This document discusses the application of fuzzy logic to optimal capacitor placement in distribution systems. It begins with definitions of fuzzy logic and fuzzy sets. It then describes the key components of a fuzzy logic system including fuzzification, fuzzy inference rules, and defuzzification. It proposes using power loss reduction index and bus voltage as input variables, and capacitor placement suitability index as the output variable, to determine the optimal locations and sizes of capacitors. The goal is to minimize power losses and maximize annual savings using fuzzy logic techniques.

1. FUZZY LOGIC & ITS
APPLICATION TO
DISTRIBUTION SYSTEM
SUBMITTED TO: SUBMITTED BY:
DR. RANJAN KU JENA PRANAYA PIYUSHA JENA
DR.ABHIMANYU MAHAPATRA REGD NO: 0901106213
ELECTRICAL ENGG

2.  Definition of fuzzy
 Fuzzy – “not clear, distinct, or precise; blurred”
 Definition of fuzzy logic
1. it deals with reasoning that is approximate rather than fixed and
exact. In contrast with traditional logic theory, where binary sets
have two-valued logic, true or false, fuzzy logic variables may
have a truth value that ranges in degree between 0 and 1.
2. Fuzzy logic has been extended to handle the concept of partial
truth, where the truth value may range between completely true
and completely false.

3. Fuzzy sets
 Fuzzy sets are sets whose elements have degrees of
membership.
Binary set :
1 T>40°
High= 0 T≤40°
Fuzzy set:
1 T>40°
High= T−30 ∕ 10 30°< T≤40°
0 T≤30°

4.  Membership Function
 A curve that defines how each point in the input
space is mapped to membership value between 0
and 1.

5.  Types Of Membership Function
1. Triangular Function
2. Trapezoidal Function
3. Bellshaped Function

6.  Linguistic Variable
 It is a variable whose values are in words or in a natural
language.
 Ex: speed=(fast, slow, moderate, very slow etc.)

7. FUZZY LOGIC SYSTEM

8. FUZZIFICATION
 Input values are translated to linguistic concepts, which
are represented by fuzzy sets.
 In other words, membership functions are applied to the
measurements, and the degree of membership in each
premise is determined.

9.  FUZZY INFERENCE
 Fuzzy inference is a computer paradigm based on
fuzzy set theory, fuzzy if-then-rules and fuzzy
reasoning.
 Linguistic rules describing the control system
consist of two parts; an antecedent block (between
the IF and THEN) and a consequent block (following
THEN)

10.  DEFUZZIFICATION
 A fuzzy system will have a number of rules that transform
a number of variables into a "fuzzy" result, that is, the
result is described in terms of membership in fuzzy sets.
 extraction of a crisp value that best represents the fuzzy
set.

12. OPTIMAL CAPACITOR PLACEMENT IN
DISTRIBUTION SYSTEM USING
FUZZY TECHNIQUES

13.  The power loss in a distribution system is
significantly high because of lower voltage and hence
high current, compared to that in a high voltage
transmission system.
 The pressure of improving the
overall efficiency of power delivery has forced the
power utilities to reduce the loss, especially at the
distribution level
 This can be achieved by placing
the optimal value of capacitors at proper locations
in radial distribution systems.

14.  The objective of the capacitor placement
problem is to determine the locations and sizes of
the capacitors so that the power loss is minimized
and annual savings are maximized.
 fuzzy logic is a powerful tool in meeting challenging
such problems in power systems .
 Node voltage measures and power loss in the
network branches have been utilized as indicators
for deciding the location and also the size of the
capacitors in fuzzy based capacitor placement
methods.

15.  The fuzzy system take two input variable as
1. Power loss reduction index(PLRI)
2. Bus voltage
 And one output variable as
1. Capacitor placement suitability index(CPSI)

17.  Decision matrix/Rule base

18. Based on these two values capacitor placement
suitability index (CPSI) for each bus is determined
by using fuzzy toolbox in MATLAB.
 The bus which is in urgent need of balancing will give
maximum CPSI.
 Buses which are already balanced will give lesser
values.

19.  Bus location for capacitor placement

20.  REFERENCE
 I.J.Nagrath & M. Gopal. ‘control system engineering’ .5th
edition.
 S.K.Bhattacharya, and S.K.Goswami, “Improved Fuzzy Based
Capacitor Placement Method for Radial Distribution
System”.IEEE Trans. Power Apparatus and Systems, vol.
108, no. 4, pp.741–944, Apr. 2008.
 http://en.wikipedia.org/wiki/Fuzzy_logic
 C. Chin, W. M. Lin, “Capacitor Placements for Distribution
Systems with Fuzzy Algorithm”, Proceedings of the 1994
Region 10 Ninth Annual International Conference, 1994, pp-
1025 - 1029.

21. THANK YOU