See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/310835567
Advanced Pareto Front Non-Dominated Sorting Multi-Objective Particle
Swarm Optimization for Optimal Placement and Sizing of Distributed
Generation
Article in Energies · November 2016
DOI: 10.3390/en9120982
CITATIONS
READS
60
7,885
3 authors:
Mahesh Kumar
Perumal Nallagownden
Mehran University of Engineering and Technology
Universiti Teknologi PETRONAS
40 PUBLICATIONS 290 CITATIONS
126 PUBLICATIONS 2,218 CITATIONS
SEE PROFILE
SEE PROFILE
Irraivan Elamvazuthi
Universiti Teknologi PETRONAS
310 PUBLICATIONS 4,883 CITATIONS
SEE PROFILE
Some of the authors of this publication are also working on these related projects:
http://www.igi-global.com/book/applied-behavioral-economics-research-trends/166083 View project
Manufacturing View project
All content following this page was uploaded by Mahesh Kumar on 27 November 2016.
The user has requested enhancement of the downloaded file.
energies
Article
Advanced Pareto Front Non-Dominated Sorting
Multi-Objective Particle Swarm Optimization
for Optimal Placement and Sizing of
Distributed Generation
Kumar Mahesh, Perumal Nallagownden * and Irraivan Elamvazuthi
Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Seri Iskandar 32610,
Perak Darul Ridzuan, Malaysia; rathii.mahesh@gmail.com (K.M.); irraivan_elamvazuthi@petronas.com.my (I.E.)
* Correspondence: perumal@petronas.com.my; Tel.: +60-12-538-9927
Academic Editor: João P. S. Catalão
Received: 29 June 2016; Accepted: 15 November 2016; Published: 25 November 2016
Abstract: This paper proposes an advanced Pareto-front non-dominated sorting multi-objective
particle swarm optimization (Advanced-PFNDMOPSO) method for optimal configuration (placement
and sizing) of distributed generation (DG) in the radial distribution system. The distributed generation
consists of single and multiple numbers of active power DG, reactive power DG and simultaneous
placement of active-reactive power DG. The optimization problem considers two multi-objective
functions, i.e., power loss reduction and voltage stability improvements with voltage profile and
power balance as constraints. First, the numerical output results of objective functions are obtained
in the Pareto-optimal set. Later, fuzzy decision model is engendered for final selection of the
compromised solution. The proposed method is employed and tested on standard IEEE 33 bus
systems. Moreover, the results of proposed method are validated with other optimization algorithms
as reported by others in the literature. The overall outcome shows that the proposed method for
optimal placement and sizing gives higher capability and effectiveness to the final solution. The study
also reveals that simultaneous placement of active-reactive power DG reduces more power losses,
increases voltage stability and voltage profile of the system.
Keywords: distributed generation; placement and sizing; distribution system; power loss reduction;
voltage stability; multi-objective particle swarm optimization (PSO); non-dominated sorting
1. Introduction
The distribution system is mostly configured radially with high resistance to reactance ratio, hence it
contributes a major share of power losses in the electric network [1]. Besides this, the load demand is
also increasing exponentially which eventually increases more power losses, decrease voltage profile
and imbalance reactive power needs. Therefore, the installation of distributed generation witnesses
many technical and economic benefits in the distribution system. Few of major benefits are; it reduces
system power losses, improves voltage profile, strengthens voltage stability, increases overall network
security, lessens the investment cost and elevates reliability of the system [2,3].
Despite many positive benefits from distributed generation (DG), it is a fact that after installation
of DG in the distribution system, the operational and control behaviour will change. The non-optimal
placement and sizing of distributed generation will increase more system losses, raises more fluctuations
in the voltage profile and deteriorates voltage stability and power quality of the system as compared to
existing one. Hence, in order to get maximum compensation from DG, it should be connected optimally
in the network along with appropriate DG placement and sizing [4].
Energies 2016, 9, 982; doi:10.3390/en9120982
www.mdpi.com/journal/energies
Energies 2016, 9, 982
2 of 23
The DG placement (siting) and sizing (capacity) are mostly attained using optimization algorithms.
Many power system researchers and planners have used diverse types of algorithms for optimal
integration of DG placement and sizing in the distribution system. Most of the algorithms used are
an analytical method, classical optimization technique, artificial intelligence (meta-heuristic) techniques
and other miscellaneous techniques [5]. The authors [6–9] used the analytical method for optimal DG
placement and sizing problem of different objective functions. The drawback of this algorithm is that
it only handles the single-objective optimization problem. Optimal placement and sizing method using
classical optimization algorithm have been used by [10–13]. Some authors had also used meta-heuristic
based optimization algorithm. These algorithms include single-objective or multi-objective optimization
techniques. The algorithms are mainly named as genetic algorithm (GA) [14], bat algorithm (BA) [15],
artificial bee colony (ABC) [16], bacterial forging optimization algorithm (BFOA) [17,18], back-tracking
and fuzzy expert [19], big-bang big crunch method (BB-BC) [20], imperialist competitive algorithm
(ICA) [21], and PSO [2,22–24] are used for stressed problem. It is concluded that most of the research
works are focused on the single objective. However, a few of the authors had worked on the multiobjective optimization with weighted techniques [16,25].
The integration of DG in the distribution system is a complex combinatorial multi-objective
optimization problem, which needs to be solved with many practical objective functions and constraints.
Practically, many objective functions have incommensurability and conflicts between them. It is not
obligatory that all objective functions give a unique solution. Hence, the authors [26–28] worked for
optimal sitting and sizing of multi-objective DG problem with respect to cost as objective functions.
The authors [29–31] used the non-dominated sorting based multi-objective optimization algorithms,
which basically maintains the diversity in the population and gives the final Pareto-solution.
However, this paper proposes an advanced-PFNDMOPSO algorithm for identifying the optimal
placement and sizing of DG in the distribution system. An optimal power flow model is presented for
both single-objective as well as for multi-objective optimization. Two objective functions are considered
for this research (I) minimization of total power loss and (II) maximization of voltage stability index,
while maintaining the technical constraints. For the single objective optimization, the priority is given
to 1st and 2nd objective function respectively, aiming to see the compatibility of proposed method.
Whereas, for multi-objective optimization, both objective functions are optimized simultaneously.
In addition to this, the performance of proposed algorithm is also modified in convergence speed using
mutation operator. The fast convergence is preferable in any algorithm but it is feared that it may result
in false Pareto-solution in the context of multi-objective optimization. Therefore, this operator helps
in maintaining the particles within the search space. Basically, the mutation operator increases the
explorative behaviour for all particles at the start of the algorithm and later its effect ceases gradually.
The results showed that the proposed advanced PFNDMOPSO method gives higher capability and
performance than other single and multi-objective optimization methods for optimal placement and
sizing of DG problem.
Meanwhile, the rest of the paper contents such as Section 2 shows the DG modeling. Section 3
presents the problem formulation for load flow technique and objective functions including constraints.
In Section 4, detailed explanation of multi-objective PSO optimization method is presented while,
Section 5 provides fuzzy decision model. Section 6 presents the case studies of the problem and results
respectively. Lastly, Section 7 presents the conclusion.
2. Distributed Generation (DG) Modeling
In most of the literature, the DG is modeled as an active power DG, which transfers only real
power in the distribution system. Though, nowadays, various kinds of distributed generators are being
integrated into the distribution system as they are identified with different types [2,32]. Such as Type-1
(Distributed Generator that injects only active power P, i.e., it could be photovoltaic, fuel cells, and
micro-turbines with power factor 1), Type-2 (Distributed Generator that injects only reactive power Q,
i.e., synchronous condenser/shunt capacitors or distributed static compensator (DSTATCOM), Type-3
Energies 2016, 9, 982
3 of 23
(Distributed Generator that injects both active and reactive power PQ, i.e., synchronous generator,
combine heat transfer (CHP), gas turbine or cogeneration) and Type-4 (Distributed Generator that
injects active power but at the same time absorbs reactive power, i.e., induction generator). This paper
utilizes the first three types of DGs, which are represented as negative P, Q and PQ loads respectively.
The boundary condition of the real and reactive power DGs are also restricted, which is given as in
Equations (1) and (2).
min
max
PDG
≤ PDG ≤ PDG
(1)
max
Qmin
DG ≤ Q DG ≤ Q DG
(2)
3. Problem Formulation
3.1. Load Flow Technique
The traditional load flow techniques, which are modeled for power transmission system are
not appropriate for distribution system due to its high resistance to reactance ratio [24]. Hence this
paper utilizes a specially designed Backward/Forward Sweep Load Flow algorithm [33]. This load
Energies
2016, 9, 982
of 23
flow
technique
works on two sweeps, the backward sweep (updating current or power flow from3 the
last junction to source junction) and forward sweep (updating voltage from the first junction to the
(DSTATCOM),
Type-3
(Distributed
that injects
both
active
powerthrough
, i.e.,
last
junction). Figure
1 represents
the Generator
one-line diagram
of two
buses
m1 and
and reactive
m2, connected
synchronous
generator,
combine
heat
transfer
(CHP),
gas
turbine
or
cogeneration)
and
Type-4
branch i. The power flow for referred distribution system at branch i can be computed by the following
(Distributed
Generator
injects active power but at the same time absorbs reactive power, i.e.,
set
of recursive
Equationsthat
(3)–(5).
induction generator). This paper utilizesPi the
three types of DGs, which are represented(3)
as
= Pfirst
m2 + Pi loss
negative ,
and
loads respectively. The boundary condition of the real and reactive power
Qm2 + Qi(1)
(4)
i =
lossand (2).
DGs are also restricted, which is given asQin
Equations
Vm2 = Vmin
maxi )
m1 − Ii ( Ri + jX
(5)
(1)
where Pi and Qi , are the real and reactive powers of the branch i interconnecting bus m1 with bus
m2. Pm2 and Qm2 are the real and reactive loads
min at bus m2.maxVm1 and Vm2 are the voltage profiles of
(2)
Q
≤ Q resistance
≤ QDG and reactance of the branch i. I is the
DG
the buses m1 and m2 respectively. Ri , and Xi are theDG
i
current flowing from m1 to m2. The power losses across each branch and of the whole system can be
computed
using
Equations (6)–(8):
3. Problem
Formulation
PDG ≤ PDG ≤ PDG
2 + Q2 )
( Pm2
m2
(6)
2
Vm2
The traditional load flow techniques, which are modeled for power transmission system are not
appropriate for distribution system due to its high (resistance
P2 + Q2 to
) reactance ratio [24]. Hence this paper
(7)
Qi loss = Xi × m2 2 m2
utilizes a specially designed Backward/Forward Sweep
Load
Flow algorithm [33]. This load flow
Vm2
technique works on two sweeps, the backward sweep (updating current or power flow from the last
i =nb−1
i =nb−1
junction to source junction) andTforward
sweep
(updating
=
P
+
j
Qi loss from the first junction to the last
(8)
∑ i loss
∑ voltage
loss
junction). Figure 1 represents the one-line
diagram
of
two
buses
1 and 2, connected through
i =1
i =1
branchP . The
power flow for referred distribution system at branch i can be computed by the
where
i loss and Qi loss are the real and reactive power losses for the branch i respectively, while Tloss
following
set
of
recursive
is the total network
loss. Equations (3)–(5).
