spring, weekday, low-load
Fall/Spring, weekend, high-load
Fall/Spring, weekend, low-load
Summer, weekday, high-load
Summer, weekday, low-load
Summer, weekend, high-load
Summer, weekend, low-load

0.112
0.067
0.045
0.027
0.223
0.134
0.089
0.054
0.112
0.067
0.045
0.027

92
85
72
67
69
63
54
50
85
92
67
72

3. Problem formulation
It is difficult to anticipate that the prediction of the load is true
due to the sources of uncertainties. Hence, an error is introduced to
the optimal process of power flow. That is why the electrical network must be organized on the basis of random load variations
and deemed with an optimal probabilistic load flow analysis.
Fig. 8 presents the flow chart of the OPLF approach. This approach
begins with reading the system data and ends with redistributing
the RDGs based on losses reduction.
The Gravitational Search Algorithm (GSA), Bat Algorithm (BA),
Imperialist Competitive Algorithm (ICA) and Flower Pollination
Algorithm (FPA) are implemented for optimal loss reduction of
power distribution network using the optimal probabilistic load

flow analysis. The OPLF solutions are carried out with different
loading levels and with several amounts of power generation from
RDGs. These data are generated from the models of the probability
density function of WT module, PV module and load variation
obtained by the methods proposed in Section 2.
In this work, the OPLF analysis starts with introducing the system data and the uncertain parameters affecting the system
expected, then load flow analysis for the study system are accomplished using forward-backward Sweep method, ending with the
allocation of the wind farms and PV generators after decreasing
the system losses, Probpowerlosses describes the probable power losses
of the system under uncertainty at certain level of (RDGs) output
power and certain level of loading variation. Each RDG is represented as active and reactive source for each load level as described
in the following equations:

Ploadupdated ¼ Pload PDG

ð5Þ

Q loadupdated ¼ Q load Q DG

ð6Þ

where Pload is the load at each bus, Powerloss indicates the losses of
the system under certain input variables

Probpowerlosses ¼ Power loss ProbDG ProbLoading

ð7Þ

The objective function of this research focused in minimizing
the total system loss taken into consideration the entire probabilistic parameters as illustrated in Eq. (8):

Min Total ProbPower

losses

¼

X

Probpower

losses

ð8Þ

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

5

A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx

where Total ProbPower losses denotes the total probable power losses
under uncertainty taking into consideration the output power of
all penetration levels of WT units and PV units in addition to load
variations.
The above mentioned problem, when applied to the IEEE 69-bus
standard system, can be formulated as follows:

Min Ploss ¼

X

I2n Rn

ð9Þ

n

where n is the number of feeders of the lateral system, In and Rn is
the current and resistance of feeder n, respectively.
The optimized variables are the locations of the installed RDGs
and the number of installed units at each selected bus.The constrains of the problem can be listed as follows:

1

V min V i V max

ð10Þ

whereV i is the bus i voltage in per unit, V min equals 0.95 per unit and
V max equals 1.05 per unit.
2– For any selected bus i, the number of installed RDGs 2 units.

Pgenerated þ PDG ¼ PLoad þ PLosses

ð11Þ

where, P generated is the generated active power, P DG is the active
power supplied by the RDGs P Load is the load active power and P
Losses is the active power losses in the feeders.

