A hybrid algorithm for voltage stability enhancement of distribution systems

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 1, February 2022, pp. 50~61
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i1.pp50-61  50
Journal homepage: http://ijece.iaescore.com
A hybrid algorithm for voltage stability enhancement of
distribution systems
Hazim Sadeq Mohsin Al-Wazni, Shatha Suhbat Abdulla Al-Kubragyi
Department of Electrical Engineering, Technology University, Baghdad, Iraq
Article Info ABSTRACT
Article history:
Received Feb 26, 2021
Revised Jun 18, 2021
Accepted Jun 29, 2021
This paper presents a hybrid algorithm by applying a hybrid firefly and
particle swarm optimization algorithm (HFPSO) to determine the optimal
sizing of distributed generation (DG) and distribution static compensator
(D-STATCOM) device. A multi-objective function is employed to enhance
the voltage stability, voltage profile, and minimize the total power loss of the
radial distribution system (RDS). Firstly, the voltage stability index (VSI) is
applied to locate the optimal location of DG and D-STATCOM respectively.
Secondly, to overcome the sup-optimal operation of existing algorithms, the
HFPSO algorithm is utilized to determine the optimal size of both DG and
D-STATCOM. Verification of the proposed algorithm has achieved on the
standard IEEE 33-bus and Iraqi 65-bus radial distribution systems through
simulation using MATLAB. Comprehensive simulation results of four
different cases show that the proposed HFPSO demonstrates significant
improvements over other existing algorithms in supporting voltage stability
and loss reduction in distribution networks. Furthermore, comparisons have
achieved to demonstrate the superiority of HFPSO algorithms over other
techniques due to its ability to determine the global optimum solution by
easy way and speed converge feature.
Keywords:
D-STATCOM
HFPSO algorithm
Smart distribution grid
Voltage stability
This is an open access article under the CC BY-SA license.
Corresponding Author:
Hazim Sadeq Mohsin Al-Wazni
Department of Electrical Engineering, Technology University
Industrial Street, Baghdad, Iraq
Email: hazimwazni83@gmail.com
NOMENCLATURE
𝑉𝑅 : The voltage at receiving end bus 𝑥𝑖(𝑡) : Size of particles
𝑉𝑆 : The voltage at sending end bus 𝑥𝑖(𝑡 + 1) : Updated size of the particles
𝑉𝑅𝑛𝑒𝑤 : The voltage at receiving end bus after
compensated
𝑉𝑖(𝑡)
𝑣𝑖(𝑡 + 1)
: Velocities of the particles
: Updated velocities of the particles
𝜃𝑛𝑒𝑤 : Phase angle between 𝑉𝑅𝑛𝑒𝑤 and 𝑉𝑆 𝑡 : Number of iteration
𝛿 : Phase angle of sending end voltage 𝐼𝐷−𝑆𝑇𝐴𝑇𝐶𝑂𝑀 : The injected current of D-STATCOM
𝛼 : Phase angle of Current pass between
two buses
𝑆𝑡𝑜𝑡𝑎𝑙 𝑙𝑜𝑠𝑠
𝑅𝑆𝑅 + 𝑗𝑋𝑆𝑅
: Total power losses
: Impedance of branch between bus 'S' and 'R'
𝑉𝑅,𝑚𝑖𝑛 : Minimum Voltage limit of bus 'R' 𝛽2 and 𝛽3 : Weighting factors of objective functions β_1
𝑉𝑅,𝑚𝑎𝑥 : Maximum Voltage limit of bus 'R' 𝑄𝐷𝑆𝑇𝐴𝑇𝐶𝑂𝑀(𝑅) : Reactive power of D-STATCOM at bus ‘R’
𝑃𝑅(𝑅)
𝑉𝑆𝐼𝑅
: Real power of DG at bus ‘R’
: Voltage stability index of node 'R'
𝑃𝑇𝐿 : Total real loss before insert DG and D-
STATCOM
𝐴𝑉(𝑥)
𝑊
: Average of buses voltages
: Weight inertia
∆𝑃𝑇𝐿
𝐷𝐺 𝐷𝑆𝑇
⁄ : Loss Reduction Index with DG and D-
STATCOM
𝑐2,𝑐1
𝐼𝐿
: Acceleration coefficients
: Current pass between two buses
𝑄𝐷𝑆𝑇𝐴𝑇𝐶𝑂𝑀(𝑅)
𝑚𝑖𝑛
, 𝑄𝐷𝑆𝑇𝐴𝑇𝐶𝑂𝑀(𝑅)
𝑚𝑎𝑥 : Minimum, maximum injected reactive power
limit of compensated bus' R'
𝑔𝑏𝑒𝑠𝑡𝑡−1 : Global best size 𝑃𝑅,min(𝑅), 𝑃𝑅,max(𝑅) : Maximum, minimum real power limit of
compensated bus 'R'

Int J Elec & Comp Eng ISSN: 2088-8708 
A hybrid algorithm for voltage stability enhancement of … (Hazim Sadeq Mohsin Al-Wazni)
51
𝑝𝑏𝑒𝑠𝑡𝑖 : Particle best size 𝑃𝑙𝑜𝑠𝑠(𝑆, 𝑅), 𝑄𝑙𝑜𝑠𝑠(𝑆, 𝑅) : Real and reactive power losses of branch
between bus 'S' and 'R'
1. INTRODUCTION
Nowadays, transmission and distribution power systems are facing a challenge to provide the power
demands for more customers with better quality and higher reliability at a lower cost. Such growing demand
increasing power transfer through lines which is limited by the thermal, voltage, and stability of lines.
