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Distributed generators providing auxiliary service are an important means of guaranteeing the safe and economic operation of a distribution system. In this paper, considering an energy storage system (ESS), switchable capacitor reactor (SCR), step voltage regulator (SVR), and a static VAR compensator (SVC), a two-stage multi-period hybrid integer second-order cone programming (SOCP) robust model with partial DGs providing auxiliary service is developed. If the conic relaxation is not exact, a sequential SOCP is formulated using convex–concave procedure (CCP) and cuts, which can be quickly solved. Moreover, the exact solution of the original problem can be recovered. Furthermore, in view of the shortcomings of the large computer storage capacity and slow computational rate for the column and constraint generation (CCG) method, a method direct iteratively solving the master and sub-problem is proposed. Increases to variables and constraints to solve the master problem are not needed. For the sub-problem, only the model of each single time period needs to be solved. Then, their objective function values are accumulated, and the worst scenarios of each time period are concatenated. As an outcome, a large amount of storage memory is saved and the computational efficiency is greatly enhanced. The capability of the proposed method is validated with three simulation cases.

Multi-Period Fast Robust Optimization for Partial Distributed Generators (DGs) Providing Ancillary Services