Q generated þ Q DG ¼ Q Load þ Q Losses

ð12Þ

where, Q generated is the generated active power, Q DG is the active
power supplied by the RDGs Q Load is the load active power and Q
Losses is the active power losses in the feeders.
4. Heuristic algorithms
In the last decade, numerous heuristic algorithms are produced
for solving many optimization problems. These comprise Gravitational Search Algorithm (GSA), Bat Algorithm (BA), Imperialist
Competitive Algorithm (ICA) and Flower Pollination Algorithm
(FPA). All of these algorithms are aimed to detect the best solution
(global optimum) through all potential inputs. This goal can be
achieved due to the high capability of these algorithms in covering
the entire search space as well as their efficient convergence capability near the best solution. In this section, a detailed description
for the above mentioned algorithms is provided.
A. Gravitational Search Algorithm (GSA)
Gravitational Search Algorithm (GSA) is a heuristic algorithm
discovered by Esmat Rashedi et al. in 2009 on the basis of Newton
gravitation theories [52].
In GSA, each solution in the search space are called agent; each
agent react with other agents through the gravity force. The performance of each agent is determined by its mass. Therefore, each
agent is represented by a particle with specific features.
Due to the force of gravity, an overall motion of all particles
towards the particles with heavier masses is achieved. The weighty
masses that move slowly than the other particles are deemed as a
good solutions. GSA explores the optimal solution by tuning the
gravitational mass and the inertial mass properly.
In order to explain the mechanism of GSA, let N agents is considered for describing a certain system. The location of each agent
in a search space of n-dimension is defined by:





X i ðtÞ ¼ xi ðtÞ; xi ðt Þ; ; xi ðtÞ; ; xi ðt Þ for i ¼ 1; 2; ; N:
1

2

d

n

ð13Þ

where xi d ðt Þ presents the location of agent i in d-dimension at time t.

The algorithm is started by setting initial values of the gravitational constant G according to Eq. (14) as follows:

GðtÞ ¼ Go e at=T

ð14Þ

where Go and a are set in the launch of the search and their
amounts are decreased over the process of the algorithm. T is the
total number of iterations.
It is important to determine the gravitational force that attracts
two agents to each other at a specific time t. If it is presumed that
agent j acts on agent i, so the gravitational force between them can
be found as follows:

F ij d ðt Þ ¼ GðtÞ


Mpi ðtÞ M aj ðtÞ d
xj ðt Þ xi d ðt Þ
Rij ðtÞ þ e

ð15Þ

where Maj is the active gravitational mass of agent j, Mpi is the passive gravitational mass of agent i, Rij ðt Þ is the Euclidian distance
between agent i and agent j ande is a constant [52]. Then, Eq. (15)
is modified as follows:

F i d ðt Þ ¼

X

randj F ij d ðtÞ

ð16Þ

j¼1;j–i

where randj is a number randomly chosen between 0 and 1. Thus,
the acceleration is specified as follows:

ai d ðtÞ ¼

F i d ðtÞ
M ii ðtÞ

ð17Þ

where Mii is the inertial mass of agent i.
During the search, agent i update its velocity and location as
illustrated in Eq. (18) and Eq. (19) respectively:

V i d ðt þ 1Þ ¼ randi V i d ðt Þ þ ai d ðt Þ;

ð18Þ

xi d ðt þ 1Þ ¼ xi d ðt Þ þ V i d ðt þ 1Þ

ð19Þ

where randi is a number randomly chosen between 0 and 1.
The gravitational and the inertial masses are updated its values
by the following sequence:

Mai ¼ Mpi ¼ M ii ¼ M i ;
mi ðt Þ ¼

i ¼ 1; 2; 3; . . . ; N:

fiti ðtÞ worstðtÞ
best ðt Þ worstðtÞ

ð20Þ

mi ðt Þ
Mi ðtÞ ¼ PN
j¼1 mj ðt Þ

ð21Þ

worstðtÞ ¼ maxj2f1; ;Ng fitj ðtÞ

ð22Þ

bestðtÞ ¼ minj2f1; ;Ng fit j ðtÞ

ð23Þ

where fit i ðtÞ is the fitness evaluation of agent i at time t. This fitness
value is determined by the gravitational and the inertial masses.
The predetermined fitness values are used to evaluate the mass
of each agent and therefore explore the agents that have heaviest
masses. The iteration-counter is increased till and the optimum
solution is generated [52].
In order to achieve the optimum solution of the research problem, the following algorithm parameters are used:
Algorithm parameter

