Optimal Capacitor Placement and Sizing for
Enhancement of Distribution System Reliability
and Power Quality Using PSO
Pravin Machhindra Sonwane,Member IEEE
Bansidhar Eknath Kushare, Member IEEE
Electrical Engg. Dept.,
K.K.Wagh Inst. of Engg. Edu. & Research
Nashik, India-422003
Professor and Head, Electrical Engg. Dept.,
K.K.Wagh Inst. of Engg. Edu. & Research
Nashik, India-422003
bekushare@kkwagh.edu.in
pm_sonwane@ieee.org
Capacitor switching and number of capacitor used is
always changing as per load and hence it is also responsible
to introduce distortion in voltage and current waveforms
results into increase in power quality problem. In this paper
total harmonic distortion is considered as one of the
constraint in addition to voltage profile and power factor
constraints.
Abstract— This paper presents optimal capacitor
placement and its sizing using Particle Swarm Optimization.
Reactive power management and planning is one of the crucial
issues in front of researcher from last four decades in addition
to voltage profile, line losses and power factor problem in
transmission and distribution system. Capacitor is a device
which is a solution to above problem if utilized in proper way.
IEEE 30 bus system is tested in this paper for optimal
configuration of capacitor with broader multi-objective
function. Reliability and its indices as discussed in IEEE std
493 and 1366 are benchmark studies followed by all
researchers. Placement of capacitor will enhance the
distribution system reliability and smart grid applicability.
Particle Swarm Optimization technique is used to evaluate
objective function for capacitor placement and sizing in IEEE
bus system.
Numerous methods are discussed to evaluate similar
problems are Artificial Neural Network[22], Fuzzy Logic
[1], Search algorithm, Simulated Annealing, Genetic
Algorithm[12-19], Tabu Search[10], Expert System[20] and
Dynamic Programming. The fact of above methods is, they
use certain control parameters that may be system
dependent and difficult to determine. The major drawback
of above methods is speed.
In this paper more practical and easy to use and
implement the multi-dimensional objective functions using
particle swarm optimization technique is presented. This
paper introduces OCP and PSO algorithm. Compensation of
KVA, losses, voltage and power factor is discussed for
before and after OCP.
Index Terms—OCP, Reliability, PSO
I. INTRODUCTION
The unpredicted nature of load and increase in power
demand in the electrical network forced the power system
operation and control in complicated mode. Increase in
power demand load results into (a) increase in number of
feeder, (b) feeder capacity, (c) more generation and/or (d)
expand the network by increasing substation capacity as
well as equipment capacity. However such changes are not
achievable in short time span and require putting lot of
burden on economy. Therefore to increase KVA margin of
substation, it will be more beneficial if system losses are
minimized by means of reactive power management through
capacitor placement. Such methods are already evaluated
and employed [1-22].
Solution techniques treat nearest capacitor size as
discrete variable rather than evaluated value of capacitor
size. Actual cost of capacitor is considered. Active power
losses and reactive power losses are evaluated separately.
Most of the assumptions are minimized. For simplicity
balanced distribution system is considered.
II.
PROBLEM FORMULATION
Optimal capacitor placement and sizing problem is
formulated based on the requirements of benefits due to
reliability cost, cost of capacitor, purchase cost, operating
cost and maintenance cost and savings due to transmission
and distribution loss is considered. Equation (1) represents
reliability cost:
1
P. M. Sonwane, Member IEEE, is pursuing Ph.D. from research
centre Electrical Department, K. K. Wagh Institute of Engineering
Education & Research, Nashik, India and working as Associate
Professor E-mail: pm_sonwane@ieee.org
2
Dr. B. E. Kushare, Member IEEE, is with K. K. Wagh Institute of
Engineering Education & Research, Nashik, Maharastra, India and
working as Head & Professor of Electrical Engg. Department. He is
Energy auditor and provides consultancy in the area of Power quality.
E-mail: bekushare@kkwagh.edu.in
(1)
1
ECOST
λi
Ccdf
Lavg
– Reliability Cost
– failure rate
– customer composite damage function
– average load
(7)
(8)
Failure rate λ is defined as the frequency of interruption.
Number of interruption or faults in given system network is
a result of weak systems and results into poor power system
operation and control. Failure rate can be decreased with
strengthening power system by means of proper reactive
power management and control, maintaining power factor
towards unity and voltage profile. Ccdf is a customer
composite damage function which varies with customer type
cost due to interruption for a customer like industrial,
commercial, agricultural, municipal or domestic is different.
