Distributed Stochastic Reserve Scheduling in AC Power Systems With Uncertain Generation

This paper presents a framework to carry out multi-area stochastic reserve scheduling (RS) based on an ac optimal power flow (OPF) model with high penetration of wind power using distributed consensus and the alternating direction method of multipliers (ADMM). We first formulate the OPF-RS problem using semidefinite programming (SDP) in infinite-dimensional spaces that is in general computationally intractable. Using a novel affine policy, we develop an approximation of the infinite-dimensional SDP as a tractable finite dimensional SDP, and explicitly quantify the performance of the approximation. To this end, we adopt the recent developments in randomized optimization that allow a priori probabilistic feasibility guarantees to optimally schedule power generating units while simultaneously determining the geographical allocation of the required reserve. We then use the geographical pattern of the power system to decompose the large-scale system into a multi-area power network, and provide a consensus ADMM algorithm to find a feasible solution for both local and overall multi-area network. Using our distributed stochastic framework, each area can use its own wind information to achieve local feasibility certificates, while ensuring overall feasibility of the multi-area power network under mild conditions. We provide numerical comparisons with a new benchmark formulation, the so-called converted dc (CDC) power flow model, using Monte Carlo simulations for two different IEEE case studies.