Fuzzy expert system based optimal capacitor allocation in distribution system-2

INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
Proceedings of the 2nd International Conference on Current Trends in Engineering and Management ICCTEM -2014
TECHNOLOGY (IJEET)
17 – 19, July 2014, Mysore, Karnataka, India
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 5, Issue 8, August (2014), pp. 86-99
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IJEET
© I A E M E
FUZZY-EXPERT SYSTEM BASED OPTIMAL CAPACITOR ALLOCATION
IN DISTRIBUTION SYSTEM
Maruthi Prasanna. H. A.1,*, Likith Kumar. M. V.1, T. Ananthapadmanabha2, & A. D.
Kulkarni2
1Research Scholar, Department of EEE, The National Institute of Engineering, Mysore, India
2Professor, Department of EEE, The National Institute of Engineering, Mysore, India
86
ABSTRACT
A fuzzy logic approach for determining the optimal location and size of capacitors is reported
in this work. The impacts of capacitors of various sizes at various locations in distribution system are
evaluated with two indices viz. Power Loss Reduction Index (PLRI) and Voltage Deviation
Reduction Index (VDRI). These two indices are fuzzified to obtain Capacitor Placement Suitability
Index (CPSI) through proposed fuzzy-expert system. The proposed method is applied for IEEE-
33bus Radial distribution system using MATLAB R2009b. The allocation of single, two and three
capacitor units has been carried out. The capacitor combination which results in the minimum power
loss is decided as optimal allocation. The results are compared with those existing in literature in
order to prove the effectiveness of the proposed fuzzy approach.
Keywords: Distribution System, Capacitors, Power loss reduction, Voltage deviation reduction,
Fuzzy logic, Load flow, optimal placement.
1. INTRODUCTION
Loss minimization in distribution systems has assumed greater significance recently since the
trend towards distribution automation will require the most efficient operating scenario for economic
viability. Studies have indicated that as much as 13% of total power generated is consumed as I2R
losses at the distribution level. Reactive currents account for a portion of these losses. However, the
losses produced by reactive currents can be reduced by the installation of shunt capacitors. In
addition to the reduction of energy and peak power losses, effective capacitor installation can also
release additional kVA capacity from distribution apparatus and improve the system voltage profile.
Reactive power compensation plays an important role in the planning of an electrical system. Its aim
is principally to provide an appropriate placement of the compensation devices to ensure a
satisfactory voltage profile while minimizing the cost of compensation.

Installation of shunt capacitors on distribution networks is essential for power flow control,
improving system stability, power factor correction, voltage profile management and losses
minimization. Therefore it is important to find optimal location and sizes of capacitors required to
minimize feeder losses. The solution techniques for loss minimization can be classified into four
categories: Analytical, numerical programming, heuristics and artificial intelligence based. Capacitor
allocation problem is a well researched topic and all earlier approached differ from each other either
in their problem formulation or problem solution methods employed [1].
In large distribution networks it is very difficult to predict the optimum size and location of
capacitor which finally results not only in reducing losses but also improves the overall voltage
profile [2]. Though many conventional models and techniques are used for this purpose but it
becomes a cumbersome task as the complexity of the system increases. [3, 4, 5] Linear and nonlinear
programming methods have been proposed earlier to solve the placement problem.
Capacitors are commonly used to provide reactive power support in distribution systems. The
amount of reactive compensation provided is very much related to the placement of capacitors in
distribution feeders. The determination of the location, size, number and type of capacitors to be
placed is of great significance, as it reduces power and energy losses, increases the available capacity
of the feeders and improves the feeder voltage profile. Numerous methods for solving this problem
in view of minimizing losses have been suggested in the literature [6–11].
A fuzzy-expert system (FES) is developed in this paper for determining the location for
connecting capacitor unit/s in distribution system to reduce the real power losses and to improve the
voltage profile. The proposed fuzzy inference system is of mamdani type consisting of two fuzzy
input variables and one fuzzy output variable. For determining the suitability of capacitor placement
at a particular node, a set of multiple-antecedent fuzzy rules has been established. The inputs to the
rules are the power loss reduction and voltage deviation reduction indices and the output is the
suitability of capacitor placement. The proposed fuzzy logic approach is developed in MATLAB
R2009b and in order to validate the proposed capacitor placement technique, the methodology is
tested on IEEE-33 bus Radial Distribution system. Comparison of obtained results with those in
recent publications showed that the proposed algorithms are capable of producing high-quality
solutions with good performance of convergence, and demonstrated viability. The fuzzy based
optimal capacitor placement can provide approximate global optimum solution.
The organization of this paper is as follows; section 2 introduces fuzzy-expert system, section
3 defines the DG placement evaluation indices, Section 4 explains about the proposed FEM for
optimal DG placement, Section 5 shows the proposed algorithm for optimal DG placement using
FEM, Section 6 discusses the Results obtained by the proposed method and finally section 7
concludes the paper.
2. INTRODUCTION TO FUZZY-EXPERT SYSTEM
Fuzzy logic refers to a logic system that generalizes the classical two-valued logic for
reasoning under uncertainty. It is motivated by observing that human reasoning can utilize concepts
and knowledge that do not have well-defined or sharp boundaries [12], [13].
Unlike the classical Boolean set allowing only 0 or 1 value, the fuzzy set is a set with a
smooth boundary allowing partial membership. The degree of membership in a set is expressed by a
number between 0 and 1, with 0 indicating entirely not in the set, 1 indicating completely in the set
and a number in between meaning partially in the set. In this way, a smooth and gradual transition
from the regions outside the set to those in the set can be described. A fuzzy set can thus be defined
by a function that maps objects in the domain of concern (i.e. the universe of discourse) to their
membership values in the set. Such a function is called the membership function. The two most
widely used membership functions are the triangular and trapezoidal functions [12], [13].
87