Hence this factor is dependent and consider here as per the
type of load selected for given system network for
evaluation. Lavg is the average load converted to given bus
which changes time to time at the same time as capacitor in
discrete form is adding in a bus, the overall load is going to
change. Then Capacitor cost is given by,
For the following constraint,
Constraints
Vmin < V< Vmax
Pf min< pf
THDi < THD max
Following assumptions are considered
development of the objective function:
the
Balanced network is considered for simplicity
Capacitors are available in step size.
Capacitor placement affects only the flow of
reactive power in the feeder.
Dedicated software using visual studio with SQL server
at back end to store huge data is developed and installed in
research lab to evaluate above objective function for optimal
capacitor configuration for enhancement of distribution
system reliability and power quality. In addition to this load
flow studies are carried out using ETAP and POWER
FACTORY DIgSAILENT software. ETAP and POWER
FACTORY software are having limitations to solve OCP
program and hence solution of these software are denied. In
PMS_PSO software the limitations are eliminated. Figure
(1) shows dash view of software.
(2)
(3)
(4)
First component of equation (4) is fundamental
component where as second component of equation (4) is
harmonic component treated separately for evaluation
matrix of active and reactive power losses separately.
CC
Xi
C0i
Qci
C1i
Bi
C2i
T
Ti
PLi
El
Nbus
in
Cost of Capacitor bank
0/1 [0 for no capacitor / 1 for capacitor]
installation cost
KVAr rating of capacitor bank
Rs/KVAr for bank
number of capacitor in a bank
operating cost / bank /yr
Planning period in yr
time duration in hours
total system loss at load level
Energy loss
Bus number at evaluation is carried out
Fig. 1 PSO PMS software
III.
Now the problem can be stated as follows
PARTICAL SWARM OPTIMIZATION
PSO is developed by Kennedy and Elberhart in 1995. It
is meta-heuristic method to optimize the function. In this
method population called as swarm is randomly generated.
The swarm consist of individuals called as particles. Each
particle is represented here by coordinate and keeps the
track in hyperspace which is based on best solution of
fitness function and is represented by Pbest. [4-9,16] All such
(5)
(6)
2
Pbest values are remained with individual particles in a global
space to achieve best amongst all solutions and is called as
gbest.
in the range 0 to 1. The C1 and C2 are learning parameters
and here it is taken as 2.
Developed software is in two modules. First module is
based on evaluation of objective function with various
constraints. Regression analysis on objective function yields
to polynomial equation which is used in PSO as second
module. PSO which is suitably using rosenbrok equation
now can work with OCP equation to find out fitness
function. PSO is initialized with two dimensional,
population size 40, maximum velocity 10, maximum
positions 100, and maximum number of iterations 200,
inertia weight 0.9 and minimum error as 0.00001.
As on today PSO algorithm is having much more better
performance as compared with other intelligent tools based
on calculation speed, required number of parameter to be
evaluated and memory occupation and hence it is observed
that PSO is most suitable to tackle multi-dimensional
objective functions. Various structure of PSO is developed
like Hybrid Particle Swarm Optimization (HPSO),
Hierarchical Structure Poly-Particle Swarm Optimization
(HSPPSO), Binary version of PSO developed by Kennedy
and Mohan, Modified PSO by Hu.at el. In all methods of
PSO only gbest information shared with others /neighbours.
Then each particle update its coordinate based on search
experience pbest and gbest according to the following
equation.
vij
1
k 1
id
x
wvij
k
id
x
c1r1 ( pbi j
k 1
id
v
xij ) c2 r2 ( gbdj
xidj )
IV.
IEEE 30 bus system is described in Fig. (1). In this
system five generators placed at bus numbers 1,2,5,8,11and
13. Transformers of rating 100MVA are placed between the
buses as 4-12; 6-9; 6-10; 9-11; 12-13 and 28-27
respectively. IEEE bus system is benchmark system
available for the study case and the operations like load flow
study can be compared. The system is also represented in
table (1) and table (2). This network consist of 30 buses, 41
branches, and 23 loads. It is observed that in this system 29
busses are rated with 33 kV, 9 buses are rated with 132 kV
and 2 buses are rated with 11 KV. Considering this in mind
we treat those buses which are 33 kV are part of distribution
system. After load flow study, it is observed that
300.703MWand 80.538 Mvar. generation is required and
this test system has initial losses in active power is 17.719
MW and 41.505 MW
(9)
(10)
(11)
2
ΔV= (Kvar)(XL) /10(KV)
Fig. 2
IEEE 30BUS SYSTEM
(12)
PSO Algorithm
If new velocity
Then new velocity
If new velocity
Then new velocity
Figure (2) indicates the flow chart of PSO process.