Consequently, when the lines are operated near to their critical limits of power angles or voltage limits, any
increased demand in this system would results instability like power system oscillation and voltage collapse
occurrence which may lead to generator outages and ultimately blackout [1].
Different techniques have been suggested by researchers for solving the voltage system stability
issues and minimizing losses in distribution systems. Previosly, system planners are inclined to develop new
lines. However, such technique is difficult to implement due to some of the economic and environmental
concerns [2], [3]. So, these various restrictions on the construction of new transmission lines have persuaded
the power system designers to look for some alternative solutions,so to increase the power system stability
and efficiently transmit power over the transmission lines [4].
To minimize the probability of voltage collapse happening and enhance voltage stability as well as
improve voltage profile, some researchers have proposed to add capacitors in an optimal location with
optimal size by using different optimization techniques such as harmonic search (HS) algorithm [5], dice
game optimization (DGO) [6], and modified biogeography based optimization (MBBO) algorithm [7].
However, these shunt capacitors are not capable to constantly produce a variable reactive power and exhibit
some of the operational problems like resonance [2]. Such restrictions of the construction of shunt capacitors
have persuaded the power system designers to look for some alternative solutions.
Recently, distribution generators (DG) are widely known as "an electric power source connected
directly to the distribution network or on the customer side of the meter'', that form the key part of the
solutions [8]. DGs are known as small distributed generators which are consisted of renewable and
nonrenewable power sources. DGs are contributed to the centralized power grids that are managed at the
distribution level [9]. The integration of renewable energy sources in the conventional distribution system is
becoming valuable and more attractive due to their economic and technical impacts [10]. Many researcher
have adopted various types of renewable sources (fuel cell, PV, battery, biomass, wind) [11]-[14]. However,
advanced devices are required to control and manage the new smart distribution grids to operate with
bidirectional power flow using power electronics and energy storage units [15]. Combining the use of the
distributed flexible ac-transmission system (D-FACTS) as a power electronic device with DG in the
distribution networks will mitigate the problems of environmental, reliability, and stability issues [2].
The distributed static synchronous compensator (D-STATCOM) is the most important type of
shunt-connected D-FACTS device, it is connected directly to low voltage distribution grids without any
ancillary components which represents as an efficient shunt capacitors substitute [2]. It acts as a reactive
power compensation source, harmonics reduction, power factor correction, and controlling the voltage of the
distribution network [16]. Recently, the combination of DG and D-STATCOM was suggested which could
compensate for the active and reactive power in smart distribution grids. The optimal location and the
capacity of DGs of these sources are some of the main factors of contribution in affecting the improvement of
the power quality indices such as the reduction of the distribution systems losses and maintaining the voltage
profile within acceptable limits [17].
A DG with D-STATCOM was tested under different conditions to enhance the voltage stability of
different load models [2], [18]. Several studies have been presented under the name of metaheuristic
techniques such as “whale optimization algorithm (WOA) [17], noval light search algorithm (LSA) [2],
gravitational search algorithm (GSA) [19], a combination of genetic algorithm and particle swarm
optimization (GA and PSO) [20], grey wolf optimization algorithm (GWOA) [21], vortex searching
algorithm [22], imperialist competitive algorithm (ICA) [8], and hybrid genetic and ant colony algorithm
[16]” to determine the optimal placement problem of DG and D-STATCOM in smart power systems. Many
of the above studies mentioned above have been carried out to locate the optimal location and size problems
of DG and D-STATCOM devices separately or simultaneously.
Remarkably, a comprehensive study is lacking in using intelligent algorithms in exploiting the
potentials of the DGs with D-STATCOM. Although, several studies have presented under the name of
metaheuristic techniques. PSO and general algebraic modeling systems were proposed to solve the sizing and
location of single and multiple D-STATCOM in [23]. An artificial fish swarm optimization algorithm
(AFSOA) using voltage stability index (VSI) and loss sensitivity factor (LSF) was applied to deduce the size
and optimal locations of DGs and D-STATCOM in [24].

