Unit Commitment Optimization Using Gradient-Genetic Algorithm and Fuzzy Logic Approaches - Complex System Modelling and Control Through Intelligent Soft Computations - page 680

constrained problem into a linear unconstrained problem, we consider the following
Lagrangian function:

N g N g

X X X

H
h¼1 ½ / i ð P ih Þþ ST i ð

L ¼ 1 U i ð h 1 Þ Þ U ih þ g ð P dh P Lh P i U ih Þð 9 Þ

i¼1 i¼1

cient.
The hypothesis being tested in this chapter is that the dynamic unit commitment
can combines such solutions to obtain the

Herein, g is the Lagrange coef

final unit commitment over the entire

planning period. Since the final unit commitment must not only satisfy the demand

and reserve constraints, but also minimum-up and minimum-down time constraints,
such combinations of independent solutions may not always be found. Therefore,
heuristic rules must be applied to the solution of the start-up cost at each consec-
utive time interval in order to satisfy the time-coupling constraints, since an
incorrect choice of the committed units at time t may affect the solutions for the rest
of the optimization period.

4 Methodology of Resolution

We have adopted two strategies for solving the Unit Commitment problem, the rst

one is based on the combination of two calculations methods, the genetic algorithm
and the gradient method and the second one based on the fuzzy logic approach. The
resolution of the of the Unit Commitment problem through Gradient genetic
algorithm method is provided by a speci

c adjustment of the Lagrangian multipliers
k i of the Lagrangian function. The combined choice of these two methods is due to
inquire about the rapidity of the genetic algorithm in the search for global minimum
in

ts the gradient method in a second step, since it
is effective in terms of the quality of the obtained optimal solutions. Besides, the use
of the fuzzy logic approach to resolve this problem is depicted to the effectiveness
of this optimization method in solving nonlinear dif

rst step, and to operate the bene

cult problems.

4.1 Fuzzy Logic

Fuzzy logic provides not only a meaningful and powerful representation for mea-
surement of uncertainties but also a meaningful representation of blurred concept
expressed in normal language. Fuzzy logic is a mathematical theory, which

encompasses the idea of vagueness when de ning a concept or a meaning. For

example, there is uncertainty or fuzziness in expressions like

, since
these expressions are imprecise and relative. Thus, the variables considered are
termed

' low ' or ' high '

' fuzzy ' as opposed to ' crisp ' . Fuzziness is simply one means of describing