Application of Genetic Algorithm to Economic Load Dispatch Seminar

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Application of Genetic Algorithm to Economic Load Dispatch

ABSTRACT:

This paper presents an approach based on genetic algorithm to solve the economic load dispatch (ELD) problem with losses for three thermal plant systems. Genetic algorithms are adaptive search methods that simulate some of the natural processes: selection, information, inheritance, random mutation and population dynamics. This approach was tested for three thermal plant systems. The performance of Genetic Algorithm - intelligent approach (GAs) is compared with the classical Kirchmayer method and it is observed that this method is accurate and may replace effectively the conventional practices presently performed in different central load dispatch centers.
INTRODUCTION:
Economic load dispatch (ELD) is a sub problem of the optimal power flow (OPF) having the objective of fuel cost minimization. The classical solutions for ELD problems have used equal incremental cost criterion for the loss-less system and use of penalty factors for considering the system losses. The lambda-iterative method has been used for ELD. Many other methods such as gradient methods, Newton’s methods, linear and quadratic programming, etc have also been applied to the solution of ELD problems. However, all these methods are based on assumption of continuity and differentiability of cost functions. Hence, the cost functions have been approximated in the differentiable form, mostly in the quadratic form. Further, these methods also suffer on two main counts. One is their inability to provide global optimal solution and getting stuck at local optima. The second problem is handling the integer or discrete variables.
Genetic algorithms (GAs) have been proved to be effective and quite robust in solving the optimization problems. GAs can provide near global solutions and can also handle effectively the discrete control variables. GAs does not stick into local optima because GAs begins with many initial points and search for the most optimum in parallel. GAs considers only the pay-off information of objective function regardless whether it is differentiable or continuous. Consequently, the most realistic cost characteristic of power plants can be formulated. Discontinuity and non-differentiability of cost charecteristics can be effectively handled by GAs.
This paper proposes the application of GAs to solve the economic load dispatch for three thermal plant systems and the results are compared with conventional method.
CLASSIC ECONOMIC LOAD DISPATCH PROBLEM
The objective of the ELD problem is to minimize the total fuel cost at thermal plants
n
OBJ = ∑ Fi (Pi)
i=1

Subject to the constraint of equality in real power balance

n
∑ Pi – PL – PD = 0
i=1

The inequality constraints of real power limits of the generation outputs are

Pi min < Pi < Pi max

Where
Fi (Pi) is the individual generation production in terms of its real power generation
Pi, Pi the output generation for unit i, n the number of generators in the system
Pd the total current system load demand, and Pl the total system transmission losses.
The thermal plant can be expressed as input-output models (cost function), where the input is the fuel cost and the output the power output of each unit, in practice, the cost function could be represented by a quadratic function.

Fi (Pi) = Ai * Pi2 + Bi * Pi + Ci

The incremental cost curve data are obtained by taking the derivative of the unit input-output equation resulting in the following equation for each generator:
dFi (Pi) / dPi = 2 Ai * Pi + Bi

Transmission losses are a function of the unit generations and are based on the system topology. Solving the ELD equations for a specified system requires an iterative approach since all unit generation allocations are embedded in the equation for each unit. In practice, the loss penalty factors are usually obtained using on line power flow software. This information is updated to ensure accuracy. They can also be calculated directly using the Bmn matrix loss formula.
PL = Pi Bij Pj
Where Bij are coefficients, constants for certain conditions.

GENETIC ALGORITHMS
GAs is inspired from phenomena found in living nature. The phenomena incorporated so far in GA models include phenomena of natural selection as there are selection and the production of variation by means of recombination and mutation, and rarely inversion, diploid and others. Most genetic algorithms work with one large panmictic population, i.e, in the recombination step each individual may potentially choose any other individual from the population as a mate. Then GA operators are performed to obtain the new child offspring.