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 50-61
52
Further, research on using the VSI and WOA was developed to select the proper location and best
size of DG, so to enhance the voltage stability and increase the load-ability through injecting the appropriate
active and reactive powers. However, the best DG place is allocating by using the VSI to find the most
sensitive buses [25]. The literature clarified that the researchers are continuing to develop intelligent
optimization techniques to solve global optimization problems. This paper has proposed to exploit the
advantage of firefly algorithm (FA) and PSO as a fast converge optimization algorithm with good-tuning
feature, so to easily achieve the global optimum solution for optimal placement and sizing of DG and D-
STATCOM device to support the grid’s voltage stability as well as enhance voltage profile and minimize
power losses.
The motivation of this study focuses on the tabulated results which illustrate the ability of the hybrid
firefly and particle swarm optimization algorithm (HFPSO) to determine the optimal placement and sizing of
DG and D-STATCOM device, due to its feature to find the global optimum solution. The algorithm is based
on a multi-objective HFPSO to minimize the system power losses and voltage profile enhancement as well as
increasing the system stability. The verification of the proposed algorithm is achieved on the standard IEEE
33-bus and Iraqi 65-bus radial distribution systems through simulation using MATLAB.
This paper is organized as follows. Section 2 explains the system modeling, While section 3
presents the problem formulation. A hybrid algorithm combining the firefly algorithm and particle swarm
optimization is introduced in section 4. In section 5, the simulation results of a distribution system under
different cases with the proposed algorithm are presented. Furthermore, a performance comparison of the
system is then carried out against other existing algorithms in supporting voltage stability and loss reduction
in the distribution networks. Finally, section 6 gives concluding remarks on the current work.
2. SYSTEM MODELLING
2.1. D-STATCOM modelling
D-STATCOM is well-known as an efficient power electronic device control power flow [16], [26].
The basic function of the D-STATCOM is providing reactive power that depends on the reactive power
exchange between the AC grid and the D-STATCOM with fast and uninterrupted power [16], [21], [27]. The
injected reactive power deduce by (1).
𝑄𝐷−𝑆𝑇𝐴𝑇𝐶𝑂𝑀 = 𝑉
𝑟𝑛𝑒𝑤 (𝐼𝐷−𝑆𝑇𝐴𝑇𝐶𝑂𝑀)∗
(1)
Where 𝐼𝐷−𝑆𝑇𝐴𝑇𝐶𝑂𝑀∠((
𝜋
2
) + 𝜃𝑛𝑒𝑤) is the injected current by DSTATCOM 𝑉𝑅𝑛𝑒𝑤 = 𝑉𝑅𝑛𝑒𝑤∠𝜃𝑛𝑒𝑤 is the
voltage of bus ‘R’ after correction. Figure 1(a) shows the single line diagram of two buses of a distribution
system with D-STATCOM that is installed in bus ‘R’ Voltage of bus ‘R’ changes from 𝑉𝑅 to 𝑉𝑅𝑛𝑒𝑤 as shown
in Figure 1(b).
(a) (b)
Figure 1. Single line diagram and the phasor diagram of two buses with D-STATCOM: (a) single line
diagram of two buses with D-STATCOM [21], (b) the phasor diagram of two buses with D-STATCOM [21]
𝑉𝑅𝑛𝑒𝑤∠𝜃𝑛𝑒𝑤 = 𝑉𝑆∠𝛿 − (𝑅𝑆𝑅 + 𝑗𝑋𝑆𝑅)𝐼𝐿∠𝛼 − (𝑅𝑆𝑅 + 𝑗𝑋𝑆𝑅)𝐼𝐷−𝑆𝑇𝐴𝑇𝐶𝑂𝑀∠((
𝜋
2
) + 𝜃𝑛𝑒𝑤) (2)

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DSTATCOM is one of the most efficient D-FACTS devices due to its features like zero resonance,
less harmonic distortion, low power losses, low cost, compact size and high regulatory capability [16], [28].
D-STATCOM has been employed as multi-applications at the distribution grids, so to enhance voltage
profile, minimize real power loss, improves load ability, and enhances stability [21]. However, the proper
location of D-STATCOM is important to minimize the network power loss and subject to the following
standard limits [29]:
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑙𝑖𝑚𝑖𝑡: 𝑉𝑅,𝑚𝑖𝑛 ≤ 𝑉𝑅 ≤ 𝑉𝑅,𝑚𝑎𝑥
where 𝑉𝑅,𝑚𝑖𝑛 is the minimum voltage limits of bus 'R' and 𝑉𝑅,𝑚𝑎𝑥 is the maximum voltage limits of bus 'R'.