Value

Number of agents
Maximum number of iterations (T)
Go

50
1000
100
20

a

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

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B. Bat Algorithm (BA)
Bat algorithm (BA) is a newly suggested meta-heuristic mechanism simulating the ‘‘echolocation” manner of bats for global- optimization accomplishment. BA is constructed by Xin-She Yang in
2010 [53].
Bats utilize ‘‘echolocation” to locate the food (prey) in the darkness. Bats move through the obstacles of the perimeter by launching a loud-sound pulse and receive the echo that rebound from the
surroundings. Bats employ fixed frequency signals for
‘‘echolocation”.
In order to demonstrate the BA process; population is firstly initialized in a random manner with specific limits. According to the
movement of the bats through speed vi at location xi, new solutions
are generated based on the next equations:

According to the cost function calculations, some countries are
identified as ‘‘Imperialists” that have the minimum cost function
value and the other countries as ‘‘Colonies” which controlled by
the initial imperialist countries. The normalized power of mth
imperialist countries is calculated from the following Eq.:





Cm


pm ¼ PM

j¼1imp C j

ð32Þ

where C m is the cost function after normalization and Mimp is the
size of imperialist countries. From Eq. (32) the initial number of colony countries M.C.m can be found:

M:C:m ¼ roundfpm :Mcol

ð33Þ

where f i is the frequency of the i bat, f min and f max are the limits of
the frequency and b is ranged from [0,1]. x is the present global
better location that is determined after matching all the locations
between the entire bats [53].
For the sake of improvement the local-search capability of BA,
Eq. (27) is used:

where Mcol is the size of colonies countries.
Based on this classification the primary ‘‘Empires” are formed.
The empire is classified as a powerful one if it has a considerable
number of colony countries relative to the other empires.
Assimilation and Revolution are the major factors that control
the process of this algorithm. In the search space, assimilation is
the factor that having control over the movement of colonies
which has lower cost towards the imperialist country that has bigger cost while revolution causes unexpected modification in the
colonies position.
At this stage of the algorithm, the positions of imperialist countries are substituted with the best colony countries [54]. The total
cost of the new mth empires is determined by the following Eq.:

xnew ¼ xold þ @At

T:C:m ¼ cost ðimperialistsm Þ

f i ¼ f min þ ðf max f min Þb

v i t ¼ v i t 1 þ



ð24Þ


xi t x f i

ð25Þ

xi t ¼ xi t 1 þ v i t

ð26Þ
th

ð27Þ

where xold is the former best solution, @ is ranged from -1 to 1, while
At is the mean loudness of the entire better solutions.
The loudness A and pulse-rate r are adjusted as a bat comes
nearer to its goal. Loudness A is reduced while pulse-rate r is grown
relative to Eq. (28) and Eq. (29) respectively:

Ai tþ1 ¼ aAi t

ð28Þ

r i tþ1 ¼ r i 0 ð1 ect Þ

ð29Þ

where a andc are adjustable numbers, r i 0 is primary pulse-rate
value of the ith bat. In order to achieve the optimum solution of
the research problem, the following parameters of bat algorithm
are used:
Algorithm parameter

Value

Population size
Number of points on the Pareto-front
Maximum number of iterations
loudness
Pulse-rate
a=c=

10
40
1000
0.25
0.5
0.9

C. Imperialist Competitive Algorithm (ICA)
ICA is one of the most important evolutionary computation
algorithms that are based on the idea of imperialism and colonialism. ICA was suggested by Gargari and Lucas in 2007 [54].
Firstly, a group of probable solutions of the optimization issue is
generated in the search space of M-dimension. These random solutions are named ‘‘Country”:

Country ¼ ½p1 ; p2 ; . . . ; pM

ð30Þ

Then, each country in this algorithm is measured by its power
which is calculated by the cost function:

Cost function ðcm Þ ¼ fn ðcountryÞ ¼ fn ðp1 ; p2 ; . . . ; pM Þ

ð31Þ

þ 0:1 mean fcost ðcolonies of an empirem Þg

ð34Þ

‘‘Imperialistic Competition” is a vital phase of the ICA where
powerful empires attempt to dominate colonies of weaker
empires. The probability function Pp that determines the domination of each empire is illustrated as follows:





M:T:C:m


Pp ¼ PM

j¼1imp M:T:C:m

ð35Þ

where M:T:C:m is the normalized total cost of mth empire.
Under certain arrangements based on the probability function
aforementioned, the colony countries are split through empires
[54]. Eventually, only the powerful empires that have the largest
total power of both imperialist and colony countries are withstood
while powerless empires are vanished which leads to the optimum
convergent solution.
In order to achieve the optimum solution of the research problem, the following algorithm parameters are used:
Algorithm parameter

Value

Number of initial countries
Number of initial imperialists
Maximum number of iterations
Revolution
Assimilation coefficient
Assimilation coefficient angle
Total cost of empire
Damping rate

200
8
1000
0.3
2
0.5
0.02
0.99

D. Flower pollination Algorithm (FPA)
Flower pollination algorithm (FPA) is a powerful mechanism for
solving the optimization problems. This technique is constructed
on the basis of flower-pollination operation. FPA is explored by
Xin-She Yang in 2012 [55]. FPA is ruled through four principles;

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
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A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx

global-pollination (Biotic and cross-pollination), local-pollination
(Abiotic and self-pollination), Flower-constancy and controlling
both global and local pollination by a switching probability [56].
In order to explain the operation process of the FPA, it is important to know that the algorithm is based on two major phases;
global-pollination and local-pollination.
In the first phase, pollen grains are taken by pollens carriers like
bees. Due to the spread of the bees in a wide zone, reaching the
best solution is guaranteed. The present superior solution is
marked asg . The motion of pollens carriers (bees) is obeyed Levy
flight hypnosis. FPA is constructed based on the flower-constancy
which reflects the ordination of bees to fly around specific flower,
leaving other flowers which may have more nectar. The motion of
bees is combined with flower-constancy as follows:

xi tþ1 ¼ xi t þ Lðxi t g Þ

ð36Þ

t

where xi is a vector that represtnts the initial solutions at t iteration, L is the size of each distance step that achieved by the pollens
carriers based on Levy flight distribution [55].
The second phase and flower-constancy can be merged as
follows:

xi tþ1 ¼ xi t þ ðxj t xk t Þ
t

ð37Þ

t

where xi and xk are pollen grains of various flowers (different solutions), is a stochastic number in the range of 0–1. Phase one and
phase two can be checked through switching probability p that
can be transferred between the two phases according to the location of the better solution, as the process of pollination can happen
at local or global places. Therefore, the algorithm is operated till the
best solution is found [55].
In order to achieve the optimum solution of the research problem, the following algorithm parameters are used:
Algorithm parameter

Value

Population size
probability switch
Maximum number of iterations
k (Levy flight coefficient) [40]

20
0.8
2000
1.5

5. Simulation results
In order to verify the purpose of this research, the four suggested algorithms are applied to IEEE 69-bus standard system
[57]. The studied 69-bus IEEE system is shown in Fig. 6. Different
loading time periods (12 periods) through the year is implemented.
The studied system is subjected to various penetration levels of
RDGs power generation based on the standard sizing of the each
unit (12.5 kW, 25 kW and 50 kW) and with limited locations of
RDGs (4 or 8 locations). Also, the study is accomplished through
different RDGs power injections (active power only, reactive power
only and, active and reactive power). Many detailed study cases are
examined.
OPLF solution in this study is fulfilled using GSA, BA, ICA and
FPA. The results of each algorithm were compared to the results
of the other three algorithms to validate the efficiency of the suggested algorithms.
This work is governed via two main strategies. In the first strategy, each type of RDGs (WT units and PV panels) is implemented
individually due to their geographical constraints which impose
restrictions on utilizing them simultaneously. In the second strategy, there is a limitation on the maximum numbers of the RDGs
at each bus location [58]. As the aim of this work is to allocate
the RDGs as a bulky unit at the heavy bus load, thus the second
strategy is made to validate the proposed algorithms [59].

