Application of fuzzy sets to optimal reactive power planning with security constraints

This paper presents a mathematical formulation for the optimal reactive power planning taking into account the static security constraints and the nonprobabilistic uncertainty in load values. The planning process is decomposed into investment and operation problems via the generalized Benders decomposition (GBD). Fixed and variable costs are considered in the investment problem. Linguistic declarations of load values in the operation problem are translated into possibility distribution functions. The operation problem is decomposed into 4 subproblems via Dantzig-Wolfe decomposition (DWD), and the modeling of multi-area power systems is considered by applying a second DWD to each subproblem, leading to a significant reduction in its dimensions for personal computer applications. Voltage constraints within each area are modeled as fuzzy sets for the static security analysis by biasing the final solution towards desired values of variables within their given ranges. The overall solution is a compromise between economics (lower investment and operation costs) and security (tighter feasible region). Numerical examples for the applicability of the proposed approach to multi-area power systems are discussed