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