Robust Distribution System Load Restoration with Time-Dependent Cold Load Pickup

Abstract: Service restoration is one of the critical functions to enable the future self-healing distribution system. To restore the distribution system in a timely and reliable manner, the realistic system operating conditions need to be accurately characterized. In this paper, two main factors that have great impacts on distribution system restoration (DSR) in practice are investigated. First, cold load pickup (CLPU), generally caused by thermostatically controlled loads (TCLs), is a common phenomenon after an outage and shaped by the outage duration. However, the time-dependent behaviors of CLPU are rarely considered in literature. In this paper, the operating state evolution of TCLs after an outage is analyzed to characterize time-dependent CLPU. And the time-dependent CLPU is analytically embedded in DSR to accurately represent the actual behaviors of the restored loads. Second, it is difficult to predict loads that fluctuate during DSR due to the lack of real-time measurement data. Accordingly, a robust DSR based on the information gap decision theory (IGDT) is proposed to address this challenge, fully considering the uncertainty of CLPU. The proposed models are tested in IEEE 13-node and 123-node test feeders. Simulation results demonstrate that the time-dependent CLPU model and the uncertainty modeling of CLPU can accurately capture the actual behaviors of loads with TCLs after an outage, which greatly improves DSR decisions in practice.