A fuzzy-expert system is an expert system that uses a collection of fuzzy sets and rules,
instead of Boolean sets for reasoning about data. The rule in the fuzzy-expert system usually takes
the form
If x is low and y is high; then z = medium
Where x and y are input variables, z is the output variable, and low, high and medium are
membership functions defined for x, y and z respectively. The antecedent (the rule’s premise)
describes the degree that the rule applies, while the conclusion (the rule’s consequent) assigns a
membership function to the output variable. The set of rules in a fuzzy-expert system is known as the
rule base or knowledge base. The computation of the output variable usually takes the following
steps [12, 13] and is presented in Fig 1.
Fuzzification: This step is also called Fuzzy Matching, which calculates the degree that the input
data match the conditions of the fuzzy rules.
Inference: Calculate the fuzzy set of the rule’s conclusion based on its matching degree. There
are two common approaches for the inference, namely the clipping method and the scaling method.
Both methods generate conclusion by suppressing the membership function of the consequent. The
extent to which they suppress the membership function depends on the degree to which the rule is
matched. The lower the matching degree, the more severe the suppression of the membership
functions. The clipping method cuts off the top of the membership function, whose value is higher
than the matching degree. The scaling method scales down the membership function in proportion to
the matching degree. The scaling method is used in this paper.
Composition: Because a fuzzy rule-based system consists of a set of fuzzy rules with partially
overlapping conditions, a particular input to the system often ‘triggers’ multiple fuzzy rules (i.e.
more than one rule will match the input to a non-zero degree). Therefore, the composition is needed
to combine the inference results of all the triggered rules to form a single fuzzy subset for the output
variable. The fuzzy disjunction operator Max is commonly used for constructing the output fuzzy set
by taking the point-wise maximum over all the fuzzy subsets generated from the inference step.
Defuzzification: This step is to convert the fuzzy set of the output variable to a crisp number.
Among the various types of defuzzification methods, the Center of Area (COA or Centroid) and
Maximum are the two most widely used techniques. The COA derives the crisp number by
calculating the weighted average of the output fuzzy set while the Maximum method chooses the
value with maximum member-ship degree as the crisp number.
Fig. 1: General Fuzzy – Expert System Approach.
88

3. CAPACITOR PLACEMENT EVALUATION INDICES
In order to determine benefits from capacitor integration, two sets of indices are proposed in
this paper Viz PLRI and VDRI. They are explained below.
ij i j i j ij i j i j PL PP QQ QP PQ
b = d −d
( ) (min)
PL i PL
spec is the Voltage specified in pu. In this paper, it is taken as 1 pu; Vi is the Voltage at the
( ) (min)
VDI i VDI
89
3.1 Power Loss Reduction Index (PLRI)
The total real power loss in a distribution system with ‘N’ buses as a function of active and
reactive power injection at all buses can be calculated using the following equation [14].
N
[ ]
= =
= + + −
i
N
1 j
1
a ( ) b ( )
(1)
Where,
a = d −d
cos( ) i j
r
ij
ij V V
i j

