Optimal Placement and Sizing of Distributed Generation Units Using Co-Evolutionary Particle Swarm Optimization Algorithms

TELKOMNIKA Indonesian Journal of Electrical Engineering
Vol. 13, No. 2, February 2015, pp. 247 ~ 256
DOI: 10.11591/telkomnika.v13i2.7026  247
Received November 14, 2014; Revised December 29, 2014; Accepted January 12, 2015
Optimal Placement and Sizing of Distributed
Generation Units Using Co-Evolutionary Particle Swarm
Optimization Algorithms
Alireza Kaviani-Arani
Department of Electrical Engineeing, Majlesi Branch, Islamic Azad University, Isfahan, Iran
Shahid Rajaee Center, Department of Technical and Vocational Education in Isfahan Province
E-mail: A.Kaviani@iaumajlesi.ac.ir, A.Kaviani@etvto.ir
Abstract
Today, with the increase of distributed generation sources in power systems, it’s important to
optimal location of these sources. Determine the number, location, size and type of distributed generation
(DG) on Power Systems, causes the reducing losses and improving reliability of the system. In this paper
is used Co-evolutionary particle swarm optimization algorithm (CPSO) to determine the optimal values of
the listed parameters. Obtained results through simulations are done in MATLAB software is presented in
the form of figure and table in this paper. These tables and figures, show how to changes the system
losses and improving reliability by changing parameters such as location, size, number and type of DG.
Finally, the results of this method are compared with the results of the Genetic algorithm (GA) method, to
determine the performance of each of these methods.
Keywords: optimal size and location, distributed generation (DG), co-evolutionary particle swarm
optimization (CPSO), system losses
Copyright © 2015 Institute of Advanced Engineering and Science. All rights reserved.
1. Introduction
The simplest and the most general definition of distributed generation sources include
the source that is connected directly to distributed (the client). Usually these resources are
referred to as small-scale power plants. There are various definitions for distributed generation
source in view of different institutes. From the perspective of the International Energy Agency
(IEA), DG refers to the source that can meet customer requirements on-site, and help
distribution network in energizing. In the view of CIGRE, DG refers to a resource that is facing
features: It’s not established a centralized, it’s not centralized dispatching, it’s usually connected
to the distribution network and its value is usually less than 50MW to 100MW. In the view of
Power Research Institute, DG is the power of a few KW to 50MW.
Use the DG in power system can have advantages such as: reduce losses; improve
voltage profiles, increased reliability, lower THD and power system improvement quality. In
addition, the small size of this resource is another advantage that it’s a very short time of
installation and be in place. A number of available distributed power generation technologies in
the world are: fuel cells, wind turbines, solar powerhouses, geothermal powerhouses, micro-
turbines and so on.
Therefore, it looks essential to determining distributed generation units to achieve these
benefits. So far, several methods have been proposed such as minimizing costs, improve
voltage profiles, low THD, increased system reliability, minimizing system losses and etc. to DG
determine the optimal location and size. In each of these methods, several optimization
algorithms are used to achieve the desired goal. In [1] to [7] references, it is used GA to improve
the voltage profile and minimizing the losses, in reference [12], reduce the cost has been to
basis of accounting, in [8],[9] references, it is used ACO algorithm to reduce losses and improve
voltage, in reference [13], it is used GA in order to eliminate the shortcomings system voltage
with DG, in [10, 11] references, it has used fuzzy logic for minimizing losses, and finally, in [14]
reference, it’s used Tabu Search Algorithm for this purpose (determining the optimal location
and size of DG). In this paper, it is presented a method to determine the number, location and
size of DG with the goal of minimizing losses and improving reliability systems that in which is