7

5.1. Implementing wind farms results
The probability density function of wind farm module is divided
into 12 probability level as illustrated in Fig. 4. Table 4 demonstrates the results of the proposed algorithms; the extracted locations and the total power loss of the applied system versus the
sizes of wind turbine modules. The rated capacities of the utilized
wind turbine unit are 12.5 kW, 25 kW and 50 kW [58,59]. The
number of units installed for the wind turbine module are chosen
to be 4 or 8 units, this leads to the following range of penetration
levels: the maximum penetration level is 400 kW (50 kW for 8
units) and minimum penetration level of 50 kW (12.5 kW for 4
units). Tables 2 and 3 show the results of the proposed algorithms
of installing the wind turbine units for different penetration levels
indicating the optimal locations and the power loss of each wind
farm module when the modules supplies active power employing
4 and 8 units respectively.
Tables 4 and 5 demonstrate the results of the proposed algorithms of installing the wind turbine units for different penetration
levels indicating the locations and the power loss of each wind
farm module when the modules supplies reactive power employing 4 and 8 units respectively.
Tables 6 and 7 show the results of the proposed algorithms of
installing the wind turbine units for different penetration levels
indicating the locations and the power loss of each wind farm
module when the modules supplies active and reactive power
employing 4 and 8 units respectively.
Based on the results, implementing the WT units, as a source of
active and reactive power, provides best loss reduction than the
other cases (supplying active power only or supplying reactive
power only). Employing ICA in this optimizing problem gives superior performance over the other algorithms. The higher penetration
level introduces preferable results than the lower penetration
level. The 8 location results in all penetration levels is obtaining
better results than installing WTs at 4 location only.
5.2. Implementing PV modules results
The probability density function of PV module is divided into 12
probability level as illustrated in Fig. 5. Table 2 demonstrates the
results of the proposed algorithms; the extracted locations and
the total power loss of the applied system versus the sizes of PV
modules. The rated capacities of the utilized PV unit are 12.5
KW, 25 KW and 50 KW [58,59]. The probabilistic total power loss
of the system under study without applying RDGs is 179 KW.
The number of units installed for the RDGs are chosen to be 4 or
8 units [58,59], this leads to the following range of penetration
levels: the maximum penetration level is 400 kW (50 kW for 8
units) and minimum penetration level of 50 kW (12.5 kW for 4
units). Tables 8 and 9 show the results of the proposed algorithms
of installing the PV units for different penetration levels indicating
the optimal locations and the power loss of each PV module when
the modules supplies active power only employing 4 and 8 units
respectively.
Tables 10 and 11 demonstrate the results of the proposed algorithms of installing the PV units for different penetration levels
indicating the locations and the power loss of each wind farm
module when the modules supplies reactive power employing 4
and 8 units respectively.
Tables 12 and 13 show the results of the proposed algorithms of
installing the PV units for different penetration levels indicating
the locations and the power loss of each wind farm module when
the modules supplies active and reactive power employing 4 and 8
units respectively.
Based on the results, implementing the PV units, as a source of
active and reactive power, provides best loss reduction than the

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

8

A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx

Fig. 6. IEEE 69-bus radial distribution system.

Table 2
The results of the proposed algorithms indicating the size, the location of wind farm modules (when supplying active power using 4 units), and the power loss.
WT size

GSA

50 kW
25 kW
12.5 kW

BA

ICA

FPA

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

41 39 38 47
43 44 49 40
39 40 41 42

106.15
107.06
107.06

66 2 68 57
53 34 68 60
48 63 58 68

106.34
107.01
107.5

68 7 61 61
27 57 17 56
50 7 49 31

94.36
100.52
100.52

45 68 63 62
59 63 62 68
68 61 62 34

101.19
104.29
106.3

Table 3
The results of the proposed algorithms indicating the size, the location of wind farm modules (when supplying active power using 8 units), and the power loss.
WT size

50 kW
25 kW
12.5 kW

GSA

BA

ICA

FPA

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

38 43 39 37 36 40 26 34
39 36 32 37 34 42 43 35
37 36 33 39 42 40 36 32

104.93
106.63
107.22

36 18 10 59 33 66 61 26
43 51 20 57 59 39 64 60
66 30 36 40 6 43 60 37

105.3
106.34
107.33

66 26 14 28 16 39 58 35
26 52 51 49 15 47 28 53
5 49 60 23 10 61 8 21

65.82
82.77
94.86

37 34 53 68 62 14 39 55
6 16 66 59 49 68 55 62
34 31 68 66 43 15 60 61

97.386
102.45
105.17

Table 4
The results of the proposed algorithms indicating the size, the location of wind farm modules (when supplying reactive power using 4 units), and the power loss.
WT size

