Static security in power system operation with fuzzy real load conditions

This paper presents a mathematical formulation for optimal power flow (OPF) taking into account the fuzzy modeling of static power system security constraints due to the uncertainty in bus loads. Uncertainties in MW loads and generations are translated into possibility distribution functions. The fuzzy OPF problem is decomposed, via Dantzig-Wolfe decomposition, into subproblems corresponding to the possibility distributions of loads. The effects of phase shifters are modeled as equivalent real power injections at corresponding system buses, which preserves the Y-bus symmetry and maintains minimum memory requirements. Contingency constraints are added to the fuzzy OPF problem. Fuzzy sets are utilized to exercise a tighter control on least cost real power generation with minimum emission dispatch solution. The final solution is a compromise among cost, static security and emission considerations. Numerical results for the application of the proposed approach to test systems are discussed