Genetic Algorithm Based Multiobjective Bilevel Programming for Optimal Real and Reactive Power Dispatch Under Uncertainty

This chapter presents how multiobjective bilevel programming (MOBLP) in a hierarchical structure can be efficiently used for modeling and solving optimal power generation and dispatch problems via genetic algorithm (GA) based Fuzzy Goal Programming (FGP) method in a power system operation and planning horizon. In MOBLP formulation of the proposed problem, first the objectives of real and reactive power (P-Q) optimization are considered as two optimization problems at two individual levels (top level and bottom level) with the control of more than one objective at each level. Then the hierarchically ordered problem is fuzzily described to accommodate the impression in P-Q optimization simultaneously in the decision making context. In the model formulation, the concept of membership functions in fuzzy sets for measuring the achievement of highest membership value (unity) of the defined fuzzy goals to the extent possible by minimising their under-deviational variables on the basis of their weights of importance is considered. The aspects of FGP are used to incorporate the various uncertainties in power generation and dispatch. In the solution process, the GA is used in the framework of FGP model in an iterative manner to reach a satisfactory decision on the basis of needs and desires of the decision making environment. The GA scheme is employed at two different stages. At the first stage, individual optimal decisions of the objectives are determined for fuzzy goal description of them. At the second stage, evaluation of goal achievement function for minimization of the weighted under-deviational variables of the membership goals associated with the defined fuzzy goals is considered for achieving the highest membership value (unity) of the defined fuzzy goals on the basis of hierarchical order of optimizing them in the decision situation. The proposed approach is tested on the standard IEEE 6-Generator 30-Bus System to illustrate the potential use of the approach.