APPLICATION OF FUZZY-SETS TO OPTIMAL REACTIVE POWER PLANNING WITH SECURITY CONSTRAINTS

This paper presents a mathematical formulation for the optimal reactiv e power planning taking into account the static security constraints a nd the non-probabilistic uncertainty in load values. The planning proc ess is decomposed into investment and operation problems via the gener alized Benders decomposition (GBD). Fixed and variable costs are consi dered in the investment problem. Linguistic declarations of load value s in the operation problem are translated into possibility distributio n functions. The operation problem is decomposed into 4 subproblems vi a Dantzig-Wolfe decomposition (DWD), and the modeling of multi-area po wer systems is considered by applying a second DWD to each subproblem, leading to a reduction in its dimensions for personal computer applic ations. Voltage constraints within each area are modeled as fuzzy sets for the static security analysis by biasing the final solution toward s desired values of variables within their given ranges. The overall s olution is a compromise between economics (lower investment and operat ion costs) and security (tighter feasible region). Numerical examples for the applicability of the proposed approach to multi-area power sys tems axe discussed.