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TELKOMNIKA Vol. 13, No. 2, February 2015 : 247 – 256
248
used Co-evolutionary Particle Swarm Optimization algorithm (CPSO) for optimization
procedure.
2. Evaluation and Selection of Indicators for DG Installation
Installation of DG without the study will have a negative effect in distribution networks,
so to avoid the negative impact of DG on system parameters; it should be exist comprehensive
and total standards for control, installation and placement of these units [15]. However,
according to which choose of following purposes, it will be specified target function:
2.1. Losses Reduction Indicator
Lines are important in conditions of heavy loads, so that its cost will impose to
consumer’s form of energy by higher prices. It is obvious that losses in line are effects of power
transmission in transmission lines. Thus by using DG, we can reduce the amount of power
transmission in lines and therefore it will be reduced losses. In any case, according to the power
and location of DG there is also the possibility of increasing the losses lines.
2.2. Voltage of Profile Improvement Indicator
One of the advantages of using DG is improve the voltage profile and maintain voltage
in acceptable range in the consumer’s terminal. By using DG, because amount of active and
reactive power loads is provided by voltage profile, it will be reduced electricity in the
transmission line and therefore strengthen of voltage range for consumer.
2.3. Increase in System Loading Indicator
One other advantages of using DG is reduction of active and reactive power transition
from the transmission lines (Overall apparent power). This works leads to increase of
transmission lines capacity and therefore it will be preventing construction and development of
new lines and other installations such as transmission and distribution substations and therefore
reduces costs the related to them.
2.4. Reliability Indicator
Improving the reliability of the system is one of the objectives of using distributed
generation. But this does not mean that we should look to it as an independent objective
because if we use DG to any reason, it will affect reliability. Of course maybe we can know in
total, all these objectives for a distribution network as subset of the system's reliability.
2.5. Voltage Stability Indicator
In the network, voltage stability is associated with the system's ability to provide the
needed reactive power of network. In other words, most of reactive power reserve in system
resulted a higher degree of voltage stability in the system.
2.6. Environmental Indicator
With utilization of DG and electrical energy production, it will be more less the emissions
of greenhouse gases and other environmental pollutants compared with traditional
technologies. We can use resources that are optimal in this respect according to percent of
emissions of DG. But it is not considered as important indicators in our country.
Now, with regards to the materials above by targeting the two targets to reduce losses
and improve reliability, all indicators are provided. Because reduced losses and improved
reliability are more consistent with the philosophy of using distributed generation. The objective
function is defined as the sum of this two indicators (Reduce losses and improve reliability).
Thus our objective function is a multi-objective function (Multi-purpose) that is major difference
with the single indicator objective function that we will discuss them in the following.
3. Model of Losses Reduction Indicator
We need reduction in power losses for operation efficiently of network. Losses in
distribution system are calculated from the Equation (1), (2).

TELKOMNIKA ISSN: 2302-4046 
Optimal Placement and Sizing of Distributed Generation Units Using… (Alireza Kaviani-Arani)
249
n n
L ij i j i j ij i j i j
i 1 j 1
P A (PP Q Q ) B (Q P PQ )
 
    (1)
ij i j ij i j
ij ij
i j i j
R cos( δ δ ) R sin(δ δ )
A , B
VV VV
 
  (2)
PL : Power losses
Pi : Active power at bus i
Qi : Reactive power at bus i
Vi : Bus voltage i
i : Phase angle of bus i
The objective of solving the problem is minimizing the total power losses so that the first
part of the objective function is as follows:
scN
1 L k
i 1
F P Loss

   (3)
The constraints governing issue is as follows:
Power balance constraint
sc scN N
DGi Di L
i 1 i 1
P P P
 
   (4)
Range of active and reactive power produced by the DG
max
DGiDGi
min
DGi QQQ  (5)
max
DGiDGi
min
DGi PPP  (6)
Range of network losses
k kLoss (withDG) Loss (withoutDG)  (7)
Range of line loading
max
ijij II  (8)
4. Calculate the Reliability Index
4.1. Unit Unavailability
It is defined the probability of failure in some time intervals during the work in the next
as the unavailability of unit and it is known as the unit forced removal rate (FOR) in applications
of power systems [16]. This parameter is defined based on the ratio of the two units value as
follows:
(9)
[down time]
FOR
[down time] [up time]
r r f
m r T

  
    
  

 
That λ is expected failure rate, μ is expected repair rates, m is mean time to failure
(MTTF = 1/λ), r is mean time to repair (MTTR = 1/μ), m+ris mean time between failures (MTBF=
1/f), f is frequency period and T is since period.

