Chance Constrained Reserve Scheduling Using Uncertain Controllable Loads Part II: Analytical Reformulation

Abstract

This paper is Part II of a two-part paper that develops a multi-period chance constrained optimal power flow model to schedule generation and reserves from both generators and aggregations of uncertain but controllable electric loads. Part I developed the formulation and solved the problem using a scenario-based method. In Part II, we assume that all uncertainties follow multivariate normal distributions, allowing us to reformulate the constraints analytically to obtain a deterministic formulation that can be solved faster and with less need for real data than the scenario-based method in Part I. We test the approach on a modified IEEE 30-bus system and compare the solutions, empirical reliabilities, and computational requirements to those of the scenario-based method. We find that the analytical reformulation solved using a cutting plane algorithm requires less computational time than the scenario-based method. Additionally, its solution is less costly and less conservative; however, its empirical reliability is lower, though still close to the desired reliability.