Modeling Costs and Load Uncertainties in Optimal Power Flow Studies

Modeling uncertainties in power systems has long interested researchers. Nowadays, as in 70's, the volatility associated with generation or fuel prices, for one side, and the uncertainties related with load forecasting and generation capacity, for another, places a new emphasis on this kind of problems. As a result of this renewed interest, in this paper we are enlarging the original Fuzzy Optimal Power Flow, FOPF, model in order to consider not only load uncertainties, but also uncertainties in generation or fuel prices, specified using trapezoidal fuzzy numbers. This new approach is based on multiparametric linear programming techniques that lead to the identification of a number of critical regions covering all the uncertainty space. This contributes to build more accurate membership functions of all variables, namely generations, branch flows and power not supplied.