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produced power, the system demand, the reserve requirements and the operational
cost as fuzzy quantities. Hence, Saber et al. (
2007
), have used a twofold simulated
annealing method for the optimization of fuzzy-based Unit Commitment model.
The adopted strategy has served to offer a robust solution for Unit Commitment
problem but it deserves more computing time to converge.
The above said methods are very ef
cient for solving highly nonlinear and
combinatorial optimization problems. When the size of the problem increases, these
evolutionary methods (Marrouchi and Chebbi
2013
; Rajan and Mohan
2004
)will
locate the high performance region of the solution space at quick execution time but
they face dif
culty in locating the exact optimal solution.
3 Problem Formulation
The objective of the Unit Commitment Problem (UCP) is the minimization of total
production costs while determining the on/off states of each unit U
ih
over a period
of time H. In the Unit Commitment Production under consideration, an interesting
solution would be minimizing the total operating cost of the generating units with
several constraints being satis
ed.
The total production cost consists of the running, start-up and banking costs.
The
first term in the total production cost is associated with the unit in the
generation mode and is called the running cost. The running cost of a thermal unit is
a function of the power output. It is obtained by adding the fuel cost function and
the operational and maintenance costs. The running cost
for unit
i can be
approximated by a quadratic form as follows:
N
g
X
X
H
h¼1
½
/
i
ð
Min C
ð
U
P
Þ
;
as C
ð
X
P
Þ
¼
P
ih
Þþ
ST
i
ð
1
U
i
ð
h
1
Þ
Þ
U
ih
ð
1
Þ
;
;
i¼1
where:
/
i
ð
P
ih
Þ
: Represents the polynomial function de
ned by:
a
i
P
ih
þ
/
i
ð
P
ih
Þ
¼
b
i
P
ih
þ
c
i
ð
2
Þ
When a generation unit transits from a shut-down mode to banking or generation
mode, certain costs are incurred to bring a boiler to its working temperature and to
carry out the start-up procedure until the unit is ready to be synchronized to the
power system. These expenses are associated with the second term in the total
production cost, called start-up costs.
The start-up process of large steam generators may take several hours and the
start-up component in the total production cost for these units is very signi
cant. On
the other hand, small gas turbine units can be quickly transferred to the generation
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