Digital Signal Processing Reference
In-Depth Information
Fuzzy protection
setting
μ
Fuzzy
signal
P
P
*
I
Fig. 11.11
Comparison of fuzzy decision signal with fuzzy threshold
decision to trip the protected plant can be taken. Application of the fuzzy settings
creates a remedy for many problems with settings of classical protection relays,
being often a peculiar compromise between sensitivity and selectivity.
Figure
11.11
illustrates one of the possible ways of comparison of the fuzzy
signal with fuzzy setting. The degree of the threshold exceeding (also a value
within [0, 1]) is defined as a ratio of the areas P* and P, where P* stands for this
part of the area under the fuzzy signal MF that is also situated under the fuzzy
setting curve [
6
,
20
], i.e.
m
¼
P
P
ð
11
:
23
Þ
With such a way of comparison, if the signal m (non-fuzzy number) is
interpreted as the grade of meeting given criterion, it is not necessary to perform
its defuzzification. It can be directly used for decision-making (through
comparison with simple threshold) or working out the final decision in multi-
criteria protection schemes, where a number of various criteria signals are
analyzed and evaluated in parallel. Introducing the weighting factors w
i
for
particular criteria values, the resulting support grade for protected plant tripping
can be defined as a weighted sum
d
¼
X
N
w
i
m
i
;
ð
11
:
24
Þ
i
¼
1
and the final protection decision is taken after the value of d exceeds certain non-
fuzzy threshold D. This approach is called weighting factor aggregation method
and can be treated as a simplified version of fuzzy reasoning.
The general reasoning with FL approach is based on processing of a set of fuzzy
rules utilizing the implication operation in ''IF antecedent THEN consequent''
form. The implication p ? q can be expressed with use of the conjunction (AND),
disjunction (OR) and negation (NOT) operands as [
22
]:
p
!
q
,
p
^
q
:
ð
11
:
25
Þ
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