𝐼𝑛𝑗𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑎𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑤𝑒𝑟 𝑙𝑖𝑚𝑖𝑡: 𝑄𝐷𝑆𝑇𝐴𝑇𝐶𝑂𝑀(𝑖)
𝑚𝑖𝑛
≤ 𝑄𝐷𝑆𝑇𝐴𝑇𝐶𝑂𝑀(𝑖) ≤ 𝑄𝐷𝑆𝑇𝐴𝑇𝐶𝑂𝑀(𝑖)
𝑚𝑎𝑥
𝑖 = 1,2,3 , 𝑛𝑏
Where 𝑄𝐷𝑆𝑇𝐴𝑇𝐶𝑂𝑀(𝑅)
𝑚𝑖𝑛
is the minimum reactive power limit of the compensated bus 'R' and 𝑄𝐷𝑆𝑇𝐴𝑇𝐶𝑂𝑀(𝑅)
𝑚𝑎𝑥
is
the maximum reactive power limit of the compensated bus 'R'.
2.2. Distributed generation (DG)
DG is described as a small-scale electric power generation that has a capacity of 1 kW to 100 MW
and linked adjacent to the loads. DG consists of renewable and nonrenewable sources such as micro turbines,
induction generators, synchronous generators, solar photovoltaic, fuel cells, combustion gas turbines, wind
turbines, and other small power generation sources. DG sources are classified into the following four types
[22]:
a) DG type one: DG injects real power (P) only
b) DG type two: DG injects both real and reactive power (P and Q)
c) DG type three: DG injects real (P) power but absorbs reactive power (Q)
d) DG type four: DG injects reactive power (Q) only
The main features of DGs are mitigating the greenhouse effect and using fossil fuel, improve
voltage profile, energy security, reliability, stability, power quality, and reduces power losses [8], [9], [29].
Nevertheless, the optimal locations of DGs are also important to improve the system operation characteristics
and subject to the following standard limits [30]:
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑙𝑖𝑚𝑖𝑡: 𝑉𝑅,𝑚𝑖𝑛 ≤ 𝑉𝑆 ≤ 𝑉𝑅,𝑚𝑎𝑥
𝐼𝑛𝑗𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑎𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑤𝑒𝑟 𝑙𝑖𝑚𝑖𝑡: 𝑃𝑅,min(𝑖) ≤ 𝑃𝑅(𝑖) ≤ 𝑃𝑅,max(𝑖) 𝑖 = 1,2,3 , 𝑛𝑏
where 𝑃𝑅,min(𝑅) is the minimum real power limit of the compensated bus 'R' and 𝑃𝑅,max(𝑅) is the maximum
real power limit of the compensated bus 'R'.
3. PROBLEM FORMULATION
3.1. Load flow analysis
The direct load flow analysis is considered in this paper to find the power losses and voltage profiles
of each bus developed for the radial distribution systems. The power-flow equations are written according to
Kirchhoff's Current Law, a more detailed explanation of the power flow analysis can be found in [27]. The
sample distribution system is shown in Figure 2. The voltage at bus 'R' is written as in (3):
𝑉𝑅 = 𝑉
𝑠 − 𝐵𝑠 ∗ (𝑅𝑠𝑅 + 𝑗𝑋𝑠𝑅) (3)
where 𝐵𝑠 is the bus-currents to branch-currents matrix. The total power loss of the network is calculated by
summing the power losses of all the branch as shown in (4) [2]:
𝑆𝑡𝑜𝑡𝑎𝑙 𝑙𝑜𝑠𝑠 = ∑ 𝑃𝑙𝑜𝑠𝑠(𝑆, 𝑅)
𝑛𝑜.𝑏𝑟𝑎𝑛𝑐ℎ
𝑠=1
+ 𝑗 ∑ 𝑄𝑙𝑜𝑠𝑠(𝑆, 𝑅)
𝑛𝑜.𝑏𝑟𝑎𝑛𝑐ℎ
𝑠=1
(4)
where the power loss in a branch between buses 'S 'and 'R' is identified by using (5) and (6) for real and
reactive losses respectively.

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𝑃𝑙𝑜𝑠𝑠(𝑆, 𝑅) = (
𝑃𝑠
2
+ 𝑄𝑠
2
|𝑉
𝑠|2
) ∗ 𝑅𝑠𝑅 (5)
𝑄𝑙𝑜𝑠𝑠(𝑆, 𝑅) = (
𝑃𝑠
2
+ 𝑄𝑠
2
|𝑉
𝑠|2
) ∗ 𝑋𝑠𝑅 (6)
Figure 2. Single line diagram of two buses system [21]
3.2. Objective function
The multi-objective function should be modeled carefully to avoid conflicting between various
single objective functions. In this paper, the objective function of the proposed algorithm is adopt a number
of functions to be optimized simultaneously such as maximize voltage stability index, mitigate the power loss
and enhance the bus voltage profile with a weighting factor. The weight factors are considered to determine
the priority impact of every single objective function for DG/D-STATCOM interconnection. Due to the fact
that, power losses have a greater effect on utilities and represent the major concern in the power system
network. Therefore, it should be reduced by selected appropriate weight factors more imperative than the
influence voltage stability index and voltage profile. Mathematically, the multi-objective function has as
shown in (7):
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒(𝐹𝑖𝑡𝑡𝑛𝑒𝑠𝑠) = 𝑚𝑖𝑛 (𝛽1(∆𝑃𝑇𝐿
⁄
) + 𝛽2 (
1
𝐴𝑉(𝑥)
) + 𝛽3 (
1
∆ 𝑉𝑆𝐼𝐷𝐺 𝐷𝑆𝑇
⁄
)) (7)
where ∆𝑃𝑇𝐿
⁄
is the ratio of the total power loss after and before adding DG/D-STATCOM in radial
distribution system (RDS) which given by (8) [17].
