Detailed Calculation of the Fuzzy Power Flow

Abstract

Power flow calculations are one of the most important computational tools forplanning and operating electric power systems, since they provide information about the state ofthe system for a specific deterministic scenario of generation and load. After the stabilization ofthe deterministic power flow calculation methods, the need to capture uncertainty in loaddefinition lead first to the development of probabilistic models, and later to fuzzy approachesable to deal with qualitative declarations and other non-probabilistic information about the valueof the loads. In this framework, fuzzy power flow calculations use typically incrementaltechniques, in order to obtain a good approximation of the fuzzy state variables. However, thesemodels and procedures are not entirely satisfactory for the evaluation of the adequacy of theelectric transmission system, since they are not completely symmetric, due to the presence of aslack bus. In this paper, we show how to perform the detailed calculation of the state variables ofthe FPF problem in an exact and symmetrical way, by means of solving multiple optimizationproblems. The extension to the constrained fuzzy power flow problem is also described, alongwith numerical adequacy indices. The procedure is illustrated using the IEEE-14 test system.