GSA

50 kW
25 kW
12.5 kW

BA

ICA

FPA

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

44 37 38 36
39 49 38 41
41 40 42 39

106.4
107.19
108

51 33 68 60
68 57 68 64
53 68 40 62

106
107.16
107.52

13 46 51 35
28 56 35 27
34 10 20 67

94
100.3
104.1

67 65 60 58
59 60 67 66
65 48 67 63

105.63
106.86
107.48

Table 5
The results of the proposed algorithms indicating the size, the location of wind farm modules (when supplying reactive power using 8 units), and the power loss.
WT size

50 kW
25 kW
12.5 kW

GSA

BA

ICA

FPA

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

29 34 30 39 43 40 37 36
37 37 30 44 40 39 30 43
36 33 40 41 39 38 34 35

105
106.54
107.27

66 40 62 60 39 30 17 56
67 18 13 47 16 53 40 68
57 65 66 44 2 67 68 53

104.82
106.65
107.22

56 20 13 30 45 66 6 22
30 53 32 14 36 60 3 28
62 22 40 37 52 23 18 38

93
99.9
103.8

62 59 58 57 68 64 18 54
67 2 66 68 68 41 5 4
8 67 68 52 53 10 2 51

104
106.86
108

other cases. Employing ICA in this optimizing problem gives superior performance over the other algorithms. The higher penetration
level presents better results than the lower penetration level. The 8
locations results in all penetration levels are gaining best results
than installing PVs at 4 locations only.

5.3. Performance evaluation
As a summary of the results of this research; the efficiency of
the suggested algorithms has been proven in finding the optimal
location and sizing of RDGs in order to minimize the power losses

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

9

A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx
Table 6
The results of the proposed algorithms indicating the size, the location of wind farm modules (when supplying active and reactive power using 4 units), and the power loss.
WT size

GSA

50 kW
25 kW
12.5 kW

BA

ICA

FPA

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

44 41 47 42
40 38 43 42
42 34 46 35

99.8
104.3
106

38 66 63 68
57 31 68 60
66 68 53 57

98.87
103.75
106.11

11 32 9 39
46 61 37 65
5 42 55 8

53.7
75.66
76

45 68 63 62
40 68 66 57
56 68 37 58

99
103
106

Table 7
The results of the proposed algorithms indicating the size, the location of wind farm modules (when supplying active and reactive power using 8 units), and the power loss.
WT size

50 kW
25 kW
12.5 kW

GSA

BA

ICA

FPA

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

41 34 35 39 34 43 37 36
39 40 42 34 33 40 37 36
32 31 38 39 40 37 36 33

95
100
105

40 56 9 60 64 59 68 29
49 55 36 68 28 26 56 63
68 29 60 2 61 28 42 44

93.732
100.84
104.86

13 32 63 9 52 4 43 48
52 48 10 27 39 47 53 54
28 64 15 51 26 66 59 53

51.1
74.66
103. 8

37 34 53 68 62 14 39 55
34 15 55 57 48 68 51 36
34 31 68 66 43 15 60 61

94
101
104

Table 8
The results of the proposed algorithms indicating the size, the location of PV units (when supplying active power only using 4 units), and the power loss.
PVs size

GSA

50 kW
25 kW
12.5 kW

BA

ICA

FPA

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

40 41 42 38
38 41 40 42
43 39 42 45

106.08
107
107.07

66 63 68 38
57 31 68 60
66 67 53 68

105.82
106.67
107.08

15 32 57 18
5 49 61 23
56 20 13 30

97.29
101.7
104.4

57 66 68 54
66 68 59 54
66 60 63 68

105.74
106.56
106.97

Table 9
The results of the proposed algorithms indicating the size, the location of PV units (when supplying active power only using 8 units), and the power loss.
PVs size

