Stochastic Optimal Power Flow with Uncertain Reserves from Demand Response

Demand response (DR) can provide reserves in power systems but a fundamental challenge is that the amount of capacity available from DR is time-varying and uncertain. We propose a stochastic optimal power flow (OPF) formulation that handles uncertain energy from wind and uncertain reserves provided by DR. To handle the uncertainty, we formulate chance constraints and use a scenario based methodology to solve the stochastic OPF problem. This technique allows us to provide a-priori guarantees regarding the probability of constraint satisfaction. Additionally, we devise a strategy for the reserves, provided either by the generators or the loads, that could be deployed in real time operation. To evaluate the effectiveness of our methodology, we carry out a simulation based analysis on the IEEE 30-bus network. Our case studies show that optimizing over the reserves provided by DR, even though they are uncertain, results in lower total cost compared to the case where only generation side reserves are taken into account. We also carry out a Monte Carlo analysis to empirically estimate the probability of constraint satisfaction and demonstrate that it is within the theoretical limits.