3.1. Load Flow Technique
Pi loss = Ri ×
Figure1.1.One-line
One-linediagram
diagramof
oftwo-bus
two-busradial
radialdistribution
distributionsystem.
system.
Figure
Pi = Pm 2 + Pi ?loss
(3)
Qi = Qm 2 + Qi ?loss
(4)
Vm 2 = Vm1 − I i ( Ri + jX i )
(5)
Energies 2016, 9, 982
4 of 23
3.2. Objective Functions
A constrained non-linear optimization problem is designed for multi-objective DG placement
and sizing problem in the distribution system. The proposed optimal power flow model is designed in
such a way that it works for single objective and multi-objective optimization. The objective functions
of this paper are to reduce the active component of power losses and to improve the voltage stability
of radial distribution system.
3.2.1. Power Loss Reduction
The fact that about thirteen percent of total power generation is wasted as ( I 2 × R) losses in the
distribution system [17,19]. Therefore, the first objective of this paper is to minimize the power losses
in radial distribution system. The mathematical expression for power loss reduction can be described
as in Equation (9):
!
i =nb−1
f 1 = min
∑
Pi loss
(9)
i =1
3.2.2. Voltage Stability Index
The voltage stability index (VSI) is an indicator, which shows the stability of distribution
system [16,34,35]. This paper is intended to observe the voltage stability of the system with the
installation of different types of DGs. The Equation (10) is used to represent the VSI index of proposed
model. Equations (11) and (12) are representing the mathematical expression for voltage stability index
as second objective function. In order to maintain the security and stability of distribution system,
the VSI value should be greater than zero; otherwise distribution system is under critical condition
of instability.
VSIm2 = |Vm1 |4 − 4.0{ Pm2 × Xi − Qm2 × Ri }2 − 4.0{ Pm2 × Ri + Qm2 × Xi } |Vm1 |2
(10)
Nb
f 0 2 = max∑ (VSImi )
(11)
mi
where VSIm2 is the VSI for bus m2 and VSImi is the VSI for whole system (mi = 2, 3, 4 . . . Nb); Nb is
the total number of buses. In order to improve the voltage stability index, the second objective function
can be presented as below:
1
f2 =
(12)
f 02
3.3. Network Constraints
The Equations (13)–(16) represents the equality and non-equality constraints of the proposed model.
3.3.1. Power Balance
Psubstation + ∑ PDG =
∑ Ploss + ∑ Pload
Qsubstation + ∑ Q DG = ∑ Qloss + ∑ Qload
(13)
(14)
where Psubstation and Qsubstation are the total real and reactive power injection by substation in to the
network. ΣPDG and ΣQ DG are the total real and reactive power, injected by DG. ΣPloss and ΣQloss are
the total real and reactive power loss in the network. ΣPload and ΣQload are the total real and reactive
power losses of the network respectively.
Energies 2016, 9, 982
5 of 23
3.3.2. Position of DG
Bus 1 is the substation or slack bus, so position of the DG should not be used at bus 1.
2 ≤ DG position ≤ nbuses
(15)
3.3.3. Voltage Profile
In order to maintain the quality of power supplies, the voltage profile of every bus in the network
should satisfy the following constraint.
V min ≤ V ≤ V max
(16)
4. Multi-Objective Optimization (MOO), Dominate, Non-Dominated and Pareto Optimal Solution
In the real world, many problems have multiple objectives which need to be optimized
simultaneously. Therefore, in a multi-objective optimization (MOO) problem, one needs to find
the best compromise solution among the whole set of solution. Commonly, the non-dominated sorting
approach is executed to find the best compromise Pareto-set.
i
MOO: It can be expressed as follows:
min F (u) = [ f 1 (u), f 2 (u), . . . , f Mobj (u)], u ∈ U
subject to : gi (u) ≤ 0, i = 1, 2, . . . , m
hi (u) = 0, i = 1, 2, . . . , l
ii
where F (u) is the function of u and Mobj is the total number of objective functions. The u and U
are the decision variable and its space respectively. gi (u) and hi (u) are the constraint functions
of the problem respectively.
Dominated: Let us say a decision vector u1 is said to dominate u2 , if and only if, the following
conditions are satisfied.
The solution in decision vector u1 is no worse than decision vector u2 in all objectives.
The solution in decision vector u1 is strictly better than u2 in all objectives.
Mathematically, it can be expressed as:
n
o
∀i ∈ 1, 2, . . . , Mobj : f i (u1 ) ≤ f i (u2 )
(17)
o
n
∃ j ∈ 1, 2, . . . , Mobj : f j (u1 ) ≤ f j (u2 )
(18)
iii
Non-dominated:
iv
A solution u is said to be non-dominated or Pareto solution of set = [ui ]; where i = 1, . . . , n, if
u ∈ S, and there is no solution u0 ∈ S for which u0 dominates u.
Pareto-optimal solution:
Supposed that all the non-dominated solutions of set S are in set P, then Pareto front of set is S is
given as in Equation (19) and can be seen in Figure 2.
→
P = { f = [ f1 (u1 ), f2 (u2 ), . . . , f Mobj (u)]T , u ∈ S}
(19)
iv.
Pareto-optimal solution:
Supposed that all the non-dominated solutions of set are in set
is given as in Equation (19) and can be seen in Figure 2.
Energies 2016, 9, 982
, then Pareto front of set is

P = { f = [ f1 (u1 ), f 2 (u2 ),..., f M obj (u )]T , u ∈ S }
6(19)
of 23
Figure
solution set.
set.
Figure 2.
2. Dominated,
Dominated, non-dominated
non-dominated and
and Pareto-front
Pareto-front solution
Multi-Objective Particle
Particle Swarm
Swarm Optimization
Optimization (PSO)
(PSO) Optimization
Optimization Algorithm
Algorithm
Multi-Objective
Kennedy and
andEberhart
Eberhartinin1995
1995
introduced
PSO,
inspired
by natural
the natural
choreography
of
Kennedy
introduced
thethe
PSO,
inspired
by the
choreography
of birds
birds
flocking
or
fish
schooling
[36].
Let
and
in
search
space
are
velocity
and
position
of
the
flocking or fish schooling [36]. Let v and S in search space are velocity and position of the particle.
particle. Therfore,
the ith
particle
position
canasbe(Swritten
as ( = , , , … … , ), where is the
Therfore,
the ith particle
position
can
be written
i = Si,1 , Si,2 . . . . . . Si,d ), where d is the dimensional
dimensional
space
of
the
particle.
The
previous
best
ith
particle
space of the particle. The previous best ith particle position will be (position
Pbesti = will
Pbestbe
1 , Pbest2 . . . . . . Pbesti,d ).
(The best= particle, among… all,
… will , be
). The
best
particle
among
all,
will
be
andrepresented
velocity of the
gbest and velocity of the particle i can be
by
particle
can
be
represented
by
(
=
,
…
…
).
Each
particle’s
velocity
closest
and
,
,
,
(Vi = Vi,1 , Vi,2 . . . . . . Vi,d ). Each particle’s velocity closest to pbest and gbest is calculated by to
Equation (20).
is calculated
by Equation
(20). Moreover,
particle’s(21).
current position is updated by
Moreover,
each particle’s
current position
is updatedeach
by Equation
Equation (21).
kk++11
k
k
k k
k + c1 × rand () × pbestid − v k
vvid
=
ω
×
v
+
c
×
rand
()
×
gbest
−
v
(20)
2
d
id
id
id
(20)
id = ω × vid + c1 × rand ( ) × pbestid − vid + c2 × rand ( ) × gbest d − vid
(
)
k +1
k
k +1
Sid
= Sid
+
vid
, i = 1, 2, . . . , n, d = 1, 2, . . . , m
k +1
k
k +1
(
)
(21)
(21)
where n is the number of particle, m is the dimensional numbers of member particles, k is kth iteration,
where
the number
particle,
is the dimensional
of member
particles,
th
ω
is inertiaisweight
factor, of
c1 and
c2 are acceleration
constants,numbers
rand() is uniform
random
value inisrange
k
k
iteration,
ω
is
inertia
weight
factor,
and
are
acceleration
constants,
()
is
uniform
(0, 1), whereas vid and Sid are velocity and position of the particle i at kth iteration.
random
value in range
(0, 1),
whereas
and (MOPSO)
are velocity
and position
of the
particle
Multi-objective
particle
swarm
optimization
is the extended
version
of PSO,
whichat
handles
th
iteration.
multiple objective functions simultaneously. The operational flow of this method was first presented
Multi-objective
particledescribed
swarm optimization
is solutions
the extended
version ofgenerated
PSO, which
by [37]
in 2004. The author
that the first(MOPSO)
few initial
are randomly
in
handles
multiple
objective
functions
simultaneously.
The
operational
flow
of
this
method
was
first
the search space. Later, these solutions are used for updating the velocities and positions and finally
presentedsolution
by [37] sets
in 2004.
authorUsually,
described
thethat
first
few
initial solutions
are randomly
improved
will beThe
obtained.
it is that
known
PSO
algorithm
has a general
drawback,
generated
in the search
space.
these
are used
for updating
the
velocitiesbut
anditpositions
that
it converges
at a very
highLater,
speed.
Fastsolutions
convergence
is preferred
in any
algorithm
is feared
and
finally
improved
solution
sets
will
be
obtained.
Usually,
it
is
known
that
PSO
algorithm
has
a
that it may results in false Pareto-solution in the context of multi-objective optimization. Therefore,
the
general
drawback,
that
it
converges
at
a
very
high
speed.
Fast
convergence
is
preferred
in
any
mutation operator is introduced, which is actually applied after the particle position is updated and
algorithm
but itthe
is feared
that
it mayThe
results
in false
Pareto-solution
the
context of behaviour
multi-objective
hence
modifies
position
vector.
mutation
operator
increasesin
the
explorative
with
all the particles at beginning of search space. Later as the number of iteration increases, the effect of
this operator decreases. Hence, this operator helps in maintaining the particles within the search space.
The pseudocode of mutation operator is presented in Algorithm 1.