50 kW
25 kW
12.5 kW

GSA

BA

ICA

FPA

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

30 40 41 39 29 33 37 40
30 44 42 38 39 43 37 45
36 42 43 31 44 38 41 40

105.33
106.25
106.81

40 56 9 60 59 67 29 68
47 55 36 68 28 26 56 63
68 29 60 2 61 28 42 44

104.92
106.17
106.86

68 59 54 57 27 62 20 41
54 18 36 39 67 19 22 17
30 2 58 18 36 58 64 43

96.63
101.4
104.3

58 23 59 19 55 68 56 60
38 53 59 47 62 68 64 8
49 48 68 63 59 36 24 42

104.78
106.12
106.78

Table 10
The results of the proposed algorithms indicating the size, the location of PV units (when supplying reactive power only using 4 units), and the power loss.
PVs size

GSA

50 kW
25 kW
12.5 kW

BA

ICA

FPA

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

47 43 38 35
38 42 39 35
44 40 41 38

103
105
106

33 68 56 66
41 62 64 68
60 63 54 68

102.36
104.84
106.04

35 32 62 43
38 19 14 49
61 23 10 61

80
89.39
97.77

23 68 63 66
59 64 66 68
62 60 57 68

102.53
104.55
106.02

Table 11
The results of the proposed algorithms indicating the size, the location of PV units (when supplying reactive power only using 8 units), and the power loss.
PVs size

50 kW
25 kW
12.5 kW

GSA

BA

ICA

FPA

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

36 48 42 45 40 34 33 39
35 39 40 36 44 33 41 32
43 40 41 47 41 38 33 33

100
104
105

68 57 64 10 66 58 2 24
61 63 37 48 58 8 33 59
68 56 13 62 26 31 2 55

99.9
103.61
105.67

67 25 22 11 55 33 2 10
45 43 28 36 7 57 51 56
16 64 59 58 42 56 22 25

76.87
88.9
88.9

66 53 2 68 26 43 58 61
16 61 24 10 62 66 42 51
66 68 62 53 21 23 63 58

99
103
102.9

Table 12
The results of the proposed algorithms indicating the size, the location of PV units (when supplying active and reactive power only using 4 units), and the power loss.
PVs size

50 kW
25 kW
12.5 kW

GSA

BA

ICA

FPA

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

Locations

Loss (kW)

45 46 39 43
44 46 37 34
46 40 43 44

102
105
106

56 62 68 2
36 68 66 6
63 54 34 68

101.97
104.74
105.78

15 53 52 21
27 41 25 45
49 36 35 24

66.66
85
95.31

63 60 66 68
66 68 41 57
64 62 68 63

100.08
103.97
105.58

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

10

A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx

Table 13
The results of the proposed algorithms indicating the size, the location of PV units (when supplying active and reactive power only using 8 units), and the power loss.
PVs size

50 kW
25 kW
12.5 kW

GSA

BA

ICA

FPA

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

Locations

Loss
(kW)

43 37 35 40 34 31 36 39
40 39 42 44 41 37 34 31
31 39 37 36 39 40 32 45

97
103
105

44 51 56 48 60 4 59 40
55 60 24 48 57 68 62 45
31 40 58 59 64 66 52 68

98.02
101.56
104.65

17 34 51 37 21 68 19 3
45 60 48 47 20 32 20 53
24 43 65 6 68 49 7 30

66.12
82.95
84.22

68 64 63 62 51 28 66 42
68 32 55 56 53 47 60 58
58 62 68 61 57 47 15 44

96
101.41
104.49

of the IEEE 69-bus standard system. The system is subjected to several penetration levels (12.5 kW, 25 kW and 50 kW), different
RDGs sources (WT units and PV panels) and different power injections (active power only, reactive power only and, active and reactive power).
Based on the results extracted from this work, it is clear that
placing renewable distributed generators such as wind turbine
(WT) units gaining better results than employing photovoltaic panels (PV) from the reduction of power losses point of view. GSA, BA,

FPA and ICA are proved to be effective and valid tools to solve the
optimization problem under study. Using the RDGs as a source of
active and reactive power increases preferable outcomes over utilizing them as a source of active power or reactive power only. ICA
has proven its superiority, over GSA, BA and FPA, in finding the
optimal power loss reduction in the applied system. The superiority of employing ICA can be illustrated as shown in Figs. 7 and 8 by
comparing the results of the four suggested algorithms for some
study samples of different cases; case (1): the unit is supplying

Fig. 7. Performance comparison of the proposed algorithms (employing WT units with 50 kW unit size for 8 locations).