Inertia weight is a parameter presents here is in the range of
0.4 to 0.9 as discussed in [25]. This parameter can be
initialised within any value in between above range but this
weight factor is continuously updated as per the equation
(8). The parameters r1 and r2 are random variable generated
Fig. 3 IEEE 30 bus test system
Table 1 represents 41 branch information regarding
branch resistance, reactance, failure rate and repair rate
values.
3
10_21
10_22
12_14
12_15
12_16
12_13
25_27
27_29
27_30
28_27
14_15
15_18
15_23
16_17
18_19
19_20
21_22
22_24
23_24
24_25
25_26
29_30
0.9786
0.9612
0.9754
0.9598
0.9510
0.9838
0.9733
0.9808
0.9564
0.9818
0.9494
0.9236
0.9498
0.9494
0.9514
0.9509
0.9462
0.9506
0.9181
0.9483
0.9537
0.9537
Fig. 4 OCP Algorithm
0.0214
0.0388
0.0246
0.0402
0.049
0.0162
0.0267
0.0192
0.0436
0.0182
0.0506
0.0764
0.0502
0.0506
0.0486
0.0491
0.0538
0.0494
0.0819
0.0517
0.0463
0.0463
0.0348
0.0727
0.1231
0.0662
0.0945
0.0000
0.2198
0.2198
0.3202
0.22100
0.2210
0.1073
0.1000
0.0524
0.0639
0.0340
0.0116
0.1150
0.1230
0.1885
0.2544
0.2399
0.0749
0.1499
0.2559
0.1304
0.1987
0.14000
0.2087
0.0000
0.6027
0.4153
0.1997
0.2185
0.2020
0.1923
0.1292
0.0680
0.0236
0.1790
0.2700
0.3292
0.3800
0.45330
[SOURSE: IEEE PES]
TABLE I. BRANCH INFORMATION OF IEEE 30 BUS SYSTEM
Branch
1_2
1_3
2_4
2_5
2_6
3_4
4_6
4_12
5_7
6_7
6_8
6_28
6_9
6_10
8_28
9_10
9_11
10_17
10_20
Failure
Rate
0.9783
0.9841
0.9532
0.9786
0.9497
0.9172
0.9828
0.9660
0.9760
0.9211
0.9494
0.9536
0.9494
0.9211
0.9537
0.9509
0.9535
0.9824
0.9666
Repair
Rate
0.0217
0.0159
0.0468
0.0214
0.0503
0.0828
0.0172
0.034
0.024
0.0789
0.0506
0.0464
0.0506
0.0789
0.0463
0.0491
0.0465
0.0176
0.0334
R_pu
X_pu
0.01920
0.04520
0.05700
0.04720
0.05810
0.01320
0.01190
0.00000
0.04600
0.0267
0.0120
0.01690
0.0000
0.00000
0.0636
0.0000
0.0000
0.0324
0.0936
0.0575
0.1652
0.1737
0.1983
0.17630
0.03790
0.0414
0.2560
0.1160
0.0820
0.0420
0.0599
0.2080
0.5560
0.2000
0.1100
0.2080
0.0845
0.2090
TABLE 2 BUS DATA(GENERATOR AND LOAD DATA)
Bus PG(MW)
4
QG(MVAr)
PL(MW)
QL(MVAr)
Vpu
Ang
01
50-200
0
0
0
1.06
0.0
02
20-80
-20-100
21.700
12.700
1.045
-5.5
03
0
0
2.400
1.200
1.021
-8.0
04
0
0
7.6
1.6
1.012
-9.6
05
15-50
-15-80
94.2
19.0
1.01
-14.4
06
0
0
0
0
1.01
-11.3
07
0
0
22.8
10.9
1.002
-13.1
08
10-35
-15-60
30
30
1.01
-12.1
09
0
0
0
0
1.051
-14.4
10
0
0
5.8
-18.752
1.045
-16.0
11
10-30
-10-50
0
0
1.082
-14.4
12
0
0
11.200
7.500
1.057
-15.2
13
12-40
-15-60
0
0
1.071
-15.2
14
0
0
6.200
1.600
1.042
-16.1
15
0
0
8.200
2.500
1.038
-16.2
16
0
0
3.500
1.800
1.045
-15.8
17
0
0
9.0
5.800
1.04
-16.1
18
0
0
3.2
0.900
1.028
-16.8
19
0
0
9.500
3.400
1.026
-17.0
20
0
0
2.200
0.700
1.03
-16.8
21
0
0
17.500
11.200
1.033
-16.4
22
0
0
0
0
1.033
-16.4
23
0
0
3.200
1.600
1.027
-16.6
24
0
0
8.700
2..213
1.021
-16.8
25
0
0
0
0
1.017
-16.4
26
0
0
3.500
2.300
1.00
-16.8
27
0
0
0
0.000
1.023
-15.8
28
0
0
0
0
1.007
-12.0
29
0
0
2.400
0.900
1.003
-17.1
30
0
0
10.600
1.900
0.992
-17.9
in amount so overall objective function suggest the solution
as given in table [5].