sin( ) i j
r
ij
ij V V
i j
PL is the exact loss of the distribution system; rijis the resistance between bus i and bus j; Vi
and Vj is the voltage magnitude of buses i and j respectively; i is the voltage angle at bus i; j is the
voltage angle at bus j; Pi and Qi active and reactive power injection at bus i ; Pj and Qj is the active
and reactive power injection at bus j.
The Power Loss Reduction Index of ith bus when capacitor is connected to that bus is given
by,
( ) (min)
( )
PL base PL
PLRI i
−
−
=
(2)
Where, PL(i) is the distribution system real power loss when capacitor is connected to the ith bus;
PL(base) is the distribution system real power loss without capacitor; PL(min) is the minimum
distribution system real power loss obtained when capacitor is connected to all the buses other than
slack bus;
3.2 Voltage Deviation Reduction Index (VDRI)
The voltage deviation index (VDI) of the distribution system is given by,
b N

=
VDI = V spec
−
V
i i
i
1
2 ( )
(3)
Where, Vi
ith bus in pu.
The VDI is a measure of the voltage profile of the distribution system and it indicates how
the voltage values of the distribution nodes are nearer to the specified voltage. It is expected that this
value should be nearer to zero, so that all the nodes of the distribution system will be having voltage
nearer to the specified voltage (1 pu).
The Voltage Deviation Reduction Index (VDRI) of ith bus when capacitor is connected to that
bus is given by,
( ) (min)
( )
VDI base VDI
VDRI i
−
−
=
(4)
Where, VDI(i) is the voltage deviation index of distribution system when capacitor is connected to
ith bus; VDI(min) is the minimum voltage deviation of distribution system of a particular bus among

all the buses when capacitor is connected to each of them other than slack bus; VDI(base) is the
voltage deviation index of the distribution system without capacitor connection;
4. PROPOSED FUZZY EXPERT SYSTEM FOR OPTIMAL CAPACITOR PLACEMENT
In this FES, in order to determine optimal location for capacitor integration in distribution
system, two input and one output variables are proposed. Input variable-1 is power loss reduction
index (PLRI) and Input variable-2 is the voltage deviation reduction index (VDRI). Output variable
is Capacitor placement suitability index (CPSI). The structure of proposed FES is of mamdani type.
PLRI variable is fuzzified into three trapezoidal membership functions and scaled in the
range from 0 to 1, as shown in Fig 2. The three membership functions of PLRI are H, M and L. The
value of 0 indicates largest reduction while value of 1 indicates smallest reduction of power loss.
VDRI variable is fuzzified into five triangular membership functions and scaled in the range
from 0 to 1, as shown in Fig 3. The five membership functions of VDRI are H, HM, M, LM and L.
The value of 0 indicates better voltage profile where as value of 1 indicates poor voltage profile of
distribution system.
Fig. 2: Power Loss Reduction Index (PLRI) representation
The CPSI is the output fuzzy variable which is evaluated for each bus by considering PLRI
and VDRI as input variables to the FES using a set of rules, which are developed from qualitative
descriptions. These rules are summarized in the fuzzy decision matrix given in Table 1. CPSI is a
fuzzy variable having five triangular membership functions and scaled in the range from 0 to 1, as
shown in Fig 4. The five membership functions of CPSI are H, HM, M, LM and L. The minimum
value of CPSI indicates the best location for capacitor placement.
90

Fig. 3: Voltage Deviation Reduction Index (VDRI) representation
Fig. 4: Capacitor Placement Suitability Index (CPSI) representation
91