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250
(10)
MTTR
FOR
MTTR MTTF


In connection with the production equipment with relatively long duty cycle, FOR
parameter is a probabilistic estimates which shows that the production unit will not be able to
next time load service under similar circumstances.
4.2. Energy Index Reliability (EIR)
Area under the load curve shows the consumed energy during a specific period and can
be used to calculate not feeding energy due deficiency in manufacturing capacity. This
parameter is defined the ratio of energy lost due to manufacturing defects and total requirement
energy for feeding the network. It’s independent of time to define this parameter for the defined
period in the load curve and is usually considered for a day, a month or a year. Any
manufacturing defect causing loss of load power still be obtained its probability from the
following equation:
(11)
Pr ( ) ( )
1
n n !
m (n-m)! m!
m n mn
ob U A
m
A U
 
  
 
 
 
 
 
That m is number of units that have been damaged, n is the total number of units, U
isunit not available and A is availability of units. Probable energy loss in a Power failure is Ek Pk.
The total od this multiplies is the total energy lost or hope lost energy.
(12)
1
n
k k
k
LOEE E P

 
That Pk is possibility of exit production unit with a capacity of Qk and Ek is energy lost
due to the production unit failure with a capacity of Qk. This parameter can be normalized by
using the total energy under the load curve that is defined by E.
(13). .
1
n
k k
p u
k
E P
LOEE
E
 
The amount of LOEEp.u.is the ratio between potential energy lost due to corruption unit
and the total required energy to feed the network load. Index of reliability energy EIR is defined
as follows:
(14). .1 p uEIR LOEE 
5. Objective Function the Problem
By combining the phrase above, objective function to determine the size and location of
DG resources are provided as follows:
1 1 2 2 , 1
n
Total i
i
F w F w F w  
(15)
1 1, 2 2,Total pu puF w F w F  (16)
w1 and w2 parameters are weighting coefficients that are an indication of their relative
importance.

251
6. Particle Swarm Optimization (PSO)
PSO is an evolutionary computation technique with the mechanism of individual
improvement, population cooperation and competition, which is based on the simulation of
simplified social models, such as bird flocking, fish schooling and the swarming theory (Kennedy
and Eberhart, 1995). In PSO, it starts with the random initialization of a population (swarm) of
individuals (particles) in the search space and works on the social behavior of the particles in
the swarm. Therefore, it finds the global best solution by simply adjusting the trajectory of each
individual towards its own best location and towards the best particle of the swarm at each time
step (generation). However, the trajectory of each individual in the search space is adjusted by
dynamically altering the velocity of each particle, according to its own flying experience and the
flying experience of the other particles in the search space.
The position and the velocity of the ith particle in the dimensional search space can be
represented as Xi = [Xi1, Xi2, …, XiN]T
and Vi = [Vi1, Vi2, …, ViN]T
, respectively. Each particle has
its own best position (pbest) Pi = [Pi1, Pi2, …, PiN]T
corresponding to the personal best objective
value obtained so far at time t. The global best particle (gbest) is denoted by Pg, which
represents the best particle found so far at time t in the entire swarm. The new velocity of each
particle is calculated as follows:
(17)   ( ) ( ) ( ), 1 , 1 1 , , 2 2 , (, ) , 1, 2, ,i j t i j t i j i j t g j i j tv wv c r p x c r p x j d       
Where c1 and c2 are constants called acceleration coefficients, w is called the inertia
factor, r1 and r2 are two independent random numbers uniformly distributed in the range of [0, 1].
Thus, the position of each particle is updated in each generation according to the
following equation:
(18), 1 , ,( ) ( ) ( 1) , 1, 2, ,i j t i j t i j tx x v j d    
In the standard PSO, Equation (17) is used to calculate the new velocity according to its
previous velocity and to the distance of its current position from both its own best historical
position and its neighbors’ best position. Generally, the value of each component in Vican be
clamped to the range [Vi,min , Vi,max] to control excessive roaming of particles outside the search
space [Xi,min , Xi,max] Then the particle flies toward a new position according to Equation (18).
The process is repeated until a user-defined stopping criterion is reached [17].
6.1. Co-evolutionary Particle Swarm Optimization (CPSO)
6.1.1. Mechanism of Co-evolution
Due to the simplicity of principle and easiness to implement, the penalty function
method is the most popular technique to handle constraints. With respect to the main difficulty of
setting appropriate penalty factors, Michalewicz and Attia (1994) indicated that a self-adaptive
scheme is a promising direction. In the previous work by Coello (2000), a notion of co-evolution
was proposed and incorporated into a GA to solve constrained optimization problems. In this
paper, we will make some modifications on co evolution and incorporate it into PSO for
constrained optimization problems [17].
The principle of co-evolution model in CPSO is shown in Figure 1. In our CPSO, two
kinds of swarms are used. In particular, one kind of a single swarm (denoted by Swarm2) with
size M2 is used adapt suitable penalty factors, another kind of multiple swarms (denoted by
Swarm1,1, Swarm1,2, …, Swarm1,M2) each with size M1 are used in parallel to search good
decision solutions. Each particle Bj in Swarm2 represents a set of penalty factors for particles in
Swarm1,j, where each particle represents a decision solution. In every generation of co-evolution
process, every Swarm1,jwill evolve by using PSO for a certain number of generations (G1) with
particle Bj in Swarm2 as penalty factors for solution evaluation to get a new Swarm1,j. Then the
fitness of each particle Bj in Swarm2 will be determined. After all particles in Swarm2 are
evaluated, Swarm2 will also evolve by using PSO with one generation to get a new Swarm2 with
adjusted penalty factors. The above coevolution process will be repeated until a pre-defined
stopping criterion is satisfied (e.g., a maximum number of co-evolution generations G2 is
reached).

