Fast Solving Method for Two-Stage Multi-Period Robust Optimization of Active and Reactive Power Coordination in Active Distribution Networks

This paper considers constraints on the cycle number of energy storage systems (ESSs), travel distances of switchable capacitors reactors (SCRs), on load tap changers (OLTCs) and step voltage regulators (SVRs). The characteristics and operational constraints of these equipments are properly formulated with binaries and big-M method, obtaining desirable linear descriptions. The branch flow equations of distribution systems for active and reactive power coordination are constructed. Considering physical constraints, a multi-period mixed-integer deterministic second-order conic programming (SOCP) to minimize network losses is formulated. Then, considering uncertainties of loads and active power of renewable distributed generators (DGs), a two-stage robust model is developed. A directly iteratively solving method between the first and second stage models is proposed. In contrast to the traditional column-and-constraint generation (CCG) method, increases to variables and constraints are not needed to solve the first stage model. To solve the second stage multi-period model, only the model of each single period needs to be solved first. Then their objective function values are accumulated, and the worst scenarios of each period are concatenated. As a result, the solving complexity is greatly reduced. The capabilities of the proposed method are validated by three simulation cases. It is found that the computational rate using the proposed method is significantly enhanced with much less computer storage. Specifically, the simulation results of 4, 33 and 69-bus systems indicate that the computing rate of the proposed method is about 28 times higher than CCG method when 8 iterations are performed. Meanwhile, the precision of optimization results is also improved.