Fuzzy load flow based on α-cuts arithmetics

In order to solve the load flow problem under uncertainty, a novel algorithm is presented. This proposal uses the fuzzy number arithmetic and the network linear model to solve the problem. Once the fuzzy sets theory is reviewed, it is demonstrated that the main difficulty to solve the problem is the calculation of the subtraction between two fuzzy numbers. With the aim to overcome this difficulty, it is proposed a methodology based on the use of a more general formula based on α-cuts, for the fuzzy numbers subtraction. It is also proposed reordering the DC load flow equations in such way that the subtraction operations are performed at the end of the calculation process. The obtained results show that, It is possible to solve, from the physical point of view, the load flow for networks with radial topology. This result can improve current planning and operation approaches incorporating uncertainties explicitly. For meshed networks, the results significantly reduce the supports of the resulting fuzzy numbers. Nevertheless In this case the Kirchhoff First Law is not fully satisfied; establishing a problem to be treated on future research.