On possibilistic and probabilistic uncertainty assessment of power flow problem: A review and a new approach

Abstract As energy resource planning associated with environmental consideration are getting more and more challenging all around the world, the penetration of distributed energy resources (DERs) mainly those harvesting renewable energies (REs) ascend with an unprecedented rate. This fact causes new uncertainties to the power system context; ergo, the uncertainty analysis of the system performance seems necessary. In general, uncertainties in any engineering system study can be represented probabilistically or possibilistically. When sufficient historical data of the system variables is not available, a probability density function (PDF) might not be defined, while they must be represented in another manner i.e. possibilistically. When some of system uncertain variables are probabilistic and some are possibilistic, neither the conventional pure probabilistic nor pure possibilistic methods can be implemented. Hence, a combined solution methodology is needed. This paper proposes a new analytical probabilistic- possibilistic tool for the power flow uncertainty assessment. The proposed methodology is based upon the evidence theory and joint propagation of possibilistic and probabilistic uncertainties. This possibilistic–probabilistic formulation is solved in an uncertain power flow (UPF) study problem.