S id = S id + vid , i = 1, 2,..., n , d = 1, 2,..., m
Energies 2016, 9, 982
7 of 23
Algorithm 1. Pseudocode for mutation operator
% mu = mutation rate % rr = reducing rate % iter = current iteration % maxiter = maximum
iteration % varmax = particle’s upper boundary % varmin = particle’s lower boundary
1: initialize reducing rate (rr)
rr = (1 − (iter − 1)/(maxiter − 1))ˆ(1/mu)
2: if rand < rr
3: function mutation_factor (particle, rr, varmax, varmin)
4: Calculate mutation range (m_range)
m_range = (varmax − varmin) × rr
5: Assign particle’s upper and lower bounds
ub = particle + m_range
lb = particle − m_range
6: Verify particle’s upper and lower bounds
if ub > varmax then ub = varmax
if lb < varmin then lb = varmin
7: Assign new values to particle within upper and lower bounds
particle = unifrnd (lb, ub)
8: end function
The main input parameters for the advanced-PFNDMOPSO need to be pre-defined, such as
maximum number of iteration ( Maxiter = 200), population size ( NPOP = 200), repository size
( NREP = 50), weight of inertia (w = 0.5), inertia weight damping rate (wdamp = 0.99), personal and
global learning coefficient (C1 = 1 and C1 = 2), number of grids per dimension ( NGrid = 7), inflation
rate ( al pha = 0.1), leader selection parameter (beta = 2), deletion selection parameter ( gama = 2) and
mutation rate (µ = 0.1). The complete algorithm is shown in Figure 3 and explained as follows:
Input data: random population POP (i ), fitness function POP (i ) . Objectives, up-date velocity
POP (i ) . Vel and position POP (i ) . Position at certain number of iteration with Equations (22)–
(25) respectively.
POP(i ).Vel
= w × POP(i ).Vel + C1 × rand()×
( POP(i ).Pbest − POP(i )) + C2 × rand() × ( REP(h) − POP(i ))
(22)
POP(i ).Position = POP(i ).Position + POP(i ).Vel
(23)
POP(i ).Position = max( POP(i ).Position, Varmin )
(24)
POP(i ).Position = min( POP(i ).Position, Varmax )
(25)
Result: Pareto-optimal solution uk .
Energies 2016, 9, 982
Energies 2016, 9, 982
8 of 23
8 of 23
Figure3.3.Flow
Flowchart
chart for
for optimal
optimal DG
Figure
DG configuration
configurationusing
usingproposed
proposedmethod.
method.
Steps:
Steps:
1.1.
2.2.
3.
3.
4.
4.
5.
5.
6.
6.7.
7.8.
8.9.
9.
10.
11.
10.
11.
12.
12.
13.
13.
14.
14.
15.
Initialization: initialize
initialize the
Initialization:
the population.
population.
For
=
1
Max.
For i = 1 to Max.
( ).
Initialize
.
Initialize POP (i ) . Position.
Initialize the velocity of each particle.
Initialize the velocity of each particle.
For = 1 Max.
For i = 1 to Max.
Initialize
( ).
.
Initialize
i ) . Vel.
Run loadPOP
flow (and
find the fitness function of each particle in population.
Run
loadthe
flow
and find
the fitness
Update
personal
best
. function of each particle in population.
Update
the domination
personal best
Pbest.the particles and save the non-dominated particles in repository
Determine
among
Determine
thesolutions
particlesare
andadded
save to
therepository
non-dominated
in repository
archive ( domination
). The new among
generated
and theparticles
dominated
solutions
archive
(REP).from
Therepository.
new generated solutions are added to repository and the dominated solutions
are removed
Find
the leader
(global
best) from
of every particle.
are
removed
from
repository.
In
order
to
select
the
leader
from
members
the repository front, firstly the member of
Find the leader (global best) from REP of everyofparticle.
repository
front is
gridded
the roulette
technique
is usedthe
so member
that cellsof
with
lower
In
order to select
the
leader and
fromthen
members
of the wheel
repository
front, firstly
repository
congestion
have
more
chance
to
be
selected.
Finally,
one
of
the
selected
grid’s
members
is
front is gridded and then the roulette wheel technique is used so that cells with lower congestion
chosen
randomly.
have
more
chance to be selected. Finally, one of the selected grid’s members is chosen randomly.
Update
the
speed of
of each
each particle
Update the speed
particle using
using Equation
Equation (22).
(22).
Update the new position of each particle (personal best) using Equations (23)–(25).
Update the new position of each particle (personal best) using Equations (23)–(25).
Run load flow and find the fitness function of each particle in population.
Run load flow and find the fitness function of each particle in population.
Apply mutation factor.
Energies 2016, 9, 982
15.
16.
17.
18.
19.
20.
21.
22.
9 of 23
Apply mutation factor.
Add non-dominated solution set of the recent population in the repository.
Determine the domination among the particles and save the non-dominated particles in repository
archive REP.
Check the size of the repository. If the repository exceeds the predefined limit, remove the
extra members.
If the convergence of algorithm occurs, the operation will stop, otherwise, go to step 6.
The rest of the members in the repository will be taken for the final solution.
For single-objective, the priority is given to only that objective function.
For multi-objective, the optimal compromise solution will be chosen.
5. Fuzzy Decision Model
In order to get the best compromise solution from non-dominated Pareto-front solution, fuzzy decision
model is proposed. For every solution in kth Pareto-front, the linear membership function αik is
introduced, which represents the proper goal of ith objective function. Figure 4 shows the linear
membership
trend and mathematically can be expressed in Equation (26).
Energies 2016, 9, function
982
9 of 23


1 the recentifpopulation
f i ≤ f i min in the repository.
16. Add non-dominated solution set

 of max
f i the
− f i kparticles
17. Determine the domination
the non-dominated particles(26)
in
αi k =among
< f save
< f i max
if f i minand
f i max − f i min


repository archive
.
 0
if f i ≥ f i max
18. Check the size of the repository. If the repository exceeds the predefined limit, remove the extra
members.
where
f imin and f imax are the minimum and maximum values of ith objective function in all
19. If the convergence
algorithm occurs,
the operation
will stop,
otherwise,
go to step
6. between
non-dominated
solutionsofrespectively.
The value
of membership
function
α generally
varies
20.
The
rest
of
the
members
in
the
repository
will
be
taken
for
the
final
solution.
0 to 1, if αi = 0, then the solution shows the incompatibility with set and if αi = 1, then the solution
21. For
single-objective,
to only
function.solution k can be found
shows
full
compatibility. the
Thepriority
degree is
ofgiven
preference
ofthat
eachobjective
non-dominated
22. For
multi-objective,
the optimal
using
normalized
membership
value compromise
αk as follows:solution will be chosen.
5. Fuzzy Decision Model
Nobj
∑ αik
In order to get the best compromise solution
from
non-dominated Pareto-front solution, fuzzy
i
=
1
αk =
(27)
Nobj Pareto-front, the linear membership function
decision model is proposed. For every solution Minnd kth
k
∑ of∑ithαiobjective function. Figure 4 shows the linear
α is introduced, which represents the proper goal
k =1 i =1
membership function trend and mathematically can be expressed in Equation (26).
Figure 4.
4. Linear
Linear fuzzy-decision
fuzzy-decision model.
model.
Figure
αik
1
if f i ≤ f i min
 max
k
 fi − fi
if f i min < f < f i max
=  max
min
f
−
f
i
 i
0
if f i ≥ f i max

(26)
where
and
are the minimum and maximum values of ith objective function in all
non-dominated solutions respectively. The value of membership function α generally varies
Energies 2016, 9, 982
10 of 23
6. Case Studies
This section provides the optimal placement and sizing of single and multiple distributed
generation resources using the advanced-PFNDMOPSO method. Two case studies are performed
2016, 9, 982 and multi-objective optimization for power loss reduction and voltage 10
of 23
as Energies
single-objective
stability
Energies 2016, 9,In
982
10 of 23
improvement.
single objective optimization, the priority is given to 1st and 2nd objective function
improvement.
In single objective
optimization,
the priority
is given
to 1st and 2nd objective
functionthe
after
getting pareto-results
obtained
from proposed
model.
In multi-objective
optimization,
improvement.
In single objective
optimization,
the model.
priorityInismulti-objective
given to 1st andoptimization,
2nd objectivethe
function
after
getting
pareto-results
from
trade-off
between
these twoobtained
functions
hasproposed
been taken
out. The proposed model
is tested ontradeIEEE 33
after
gettingthese
pareto-results
obtained
In multi-objective
the33
tradeoff
between
two functions
has from
beenproposed
taken out.model.
The proposed
model isoptimization,
tested on IEEE
bus
bus system. The technical specification for this test system are taken from ref. [2]. The base case values
off between
these twospecification
functions has
out. The
model
is tested
on IEEE
33 bus
system.
The technical
forbeen
this taken
test system
are proposed
taken from
ref. [2].
The base
case values
for both case studies are 1 MVA and 12.66 kV respectively. Each case study is further investigated
system.
The studies
technicalare
specification
this kV
testrespectively.
system are taken
ref. [2].is The
baseinvestigated
case values
for
both case
1 MVA andfor
12.66
Each from
case study
further
with different types of DGs. The DG types are demarcated as; Type-1: Active power DG, Type-2:
for both
case studies
1 MVA
and types
12.66 kV
Each
case study
is further
investigated
with
different
types ofare
DGs.
The DG
are respectively.
demarcated as;
Type-1:
Active
power DG,
Type-2:
Reactive
Power DG
and
Type
3:
Active-Reactive
power DG.as;
The
size of
real power
DG
should
be
with
different
types
of
DGs.
The
DG
types
are
demarcated
Type-1:
Active
power
DG,
Type-2:
Reactive Power
DG and Typemax
3: Active-Reactive power DG. The size of real power DG should
be in
min
in range
range
p DG= =
0 MW,
p DG3:
≤
2 and
MWthe
and
the
sizeDG.
reactive
power
DG
Reactive
and Type
Active-Reactive
power
The size
of
real
power
DG be
should
be in of
ofof Power
0DG
MW,
2 MW
size
reactive
power
DG
should
beshould
in range
ofin range
max = 2 MVAr, the voltage limits for Type-1 and Type-3 are V
Qmin
=
0
MVAr,
Q
=
0.95
p.u
(
) and
min
range
0 MW,
MW
and the
size for
reactive
power
DG should
range
DG
(p. u) and
= of
0 MVAr,= DG
= 2 MVAr,2the
voltage
limits
Type-1
and Type-3
are be in =
0.95of
Vmax ==1.05
p.u
,
whereas,
the
voltage
limits
for
Type-2
are
V
=
0.92
p.u
and
V
=
1.05
(
)
(
)
(p.u)
max (p. u) and
=1.05
0 MVAr,
= 2 MVAr,
the voltage
for Type-1
and=Type-3
(p. u), whereas,
the voltage
limits limits
for Type-2
are min
0.92 (p.are
u) and = 0.95
respectively.