The MAX–MIN METHOD involves truncating the consequent membership function of each
fired rule at the minimum membership value of all the antecedents. A final aggregated membership
function is achieved by taking the union of all the truncated consequent membership functions of the
fired rules [15]. For the capacitor location problem, resulting capacitor placement suitability
membership function μs of node i for k fired rules is given by,
max (min( (i), (i))) s k p v μ = μ μ
( )
μ
z zdz
s
( )
92
(5)
Where p μ
and v μ
are the membership functions of the PLRI and VDRI variables respectively. The
CPSI values must be defuzzified in order to determine the node suitability ranking for capacitor
placement. This is achieved by Centroid method of defuzzification [15].
The capacitor placement suitability index (CPSI) is determined by
=
z dz
CPSI
s
μ
(6)
Table 1: Fuzzy Decision Matrix for CPSI
AND
VDRI
H HM M LM L
PLRI
H H H HM M LM
M M M LM L L
L LM LM LM L L
5. PROPOSED ALGORITHM FOR OPTIMAL CAPACITOR PLACEMENT BY FES
The procedural steps that have been adopted in finding optimal location for capacitor
placement in distribution system using Fuzzy-Expert System is shown in Fig 5.
6. SIMULATION RESULTS
The proposed methodology using FES is tested on IEEE-33bus Radial Distribution System
(RDS) shown in Fig. 6 [16] having following characteristics:
Number of buses=33; Number of lines=32; Slack Bus no=1; Base Voltage=12.66KV; Base
MVA=100 MVA;
The test system is simulated in MATLAB R2009b the proposed FES methodology has
been tested, whose results are as shown below. The forward backward method of load flow (FBLF)
is employed in this paper, whose details are given in [17]. The objective of this paper is to determine
the optimal locations for the capacitor units to be placed in distribution system so that maximum loss
reduction and voltage deviation reduction is achieved. Initially, the base case FBLF is run for the
IEEE 33bus RDS and the base case voltage profile is shown in Fig 7. The base case real power loss
is 210.97 kw and base case VDI is 0.1338 pu.

Fig. 5: Optimal Capacitor Placement using Fuzzy-Expert System
93

Fig. 6: Single line diagram of IEEE-33 bus RDS
Fig. 7: Base Case Voltage Profile of IEEE-33 bus RDS
In this paper, 3 scenarios of optimal capacitor placement are carried out:
Scenario-1 in which a single capacitor is to be placed;
Scenario-2 in which two capacitor units of unity pf are to be placed;
Scenario-3 in which three capacitor units of unity pf are to be placed.
The procedure of determining optimal location for capacitor units is explained in Fig 5. In
each scenario, the practically available capacitor sizes are considered. The details of available
capacitors can be found in [18]. The results of each scenario are tabulated in Table 2, Table 3 and
Table 4 respectively. Table 2 corresponds to Scenario-1, Table 3 corresponds to Scenario-2 and
Table 4 corresponds to Scenario-3. In Table 2 and Table 3, the total capacity of capacitors is
restricted to 1800KVAr. In each scenario, the power loss with capacitor is compared with the base
case power loss and Loss reduction in Kw by Capacitor injection is tabulated and similarly the VDI
with capacitor is compared with base case VDI and VDI reduction in pu by Capacitor injection is
tabulated.
To demonstrate the validity of the proposed method, the obtained results are compared with
those existing in literature. Table 5 presents the comparison of the performance parameters of the
distribution system with the capacitor allocation using the proposed fuzzy approach with the other
techniques present in the literature. In order to compare the different capacitor allocations, the loss
savings from the capacitor allocation is evaluated as loss savings per MVAr injection of capacitor.
Through this index, it is very clear from Table 5 that the proposed method yields maximum loss
94

reduction of 48.70 Kw/MVAr with 3 capacitor units of 450KVAr optimally located at bus 33, 16,
and 30 of IEEE 33 bus RDS.
Fig 8 shows the distribution system loss reduction for increasing penetration of 450kvar
capacitor units through each scenario. It is observed that, there will be significant reduction in power
loss for each capacitor unit injection at the optimal locations of 450KVAr capacitor unit/s given in
sl.no 3 of Table 2, Table 3 and Table 4 respectively. Similarly, Fig 9 shows the improvement in the
voltage profile of the IEEE 33 bus RDS for increasing penetration of 450KVAr capacitor units
through each scenario. It is observed that, as the VDI is reducing for each scenario, there will be an
improvement in the voltage profile.
Table 2: Optimal Capacitor Placement Results of IEEE 33 bus RDS for Scenario-1 for various
Capacitor ratings
95
Sl.
no
Capacitor
size in
KVAr
Optimal
location
Base
case
power
loss in
kw
Base
case
VDI
in pu
Power
loss with
Capacitor
in kw
VDI with
Capacitor
in pu
Loss
reduction
in kw
VDI
reduction
in pu
1 150 33 210.97 0.1338 196.84 0.1259 14.13 0.0079
2 300 33 210.97 0.1338 185.27 0.1185 25.69 0.0153
3 450 33 210.97 0.1338 176.03 0.1115 34.93 0.0223
4 600 33 210.97 0.1338 169.28 0.1051 41.68 0.0287
5 900 32 210.97 0.1338 160.55 0.0936 50.41 0.0402
6 1000 31 210.97 0.1338 159.78 0.0901 51.18 0.0437
7 1200 32 210.97 0.1338 158.32 0.0838 52.64 0.0500
Capacitor ratings
Sl.
no
Capacitor
size in
KVAr
Optimal
location
Base case
power
loss in kw
Base
case
VDI
in pu
Power
loss with
Capacitor
in kw
VDI with
Capacitor
in pu
Loss
reduction
in kw
VDI
reduction
in pu
1 150
33
18
210.97 0.1338 185.73 0.1114 25.23 0.0224
2 300
33
10
210.97 0.1338 168.64 0.0981 42.32 0.0357
3 450
33
16
210.97 0.1338 158.32 0.0767 52.64 0.0571
4 600
33
14
210.97 0.1338 152.66 0.0639 58.30 0.0699
5 900
32
9
210.97 0.1338 150.52 0.0516 60.44 0.0822