∆𝑃𝑇𝐿
⁄
=
𝑃𝑇𝐿
⁄
𝑃𝑇𝐿 (8)
⁄
is the ratio of the voltage stability index of weaken bus after and before adding
DG/D-STATCOM in RDS which is given by (9) [2].
⁄
=
𝑉𝑆𝐼𝑎𝑓𝑡𝑒𝑟
⁄
𝑉𝑆𝐼𝑏𝑒𝑓𝑜𝑟 (9)
𝐴𝑉(𝑥) is the average of buses voltages which is given by (10) [15].
𝐴𝑉(𝑥) = (
∑ 𝑉𝑖(𝑥)
𝑛
𝑖=1
𝑛
) (10)
𝛽1, 𝛽2 and 𝛽3 are the weighting factors of the minimization power loss and maximization AV and VSI
respectively which are considered as (0.7), (0.3), and (0.3) respectively.
3.3. Voltage stability index
Voltage stability is the ability of a power system to meet the increasing demand and maintain the
voltage at all buses in an acceptable limit and to avoid the occurrence of the voltage collapse. The voltage

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collapse is defined as a very low voltage profile in a significant number of the system buses with a sequence
of events accompanying voltage instability [1], [31].
The power system security level can be reflected by many possible indices. In this part, the VSI is
applied pre-identify to identify the weak buses of radial distribution networks, in order to strengthen these
buses and maintain system voltages at an acceptable level. It will add DGs and D-STATCOM in an optimal
location. Then, to overcome the sup-optimal operation of the existing algorithms, the HFPSO algorithm is
utilized to determine the optimal size of both DG and D-STATCOM. Moreover, the predetermining
advantage of the optimal location by using VSI to minimize the search space of the optimization algorithm.
The monetary value of voltage stability index can be formulated as relation in (11) [22], [24]:
𝑉𝑆𝐼𝑅 =∣ 𝑉𝑆 ∣4
− 4(𝑃𝑅𝑋𝑆𝑅 − 𝑄𝑅𝑅𝑠𝑅)2
−∣ 𝑉
𝑠 ∣4 (𝑃𝑅𝑅𝑠𝑅 + 𝑄𝑅𝑋𝑠𝑅) (11)
where 𝑉𝑆𝐼𝑅 is the voltage stability index of node 'R' for the distribution system, which is shown in Figure 3.
4. HYBRID FIREFLY AND PARTICAL SWARM OPTIMIZATION (HFPSO)
A HFPSO is used in this study so to find the optimum DG and D-STATCOM placement and sizing.
The HFPSO is introduced firstly by [32] to solve the optimization problem. The performance of the proposed
hybrid optimization algorithm has significant improvements over the standard PSO and FA algorithms due to
the combination of the advantages and strengths of PSO and FA, and also because it mitigates the
disadvantages of these algorithms. Generally, it provides a fast convergence as PSO feature and easily
achieves the global optimum solution as a good-tuning feature of FA [32]. Figure 3 shows the flowchart of
the proposed hybrid of FA and PSO.
Figure 3. Flowchart of HFPSO algorithm [32]

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56
To illustrate the HFPSO algorithm, the steps of the algorithm steps are described below:
1. Input the parameters that are used by both algorithms and initialize particles with random positions and
velocities. In the considered case, the location of D-STATCOM and DG are generated in a form of
vectors as algorithm particles.
2. Run the load flow program to calculate the fitness of each particle according to (7).
3. Calculate the global and personal best particles and then assigned
4. An improvement is done in its fitness value in the last iteration according to (12).
𝑓(𝑖, 𝑡) = {
𝑡𝑟𝑢𝑒, 𝑖𝑓 𝑓𝑖𝑡𝑛𝑒𝑠𝑠(𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑖
𝑡
) ≤ 𝑔𝑏𝑒𝑠𝑡𝑡−1
𝑓𝑎𝑙𝑠𝑒. 𝑖𝑓 𝑓𝑖𝑡𝑛𝑒𝑠𝑠(𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑖
𝑡
) > 𝑔𝑏𝑒𝑠𝑡𝑡−1 (12)
5. Save the current position in a temp variable (𝑥𝑖−𝑡𝑒𝑚𝑝) and calculate the new position and velocity
according to (13) and (14).
