24-08-2012, 04:57 PM
Unit Commitment Problem Solution Using Shuffled Frog Leaping Algorithm
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Abstract
A new evolutionary algorithm known as the shuffled
frog leaping algorithm is presented in this paper, to solve the unit
commitment (UC) problem. This integer-coded algorithm has
been developed to minimize the total energy dispatch cost over the
scheduling horizon while all of the constraints should be satisfied.
In addition, minimum up/down-time constraints have been directly
coded not using the penalty function method. The proposed
algorithm has been applied to ten up to 100 generating units,
considering one-day and seven-day scheduling periods. The most
important merit of the proposed method is its high convergence
speed. The simulation results of the proposed algorithm have
been compared with the results of algorithms such as Lagrangian
relaxation, genetic algorithm, particle swarm optimization, and
bacterial foraging. The comparison results testify to the efficiency
of the proposed method
INTRODUCTION
UNIT COMMITMENT (UC) is used to schedule the operation
of the generating units in order to satisfy load demand
such that the total system operational cost over the scheduled
horizon be minimized as subject to many system and generator
operational constraints [1]. The solution to this problem implies
a simultaneous solution of two subproblems: the mixed-integer
nonlinear programming problem of determining the generating
units to be running during each hour of the planning horizon,
considering system capacity requirements; and the quadratic
programming problem of optimally dispatching the forecasted
load among the committed units during each specific hour of
operation [2].
SHUFFLED FROG LEAPING ALGORITHM
The SFLA is a meta-heuristic optimization method which
is based on observing, imitating, and modeling the behavior
of a group of frogs when searching for the location that has
the maximum amount of available food [27]. SFLA, originally
developed by Eusuff and Lansey in 2003, can be used to solve
many complex optimization problems, which are nonlinear,
nondifferentiable, and multi-modal [28]. SFLA has been successfully
applied to several engineering optimization problems
such as water resource distribution [29], bridge deck repairs
[30], job-shop scheduling arrangement [31], and traveling
salesman problem (TSP) [32]. The most distinguished benefit
of SFLA is its fast convergence speed [33]. The SFLA combines
the benefits of the both the genetic-based memetic algorithm
(MA) and the social behavior-based PSO algorithm [34].
APPLICATION OF SFLA ON UC PROBLEM
Frog (Solution) Definition
In the integer coded SFLA, the frog position consists of
a sequence of integer numbers, representing the sequence of the
ON/OFF cycle durations of each unit during the UC horizon. A
positive integer in the represents the duration of continuous
unit operation (ON status), while a negative integer represents
the duration of continuous reservation (OFF status) of the unit.
The number of a unit’s “ON/OFF” cycles during the UC horizon
depends on the number of load peaks during the UC horizon and
the sum of the minimum up and down times of the unit [17].
Fig. 3 shows a daily load profile with two load peaks used to
determine the number of ON/OFF cycles of units.
Fitness Function Computation
The objective function of SFLA has two terms. The first
term is the total operation cost over scheduling horizon and
the second term is the penalty function that penalizing the
violation of system constraints. All the generators are assumed
to be connected to the same bus supplying the total system
demand. Therefore, the network constraints are not considered.
In the first step, an ED should be performed for the scheduling
horizon. It is an important part of UC [3]. Its goal is to minimize
the total generation cost of a power system for each hour while
satisfying constraints.
CONCLUSION
This paper has proposed a new evolutionary algorithm known
as SFLA to solve the UC problem. The combination of the local
search with information exchange of groups results in performance
improvement of SFLA. In the UC problem, the minimum
up and down-time constraints have been considered during generating
the feasible solutions. Therefore, there is no need to use
the penalty functions method.
The efficiency of the proposed algorithm has been studied
considering periods of one-day and seven-day scheduling for
ten up to 100-unit systems. The proposed method has been compared
with other methods. The simulation results show that the
computation times and production costs of SFLA are less than
other algorithms such as LR, GA, PSO, and BF.