3.4 Formulation Of GA And Neural Network

3.1 PROBLEM FORMULATION:
The objective of the economic load dispatch problem is to minimize the total fuel cost. 3.2 ECONOMIC LOAD DISPATCH NEGLECTING LOSSES
LAGRANGIAN MULTIPLIER (LAMBDA-ITERATION) METHOD: Where λ is the Lagrangian Multiplier.
Now, differentiating F with respect to the generation Pn and equating to zero gives the condition for optimal operation of the system. The incremental production cost of a given plant over a limited range is represented by Fn/dPn =FnnPn+ fn
Fnn= slope of incremental production cost curve fn= intercept of incremental production cost curve
The active power generation constraints are accepted into account for solving the equations which are derived above. If these constraints are irreverently for any generator it is
The generation with highest positive incremental transmission loss will operate at the lowest incremental cost of production.
3.4 Formulation of GA and Neural Network
A genetic algorithm (GA) is a method for solving both constrained and unconstrained optimization problems depend on a natural selection process that mimics biological evolution. The algorithm has restated modifies a population of individual solutions. At each step, the genetic algorithm randomly selects individuals from the current population and uses them as parents to produce the children for the next generation. Over successive generations, the population "evolves" toward an optimal solution.
Constrained Minimization Problem
We want to minimize a simple fitness function of two variables x1 and x2 min f(x) = 100 * (x1^2 - x2) ^2 + (1 - x1)^2; x
Such that the following two nonlinear constraints and bounds are satisfied x1*x2 + x1 - x2 + 1.5 <=0, (nonlinear constraint) 10 - x1*x2 <=0, (nonlinear constraint) 0 <= x1 <= 1, and (bound) 0 <= x2 <= 13 (bound)
Coding the Fitness Function
We create a MATLAB file named simple_fitness.m with the following code in it: function y =