Journal of Engineering Research and Studies
E-ISSN 0976-7916
Research Article
AN EFFICIENT APPROACH FOR CAPACITOR SIZING AND
LOCATION ON A RADIAL DISTRIBUTION SYSTEM USING
ARTIFICIAL INTELLIGENCE TECHNIQUE
Shikha Gupta1, Gursewak Singh Brar2
Address for Correspondence
Department of Electrical Engineering, Chitkara Institute of Engg. & Tech., Rajpura, District Patiala-147001
Department of Electrical Engineering, B.B.S.B.E.C., Fathegarh Sahib, Punjab
E Mail shikhagupta157@gmail.com, brargs77@yahoo.com
ABSTRACT
This paper undertakes the problem of optimal shunt capacitor placement for loss reduction in a radial distribution feeder. The
objective is to determine the optimum size and location of the capacitors to be placed on a radial distribution system. The objective
function is to have maximization of saving due to reduction of energy losses thereby taking into consideration cost of capacitor. The
solution methodology used divides the problem into two parts. In first part, load flow solution for the radial feeder is obtained and
followed by a loss sensitivity analysis to select the candidate capacitor installation locations. In second part, Genetic algorithm is
used as an optimization tool, which obtains the optimal value of capacitors to be installed. The solution algorithms have been
implemented into and tested on a 33-bus radial distribution system. Test results demonstrate the effectiveness of the developed
algorithm. Computational results are calculated in MATLAB 7.
KEYWORDS: Radial Distribution System (RDS), Capacitor placement, Loss reduction, Loss sensitivity factor (LSF), Genetic
algorithm (GA).
I. INTRODUCTION
The analysis of the customer failure statistics of most
utilities indicates that the distribution system makes the
greatest individual contribution to the unavailability of
supply to a customer. Therefore, the analysis of a
distribution system is an important area of activity. It is
well known that losses in a distribution system are
significantly high. The economic reduction of loss in
power systems is considered one of the most important
issues in the economy of all countries. Because of the
growing effort to reduce system losses, many papers
have been published in recent years referring to
optimal distribution planning. Researches in this field
show that loss reduction is more economical than
increasing generation. Reduction of loss in the
distribution systems with the maximum saving is
achieved through various methods. One of the methods
is the optimal selection of capacitors in such networks.
The installation of shunt capacitors on radial
distribution systems is essential for power flow control,
improving system stability, power factor correction,
voltage profile management and losses minimization.
Therefore it is important to find the optimal size and
location of capacitors required to minimize energy
losses. A variety of methods have been devoted for
load flow analysis and capacitor placement problems
by many researchers. D. Shirmohammadi and A.
Semlyen [3] presented a new compensation-based
power flow method for the solution of weakly meshed
distribution and transmission networks.S. Ghosh and
D. Das [4] proposed a simple and efficient method for
the load flow of radial distribution network using the
evaluation based on algebraic expression of receiving
JERS/Vol.II/ Issue II/April-June, 2011/50-54
end. Goswami and Basu [5] have presented a direct
method for solving radial and meshed distribution
networks. Sundhararajan and Pahwa [7] have solved
the general capacitor placement problem in a
distribution system using a genetic algorithm. ChingTzong Su, Chu-S. Lee and Chin-S. Ho [8] has
presented an optimal capacitor placement method
which employs simplified power flow formulations,
genetic algorithms and sensitivity factors for a given
load pattern. Prakash and M. Sydulu[12] presented a
novel Particle Swarm Optimization based approach for
capacitor placement on Radial Distribution Systems. In
this paper capacitor placement problem for loss
minimization of distribution system is solved using
GA. In order to demonstrate the effectiveness of GA an
example from the literature is solved and the
computational results are obtained.
II. PROBLEM FORMULATION
The problem of capacitor placement consists of
determining the location, size and number of capacitors
to be installed in a distribution system.
III. OBJECTIVE FUNCTION
The objective is to reduce the energy losses on the
system while striving to minimize the cost of capacitor
in the system. It thus consists of two terms. The first is
the cost of capacitor placement and the second is the
cost of the total energy losses. The cost associated with
capacitor placement is composed of a fixed installation
cost and a purchase cost. The total cost of the energy
losses is obtained by summing up the real power losses
for each load level multiplied by the corresponding
duration.
