Chance Constrained Reserve Scheduling Using Uncertain Controllable Loads Part I: Formulation and Scenario-Based Analysis

This paper develops a multi-period chance constrained optimal power flow model to schedule generation and reserves from both generators and aggregations of controllable electric loads. In contrast to generator-based reserve capacities, load-based reserve capacities are less certain because they depend on load usage patterns and ambient conditions. This paper is divided in two parts. In part I, we develop a reserve scheduling framework managing uncertain power from wind and uncertain reserves provided by controllable loads, and solve the problem using a probabilistically robust optimization method that may require large numbers of uncertainty scenarios but provides a priori guarantees on the probability of constraint satisfaction, assuming no knowledge of the uncertainty distributions. The solution of this problem offers us a policy-based strategy for real-time reserve deployment. We derive simple rules, based on the cost parameters of the resources, to determine when load-based reserves will be preferable. In part II, we reformulate the problem assuming the uncertainty follows multivariate normal distributions and re-solve the problem, comparing the results against the randomized technique. To evaluate the performance of the methods, we conduct simulations using the IEEE 30-bus network.