Symmetric AC fuzzy power flow model

Power flow calculations are one of the most important computational tools for planning and operating electric power systems. After the stabilization of the deterministic power flow calculation methods, the need to capture uncertainty in load definition lead first to the development of probabilistic models, and later to fuzzy approaches able to deal with qualitative declarations and other non-probabilistic information about the value of the loads. Present fuzzy power flow (FPF) calculations use typically incremental techniques, in order to obtain a good approximation of the fuzzy state variables. However, these models and procedures are not entirely satisfactory for the evaluation of the adequacy of the electric transmission system, since they are not completely symmetric. In this paper, we show how to perform the detailed calculation of the state variables of the FPF problem in an exact and symmetrical way, by means of solving multiple optimization problems. The procedure is illustrated using the IEEE 118 test system.