Journal of Engineering Research and Studies
Mathematical Representation:
It is expressed mathematically by the equations below:
1. Capacitor Cost (KC):
Capacitor cost is divided into two terms: constant
installation cost and variable cost which is proportional
to the rating of capacitors. Therefore capacitor cost is
expressed as:
ncap
KC =
∑K
i
+ K ×Q
c
ci
i =1
(1)
Where,
Ki is the constant installation cost of capacitor.
Kc is the purchase rate of capacitor per kVAR.
Qci is the rating of capacitor on bus in kVAR.
2: Energy Loss Cost (ELC):
The Energy loss cost (ELC) can be calculated by
multiplying EL with the energy rate (Ke)
ELC = EL x Ke
(2)
where
ELi, is energy loss (kW) in section–i in time duration
T.
Ke is the energy rate
The cost function ‘S’ [7] is expressed as:
Minimize
n
ncap
S = K e × ∑ EL j + ∑ K i + K c × Q ci
j =1
i =1
F is the fitness function
1
F( f ) =
1+ S
(3)
(4)
Net saving = BEL – KC
(5)
Where
BEL is benefit due to energy loss reduction
BEL = ELC(without capacitor) - ELC(with capacitor)
ELC(without capacitor) is energy loss cost without capacitor.
ELC(with capacitor) is energy loss cost with capacitor.
KC is the total capacitors cost as expressed by
equation.
IV. METHODOLOGY USED
The solution procedure solves the problem in two
steps. Firstly load flow analysis of uncompensated
system is carried out to calculate bus voltages and line
losses followed by Loss Sensitivity Factor to identify
the candidate buses for shunt capacitor placement.
Then Capacitor allocation is done using Genetic
Algorithm and finally load flow analysis of
compensated system is carried out to obtain optimal
solution.
JERS/Vol.II/ Issue II/April-June, 2011/50-54
E-ISSN 0976-7916
V. CAPACITOR SIZING AND LOCATION USING
GENETIC ALGORITHM
The developed algorithm for identifying the sizing and
location is based on Genetic Algorithm (GA).
The various steps performed for Genetic Algorithm
[12] are given as follow:
The algorithm procedure can be summarized as:
Step 1: Read the line and load data of distribution.
Step 2: Run the Load Flow of Distribution System to
find out voltage magnitudes at the buses and total
power loss.
Step 3: Select the candidate buses.
Step 4: Set GEN = 0
Step 5: Form initial population of real numbers, which
is randomly selected value of capacitors to be installed
at the candidate buses for compensation.
Step 6: Update the reactive power at candidate buses.
Step 7: Run the Load Flow of Distribution System
with updated reactive power at the candidate buses for
each population. Also calculate total power loss for
each population.
Step 8: Calculate the total Energy Loss Cost (ELC)
and Capacitor Cost (KC) for population.
Step 9: For each population, evaluate the objective
function and the fitness value. The objective function
for each population is the total energy loss cost and the
cost of capacitors given in eq. (3).
Step 10: GEN = GEN + 1
Step 11: Select the solutions in pool from initial
population by using Roulette Wheel Selection
procedure.
Step 12: Perform Crossover on the solutions selected
randomly from the pool using procedure and generate
two off springs.
Step 13: Perform Mutation on the offspring generated
by the crossover operation using the procedure and
generate the offspring.
Step 14: Calculate Energy Loss Cost (ELC) and
capacitors cost (KC). Also evaluate objective function
and Fitness Function of each off springs.
Step 15: Combine the solutions of the pool and the off
springs and refer them as new population.
Step 16: Replace new population with initial
population for next generation.
Step 17: Go to step 10, till the solution converges.
Step 18: STOP
The above set of steps for the capacitor placement is
depicted in flowchart as shown in Fig. 1 below.
Journal of Engineering Research and Studies
E-ISSN 0976-7916
Table1. The proposed method and the algorithm are
implemented by using MATLAB 7.
Table 1: Comparison of the results obtained on 33 Bus RDS before and after placing the capacitors
Minimum System
Voltage (p.u.)
Power Loss (kW)
Loss reduction (%)
Buses
Capacitor
(kVAr)
and
size
Total
Compensation
Total Energy Loss
Cost
Total
capacitors
cost
Total Cost
Total
savings
annual
Uncompensated
0.9041
Compensated
0.9304
177KW
-----
104KW
41.24%
(73kW)
7 250
12 350
16 250
27 200
1050 kVAr
---
-$93,031.2
= Rs. 46,51,560
--$93,031
= Rs. 46,51,560
--
$54,662
=Rs.27,33,120
$7,150
= Rs. 3,57,500
$ 61,812
=Rs.30,90,620
$ 31,219
=Rs.
