Hybrid Stochastic-Deterministic Multiperiod DC Optimal Power Flow

Abstract

Stochastic optimal power flow (OPF) formulations that minimize the expected operating costs over forecast scenarios generally result in lower costs than the standard (deterministic) OPF problem for power systems with significant forecast error, for example, from renewable energy sources. However, this type of stochastic OPF problem is more computationally demanding than the deterministic OPF, and even more so when storage units or ramp-constrained generators are included, as they require solving a multi-period OPF problem. We propose a hybrid method approaching the cost performance of the stochastic OPF problem and the computational burden of the deterministic OPF problem. Our method decomposes the problem into stochastic and deterministic subproblems, and relies on Benders’ Cuts to interface them. We present three versions of the method, which achieve different cost/computational burden trade-offs. The versions can be parametrized so that they scale well with the problem dimension. For one of the versions, we develop a multi-dimensional formulation of the Sandwich Algorithm , which is used to iteratively approximate a convex function. Through a case study using a 118-bus system, we find that our hybrid method achieves between 25% and 81% of the cost improvement of the stochastic OPF, but requires only 12 to 41% of the increased computation time required by the stochastic OPF. Both the hybrid method and the multi-dimensional Sandwich Algorithm can be used for problems outside of the field of power systems.