Each
type
of DG the
is further
processed
with
installation
single
number
1.05
(p.u)
u),
whereas,
voltage
limits
forisType-2
are
= of
0.92
(p.installation
u)and
andmultiple
==1.05
(p.
respectively.
Each
type
of DG
further
processed
with
of single
and of
DGs
as
shown
in
Figure
5.
=
1.05
(p.
u)
respectively.
Each
type
of
DG
is
further
processed
with
installation
of
single
and
multiple number of DGs as shown in Figure 5.
multiple number of DGs as shown in Figure 5.
Figure5.5.The
The conceptual
conceptual framework
Figure
frameworkof
ofcase
casestudies.
studies.
Figure 5. The conceptual framework of case studies.
The one-line diagram of IEEE 33 bus system is given in Figure 6. The total real and reactive
The one-line
diagram ofofIEEE
3333bus
is
in Figure
Figure 6.6. The
Thetotal
totalreal
realand
and
reactive
one-line
IEEE
bussystem
system
is given
given
reactive
powerThe
demands
arediagram
3720 kW and
2300
kVAr
respectively.
The proposed
methodology
is carried
out
power
demands
areare
3720
kW
and
2300
kVAr
respectively.
The proposed
proposedmethodology
methodologyis is
carried
power
demands
3720
kW
and
2300
kVAr
respectively.
carried
outout
by simulation using Intel core i5, 4096 MB RAM personal computer using MATLAB (2015a) software
by simulation
using
Intel
core
, 4096MB
MBRAM
RAM personal
personal computer
(2015a)
bypackage
simulation
Intel
core
i5 ,i54096
computerusing
usingMATLAB
MATLAB
(2015asoftware
) software
[38].using
package
[38].
package
[38].
Figure 6. IEEE 33 radial distribution system.
Figure 6. IEEE 33 radial distribution system.
Figure 6. IEEE 33 radial distribution system.
6.1. Case Study-I: Single-Objective Optimization
6.1. Case Study-I: Single-Objective Optimization
The purpose of this case study is to validate competency of the proposed method for various
The purpose of this case study is to validate competency of the proposed method for various
types of distributed generators in the distribution system. For this, among the pareto results
types of distributed generators in the distribution system. For this, among the pareto results
produced by the proposed method, the priority is given to only specific objective function i.e., power
produced by the proposed method, the priority is given to only specific objective function i.e., power
Energies 2016, 9, 982
11 of 23
6.1. Case Study-I: Single-Objective Optimization
The purpose of this case study is to validate competency of the proposed method for various types
of distributed generators in the distribution system. For this, among the pareto results produced by
the proposed method, the priority is given to only specific objective function i.e., power loss reduction
(Ploss) or voltage stability improvement (VSI). However, other associated objective function values are
also recorded.
6.1.1. Priority to 1st Objective Function (Ploss)
In this case, the priority is given only to a 1st objective function which is active power loss reduction
(i.e., ploss). The optimal placement and sizing are found for three types of DGs and each having three
numbers of DG units, i.e., Type-1 (1 DG), . . . , Type-1 (3 DG), Type-2 (1 DG), ..., Type-2 (3 DG) and
Type-3 (1 DG), . . . , Type-3 (3 DG) respectively. The results of the proposed method are also compared
with the literature that has worked for minimization of power loss. Table 1 is showing the optimal
location, size and power loss reduction by each DG along with voltage stability improvement.
Table 1. Optimal placement and sizing of DG for case study-I as single-objective function with priority
to 1st objective function.
Reduction in
Ploss (%)
DG-Type
DG No.
DG Location
DG Size (MW)
Ploss (kW)
VSI
Base-case
-
-
-
211
25.125
Type-1
1 DG
2 DG
3 DG
7
13, 31
14, 24, 27
2.0
1.1115, 1.4882
0.70027, 1.0089, 1.62850
115.17
87.8
79.4
27.326
28.75
29.05
45.41
57.42
62.37
Type-2
1 DG
2 DG
3 DG
30
12, 30
30, 30, 12
1.2807
0.44219, 1.2062
1.06288, 0.3525, 0.4533
151.4
142.5
140
26.192
26.75
26.83
28.24
32.46
33.64
1-1 DG (P)
1-1 DG (Q)
8
30
1.911
1.253
64.78
29.19
69.29
2-2 DG (P)
2-2 DG (Q)
15, 31
30, 20
0.8258, 1.1288
1.4424, 0.3717
40.2
30.025
80.94
3-3 DG (P)
3-3 DG (Q)
20, 29, 13
12, 5, 33
0.447, 1.3574, 0.9058
0.663, 0.6557, 0.78976
34.5
31.173
83.64
Type-3
It can also be seen that with the use of different types of DGs, the placement and sizing varies
largely, which eventually affect overall objective functions. This revealed that with maximum (3)
number of DG units of (Type-1, Type-2 and Type-3), the objective 1 is improved up to 62.37 percent,
33.64 percent, and 83.64 percent respectively. The results had revealed that integration of Type-3 DG
gives better performance as compared to Type-1 and Type-2 DG.
The results of the proposed model are compared with Type-1 DG with following algorithms.
The Type-1 DG with one DG unit is compared with flower pollination algorithm (FPA) [39], GA [6],
grid search algorithm (GSA) [40] and PSO [2], for two-DG units with FPA [39] and for three-DG units
with GA [41], PSO [41], genetic algorithm and particle swarm optimization algorithm (GA/PSO) [41],
dynamic adoption of PSO (DAPSO) [42], parto frontier differential evolution (PFDE) [43] and loss
sensitivity factor and simulated annealing (LSFSA) [44]. Table 2 shows the comparisons of proposed
method with other algorithms.
It can be seen from Table 2 that with the use of only 1 DG, the proposed method gives better
loss reduction compared to FPA [39]. However, when compared with analytical method (AM) [6],
GSA [40] and PSO [41], optimization algorithms, the loss reduction by proposed method is same but
the DG capacity is lesser. Similarly, for 2 DG the performance of proposed algorithm is better in terms
of loss reduction and DG capacity as compared to FPA [39] algorithm. Moreover, for 3 DG, it can be
Energies 2016, 9, 982
12 of 23
seen that the loss reduction is maximum by the proposed method compared to other methods such as
LSFSA [44], PFDE [43], DAPSO [42], GA/PSO [41], PSO [41], GA [41] reported in the literature.
Table 2. Comparison of the proposed method with other algorithms for Type-1 DG (1st objective function).
Method
DG Size & Location
Ploss (kW)
Method
DG Size & Location
1 DG
2.0 at 7
2.589 x at 06
Proposed
method
Ploss (kW)
2 DG
115.17
111.0
AM [6]
2.600 at 06
111.0
GSA [40]
2.600 at 06
111.0
PSO [2]
2.600 at 06
111.0
FPA [39]
2.000 at 07
115.17
Method
DG Size & Location
Ploss (kW)
1.2603 at 29
0.9277 at 13
Proposed
method
87.8
1.0339 at 12
FPA [39]
89.2
1.0866 at 30
Method
DG Size & Location
Ploss (kW)
3 DG
Proposed
method
0.70027 at 14
1.0089 at 24
1.62850 at 27
79.40
GA/PSO [41]
1.2000 at 32
0.8630 at 16
0.9250 at 11
103.40
LSFSA [44]
1.1124 at 06
0.4874 at 18
0.8679 at 32
82.80
PSO [41]
0.9816 at 13
0.8297 at 32
1.1768 at 08
105.30
PFDE [43]
0.9100 at 13
1.2500 at 26
0.8800 at 32
88.00
GA [41]
1.5000 at 11
0.4228 at 29
1.0714 at 30
106.30
DAPSO [42]
0.6810 at 10
0.600 at 18
0.7190 at 31
92.55
x
All constraints are appreciated except µ.
The voltage profile and voltage stability are two main parameters of the radial distribution system.
The voltage profile of each node defines the performance of the system, whereas, the voltage stability
indicates the ability of a system to maintain its stability. Optimal placement and sizing of DG along
with power loss reduction increases the voltage profile and voltage stability of each bus of the system.
The results of both parameters for single-objective optimization with priority to 1st objective function
are depicted in Table 3.
Table 3. The voltage profile and voltage stability of the system for 1st objective function.
DG No.
Voltage (p.u)
Voltage Stability (p.u)
Min
Max
Min
Max
Base Case
0.9037 at 18
1.00 at 1
0.6669 at 18
1.00 at 1
Type-1
1 DG
2 DG
3 DG
0.9424 at 18
0.9647 at 18
0.9728 at 18
1.00 at 1
1.00 at 1
1.00 at 1
0.7888 at 18
0.8661 at 18
0.8953 at 18
1.00 at 1
1.00 at 1
1.00 at 1
Type-2
1 DG
2 DG
3 DG
0.9160 at 18
0.9295 at 18
0.9297 at 18
1.00 at 1
1.00 at 1
1.00 at 1
0.6984 at 18
0.7405 at 18
0.7410 at 18
1.00 at 1
1.00 at 1
1.00 at 1
Type-3
1 DG
2 DG
3 DG
0.9492 at 18
0.9859 at 18
1.0051 at 18
1.00 at 1
1.00 at 1
1.00 at 1 & 33
0.8116 at 18
0.9449 at 18
1.020 at 18
1.00 at 1
1.00 at 1
1.00 at 1
DG Type
Energies 2016, 9, 982
13 of 23
The base case voltage profile values for IEEE 33 bus is 0.9037 p.u at bus 18 before installing the DG.
Energies 2016,it9,can
982
13 of 23
However,
Energies 2016, 9, 982 be seen that with the installation of Type-1 DG the voltage profile can be improved
13 of 23
up to 0.9728 p.u. With the installation of Type-2 DG, it can be improved up to 0.9297 p.u and with
and with the installation
of
Type-3
DG,
it can be improved
up
torespectively.
1.0 p.u respectively.
Similarly,
for
the
of Type-3 of
DG,
it canDG,
be improved
up to 1.0 up
p.uto
Similarly,Similarly,
for voltage
andinstallation
with the installation
Type-3
it can be improved
1.0 p.u respectively.
for
voltage
stability
the
base
case
values
are
0.6669
p.u
without
installation
of
DG.