Fig. 8. Performance comparison of the proposed algorithms (employing PV units with 25 kW unit size for 4 locations).

Fig. 9. Convergence of the suggested algorithms (employing PV units, supplying active and reactive power, with 50 kW unit size for 8 locations).

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003

A.M. Ibrahim, R.A. Swief / Ain Shams Engineering Journal xxx (xxxx) xxx

active power, case (2): the unit is supplying reactive power and
case (3): the unit is supplying active and reactive power.
The convergence characteristics of the suggested algorithms
proved the appropriate selection of the parameters of each algorithm. The convergence of the utilized algorithms for a case of
using PV units, supplying active and reactive power, with 50 kW
unit size for 8 locations as illustrated in Fig. 9 is used as an evident
for the superiority of employing ICA over the other algorithms in
terms of reaching the best optimal solution with fewer iterations.

6. Conclusion
This paper proposes an optimal probabilistic load flow (OPLF)
method for finding out the power loss reduction for a distributed
network equipped with RDGs (WT or PV units). The Load flow
has been executed utilizing forward-backward sweep methodology. The wind speed random behavior is modeled using Weibull
Probability Density Function (WPDF). Also, the solar irradiance
data taken from official site is modeled using WPDF taking into
consideration the load level variations at each bus. These models
are combined to participate in the optimization problem for determination of the optimum location and for sizing the RDGs modules
that minimize the system power losses on the feeders. The optimization problem is performed using four modern heuristic algorithms; Gravitational Search Algorithm (GSA), Bat Algorithm (BA),
Imperialist Competitive Algorithm (ICA) and Flower Pollination
Algorithm (FPA). The penetration levels of RDG units with different
modes of power generation are considered. Based on the results,
the use of WTs module, on IEEE 69-bus standard system, gives better results than using PVs module. Also results indicate that utilizing WT units or PV panels, with high penetration level, as a source
of active and reactive power provides best loss reduction than the
other cases (supplying active power only or supplying reactive
power only). The 8 locations results in all penetration levels are
gaining best results than installing PVs or WTs at 4 locations only.
The results indicate the validity and the effectiveness of the proposed algorithms in achieving the target of the research. ICA
results demonstrate its efficiency and superiority, in finding the
optimal location and in sizing of PV/WT units on the distribution
network for the purpose of reducing power loss, over the other
suggested algorithms.
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Dr. Amr. M. Ibrahim was born in Egypt in 1975. He
received the B.Sc., M.Sc. and the Ph.D. (2008) degrees in
electrical engineering from Ain Shams University, Cairo,
Egypt. He is currently an Assistant Professor in the
Department of Electric Power and Machines, Ain Shams
University. He has supervised 10+ Ph.D. and M.Sc. theses in the field of electrical power system. He has taught
tens of undergraduate and graduate courses in this field.
He has authored and co-authored more than 30 papers.
He is interested in many research areas such as: distributed generation, renewable Energy, and power system protection.

Dr. Rania A. Swief got her B.Sc., M.Sc., and Ph.D from
Ain Shams University, Cairo, Egypt on 1998 , 2004 , and
2010 respectively. Ph.D was in the area of Deregulated
market and price load market relations. Contributed in
many paper nationally and internationally. She has
many publications in local and international conferences. Supervised many Ph.D and Master degrees in the
areas of Smart grid, Protection, Deregulated market and
Renewable Energy. Her Fields of Interests lie in Power
System Analysis, Planning, and Renewable Energy.

Please cite this article as: A. M. Ibrahim and R. A. Swief, Comparison of modern heuristic algorithms for loss reduction in power distribution network
equipped with renewable energy resources, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2017.11.003


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