Multi-period Two-stage Robust Optimization of Radial Distribution System with Cables Considering Time-of-use Price

In the existing multi-period robust optimization methods for the optimal power flow in radial distribution systems, the capability of distributed generators (DGs) to regulate the reactive power, the operation costs of the regulation equipment, and the current of the shunt capacitor of the cables are not considered. In this paper, a multi-period two-stage robust scheduling strategy that aims to minimize the total cost of the power supply is developed. This strategy considers the time-of-use price, the capability of the DGs to regulate the active and reactive power, the action costs of the regulation equipment, and the current of the shunt capacitors of the cables in a radial distribution system. Furthermore, the numbers of variables and constraints in the first-stage model remain constant during the iteration to enhance the computation efficiency. To solve the second-stage model, only the model of each period needs to be solved. Then, their objective values are accumulated, revealing that the computation rate using the proposed method is much higher than that of existing methods. The effectiveness of the proposed method is validated by actual 4-bus, IEEE 33-bus, and PG 69-bus distribution systems.