The
installation
of
stability
the base case
values
arevalues
0.6669are
p.u0.6669
without
of DG. Theof
installation
of Type-1 DG
voltage stability
the base
case
p.uinstallation
without installation
DG. The installation
of
Type-1
DG also
improves
voltage
stability
by 0.8953
p.u. The installation
ofType-3
Type-2 and
Type-3
DG
also
improves
voltage
stability
by 0.8953
p.u.
installation
Type-2 andof
improve
Type-1
DG also
improves
voltage
stability
byThe
0.8953
p.u. Theofinstallation
Type-2DG
andcan
Type-3
DG
can
improve
the
voltage
stability
up
to
0.7410
p.u
and
1
p.u
respectively.
the
stability
up tostability
0.7410 p.u
1 p.u p.u
respectively.
canvoltage
improve
the voltage
up and
to 0.7410
and 1 p.u respectively.
Before
adding
the
distributed
generation
sources in IEEE
IEEE 33 bus
bus system, the
the substation bus
bus has
Before
Before adding
adding the
the distributed
distributed generation
generation sources
sources in
in IEEE 33
33 bus system,
system, the substation
substation bus has
has
highest voltage profile
profile of 1.00
1.00 p.u, however,
however, thebus
bus 18has
has lowestvoltage
voltage profile.After
After integrating
highest
highest voltage
voltage profile of
of 1.00 p.u,
p.u, however, the
the bus18
18 haslowest
lowest voltageprofile.
profile. After integrating
integrating
DG, it can be
be seen that
that the Type-1
Type-1 and Type-3
Type-3 increases more
more voltage profile
profile as compared
compared to Type-2
Type-2
DG,
DG, itit can
can be seen
seen that the
the Type-1 and
and Type-3 increases
increases more voltage
voltage profile as
as compared to
to Type-2
DG. Similarly,Figures
Figures 7 and88shows
shows thevoltage
voltage profileofofeach
each busofofthe
the system.
DG.
DG. Similarly,
Similarly, Figures77and
and 8 showsthe
the voltageprofile
profile of eachbus
bus of thesystem.
system.
1.02
1.02
Voltage
Voltage(p.u)
(p.u)
1
1
0.98
0.98
0.96
0.96
0.94
0.94
0.92
0.92
0.9
0.9 0
0
without DG
without
DG
with Type-1(1DG)
with
with Type-1(1DG)
Type-1(2DG)
with
with Type-1(2DG)
Type-1(3DG)
with
with Type-1(3DG)
Type-3(1DG)
with
with Type-3(1DG)
Type-3(2DG)
with
with Type-3(2DG)
Type-3(3DG)
with Type-3(3DG)
5
10
5
10
15
15
20
20
Bus numbers
Bus numbers
25
25
30
30
35
35
Figure
7. Voltage
profile for 33
33 bus with
with Type-1and
and Type-3DG
DG for1st
1st objectivefunction.
function.
Figure 7.
7.
Voltage profile
Figure
Voltage
profile for
for 33 bus
bus with Type-1
Type-1 andType-3
Type-3 DGfor
for 1stobjective
objective function.
Figure 8. Voltage profile for 33 bus with Type-2 DG for 1st objective function.
Figure 8. Voltage profile for 33 bus with Type-2 DG for 1st objective function.
Figure 8. Voltage profile for 33 bus with Type-2 DG for 1st objective function.
It can be seen from Figures 9 and 10 that the voltage stability of substation bus is highest.
It can be seen from Figures 9 and 10 that the voltage stability of substation bus is highest.
However, the bus 18 and bus 65 has lowest values without adding the distributed generation sources.
However, the bus 18 and bus 65 has lowest values without adding the distributed generation sources.
After integrating DG, similar to voltage profile, the voltage stability is also increased more by
After integrating DG, similar to voltage profile, the voltage stability is also increased more by
Type-1 and Type-3 DG as compared to Type-2 DG.
Type-1 and Type-3 DG as compared to Type-2 DG.
Energies 2016, 9, 982
14 of 23
It can be seen from Figures 9 and 10 that the voltage stability of substation bus is highest.
However, the bus 18 and bus 65 has lowest values without adding the distributed generation sources.
After integrating DG, similar to voltage profile, the voltage stability is also increased more by Type-1
and Type-3
Energies
2016, 9,DG
982as compared to Type-2 DG.
14 of 23
Figure9.9.Voltage
Voltage stability
stability for
for 33
33 bus
bus with
with Type-1
Type-1 and Type-3 DG for 1st objective function.
Figure
function.
Figure
for 1st
1st objective
objective function.
function.
Figure 10.
10. Voltage
Voltage stability
stability for
for 33
33 bus
bus with
with Type-2
Type-2 DG
DG for
6.1.2.
6.1.2. Priority
Priority to
to 2nd
2nd Objective
Objective Function
Function (VSI)
(VSI)
Among
Among the
the pareto
pareto results
results observed
observed by
by the
the proposed
proposed method,
method, priority
priority is
is given
given to
to the
the second
second
objective
function,
which
is
voltage
stability
improvement.
The
detailed
discussion
is
available
for
objective function, which is voltage stability improvement. The detailed discussion is available for two
two
types
of DGs
i.e., Type-1
(1and
DG 2and
2 DG)
and Type-3
(1 in
DG)
in Table
4.
types
of DGs
i.e., Type-1
(1 DG
DG)
and Type-3
(1 DG)
Table
4.
It can be seen that by giving priority to VSI, a significant VSI had been improved. The results
Table 4. Optimal placement and sizing of DG for case-1 as single-objective function with priority to
show that with Type-1 (2 DG) VSI is improved upto 27.62 percent, whereas, with Type-3 (1 DG) it is
2nd objective function.
improved by 31.23 percent.
DG
DG Size
Reduction
(
)
DG-Type
DG No.
Location
(MW)
in VSI (%)
1 DG
16
1.999
194.9
29.767
18.47
Type-1
2 DG
14, 30
1.972, 1.860
188.7
32.067
27.62
1-1 DG (P)
15
1.956
Type-3
179.4
32.974
31.23
1-1 DG (Q)
10
2.0
It can be seen that by giving priority to VSI, a significant VSI had been improved. The results
Energies 2016, 9, 982
15 of 23
Table 4. Optimal placement and sizing of DG for case-1 as single-objective function with priority to
2nd objective function.
DG-Type
DG No.
DG Location
DG Size (MW)
Ploss (kW)
VSI
Reduction in VSI (%)
Type-1
1 DG
2 DG
16
14, 30
1.999
1.972, 1.860
194.9
188.7
29.767
32.067
18.47
27.62
Type-3
1-1 DG (P)
1-1 DG (Q)
15
10
1.956
2.0
179.4
32.974
31.23
The results for VSI as an objective function are also validated against backtracking search
algorithm (BSA) [19] as shown in Table 5.
Table 5. Comparison of the proposed method with other algorithms for Type-1 (1 DG) and Type-3
(1 DG) for 2nd objective function.
Type-1 (1 DG)
Parameters
DG Size (MVA)
Vmin (p.u)
Vmax (p.u)
VSImin
VSImax
1/ ∑ VSI
Ploss (kW)
Qloss (kVAR)
Type-3 (1 DG)
Proposed Method
BSA
Proposed Method
BSA
1.984 at 10
0.9440 at 33
0.9982 at 2
0.7974 at 33
0.9927 at 2
29.240
133.0
94.1
1.857 at 11
0.9438 at 33
0.9981 at 3
0.7934 at 33
0.9926 at 2
29.237
133.01
93.53
1.975 at 13 + j2 at 8
0.9629 at 33
1.049 at 15
0.8630 at 33
1.229 at 13
32.53
137.6
106.3
1.618 + j1.895 at 11
0.9604 at 33
1.0049 at 11
0.8507 at 33
1.2058 at 12
32.051
138.74
105.35
For Type-1 (1 DG) and Type-3 (1 DG), the proposed method gives better results in voltage stability
improvement as compared to BSA presented in [19]. The voltage stability improvement by proposed
method is higher as at 29.767 and 32.974 as compared to BSA 29.237 and 32.051 respectively. Even the
VSI values were deeply checked in relating to power loss as referred by BSA. It is realized that the
outcomes are higher even in this case as compared to BSA. Moreover, the minimum and maximum
voltage profile and voltage stability of the proposed method are also upfront.
By giving priority to VSI as an objective function, the significant voltage profile and voltage
stability improvement had been observed. The results of both parameters are depicted in Table 6.
Table 6. The voltage profile and voltage stability of the system for 2nd objective function.
DG No.
Voltage (p.u)
Voltage Stability (p.u)
Min
Max
Min
Max
Base Case
0.9037 at 18
1.00 at 1
0.6669 at 18
1.00 at 1
Type-1
1 DG
2 DG
0.9440 at 18
0.9836 at 25
1.00 at 1
1.037 at 14
0.7974 at 18
0.9360 at 25
1.00 at 1
1.159 at 14
Type-3
1 DG
0.9629 at 33
1.052 at 13
0.86303 at 31
1.229 at 13
DG Type
It can be seen that with installation of Type-1 (1 DG) and Type-1 (2 DG), the minimum voltage
profile can be improved upto 0.9440 p.u and 0.9836 p.u respectively. Whereas, with installation of
Type-3 (1 DG) it can be improved upto 0.9629 p.u. Similarly, the installation of DG improves voltage
stability as 0.7974 and 0.9360 with Type-1 (1 DG) and Type-1 (2 DG) respectively. The installation of
Type-3 (1 DG) can improve the voltage stability upto 0.86303. The voltage profile and voltage stability
on each bus can be realized in Figures 11 and 12 respectively.
Energies 2016, 9, 982
16 of 23
Voltage (p.u)
16 of of
23 all
seen from Figure 11 and in Figure 12 that the voltage profile and voltage stability
buses satisfy the minimum voltage profile and voltage stability standard. However, Type-3 (1 DG)
Energies
2016,
9, 982
16 of 23
gave
more
improvement
in results as compared to Type-1 DG.
Voltage (p.u)
Energies 2016,
9, 982
It can
be
Figure 11. Voltage profile for 33 bus with Type-1 (1 DG and 2 DG) and Type-3 (1 DG) for 2nd
objective function.
Figure
profile
for 33
Type-1
(1 DG and
2 DG)
Type-3
(1Type-3
DG) for (1
2nd
objective
function.
Figure11.
11.Voltage
Voltage
profile
forbus
33 with
bus with
Type-1
(1 DG
andand
2 DG)
and
DG)
for 2nd
objective function.
Figure
12. Voltage
stability
for 33for
bus33with
(1 DG (1
and
2 DG)
Type-3
DG) for
Figure
12. Voltage
stability
bus Type-1
with Type-1
DG
andand
2 DG)
and (1
Type-3
(1 2nd
DG) for 2nd
objective
function.
objective
function.