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In brief, two kinds of swarms evolve interactively, where Swarm1,j is used to evolve
decision solutions while Swarm2 is used to adapt penalty factors for solution evaluation. Due to
the co-evolution, not only decision solutions are explored evolutionary, but also penalty factors
are adjusted in a self-tuning way to avoid the difficulty of setting suitable factors by trial and
error.
Figure 1. Graphical illustration for the notion of co-evolution
6.1.2. Evaluation function for Swarm1,j
For constrained optimization problems, we design the penalty function following the
guidance suggested by Richardson et al. (1989), i.e., not only how many constraints are
violated but also the amounts in which such constraints are violated. In particular, the ith particle
in Swarm1,jin CPSO is evaluated by using the following formula:
(19)    1 2_ _i iF x f x sum viol w num viol w    
Where fi(x) is the objective value of the ith particle, sum_viol denotes the sum of all the
amounts by which the constraints are violated, num_viol denotes the number of constraints
violation, w1 and w2 are penalty factors corresponding to the particle Bjin Swarm2.
The value of sum_viol is calculated as follows:
(20)   viol
1
sum , 0
N
i i
i
g x g x

  
Where N is the number of inequality constraints (here it is assumed that all equality
constraints have been transformed to inequality constraints).
6.1.3. Evaluation function for Swarm2
Each particle in Swarm2 represents a set of factors (w1 and w2). After Swarm1,jevolves
for a certain number of generations (G1), the jth particle Bj in Swarm2 is evaluated as follows.
a) If there is at least one feasible solution in Swarm1,j, then particle Bj is evaluated using
the following formula and is called a valid particle:
(21)  feasible
num _ feasible
num _ feasible
j
f
P B  

Where feasiblef denotes the sum of objective function values of feasible solutions in Swarm1,j,
and num_feasible is the number of feasible solutions in Swarm1,j. The reason for only
considering feasible solutions is to bias the Swarm1,jtowards feasible regions. Moreover, the
subtraction of num_feasible in Equation (21) is to avoid Swarm1,j stagnating at certain regions in
which only very few particles will have good objective values or even be feasible. Consequently,

253
Swarm1,jwill be encouraged to move towards regions including a lot of feasible solutions with
good objective values. In addition, num_feasible also acts as a scaling factor when used to
divide feasiblef .
b) If there is no feasible solution in Swarm1,j(it can be considered that the penalty is too
low), then particle Bj in Swarm2 is evaluated as follows and is called an invalid particle.
(22)   
sum _ viol
Max num _ viol
num _ viol
j validP B P 



Where Max(Pvalid) denotes the maximum fitness value of all valid particles in Swarm2,
sum_ viol denotes the sum of constraints violation for all particles in Swarm1,j, and
num _ viol counts the total number of constraints violation for all particles in Swarm1,j.
Obviously, by using Equation (22), the particle in Swarm2 that results in a smaller
amount of constraints violation of Swarm1,j is considered better. Consequently, the search may
bias Swarm1,j to the region where the sum of constraints violation is small (i.e. the boundary of
the feasible region). Moreover, the addition of item Max(Pvalid) is to assure that the valid particle
is always better than the invalid one to guide the search to the feasible region. In addition,
num _ viol acts as a scaling factor. Figure 2 shows the flow chart of a CPSO algorithm.
Figure 2. The process computational algorithm (CPSO)

