Three-phase optimal power flow based on Affine Arithmetic

This paper presents a non-linear stochastic mathematical formulation for the three-phase optimal power flow problem, which addresses the uncertainties of both the load and the renewable generation using the self-validation method called Affine Arithmetic. The affine shapes for tree-phase variables was performed using the theoretical approach of Reduced Affine Arithmetic together with the Chebyshev approximation method for non-affine operations. The stochastic mathematical model is formulated into as an equivalent optimization problem through a set of affine operators to later be solved by a two-stage stochastic optimization problem. Two three-phase distribution systems 19-bus and 25-bus are used to show the effectiveness of the proposed methodology.