Figure 12. Voltage stability for 33 bus with Type-1 (1 DG and 2 DG) and Type-3 (1 DG) for 2nd
6.2.6.2.
CaseCase
studyII:function.
Multi-Objective
Optimization
objective
Study-II:
Multi-Objective
Optimization
In thisthis
case
the
important objective
objectivefunctions
functionssuch
such
power
reduction
and
casestudy,
study,
the two
two important
as as
power
lossloss
reduction
and voltage
6.2. In
Case studyII: Multi-Objective
Optimization
voltage
stability
are optimized
simultaneously.
A pareto
list of pareto
solution
is recorded,
after the
getting
the
stability
are optimized
simultaneously.
A list of
solution
is recorded,
after getting
simulation
simulation
results
of
the
proposed
method.
Then,
pareto
based
fuzzy
decision-making
technique
is for
In
this
case
study,
the
two
important
objective
functions
such
as
power
loss
reduction
and
results of the proposed method. Then, pareto based fuzzy decision-making technique is applied
applied
for
choosing
the
best
compromise
solution
set
from
them.
In
this
case,
two
types
of
DGs,
i.e.,
voltage
stability
are
optimized
simultaneously.
A
list
of
pareto
solution
is
recorded,
after
getting
the
choosing the best compromise solution set from them. In this case, two types of DGs, i.e., Tyep-1 and
Tyep-1
andare
Type-3
are included,
to
theresults.
optimal
results.
Table
7fuzzy
shows
thecompromise
optimal compromise
simulation
results
of
proposed
method.
Then,
pareto
based
decision-making
technique
Type-3
included,
to the
realize
therealize
optimal
Table
7 shows
the
optimal
results
whenis
results
whenfor
Type-1
of 1DG
is used.
Furthermore,
thesetefficacy
and performance
of the
proposed
applied
choosing
the best
compromise
solution
from them.
In this case, two
types
of DGs, i.e.,
method
are and
alsoType-3
compared
with BSAto
and
GA algorithms
TheTable
pareto
solutions
Type-1compromise
(1 DG)
Tyep-1
are included,
realize
the optimal[19].
results.
7 shows
the of
optimal
is portrayed
in Figure
13. of 1DG is used. Furthermore, the efficacy and performance of the proposed
results when
Type-1
method are also compared with BSA and GA algorithms [19]. The pareto solutions of Type-1 (1 DG)
is portrayed in Figure 13.
Energies 2016, 9, 982
17 of 23
Type-1 of 1DG is used. Furthermore, the efficacy and performance of the proposed method are also
compared with BSA and GA algorithms [19]. The pareto solutions of Type-1 (1 DG) is portrayed in
Figure 13.
Energies
2016,7.9,Optimal
982
17 of 23
Table
compromise results of proposed method in comparison with BSA and GA for Type-1
(1DG) in multi-objective optimization case.
Table 7. Optimal compromise results of proposed method in comparison with BSA and GA for
Type-1
(1DG) in multi-objective
optimization
case. Method
Parameters
Base Case
Proposed
BSA
GA
DG Size (MVA)
Parameters
(MVA)
Vmin (p.u
)
Vmax (p.
(p.uu)
)
(p. u)
VSImin
VSImax
1/
∑ VSI
1/∑
kW)
Ploss ((kW)
Qloss ((kVAR)
kVAR)
Base Case
- 0.9037 at 18
0.9037
0.9970atat18
2
0.9970 at 2
0.6669 at 18
0.6669 at 18
0.9881 at 2
0.9881 at 2
Proposed
25.125
Proposed
25.125
BSA/GA-25.554
BSA/GA-25.554
211 211
143 143
1.874 + j0 Method
at 9
1.632
1.415
Proposed
BSA+ j0 at 10
GA + j0 at 10
1.874
+ j0atat339
1.632
1.415
0.9439
0.9408+atj033at 10
0.9378+atj033at 10
0.9439
at 33
0.9408
0.9378
at 233
0.9982
at 2
0.9980 at
at 233
0.9979 at
0.9982 at 2
0.9980 at 2
0.9979 at 2
0.7970 at 31
0.7834 at 33
0.7735 at 33
0.7970 at 31
0.7834 at 33
0.7735 at 33
0.99269 at 2
0.9921 at 2
0.9916 at 2
0.99269 at 2
0.9921 at 2
0.9916 at 2
28.40 28.40
124.5(40.99%)
(40.99%)
124.5
88
88
28.765
28.765
28.361
28.361
125.54
(40.46%)
(41.40%)
125.54
(40.46%) 123.55
123.55
(41.40%)
87.25
87.25
84.47
84.47
Figure 13.
13. Pareto-solution
Pareto-solution and
and optimal
optimal compromise
compromise solution
solution for
for Type-1
Type-1(1
(1DG).
DG).
Figure
It can
can be
be seen
seen that
that with
with the
the use
use of
of 11 DG
DG of
of Type-1,
Type-1,the
thePFNDMOPSO
PFNDMOPSO method
method gives
gives acceptable
acceptable
It
results in
in loss
loss reduction
reduction and
and voltage
voltage stability
stability improvement
improvement as
as compared
compared to
to the
the BSA
BSA and
and GA
GA
results
algorithms
[19].
Specifically,
power
loss
reduction
by
the
proposed
method
is
higher
as
49.99
%
as
algorithms [19]. Specifically, power loss reduction by the proposed method is higher as 49.99 % as
compared
to
BSA
40.46%.
However,
GA
marginally
reduces
more
power
loss
as
compared
to
the
compared to BSA 40.46%. However, GA marginally reduces more power loss as compared to the
proposed method.
method. Similarly,
Similarly,for
for voltage
voltage stability
stability the
the proposed
proposed method
method gives
gives higher
higher voltage
voltage stability
stability
proposed
than
the
GA
and
BSA.
Moreover,
the
minimum
and
maximum
voltage
profile
and
voltage
stability
than the GA and BSA. Moreover, the minimum and maximum voltage profile and voltage stability of
of the
proposed
method
give
higher
in results
as compared
to BSA
the
proposed
method
alsoalso
give
higher
in results
as compared
to BSA
andand
GA.GA.
In order
orderto
tocheck
checkthe
thevalidity
validityand
andperformance
performanceofofthe
theproposed
proposed
method,
proposed
method
In
method,
thethe
proposed
method
is
is
extended
by
hosting
2
DG
for
Type-1
and
1
DG
for
Type-3.
The
numerical
outcomes
of
Type-1
extended by hosting 2 DG for Type-1 and 1 DG for Type-3. The numerical outcomes of Type-1 (2 DG)
(2 DG)
and(1
Type-3
(1 DG)
and its compared
results
BSAare
and
GA are
shown
in Table
8. The
and
Type-3
DG) and
its compared
results with
BSA with
and GA
shown
in Table
8. The
pareto-optimal
pareto-optimal
solutions
of DG)
theseand
Type-1
(2 DG)
and
Type-2
DG)
are shown
solutions
of these
Type-1 (2
Type-2
(1 DG)
are
shown(1in
Figures
14 andin15 respectively.
Figures 14 and 15 respectively.
Energies 2016, 9, 982
18 of 23
Energies 2016, 9, 982
Energies 2016, 9, 982
18 of 23
18 of 23
Figure 14. Pareto-solution and optimal compromise solution for Type-1 (2 DG).
Figure 14.
14. Pareto-solution
Pareto-solution and
and optimal
optimal compromise
compromise solution
solution for
for Type-1
Type-1 (2
Figure
(2 DG).
DG).
Figure 15. Pareto-solution and optimal compromise solution for Type-3 (1 DG).
Figure 15. Pareto-solution and optimal compromise solution for Type-3 (1 DG).
Figure 15. Pareto-solution and optimal compromise solution for Type-3 (1 DG).
Table 8. Optimal compromise results of multi-objective function for Type-1 (2 DG) and
Table 8. Optimal compromise results of multi-objective function for Type-1 (2 DG) and
Table
8. Optimal
Type-3
(1 DG). compromise results of multi-objective function for Type-1 (2 DG) and Type-3 (1 DG).
Type-3 (1 DG).
Type-1 (2 DG)
Type-1
(2 DG) Type-1 (2 DG)
Proposed
Proposed
Method BSA BSA
Proposed
Method
BSA
Method
1.1155
11
1.126+ +
DGSize
1.1155 atat11
1.126
j0j0atat1313
(MVA) 1.1155 at 11
(MVA)
1.126
+
j0
at
1.4882
at
29
0.730
+
1.4882 at 29
0.730 + j0j0
atat13
3131
(MVA)
1.4882
at
29
0.730
+
j0
at
31
(p.
u)
0.9766
at
33
0.9631
at
33
Vmin (p.u)
0.9766 at 33
0.9631 at 33
(p. u)
0.9766
at 33
0.9631
at
u))
0.9986
0.9982
at 33
2at 2
Vmax(p.