𝑥𝑖(𝑡 + 1) = 𝑥𝑖(𝑡) + 𝐵°𝑒−𝛾𝑟2𝑖𝑗
(𝑥𝑖(𝑡) − 𝑔𝑏𝑒𝑠𝑡𝑡−1
) + ᵃ∈𝑖 (13)
𝑣𝑖(𝑡 + 1) = 𝑥𝑖(𝑡 + 1) − 𝑥𝑖−𝑡𝑒𝑚𝑝 (14)
6. Start the local search and handle particle by an imitative FA if a particle has a better or equal fitness value
than the previous global best, otherwise, PSO continues its standard processes with a particle according to
(15) and (16) so to handle this particle.
𝑉𝑖(𝑡 + 1) = 𝑤𝑉𝑖(𝑡) + 𝑐1𝑡1(𝑝𝑏𝑒𝑠𝑡𝑖(𝑡) − 𝑥𝑖(𝑡)) + 𝑐2𝑡2(𝑔𝑏𝑒𝑠𝑡𝑖(t) − 𝑥𝑖(t)) (15)
𝑥𝑖(𝑡 + 1) = 𝑥𝑖(𝑡) + 𝑉𝑖(𝑡 + 1) (16)
7. Run the load flow to calculate the fitness of each particle, select the dominant one and consider it as best
global fitness if it was better than the previous global fitness.
8. Update the best position of each particle by comparing the new position to the best global position.
9. If the algorithm converges, the optimization process is over. Print the optimal solution, or otherwise, go to
step 4.
5. RESULTS AND DISCUSSION
To demonstrate the performance of the HFPSO method, a standard IEEE 33-bus RDS and 65-bus
Iraqi RDS are used and simulated using the MATLAB. The losses and bus voltage for all the systems are
calculated through the direct load flow analysis. The optimal location and sizing of DG and D-STATCOM
are obtained by the proposed optimization algorithm HFPSO. To demonstrate the effectiveness of the
proposed algorithm, the overall findings/results are compared with other optimization techniques such as;
bacterial foraging optimization algorithm (BFOA) [18] and the PSO [10], [33], [34] for four different cases
as follows: i) case 1 the system without DG and D-STATCOM, ii) case 2 the system with only D-
STATCOM, iii) case 3 the system with only DG and iv) case 4 the system with multi DG and D-STATCOM.
5.1. 33-bus test system
A bus test radial distribution system is considered in this paper. To show the effectiveness of the
proposed method, four different case studies have been tested. The data of the system are taken from [35].
The total load of the system is 3715 kW and 2300 KVar with the base apparent power and base voltage are
100 MVA and 12.66 kV respectively. The comparative simulation results of the proposed algorithm and
other optimization techniques are shown in Table 1. Firstly, the system without DG and D-STATCOM as a
base case is simulated. So, the active power losses, the minimum VSI, and the minimum voltage are
210.77 kW, 0.66734 p.u, and 0.90383 p.u, respectively as indicated in Table 1.
Then, the D-STATCOM is placed at 30th
bus as the optimal location (case 2), the total power loss
has been reduced to 143.6 kW and the minimum VSI is enhanced to 0.7355 p.u, while the results obtained in
[18] are 144.38 kW and 0.7228 p.u respectively. In this case, the authors have taken the line data of RDS
presented in [36], [37] which differs from the line data considered in this paper but the same line data
considered in [27] in case placement D-STATCOM. In case 3, one DG (type one) is optimally placed in the
6th
, bus with 2720 kW as an optimal size. The total power loss is reduced to 111.23 kW and the minimum

57
VSI of this system is enhanced to 0.7949 p.u. Clearly, the power loss reduction and VSI enhancement, in this
case, are better than other optimization methods as illustrates in Table 1. Finally, in case 4, three DG and
three D-STATCOM are placed in the system at optimal locations to reduce the power losses and to improve
the minimum VSI of this system. The obtained results are presented in Table 1. The total power loss is
reduced to 13.8 kW and the minimum VSI is enhanced to 0.9415 p.u. It is noticed that the results in case 4
are better than the results of other algorithms. Obviously, the HFPSO gives a good reduction in losses and the
voltage profile of the system has been improved noticeably compared to other algorithms. A comparison of
the voltage profile, stability voltage index and the total power losses for the four different cases are shown in
Figure 4(a), 4(b), and 4(c) respectively.
