Optimizing Instantaneous and Ramping Reserves With Different Response Speeds for Contingencies—Part I: Methodology

The need to efficiently manage different reserve types, inertia, and the largest credible contingency is critical to the continued uptake of variable renewable energy (VRE) and security of a power system. This article presents an optimization formulation for the dispatch of contingency reserves to satisfy frequency limits. Reserve options are divided into two categories: instantaneous reserve (a stepped response with a time delay) and a ramped response with both a time delay and ramp rate. The problem is to optimally select reserve capacity from a set of offers with different response speeds, i.e. different time delays, ramp rates, and prices. The optimal reserve dispatch requires the frequency transient for a contingency to be constrained against frequency limits that occur at specified times after the contingency. The first result of this article is the demonstration of convexity of the feasible solution space; thereby, retaining desirable uniqueness properties of the optimal solution, and polynomial time performance of a solver. The feasible solution space is characterized by piecewise constraints whose components are quadratic. The second result of this article is the development of a solving methodology that utilizes the convex properties of the proposed formulation.