0.9986atat22
0.9982
(p.u
(p. u)
0.9986
at
2
0.9982
at
0.9129 at 31
0.8503 at 231
VSImin
0.9129 at31
31
0.850331
at 31
0.9129
0.8503
0.9944 at
at 2
0.9927 at
at 2
VSI
0.9944
at
2
0.9927
0.9944
0.9927
1/∑ max
29.293 at 2
29.284 at 2at 2
1/∑
29.293
29.284
1/ ∑(kW)
VSI
29.284
93.029.293
(55.92%) 93.39 (55.71%)
(kW)
93.0
(55.92%) 93.39
(55.71%)
65.0
63.41
Ploss(kVAR)
93.0 (55.92%)
93.39 (55.71%)
(kW)
(kVAR)
65.0
63.41
Qloss (kVAR)
65.0
63.41
Parameters
Parameters
Parameters
GA GA
GA
1.139++j0j0at
at 13
13
1.139
1.139
+
j0
at
13
0.0717
+
j0
at
31
0.0717
31
0.0717
+
j0
at
31
0.9627
at
33
0.9627 at 33
0.9627
at
0.9982
at 33
2at 2
0.9982
0.9982
at
0.8497 at 231
0.8497 at
31
0.8497
0.9927 at
at 31
2
0.9927
at
0.9927
29.291 at 2 2
29.291
93.8529.291
(55.49%)
93.85
(55.49%)
63.72
93.85 (55.49%)
63.72
63.72
Type-3 (1 DG)
Type-3
(1 DG)
Proposed
Proposed
Method
Proposed
Method
Method
1.991
at
9
+
1.991 at j1.60
9 +
at1.991
33
j1.60 atat339 +
j1.60
at at
33at3333
0.9825
0.9825
0.9825
at
33
1.00
at
9,10,11
1.00 at 9, 10, 11
1.00
at
9,10,11
0.9353 at 31
0.9353
0.9353
atat
3131
1.0 at 9,10,11
1.0
at
9,
10,
1.0
at 9,10,1111
30.085
30.085
30.085
76.9 (63.55%)
76.9
(63.55%)
58.6
76.9 (63.55%)
58.6
58.6
Type-3 (1 DG)
BSA BSA
BSA
1.858 ++ j1.493
1.858
j1.493
at 8
1.858
at 8 + j1.493
at
80.9578
0.9578
at 33
at 33
0.9578
at
33
1.0125
at
1.01258at 8
1.0125
0.8417 at
at 833
0.841733
at 33
0.8417
1.0269 at
at 9
1.0269
1.0269
30.276 at 9at 9
30.276
85.73 30.276
(59.34%)
85.73
(59.34%)
66.08
85.73 (59.34%)
66.08
66.08
GA
GA
GA
1.802
1.802++j1.152
j1.152
at 2 + j1.152
1.802
at 2
at
2 at
0.9541
at33
33
0.9541
0.9541
at
33
1.0045
at
8
1.0045 at 8
1.0045
0.8287 at
at 833
0.8287
at 33
0.8287
0.9945 at
at 33
9
0.9945
0.9945
at99
29.798at
29.798
29.798
82.71 (60.77%)
82.71
(60.77%)
61.51 (60.77%)
82.71
61.51
61.51
For Type-1 (2 DG), the proposed method gives better results in loss reduction and voltage
For Type-1
(2 DG),asthecompared
proposedtomethod
gives
better
results in
lossSpecifically,
reduction and
voltage
stability
improvement
BSA
and
GA
algorithms
[19].
power
loss
For
Type-1
(2
DG),
the
proposed
method
gives
better
results
in
loss
reduction
and
voltage
stability
stability
improvement
as
compared
to
BSA
and
GA
algorithms
[19].
Specifically,
power
loss
reduction by proposed
method
is higher
as at
55.92% as[19].
compared
to BSApower
55.71%
and GA 55.49%
improvement
as compared
to BSA
and GA
algorithms
Specifically,
loss
by
reduction
by Similarly
proposed
method
is higher
as the
at
55.92%
as compared
to BSA
55.71%
andreduction
GA
respectively.
for
voltage
stability,
proposed
method gives
higher
outcomes
as55.49%
29.293
respectively.
Similarly
for
voltage
stability,
the proposed
methodand
gives
higher outcomes
as 29.293
compared to BSA
29.284
and
GA 29.291.
Moreover,
the minimum
maximum
voltage profile
and
compared to BSA 29.284 and GA 29.291. Moreover, the minimum and maximum voltage profile and
Energies 2016, 9, 982
19 of 23
proposed
method
Energies 2016,
9, 982 is higher as at 55.92% as compared to BSA 55.71% and GA 55.49% respectively.
19 of 23
Energies 2016, 9, 982
19 of 23
Similarly
for voltage stability, the proposed method gives higher outcomes as 29.293 compared
to
minimum
and GA
maximum
stability
of the proposed
method voltage
are higher
in results
as compared
BSA
29.284 and
29.291. voltage
Moreover,
the minimum
and maximum
profile
and minimum
and
minimum and maximum voltage stability of the proposed method are higher in results as compared
to BSA and
GA. stability of the proposed method are higher in results as compared to BSA and GA.
maximum
voltage
to BSA and GA.
ForType-3
Type-3(1(1DG),
DG),the
thepower
powerloss
lossreduction
reductionby
by the
the proposed
proposed method is higher
For
higher as
as at
at 63.55%
63.55% as
as
For Type-3 (1 DG), the power loss reduction by the proposed method is higher as at 63.55% as
comparedtotoBSA
BSA59.34%
59.34%and
andGA
GA60.77%
60.77%respectively.
respectively. However,
However, voltage stability
stability of
compared
of the
the proposed
proposed
compared to BSA 59.34% and GA 60.77% respectively. However, voltage stability of the proposed
methodgives
giveshigher
higheroutcomes
outcomesas
as30.085
30.085 compared
compared to
to BSA
BSA 30.276
30.276 and
and GA
GA 29.798.
29.798. Moreover,
method
Moreover, the
the
method gives higher outcomes as 30.085 compared to BSA 30.276 and GA 29.798. Moreover, the
minimum
and
maximum
voltage
profile
and
voltage
stability
of
the
proposed
method
in
this
are
also
minimum and maximum voltage profile and voltage stability of
this are also
minimum and maximum voltage profile and voltage stability of the proposed method in this are also
higherininresults
resultsasascompared
comparedtotoBSA
BSAand
andGA.
GA.
higher
higher in results as compared to BSA and GA.
VoltageProfile
Profileand
andVoltage
VoltageStability
Stabilityfor
forCase
CaseStudy-II
Study-II
Voltage
Voltage Profile and Voltage Stability for Case Study-II
TheFigures
Figures1616and
and17
17shows
showsthe
thevoltage
voltage profile
profile and
and voltage stability analysis for
The
for multi-objective
multi-objective
The Figures 16 and 17 shows the voltage profile and voltage stability analysis for multi-objective
optimizationcase.
case.
optimization
optimization case.
Figure 16. Voltage profile for Type-1 (1 DG and 2 DG) and Type-3 (1 DG).
Figure
DG) and
and Type-3
Type-3 (1
(1 DG).
DG).
Figure 16.
16. Voltage
Voltage profile
profile for
for Type-1
Type-1 (1
(1 DG
DG and
and 22 DG)
Figure 17. Voltage stability for Type-1 (1 DG and 2 DG) and Type-3 (1 DG).
Figure 17. Voltage stability for Type-1 (1 DG and 2 DG) and Type-3 (1 DG).
Figure 17. Voltage stability for Type-1 (1 DG and 2 DG) and Type-3 (1 DG).
It can be seen from Figure 16, that with the installation of Type-1 (1 DG) and Type-1 (2DG) the
It can be seen from Figure 16, that with the installation of Type-1 (1 DG) and Type-1 (2DG) the
minimum voltage profile is improved upto 0.9439 p.u and 0.9766 p.u at bus 33 respectively, while
minimum voltage profile is improved upto 0.9439 p.u and 0.9766 p.u at bus 33 respectively, while
maximum voltage profile is improved upto 0.9982 p.u and 0.9986 p.u at bus 2 respectively. With the
maximum voltage profile is improved upto 0.9982 p.u and 0.9986 p.u at bus 2 respectively. With the
Energies 2016, 9, 982
20 of 23
It can be seen from Figure 16, that with the installation of Type-1 (1 DG) and Type-1 (2DG)
the minimum voltage profile is improved upto 0.9439 p.u and 0.9766 p.u at bus 33 respectively,
while maximum voltage profile is improved upto 0.9982 p.u and 0.9986 p.u at bus 2 respectively. With
the installation of Type-3 (1DG), the minimum voltage profile is improved upto 0.9825 p.u at bus 33
and maximum voltage is improved upto 1.00 p.u at bus 9, 10 and 11 respectively.
Moreover, Figure 17 shows that with the installation of Type-1 ( 1 DG) and Type-1 (2 DG)
the minimum voltage stability is improved upto 0.7970 p.u and 0.9129 p.u at bus 31 respectively,
while maximum voltage stability is improved upto 0.99269 p.u and 0.9944 p.u at bus 2 respectively.
With the installation of Type-3 (1 DG), the minimum voltage stability is improved upto 0.9353 p.u at
bus 31 and maximum voltage is improved upto 1.00 p.u at bus 9,10 and 11 respectively.
The overall analysis shows that the voltage profile and voltage stability for both test systems at
every node are improved, hence it can be concluded that the performance of the proposed methodology
for optimal placement and sizing are better as compared to the literature algorithms.
7. Conclusions
In this manuscript, an advanced-PFNDMOPSO has been applied for optimal placement and sizing
of distributed generation sources. The proposed method consists two case studies as single-objective
optimization and multi-objective optimization for power loss reduction and voltage stability improvement.
Three types of distributed generation sources i.e., active power DG, reactive power DG and
active-reactive power DG (i.e., simultaneously placement Type-1 and Type-2) are proposed in the
methodology. Furthermore, each case study consists of single and multiple numbers of DG(s).
An advanced-non-dominated sorting MOPSO method is effectively utilized. For the case study-I,
the preference is only given to only one objective function at a time (i.e., power loss reduction or voltage
stability improvement). Whereas, for case study-II the optimal compromise results were chosen from
trade-off solution using fuzzy decision model. The proposed methodology is tested on IEEE 33 bus
system. The results of the proposed method are also compared with the literature algorithms. It can be
concluded that the proposed method gives better results in terms of optimal placement and sizing
of DG problem for both case studies. Additionally, the study also demonstrates that simultaneous
installation of active and reactive power DG (Type-3) gives better performance in terms of power loss
reduction, voltage stability and voltage profile improvement in the distribution system.
Acknowledgments: The authors would like to gratefully acknowledge Universiti Teknologi PETRONAS,
Malaysia for providing continuous technical and financial support to conduct this research. This research
is supported by Fundamental Research Grant from the Ministry of Higher Education, Malaysia (Grant No.
FRGS/2/2014/TK03/UTP/02/9).
Author Contributions: Perumal Nallagownden proposed the ideas of distributed generation in the distribution
system and gave suggestions for the manuscript. Kumar Mahesh performed the simulation, analyzed the
results critically and wrote this paper. Irraivan Elamvazuthi assisted in optimization algorithm and reviewed
the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
V
kW/MW
KVA/MVA
KVar/MVar
m1, m2
i
p.u
PDG
min
PDG
max
PDG
Volt
Kilo/mega watt
Kilo-volt/mega-volt ampere
Kilo-volt/mega-volt ampere reactive
m1 and m2 are buses name
i is the branch name connected between bus m1 and m2
Per unit
Active power DG
min. value of Active power DG
max. value of Active power DG
Energies 2016, 9, 982
Q DG
Qmin
DG
Qmax
DG
VSI
MOO
MOPSO
DSTATCOM
Obj-1
Obj-2
BA
ABC
BSA
21 of 23
reactive power DG
min. value of reactive power DG
max. value of reactive power DG
Voltage stability indicator
Multi-objective optimization
Multi-objective particle swarm optimization
Distribution static compensator
Objective-1
Objective-2
Bat algorithm
Artificial bee colony
Backtracking search algorithm
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
El-Fergany, A. Optimal allocation of multi-type distributed generators using backtracking search optimization
algorithm. Int. J. Electr. Power Energy Syst. 2015, 64, 1197–1205. [CrossRef]
Kansal, S.; Kumar, V.; Tyagi, B. Optimal placement of different type of DG sources in distribution networks.