Figure (4) is a flow chart that represents the PSO based
OCP algorithm. Load flow data is provided in addition to
capacitor information. PMS_PSO software evaluates the
objective function considering all constraint and memorised
in the backend database. As per the requirements and
customer type reliability cost is evaluated based on above
equations. PSO will initialize it’s parameters as per
constraint selected and evaluated a fitness function as given
in figure (4).
Table [5] shows the loss reduction in branches in the
system shown. The capacitor placement can help to modify
voltage parameters in the system. In Figure (6), profit during
planning period is shown. It is observed that within two year
the capacitor cost including operating cost is recovered and
accumulative profit starts afterwards. Apart from this before
and after capacitor placement evaluates as 13.81MVA
capacity is released in this system. In most of cases power
factor is improved and voltage is within the limits as per
standard as shown in table [6]. Harmonic distortion as per
equation (8) is also not violated.
Reliability Indices:
At the same time capacitor bank also contribute in
reactive power, so wherever local reactive power is
required, capacitor placed as suggested by PSO and it is
general practice that the distribution engineer locally apply
the capacitor for this purpose, which is the solution for local
case. PSO evaluates its fitness function in local and global
platform as shown in figure (5).
(15)
TABLE [5]. BRANCH LOSSES BEFORE AND AFTER OCP
Source of equations (13-15) is from IEEE standard 1366,
2001. These indices are depending on failure rate, duration
of interruptions and number of customers interrupted. Most
of the time, it is observed that as capacitor as a component is
added in the network, overall system failure is increasing.
For simplicity this fact is neglected in this paper also it is
presumed that capacitor placement is decreasing. In
previous research paper, modified failure rate is depending
on compensated and uncompensated failure rate and in most
cases it was predicted values. Modified failure rate, in this
paper is calculated as per thermal loading of transformers
and line loading and then used in evaluation process of
objective function.
V.
RESULTS
It is observed that the capacitor placement reduces the
power losses as active power reduction is (17719.8317484.9)=234.93KW and reactive power reduction is
(41505.82-41246.02)=259.8KVAR. It is observed that
Reliability Indices are improved as compared in Table [3]
before capacitor placement and Table [4] after capacitor
placement. Few branches are found that KW and KVA
losses are increasing, it is due to (a)it is small in amount and
(b)cost due to losses as compared to reliability cost is small
5
Branch
Before
kW
Losses
Before
kvar
Losses
After
kW
Losses
After
kvar
Losses
1_2
5176
9675
5180
9676
1_3
3129
7038
3115
6968
2_4
1035
703
1017
783
2_5
2981
8134
2954
8007
2_6
1960
2037
1945
1964
3_4
862
1617
858
1596
4_6
614
1229
625
1256
5_7
202
1543
177
1617
6_7
387
513
382
544
6_8
116
500
116
513
6_28
59.783
1093
60.002
1108
8_28
3.553
4286
2.139
4345
9_10
0
761
0
765
10_17
9.253
24.131
8.311
21.675
72.49
162
74.072
165
10_21
107
229
96.992
209
10_22
49.101
101
43.787
90.284
12_14
81.393
169
73.125
152
12_15
246
484
214
422
12_16
77.09
162
49.213
103
14_15
8.944
8.082
5.502
4.972
15_18
49.304
100
44.535
90.688
15_23
40.505
81.819
24.791
50.077
16_17
14.845
54.48
12.339
45.282
18_19
8.179
16.538
6.765
13.679
19_20
14.498
28.996
15.044
30.087
21_22
1.106
2.25
1.805
3.673
22_24
33.759
52.547
29.546
45.989
23_24
11.46
23.44
9.709
19.859
24_25
7.346
12.828
5.755
10.05
25_26
45.742
68.326
30.858
46.093
25_27
28.074
53.605
29.354
56.049
27_29
88.121
166
85.142
161
27_30
166
312
160
301
29_30
Total
Losses
34.282
64.776
33.112
62.567
17719.83
41505.82
17484.9
41246.02
Fig. 5
PSO for OCP
Cost
600
Thousands
10_20
500
400
300
200
100
0
1
2
3
4
5
Year
Fig. 6 Figure 5 Profit curve
P.F.
