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presented in the literature. However, these methods may cause the dimensions of the ED
problem to become extremely large when applied on large power systems, thus requir-
ing enormous computational efforts [37].
Recently, as an alternative to the conventional mathematical approaches, the meta-
heuristic optimization techniques such as genetic algorithm [37-39], Tabu search [40],
simulated annealing (SA) [41], ant colony (AC) [42], evolutionary programming (EP)
[43] and particle swarm optimization (PSO) [44-46] have been used to obtain global
or near global optimum solutions for ED problems. These methods are effective for
global searching due to their capability of exploring and finding high performance re-
gions in the search space at an affordable time. Also, limitations regarding the form of
the cost functions employed and the continuity of variables used for the mathematical
optimization methods can be completely eliminated.
Although various optimization methodologies have been developed for economic
dispatch problems, the complexity of the task reveals the need for developing efficient
algorithms to precisely locate the optimum dispatch solution. In this context, this
chapter focuses on the application of the HS algorithm for solving ED problems, aim-
ing to provide a practical alternative for conventional methods.
3.1 Problem Formulation for ED Problems
The goal of the ED problem is to minimize the total power generation cost that is
modeled as the sum of the cost functions of all generators. To simplify the optimiza-
tion problem and facilitate the application of classical techniques, cost functions of
generators are typically modeled by smooth quadratic function form given as:
n
∑
=
2
C
=
a
+
b
P
+
c
P
(2)
T
i
i
i
i
i
i
1
where
C
T
is the total generation cost,
n
is the total number of generating units,
a
i
,
b
i
and
c
i
are the cost coefficients of the
i
th
unit, and
P
i
is the actual power output of the
i
th
unit.
To model a more realistic cost function of generators, the valve-point effects need
to be considered. For the purpose of modeling the valve-point loading effects a recur-
ring rectified sinusoidal term is added to Eq. (2) as follows:
n
∑
=
2
min
C
=
a
+
b
P
+
c
P
+
α
d
sin(
f
(
P
−
P
))
(3)
T
i
i
i
i
i
i
i
i
i
i
1
where
d
i
and
f
i
are the valve-point coefficients of the
i
th
unit.
is the lower genera-
min
P
tion limit of the
i
th
unit.
Practically several types of fuel may be used for a unit. For a unit with k fuel op-
tions, Eq. (2) is modified as follows.
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