Int. J. Electr. Power Energy Syst. 2013, 53, 752–760. [CrossRef]
Yammani, C.; Maheswarapu, S.; Matam, S.K. A Multi-objective Shuffled Bat algorithm for optimal placement
and sizing of multi distributed generations with different load models. Int. J. Electr. Power Energy Syst. 2016,
79, 120–131. [CrossRef]
Peng, X.; Lin, L.; Zheng, W.; Liu, Y. Crisscross Optimization Algorithm and Monte Carlo Simulation for
Solving Optimal Distributed Generation Allocation Problem. Energies 2015, 8, 13641–13659. [CrossRef]
Prakash, P.; Khatod, D.K. Optimal sizing and siting techniques for distributed generation in distribution
systems: A review. Renew. Sustain. Energy Rev. 2016, 57, 111–130. [CrossRef]
Acharya, N.; Mahat, P.; Mithulananthan, N. An analytical approach for DG allocation in primary distribution
network. Int. J. Electr. Power Energy Syst. 2006, 28, 669–678. [CrossRef]
Quoc, H.D.; Mithulananthan, N. An optimal operating strategy of DG unit for power loss reduction in
distribution systems. In Proceedings of the 2012 7th IEEE International Conference on Industrial and
Information Systems (ICIIS), Chennai, India, 6–9 August 2012; pp. 1–6.
Hung, D.Q.; Mithulananthan, N.; Bansal, R. Analytical strategies for renewable distributed generation
integration considering energy loss minimization. Appl. Energy 2013, 105, 75–85. [CrossRef]
Aman, M.; Jasmon, G.; Mokhlis, H.; Bakar, A. Optimal placement and sizing of a DG based on a new power
stability index and line losses. Int. J. Electr. Power Energy Syst. 2012, 43, 1296–1304. [CrossRef]
Keane, A.; O’Malley, M. Optimal utilization of distribution networks for energy harvesting. IEEE Trans.
Power Syst. 2007, 22, 467–475. [CrossRef]
Keane, A.; O’Malley, M. Optimal allocation of embedded generation on distribution networks. IEEE Trans.
Power Syst. 2005, 20, 1640–1646. [CrossRef]
Atwa, Y.; El-Saadany, E. Probabilistic approach for optimal allocation of wind-based distributed generation
in distribution systems. IET Renew. Power Gener. 2011, 5, 79–88. [CrossRef]
Atwa, Y.; El-Saadany, E.; Salama, M.; Seethapathy, R. Optimal renewable resources mix for distribution
system energy loss minimization. IEEE Trans. Power Syst. 2010, 25, 360–370. [CrossRef]
Abdelsalam, A.A.; Zidan, A.A.; El-Saadany, E.F. Optimal DG Allocation in Radial Distribution Systems with
High Penetration of Non-linear Loads. Electr. Power Compon. Syst. 2015, 43, 1487–1497. [CrossRef]
Yuvaraj, T.; Ravi, K.; Devabalaji, K. DSTATCOM allocation in distribution networks considering load
variations using bat algorithm. Ain Shams Eng. J. 2015. [CrossRef]
Mohandas, N.; Balamurugan, R.; Lakshminarasimman, L. Optimal location and sizing of real power DG
units to improve the voltage stability in the distribution system using ABC algorithm united with chaos.
Int. J. Electr. Power Energy Syst. 2015, 66, 41–52. [CrossRef]
Devabalaji, K.; Ravi, K.; Kothari, D. Optimal location and sizing of capacitor placement in radial distribution
system using Bacterial Foraging Optimization Algorithm. Int. J. Electr. Power Energy Syst. 2015, 71, 383–390.
[CrossRef]
Energies 2016, 9, 982
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
22 of 23
Imran, A.M.; Kowsalya, M. Optimal size and siting of multiple distributed generators in distribution system
using bacterial foraging optimization. Swarm Evol. Comput. 2014, 15, 58–65. [CrossRef]
El-Fergany, A. Multi-objective Allocation of Multi-type Distributed Generators along Distribution Networks
Using Backtracking Search Algorithm and Fuzzy Expert Rules. Electr. Power Compon. Syst. 2016, 44, 252–267.
[CrossRef]
Abdelaziz, A.Y.; Hegazy, Y.G.; El-Khattam, W.; Othman, M.M. A Multi-objective Optimization for Sizing and
Placement of Voltage-controlled Distributed Generation Using Supervised Big Bang-Big Crunch Method.
Electr. Power Compon. Syst. 2015, 43, 105–117. [CrossRef]
Moradi, M.H.; Zeinalzadeh, A.; Mohammadi, Y.; Abedini, M. An efficient hybrid method for solving the
optimal sitting and sizing problem of DG and shunt capacitor banks simultaneously based on imperialist
competitive algorithm and genetic algorithm. Int. J. Electr. Power Energy Syst. 2014, 54, 101–111. [CrossRef]
Mistry, K.D.; Roy, R. Enhancement of loading capacity of distribution system through distributed generator
placement considering techno-economic benefits with load growth. Int. J. Electr. Power Energy Syst. 2014, 54,
505–515. [CrossRef]
Elsheikh, A.; Helmy, Y.; Abouelseoud, Y.; Elsherif, A. Optimal capacitor placement and sizing in radial
electric power systems. Alex. Eng. J. 2014, 53, 809–816. [CrossRef]
Devi, S.; Geethanjali, M. Optimal location and sizing determination of Distributed Generation and DSTATCOM
using Particle Swarm Optimization algorithm. Int. J. Electr. Power Energy Syst. 2014, 62, 562–570. [CrossRef]
Kayal, P.; Chanda, C. Strategic approach for reinforcement of intermittent renewable energy sources and
capacitor bank for sustainable electric power distribution system. Int. J. Electr. Power Energy Syst. 2016, 83,
335–351. [CrossRef]
Gong, Q.; Lei, J.; Ye, J. Optimal Siting and Sizing of Distributed Generators in Distribution Systems
Considering Cost of Operation Risk. Energies 2016, 9, 61. [CrossRef]
Gao, Y.; Liu, J.; Yang, J.; Liang, H.; Zhang, J. Multi-objective planning of multi-type distributed generation
considering timing characteristics and environmental benefits. Energies 2014, 7, 6242–6257. [CrossRef]
Farjah, E.; Bornapour, M.; Niknam, T.; Bahmanifirouzi, B. Placement of combined heat, power and hydrogen
production fuel cell power plants in a distribution network. Energies 2012, 5, 790–814. [CrossRef]
Liu, K.-Y.; Sheng, W.; Liu, Y.; Meng, X.; Liu, Y. Optimal sitting and sizing of DGs in distribution system
considering time sequence characteristics of loads and DGs. Int. J. Electr. Power Energy Syst. 2015, 69, 430–440.
[CrossRef]
Sheng, W.; Liu, K.; Liu, Y.; Meng, X.; Li, Y. Optimal Placement and Sizing of Distributed Generation via
an Improved Nondominated Sorting Genetic Algorithm II. IEEE Trans. Power Deliv. 2015, 30, 569–578.
[CrossRef]
Zeinalzadeh, A.; Mohammadi, Y.; Moradi, M.H. Optimal multi objective placement and sizing of multiple
DGs and shunt capacitor banks simultaneously considering load uncertainty via MOPSO approach. Int. J.
Electr. Power Energy Syst. 2015, 67, 336–349. [CrossRef]
Aman, M.M.; Jasmon, G.B.; Bakar, A.H.A.; Mokhlis, H. A new approach for optimum simultaneous multi-DG
distributed generation Units placement and sizing based on maximization of system loadability using HPSO
(hybrid particle swarm optimization) algorithm. Energy 2014, 66, 202–215. [CrossRef]
Haque, M. Efficient load flow method for distribution systems with radial or mesh configuration. IEE Proc.
Gener. Transm. Distrib. 1996, 143, 33–38. [CrossRef]
Sajjadi, S.M.; Haghifam, M.R.; Salehi, J. Simultaneous placement of distributed generation and capacitors in
distribution networks considering voltage stability index. Int. J. Electr. Power Energy Syst. 2013, 46, 366–375.
[CrossRef]
Chakravorty, M.; Das, D. Voltage stability analysis of radial distribution networks. Int. J. Electr. Power Energy Syst.
2001, 23, 129–135. [CrossRef]
Kennedy, J. Particle swarm optimization. In Encyclopedia of Machine Learning; Springer: New York, NY, USA,
2010; pp. 760–766.
Coello, C.A.C.; Pulido, G.T.; Lechuga, M.S. Handling multiple objectives with particle swarm optimization.
IEEE Trans. Evol. Comput. 2004, 8, 256–279. [CrossRef]
Kansal, S.; Sai, B.B.; Tyagi, B.; Kumar, V. Optimal placement of distributed generation in distribution networks.
Int. J. Eng. Sci. Technol. 2011, 3, 47–55. [CrossRef]
Energies 2016, 9, 982
39.
40.
41.
42.
43.
44.
23 of 23
Oda, E.S.; Abdelsalam, A.A.; Abdel-Wahab, M.N.; El-Saadawi, M.M. Distributed generations planning using
flower pollination algorithm for enhancing distribution system voltage stability. Ain Shams Eng. J. 2015.
[CrossRef]
Gözel, T.; Eminoglu, U.; Hocaoglu, M. A tool for voltage stability and optimization (VS&OP) in radial
distribution systems using matlab graphical user interface (GUI). Simul. Model. Pract. Theory 2008, 16,
505–518.
Moradi, M.H.; Abedini, M. A combination of genetic algorithm and particle swarm optimization for optimal
DG location and sizing in distribution systems. Int. J. Electr. Power Energy Syst. 2012, 34, 66–74. [CrossRef]
Manafi, H.; Ghadimi, N.; Ojaroudi, M.; Farhadi, P. Optimal placement of distributed generations in radial
distribution systems using various PSO and DE algorithms. Elektron. Elektrotech. 2013, 19, 53–57. [CrossRef]
Moradi, M.H.; Tousi, S.R.; Abedini, M. Multi-objective PFDE algorithm for solving the optimal siting and
sizing problem of multiple DG sources. Int. J. Electr. Power Energy Syst. 2014, 56, 117–126. [CrossRef]
Injeti, S.K.; Kumar, N.P. A novel approach to identify optimal access point and capacity of multiple DGs
in a small, medium and large scale radial distribution systems. Int. J. Electr. Power Energy Syst. 2013, 45,
142–151. [CrossRef]
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
View publication stats