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254
7. Samples Network Study
The proposed method has been applied on a 69 buses test network samples. All
network data and Algorithm CPSO has been given respectively in Table 1 and 2.
Table 1. Data distribution network sample 69 buses
Network Active power (MW) Reactive power (Mvar) Total active power
losses (MW)
Total reactive
power losses (Mvar)
69 buses 3.80 2.69 230.0372 104.3791
Table 2. The CPSO algorithm data
CPSO Population size Maximum number of
repetitions Kmax
C1 = C2 w
30 100 2 0.4
Figure 3. 69 bus distribution network sample
Table 3. CPSO results to the samples network
Total real power loss(kW) Min Ave. Max
80.1933 95.4714 203.2326
Average Time (Sec.) 5.6341
Convergence characteristic of best the proposed algorithm response is shown in Figure
4. Figure 5 shows total active power losses resulting from the 100 times implementation of
CPSO-OPDG program.
Figure 4. Convergence characteristic of best the proposed algorithm response
0 20 40 60 80 100
80
82
84
86
88
90
92
94
96
98
100
Generation
TotalRealPowerLoss(kW)

255
Figure 5. Total active power losses from the 100 times implementation of program CPSO-
OPDG
Optimum location and size of DG for 69 bus system by using GA and CPSO algorithms
is shown in Table 4. As it is shown in Table, loss reduction percentage of active and reactive
power in case one DG by using the CPSO algorithm is equal to 63.05% and 60.28%, while,
these two parameters are equal to 61.64% and 58.43% by using the GA algorithm. In the case
of two DG, loss reduction percentage of active and reactive power with using of CPSO algorithm
is equal to 68.18% and 64.81%, while, it is equal to 63.51% and 60.43% by using the GA
algorithm. Also in the case of three DG, loss reduction percentage of active and reactive power
with using of CPSO algorithm is equal to 69.19% and 65.81%, but this amount is equal to
67.93% and 64.26% by using the GA algorithm. Also it should be mentioned that CPSO has this
advantage that it can be achieved true optimal solution in the first few repetition, but for GA we
need to run the algorithm with many repetitions to get the main optimum and non-local answer.
Table 4. DG Optimal Placement for 69 buses IEEE network using GA and CPSO algorithms
Method
Bus
No.
DG
Size
(MW)
Bus
No.
DG
Size
(MW)
Bus
No.
DG
Size
(MW)
Ploss
(kW)
Qloss
(kvar)
Loss Reduction
%
Real
Reactiv
e
Load Flow
Analysis
230.0
3
104.3
7
Heuristic Search 56 1.807 84.93 41.45 63.08 60.29
GA
61 1.500 88.21 43.39 61.64 58.43
62 0.861 61 0.886 83.91 41.31 63.51 60.43
62 0.736 18 0.519 61 0.809 73.76 37.31 67.93 64.26
CPSO
56 1.808 84.98 41.47 63.05 60.28
56 1.724 53 0.519 73.18 36.74 68.18 64.81
56 1.666 55 0.375 33 0.508 70.87 35.69 69.19 65.81
8. Conclusion
In this paper, it has been used an Evolutionary Intelligent Method for solving the
problem of location and optimized size of DG resources with multiple objectives. CPSO method
is very powerful and accurate, as well as is simple on Implementation. About the results of the
test network (69 buses IEEE) that is done by using two intelligent algorithms CPSO and GA, it
must be said that the simulation shows that loss reduction percentage of active and reactive
power with using of CPSO algorithm is more and better of the results obtained of GA algorithm.
Of course, the main advantage CPSO algorithm is in the time of obtains optimal values.
Because just as mentioned, CPSO in the first few repetition; indicates the right answer. But we
should be increase the number of these repetitions to find the right optimal solution in the GA.
170 180 190 200 210 220
80
100
120
140
160
180
200

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So in this context, CPSO algorithm is more efficient than genetic algorithm. So in the end, we
can be stated that simulation results of the CPSO method is more effective compared to other
methods used in this field.
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