Distributed Generation for Service Restoration Considering Uncertainties of Intermittent Energy Resources

Local distribution resources, such as distributed generations (DGs), energy storage systems, and some renewable energy resources, can be interconnected for service restoration in distribution systems and operate as an island after extreme events. High penetration of renewable energy resources makes it difficult to make decisions on restoration strategies because the power injections become uncertain. This paper proposes a chance-constrained program with relaxed second-order cone constraints (SOCC) to formulate the critical load restoration problem. The joint probability density function of power outputs of PVs and WTs is represented by a Gaussian mixture model (GMM). Using the sample average approximation method, an approximate analytical form of the chance constraints is proposed, which transforms the probabilistic program to a deterministic mixed-integer second-order cone program (MISOCP). The MISOCP can be solved by off-the-shelf optimization solvers. The effectiveness of the proposed method is validated by the simulation of the IEEE 33-node test system.