15,60,940
It has been found that if the capacitors are placed at
locations other then the above (i.e. first four highly
sensitive buses) but in the decreasing order of LSF,
although losses are reduced but in each case losses are
more than previous and total cost also increases
thereby reducing overall annual benefit. Table 2 shown
below gives the comparison of the results obtained by
capacitor placement at four different buses on different
locations in each case. Thus, it is shows that maximum
loss reduction and savings are obtained when the
capacitors are placed at first four highly sensitive buses
are per LSF.
Fig. 1 Flowchart for the capacitor placement on
RDS
VI. APPLICATION EXAMPLE AND RESULTS
The single line diagram of compensated and
uncompensated test system i.e. 33 bus system
considered in this work is shown in fig. 2 & 3 resp. It
has been found that by placing the capacitor at highly
sensitive nodes (i.e. buses 7,12,16,27) maximum
benefit can be obtained. Comparison of results of the
compensated and uncompensated RDS is presented in
Table 2: Comparison of the results obtained on 33-Bus RDS before and after placing the capacitors at four
different buses on different locations in each case
Minimum
system
voltage (p.u.)
Power Loss (kW)
Loss reduction (%)
Optimal location and
Capacitor size (kVAr)
Total kVAr
Total Energy Loss Cost
Total capacitors cost
Total cost
Net annual savings
Uncompensated
Compensated Case I
0.9041
177 KW
------
----$93,031=
Rs. 46,51,560
---$93,031=
Rs. 46,51,560
---
0.9304
Compensated
Case II
0.9281
Compensated
Case III
0.9209
Compensated
Case IV
0.9176
104 KW
41.2%
7
250
12 350
16 250
27 200
1050 kVAr
$54,662 =
Rs. 27,33,120
$7,150
=Rs. 3,57,500
$61,812 =
Rs. 30,90,620
$31,219 =
Rs. 15,60,940
114 KW
35.5%
16
300
27
150
9
200
8
200
850 kVAr
$59,918.4 =
Rs. 29,95,920
$6,550
= Rs. 3,27,500
$66,468 =
Rs. 33,23,420
$26,563 =
Rs. 13,28,140
126 KW
28.8%
27
200
9
250
8
100
30
350
900 kVAr
$66,225.6 =
Rs. 33,11,280
$6,700
= Rs. 3,35,000
$72,925 =
Rs. 36,46,280
$20,106 =
Rs.10,05,280
135 KW
23.7%
9
150
8
150
30
150
28
250
700 kVAr
$70,956=
Rs.35,47,800
$6,100
= Rs. 3,05,000
$77,056=
Rs.38,52,800
$15,975=
Rs.7,98,760
JERS/Vol.II/ Issue II/April-June, 2011/50-54
Journal of Engineering Research and Studies
The 33-bus radial distribution system [6], as shown in Fig. 2, has following characteristics:
Number of buses = 33
Number of lines = 32
Slack Bus No =1
Base Voltage=12.66 KV
Base MVA=100
Fig 2 : Single line diagram of 33 bus system
Fig 3 : Single line diagram of 33 bus system after compensation
In all the calculations following parameters are used [15]:
1. Population size = 100
2. Maximum Generation = 100
3. Crossover probability ‘Pc’=1
4. Mutation probability ‘Pm’= 0.006
5. Energy rate Ke = US $0.06/kWh (= Rs.3/kWh)
6. Installation cost of capacitor ‘Ki’ = US $1000 (=Rs.50,000/each location)
7. Purchase rate of capacitor ‘Kc’ = US $3.0/kVAR (=Rs.150/kVAR)
JERS/Vol.II/ Issue II/April-June, 2011/50-54
E-ISSN 0976-7916
Journal of Engineering Research and Studies
VII. CONCLUSION
In this paper the capacitor sizing and placement
problem is discussed using an efficient GA algorithm.
A test case of 33 bus system has been used and results
demonstrate the improvement in voltage profile and
reduction of the losses thereby maximizing net annual
savings. This method places the capacitors at less
number of locations with optimum size and offers
much net annual savings. It has been found that
maximum benefit can be obtained by placing the
capacitors at highly sensitive nodes.
ACKNOWLEDGEMENT
This work is a part of M.Tech. Thesis work of
Ms. Shikha Gupta conducted during the time period
Jan to Dec, 2010 under the able guidance of
Dr. Gursewak Singh Brar, HOD and Astt. Prof. at
B.B.S.B.E.C. Fathegarh Sahib.
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