General polynomial chaos in the current–voltage formulation of the optimal power flow problem

Abstract

Mathematical optimization techniques play a key role in enabling the power system transition to sustainable energy and are used for a variety of applications such as scenario analysis, optimal planning and operational decision making. Power flow optimization, a.k.a., optimal power flow, is a building block for many applications in network operations and planning. This paper discusses the treatment of general polynomial chaos expansion for the current–voltage formulation of the optimal power flow problem. The power flow equations of the current–voltage formulation are linear, making their Galerkin projection significantly more tractable compared to formulations in the power–voltage space, while still being exact. Furthermore, auxiliary variables and quadratic constraints enable chance constraints as second-order-cone constraints. An additional advantage of this approach is that the Galerkin projection of the quadratic constraints is significantly less complex compared to those of non-linear constraints with a polynomial degree higher than two, as would be needed for expressing the original variables’ variance without the auxiliary variables. On average, the current–voltage formulation using auxiliary variables shows more than an order of magnitude speed-up with respect to the power–voltage formulation without auxiliary variables.