Fuzzy Arithmetic for the DC Load Flow

The consideration of uncertainties in the future system operation is a key aspect in current planning methodologies. In this context, load flow studies based on probabilistic theory, fuzzy numbers, and Monte Carlo simulations have been proposed in the literature. This work analyzes in a novel way the application of fuzzy number arithmetic for the DC load flow problem. In this sense, fuzzy sets theory is reviewed and is showed that there are two alternative and valid procedures to perform a subtraction. A key aspect for the right selection of one of these procedures is the independency or dependency among the involved variables. Assuming input data as independent variables, this work is focused on analyzing the fuzzy subtraction between dependent state variables of the system, such as voltage phase angle. Accordingly, two new valid alternative methodologies are proposed and applied to case studies. Results are compared to previous related works showing the consistency of the proposed methodologies. Future research will be focused on the consideration of ohmic losses and AC network modeling in the field of expansion planning studies.