Table 1. The comparative simulation results
Variable HFPSO BFOA [18] PSO [10], [33], [34]
Case 1 Ploss (kW) 210.77 210.98 210.99
VSImin (p.u.) 0.66734 0.6610 0.6671
Vmin (p.u.) 0.90383 0.9037 0.9038
Case 2 Size in kVAr (location) 1300 (30) 1102.7 (30) 1233 (7)
Ploss (kW) 143.6 144.38 153
VSImin (p.u.) 0.7355 0.7228 0.726
Vmin (p.u.) 0.9261 0.922
Case 3 Size in kW (location) 2720(6) 2200 (6) 2895.1 (7)
Ploss (kW) 111.23 113.14 114.89
VSImin (p.u.) 0.7949 0.7640
Vmin (p.u.) 0.9442 0.9368 0.9501
Case 4 Size in kVAr (location) 390 (12)
650 (24)
840 (30)
400 (12)
350 (25)
850 (30)
603.4 (8)
466.3 (22)
856.7 (30)
Size in kW (location) 880 (12)
870 (24)
1030 (30)
850 (12)
750 (25)
860 (30)
1015.4 (9)
351.4 (24)
8445 (30)
Ploss (kW) 13.8 15.07 27.3993
VSImin (p.u.) 0.9415 0.9376
Vmin (p.u.) 0.985 0.9862 0.975
(a) (b)
(c)
Figure 4. Comparison of results for the four different cases: (a) comparison of voltage profiles for different
cases in 33-bus system, (b) comparison of VSI for different cases in 33-bus system, and (c) comparison of
line losses for different cases in 33-bus system

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5.2. The 65-bus system numerical results
The Iraqi real 65-bus radial distribution system is simulated as a second test system under four
different case studies. Figure 5 shows the system’s configuration. The system data is given in Table 2 and the
results are presented in Table 3. The total load of this RDS is 5669.1 kW and 3560.6 KVar with base
apparent power and base voltage are 100 MVA and 11 kV respectively. The active power losses, the
minimum VSI, and the minimum voltage of the base case are 446.2 kW, 0.645 p.u, and 0.8962 p.u,
respectively.
Figure 5. Iraqi real 65-bus configuration
Table 2. 65 bus system data
From To R (p.u) 𝑃𝐿 𝑄𝐿 To R (p.u) X (p.u) 𝑃𝐿 (MW) 𝑄𝐿 (MVAr)
1 1 2 0.216363 (MW) (MVAr) 33 34 0.006175 0.007538 0.1700 0.1054
2 2 3 0.18478 0.1063 0.0659 34 35 0.045125 0.055081 0.1063 0.0659
3 3 4 0.159363 0.1063 0.0659 35 36 0.032063 0.039137 0.1063 0.0659
4 4 5 0.06318 0.0 0.000 36 37 0.030875 0.037687 0.0 0.000
5 4 6 0.025650 0.1700 0.1054 37 38 0.046550 0.056820 0.1063 0.0659
6 6 7 0.011400 0 0 38 39 0.015200 0.018554 0.0 0.0
7 6 8 0.077663 0.1063 0.0659 39 40 0.056763 0.069286 0.1700 0.1054
8 8 9 0.004750 0.0 0.00 40 41 0.018763 0.022902 0.0 0.0
9 8 10 0.073625 0.1063 0.0659 41 42 0.021138 0.025801 0.1063 0.0659
10 10 11 0.022325 0.0 0.000 42 43 0.045600 0.055661 0.1700 0.1054
11 10 12 0.024938 0.1063 0.0659 43 44 0.022088 0.026961 0.1063 0.0659
12 12 13 0.066025 0.0 0.000 44 45 0.026363 0.032179 0.1700 0.1054
13 12 14 0.032300 0.1700 0.1054 45 46 0.037525 0.045804 0.0 0.00
14 14 15 0.030875 0.1700 0.1054 46 47 0.055813 0.068127 0.1063 0.0659
15 15 16 0.031588 0.0 0.0 47 48 0.007600 0.009277 0.1063 0.0659
16 15 17 0.089538 0.1700 0.1054 48 49 0.021375 0.026091 0.0 0.000
17 17 18 0.017100 0.0 0.0 49 50 0.009975 0.012176 0.1063 0.0659
18 17 19 0.014725 0.1063 0.0659 50 51 0.029688 0.036238 0.1700 0.1054
19 19 20 0.015675 0.0 0.000 51 52 0.006413 0.007827 0.0 0.000
20 19 21 0.095238 0.1063 0.0659 52 53 0.081225 0.099146 0.1700 0.1054
21 21 22 0.121838 0.0 0.0 53 54 0.016150 0.019713 0.0 0.000
22 21 23 0.113050 0.1700 0.1054 54 55 0.018525 0.022612 0.1700 0.1054
23 23 24 0.016388 0.0 0.0 55 56 0.018763 0.022902 0.1700 0.1054
24 23 25 0.011400 0.1700 0.1054 56 57 0.002850 0.003479 0.1063 0.0659
25 25 26 0.001663 0.0 0.0 57 58 0.013538 0.016524 0.1063 0.0659
26 25 27 0.027550 0.1063 0.0659 58 59 0.012588 0.015365 0.0 0.00
27 27 28 0.008550 0.0 0.0 59 60 0.009500 0.011596 0.1063 0.0659
28 28 29 0.011638 0.1063 0.0659 60 61 0.050113 0.061169 0.1700 0.1054
29 29 30 0.020900 0.1700 0.1054 61 62 0.026125 0.031889 0.1063 0.0659
30 27 31 0.015675 0.1700 0.1054 62 63 0.022800 0.027830 0.0 0.000
31 31 32 0.021613 0.0 0.0 63 64 0.021138 0.025801 0.1700 0.1054
32 31 33 0.069113 0.1700 0.1054 64 65 0.024938 0.030439 0.1700 0.1054
It is depicted from Table 3 the total power loss is reduced to 300.3 kW and the minimum VSI is
enhanced to 0.7941 p.u after D-STATCOM is placed at the 33th
