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Table 1 Fuzzy rules relating input/output fuzzy variables
LCG IC IL PRC LCG IC IL PRC LCG IC IL PRC
L L Z L BAV LG Z BAV AAV M Z AAV
L L S L BAV LG S BAV AAV M S AAV
L L LG L BAV LG LG BAV AAV M LG AAV
L M Z L AV L Z AV AAV LG Z AAV
L M S L AV L S AV AAV LG S AAV
L M LG L AV L LG AV AAV LG LG AAV
L LG Z L AV MZ AV H L Z H
L LG S L AV MS AV H L S H
L GGL VMGVH L GH
BAV
L
Z
BAV
AV
LG
Z
AV
H
M
Z
H
BAV
L
S
BAV
AV
LG
S
AV
H
M
S
H
BAV
L
LG
BAV
AV
LG
LG
AV
H
M
LG
H
BAV
M
Z
BAV
AAV
L
Z
AAV
H
LG
Z
H
BAV
M
S
BAV
AAV
L
S
AAV
H
LG
S
H
BAV
M
LG
BAV
AAV
L
LG
AAV
H
LG
LG
H
R
1
1
C
P
l
C
ðÞ
dC
P
production Cost
¼
ð
13
Þ
R
1
1
l
C
ðÞ
dC
P
with:
lð
C
P
Þ
Membership degree of the production cost vector.
Based on the aforementioned fuzzy sets, membership functions are selected for
each fuzzy input and the fuzzy output variables. For our case study, a triangular
shape is used to illustrate the considered membership functions. Once the mem-
bership functions are set, the input variables are then linked to the output variable
by IF-THEN rules as shown in the following scheme (Fig.
2
).
The Unit Commitment problem can be considered as two linked optimization
sub-problems, namely the unit-scheduling problem and the economic load dispatch
problem. The second proposed optimization method integrates genetic algorithm
with the gradient optimization method to solve the UC problem.
4.2 Gradient-Genetic Algorithm Method
The purpose of this strategy is to validate an approach to apprehend the whole
problem by combining an economic model with a model having operational con-
straints. To achieve this purpose, the approach is to combine a classical gradient
method with a meta-heuristic method, genetic algorithm, well suited to take into
account new constraints. The fundamental principle of a genetic algorithm is to
represent the natural evolution of organisms (individuals).
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