Best Compromise Solutions for Stochastic Multi-Objective Environmental/Economic Dispatch of Power Systems using Evolutionary Chance-Constrained Nonlinear Programming and Latin Hybercube Sampling

Abstract

In power systems optimization, the stochastic environmental/economic dispatch problem consists of    simultaneously minimizing the fuel cost of generation and NO_x emission to environment considering decision  variables, power system loads and objective functions as stochastic. This stochastic approach represents a more  realistic model since acquired data are subject to inaccuracies from measuring and forecasting of input data and   changes of unit performance during the period between measuring and operation. The Non-Dominated Sorting  Genetic Algorithm (NSGA-II) is used to generate the set of non-dominated solutions of the multi-objective  problem  formulated by a chance-constrained programming technique. Latin Hypercube Sampling is used to yield  more precise estimates of these stochastic variables. The decision maker or power system operator may have imprecise or fuzzy goals for each objective function. In order to help the operator in selecting an operating point  from the obtained set of Pareto-optimal solutions, fuzzy logic theory is applied to each objective function to obtain  a fuzzy membership function. The best non-dominated solution can be found when the normalized sum of  membership function values for all objectives is highest. This paper analyzes the changes in the best compromise  solutions obtained from the evolutionary algorithm for coefficient of variation of 0.05, 0.1 and 0.2 under system  reliability of 68.3% and 95.5% respectively. Simulation results are presented for the standard IEEE 30-bus test  system.

Keywords: Power Systems, Environmental/Economic Dispatch, Multi- Objective Optimization, Evolutionary   Algorithms, Fuzzy Logic.