Capacitor ratings
96
Sl.
no
Capacitor
size in
KVAr
Optimal
location
Base
case
power
loss in
kw
Base
case
VDI in
pu
Power
loss with
Capacitor
in kw
VDI with
Capacitor
in pu
Loss
reduction
in kw
VDI
reduction
in pu
1 150
18
15
33
210.97 0.1338 174.95 0.1044 36.01 0.0294
2 300
18
31
9
210.97 0.1338 154.52 0.0862 56.44 0.0476
3 450
17
33
27
210.97 0.1338 145.23 0.0624 65.73 0.0714
4 600
16
33
5
210.97 0.1338 147.67 0.0475 63.29 0.0863
Table 5: Performance of the Proposed Fuzzy-Expert System based Capacitor Placement
Referen
ces
Before
Capacitor
Placement
Optimal Capacitor Allocation After Capacitor Placement
Losses (Kw) Location
Size in
KVAr
Total
Size
in
MVA
r
Losses
(Kw)
Loss
Savings
in Kw
Loss
Savings/
Capacitor
MVAr
injection
[19] 203.00
8, 15, 20, 21, 24,
26, 28
27
300
600
2.700 135.00 68.00 25.85
[20] 210.97
13, 14, 15, 16,
31, 32
30
150
750
1.650 146.25 64.72 39.22
[21] 210.97
6
8
1200
150
1.350 163.37 47.60 35.26
[22] 210.97
28
6
29
8
30
9
25
475
300
175
400
350
1.725 141.23 69.74 40.42
Propose
d
Method
210.97
33
16
30
450
450
450
1.350 145.23 65.74 48.70

Base case 1 CAP of 450 KVAr 2 CAP of 450 KVAr 3 CAP of 450 KVAr
210.97
176.03 158.32 145.23
Power loss reduction pattern
Fig. 8: Reduction of Power loss in IEEE 33 bus RDS with penetration of 450KVAr Capacitors for
three scenarios
1
0.99
0.98
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0.9
Base case
1 CAP of
450kVAr
2 CAP of
450kVAr
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Voltage in Pu
Distribution Network Nodes
Fig. 9: Improvement of voltage profile of IEEE 33bus RDS with penetration of 450KVAr Capacitor
Units for three scenarios
97
7. CONCLUSION
A fuzzy-expert system is developed for optimal allocation of capacitor units in distribution
system. The optimal locations for capacitor placement are decided in order to provide maximum
power loss reduction and voltage profile improvement. The proposed fuzzy-expert system provides
Capacitor placement suitability index by PLRI and VDRI fuzzy variables. The proposed
methodology is tested on IEEE-33bus Radial distribution system using MATLAB 9.0 for placement
of single capacitor unit, two capacitor units and three capacitor units. From the results it is apparent
that the proposed fuzzy-expert system provides optimal loss reduction and voltage profile
improvement. The results were also compared with those existing in literature, through which, it is
apparent that the proposed method provides maximum loss reduction saving per capacitor MVAr
injection.

98
ACKNOWLEDGEMENT
The authors Maruthi Prasanna. H. A. and Likith Kumar. M. V. acknowledge the Technical
Education Quality Improvement Programme (TEQIP)-II of All India Council for Technical
Education (AICTE), New Delhi, India and Dr. G. L. Shekar, Principal, NIE, Mysore for providing
financial assistance for carrying out this research work.
The author Maruthi Prasanna. H. A. also acknowledge the Karntaka Power Transmission
Corporation Limited (KPTCL), Karnataka for providing leave to pursue Integrated M.Tech + PhD
programme.
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