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The penetration of distributed energy resources (DERs) is increasingdramatically. Due to the uncertainty of DERs, the operation of the distributionsystem is facing higher risks and challenges. To overcome such challenges, atwo-stage chance-constrained convex AC optimal power flow (ACOPF) model isproposed in this paper, which can increase the economic efficiency ofdistribution system operation and manage the intermittency of DERs. In thefirst stage, a convex second-order cone programming (SOCP)-based ACOPF model isproposed in which the detailed models and limitations of DER, namely, demandresponse (DR), energy storage units, and rooftop PV systems are modeled toobtain participation ratio of DERs. In the second stage, Monte Carlo simulationis utilized to model the uncertainties of DERs. A probability violation indexis introduced to make a trade-off between scheduling more DERs and imposing ahigher risk to the distribution system. In this stage, power flow analysis isconducted for each scenario to determine the probability violation index ofsystem. Then, a modified SOCP-based ACOPF is proposed to satisfy the systemprobability violation criterion. Simulation results illustrate that theproposed two-stage chance-constrained model improves economic efficiency andreliability of real-time operation of the distribution system.

Two-Stage Distributed Energy Resources Scheduling via Chance-Constrained AC Optimal Power Flow: A Second-Order Cone Programming Approach