bus as the optimal location in case 2. While

59
in case 3, one DG (type one) is optimally placed in the 33th
bus with 5020 kW as the optimal size. The total
power loss is reduced to 122 kW and the minimum VSI of this system is enhanced to 0.8367 p.u. In case 4,
both three DG and one D-STATCOM are installed at optimal locations to reduce the power losses and to
improve the minimum VSI of this system. The obtained results are presented in Table 3. However, the total
power loss is reduced to 12.2 kW and the minimum VSI is enhanced to 0.9707 p.u after a multi DG and D-
STATCOM are placed at the optimal locations. A comparison of the voltage profile, stability voltage index,
and the total power losses for the four different cases are shown in Figure 6(a), 6(b), and 6(c) respectively.
Table 3. 65-bus numerical results
Case 1 Case 2 Case 3 Case 4
Size in MVAr (location) 3.34 (33) 2.77 (33)
Size in MW (location) 5.02 (33) 3.96 (34)
0.39 (39)
1.62 (3)
Ploss (kw) 446.2 300.3 122 12.2
Qloss (kvar) 544.6 367 148.9 14.9
VSImin (p.u.) 0.645 0.7941 0.8367 0.9707
Vmin (p.u.) 0.8962 0.9440 0.9564 0.9926
(a) (b)
(c)
Figure 6. Comparison of results losses for the four different cases: (a) comparison of voltage profiles for
different cases in Iraqi 65-bus system, (b) comparison of VSI for different cases in Iraqi 65-bus system, and
(c) comparison of line losses for different cases in Iraqi 65-bus system
6. CONCLUSION
In this paper, a new optimization technique based on HFPSO has been proposed to enhance the
system stability of smart distribution grids. The main advantage of the proposed algorithm is to combine the
advantages and strengths of PSO and FA and to mitigate the disadvantages of these algorithms. HFPSO is
employed to solve a multi-objective function including voltage stability enhancement and minimizing the

 ISSN: 2088-8708
60
total power loss by finding the optimal locations and sizes of DG and D-STATCOM in the power distribution
system. Actually, The effectiveness of the proposed algorithm has been tested on two power systems.
Besides, the overall results were, compared with some other optimization techniques such as BFOA and PSO
under four different cases. Comprehensive simulation results show that the proposed HFPSO algorithm
achieves significant improvements compared to other optimization algorithms in supporting voltage stability
and in minimizing the power losses in distribution networks. Generally, HFPSO provides a fast convergence
as PSO feature and easily achieves the global optimum solution as a good-tuning feature of the firefly
algorithm. Furthermore, it could be concluded that the HFPSO would simplify the use, as an intelligent real-
time tool with any large distribution system.
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BIOGRAPHIES OF AUTHORS
Hazim Sadeq Mohsin Al-Wazni was born in 1981. He received his B.Sc. degree
in Electrical Engineering from University of Babylon, Iraq in 2003. Presently he is pursuing
M.Sc. In Electrical Power Engineering in Department of Electrical Engineering at Technology
University, Iraq. He has more than 16 years of experience in mantainus of electrical
distribution networks. His major scientific interest is focused on optimal location of DG and
D-STATCOM devices, modelling and simulation of distribution power system. He can be
contacted at email: hazimwazni83@gmail.com.
Shatha Suhbat Abdulla Al-Kubragyi received her B.Sc. and M.Sc degree in
Electrical and Electronic Engineering from University of Technology, Baghdad, Iraq, in 2000
and 2003, respectively. She was awarded a Ph.D. degree from University of Cranfield, UK in
2018. Since 2005, she has been a Lecturer in Electrical Engineering in the Department of
Engineering at the University of Technology. Her research interests includes power system
analysis, microgrids , renewable energy technologies, FACTS devices, and power system
operation and control. She can be contacted at email: Shatha.S.Abdulla@uotechnology.edu.iq.

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