Connecting a large number of intermittent distributed generators (DGs) and electric vehicles (EVs) to a distribution network increases uncertainty and seriously threatens the safety and economic operation of that distribution network. Robust optimization is an important method of hedging against the adverse effects of uncertainty. However, the existing literature on robust optimization of distribution networks has not taken into account constraints on the travel distances of regulating equipment. In response to this deficiency, this paper considers constraints on the cycle period of energy storage systems (ESSs), travel distances of switchable capacitors and reactors, and load tap changers (OLTCs) and step voltage regulators (SVRs). A two-stage multi-period mixed-integer second-order cone robust model for coordinated active and reactive power optimization of a distribution network is formulated based on branch flow equations. There are not any dummy variables in the second stage model. In contrast to the deficiency of the low computational rate of the column-and-constraint generation (CCG) method, an iterative solution to the first and second stage models is proposed based on the cutting plane. Increases to the variables and constraints are not needed to solve the first stage model. For the second stage multi-period model, only the model of each single period needs to be solved first. Then the results of the two models are accumulated. Overall, the computational speed is significantly enhanced. The capabilities of the proposed method are validated by three simulation cases.

In the existing multi-period robust optimization method of active and reactive power coordination in distribution networks, the reactive power regulation capability of distributed generators (DGs), operation costs of regulating equipment, and the current of shunt capacitance of cables are not taken into account. In this paper, based on branch flow equations, a multi-period two-stage mixed integer second-order cone programming (SOCP) robust optimization model of active and reactive coordination in distribution system with cables is developed considering the reactive power regulation capability of DG, action costs of switched capacitor reactor (SCR), on load tap changer transformer (OLTC), energy storage system (ESS), and current of shunt capacitor of cables. Further, against to the deficiency of low computational rate of column and constraint generation method (CCG), a novel method iteratively solving the first and second stage model on cutting plane is proposed. In the first stage model, the number of variables and constraints keeps constant during the iteration. In the second stage model, it only needs to solve the model of each single time period. Then their results are accumulated. Thus, the computational speed using the proposed method is much higher than CCG. The effectiveness of the proposed method is separately validated on the 4-bus, IEEE 33-bus, and PG69-bus distribution systems.