Abstract: Distributed generators (DGs) interfaced with inverters providing auxiliary service is of high value in terms of guaranteeing safe and economic operation of distribution system. In this paper, simultaneously considering the capabilities of energy storage systems, switchable capacitor reactors, on-load transformer changers, static Var compensators, and operation constraints, we developed a multi-period two-stage hybrid integer second-order conic programming (SOCP) robust model with partial DGs providing auxiliary service to minimize active power losses of ESSs and distribution network as well as abandoned wind and solar power based on branch flow equations. Meanwhile, we proposed a novel method of directly iteratively two-stage solving between master and sub-problems based on cutting plane. In comparison to columns and constraints generation algorithm (CCG), the numbers of variables and constraints in the first stage model remain constant during iteration to enhance the computing efficiency. To solve the second-stage multi-period model, only the model of each single period needs to be solved. To this end, the solving complexity and computer memory are greatly reduced. If the conic relaxation is not exact, a two-stage mixed integer sequential SOCP is formulated using convex-concave procedure and cuts, which can be quickly solved still. Moreover, the global optimal solution of the original problem can be recovered. The capabilities of the proposed method are validated with two simulation cases. The simulation results of IEEE 123-bus distribution network show that the computational rate of the proposed method is 12 to 22 times that of CCG algorithm. The proposed method provides a real-time and fast analyzing and solving tool for the optimal robust operation of distribution networks with high proportion of intermittent DGs, and improves the accommodating capabilities of renewable energy.