TABLE [6].CAPACITOR PLACEMENT AND SIZING USING OCP
Bus
14
15
16
20
22
23
27
29
Vold
1.042
1.038
1.044
1.026
1.033
1.027
1.023
1.003
Vmod
1.043
1.040
1.045
1.028
1.035
1.028
1.024
1.004
Total KVAr
800
2400
1200
2400
2400
1200
1200
800
PFold
92.59
91.63
93.18
92.22
83.50
82.30
97.84
98.69
PFmod
93.00
93.00
94.00
94.00
84.95
83.40
98.20
98.80
No of Capacitor
Fig. 7 power factor improvement for a sample bus 10
6
Thousands
CONCLUSION
Objective function
900000
800000
Particle swarm optimization is a tool to evaluate
multidimensional objective function. Evaluation of loss
reduction yield to conclude that to decide cost recovery
period due to cost of capacitor and installation cost. Result
analysis shows that optimal capacitor configuration find
proper places and size of capacitor. This placement
improves power factor, reduces active and reactive losses,
maintain voltage profile and KVA release. Apart from this
indices shows that Reliability of the system is also
improved.
700000
600000
500000
400000
300000
200000
100000
No of Capacitor
0
0
5
10
15
ACKNOWLEDGMENT
Fig. 8 objective function for sample of bus 10
Author thanks to Principal Prof. Dr. K. N. Nandurkar
and management of K. k. Wagh Institute of Engineering
education nashik for supporting to conduct this research
work in the institute research laboratory, BCUD section to
consider the research proposal and provide funding from
university to this research work, without which research
work may not be completed.
ECOST
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No of Capacitor
Fig. 9 Reliability Cost for a sample bus 10
Voltage (V=V+ΔV)
No of Capacitor
Fig. 10 Voltage profile for a sample bus 10
All above graphs are plotted on the basis of sample for a
bus number 10. Almost all other buses where capacitors are
placed are of the same nature and where capacitors are not
placed graphs will be generated with opposite nature
reasons may be due to power factor in leading mode or
voltage profile may be violating limits or VTHD may not as
per IEEE standard 519. Considering this, only sample bus
10 graphs are plotted here. PMS_PSO is capable to plot any
graph as per the selection of programmer.
7
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ABOUT THE AUTHOR
Prof. P. M. Sonwane graduated in Electrical
Engineering from Chandrapur Engineering
College, Nagpur University. He obtained
M.Tech. in Integrated power systems From
V.R.C.E. Nagpur in 2005 and pursuing Ph.D.
in University of Pune. His area of interest is
power system. Planning and Reliability,
microprocessor, microcontroller, robotics and
automation, artificial Intelligence and distribution system. He
worked in Mumbai and Pune University and taught various
subjects in last 14 Years. Currently he is working with Electrical
Engineering Department, K. K. Wagh Institute of Engg. Edu. &
Research, Nashik as Associate Professor.
Prof. Dr. B. E. Kushare graduated in
Electrical Engineering from Govt. College of
Engineering, Aurangabad and obtained Gold
Medal as University Topper in 1989. He
completed his ME Electrical Control System
from Pune University in 1992 and obtained
Ph.D. in Power Quality from Pune University
in 2006. He is also a Certified Energy auditor. He Published
around 100 International and National Papers. He is also a
consultant to various industries in India and abroad. He is working
as Professor & Head of Electrical Engg. Dept. at K.K.Wagh
Institute of Engg. Education & Research, Nashik, Maharashtra,
India.
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