Power flow problems with nested information: An approach based on fuzzy numbers and possibility theory

In this paper, we present a new approach based on possibility theory to deal with the power flow problems in electrical networks. The approach takes into account the available information of a power system that is characterized generally by big data, often uncertain, redundant or insufficient for a correct description of the network status. In particular, we present a method to deal with nested information that can be generated by inaccurate measurements of electrical parameters. In order to solve the power flow problem we define a way to model nested information in power system and formalize an AC fuzzy power flow problem. The power flow results are obtained by an innovative approach based on the solution of a simultaneous nonlinear equations fuzzy system. The effectiveness of the proposed method is proven by applying the proposed approach to two modified IEEE benchmark test systems. Simulation results show accuracy, robustness and good computational cost of the implemented method in the search of the solution.