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 are 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 generating units while simultaneously determining 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.

This paper presents a solution method for a day-ahead stochastic reserve scheduling (RS) problem using an AC optimal power flow (OPF) formulation. Such a problem is known to be non-convex and in general hard to solve. Existing approaches follow either linearized (DC) power flow or iterative approximation of nonlinearities, which may lead to either infeasibility or computational intractability. In this paper we present two new ideas to address this problem. We first develop an algorithm to determine the level of reserve requirements using vertex enumeration (VE) on the deviation of wind power scenarios from its forecasted value. We provide a theoretical result on the level of reliability of a solution obtained using VE. Such a solution is then incorporated in RS-OPF problem to determine up-and down-spinning reserves by distributing among generators, and relying on the structure of constraint functions with respect to the uncertain parameters. As a second contribution, we use the sparsity pattern of the power system to reduce computational time complexity. We then provide a novel recovery algorithm to find a feasible solution for the RS-OPF problem from the partial solution which is guaranteed to be rank-one. The IEEE 30 bus system is used to verify theoretical developments together with a comparison with DC counterpart using Monte Carlo simulations.