A fuzzy interval optimization-based approach to optimal generation scheduling in uncertainty environment

Abstract

This paper proposes a fuzzy interval optimization approach to solve the Environmental/Economic Dispatch (EED) problem with uncertain parameters in the constraints and the objective functions. The objective functions considered are fuel cost and the gaseous emissions of the generating units. Two different types of fuel cost functions are considered in this study, namely, the conventional quadratic function and the augmented quadratic function to introduce more accurate modeling that incorporates the valve loading effects. The latter model presents non-differentiable and nonconvex regions that challenge most gradient-based optimization algorithms. In the proposed approach, objective functions are fuzzified and integrated to represent the fuzzy decision value. On the other hand, load uncertainties are modeled using fuzzy intervals. This fuzzy EED problem formulation provides a modeling flexibility, relaxation in constraints and allows the method to seek a practical solution. The obtained fuzzy multi-objective optimization problem is solved using non-dominated sorting genetic algorithm-II, known for its global searching capabilities, to get the best compromise among all the objectives. The performance of this solution is examined and applied to the standard IEEE 30-bus six-generator test system and the Indian power network of 82-bus by comparing its results with that of the existing methods. Different cases with different complexities have been considered in the study reported in this paper.