Enhancing the Radiality Constraint for Multi-period Restoration and Repair Model with Optimal Number of Islands in Active Distribution Networks

Maintaining the radial topology during the system restoration is vital to ensure the resilience of distribution networks. This paper proposes a multi-period restoration and repair model that considers an optimal number of islands after N-k contingencies in active distribution networks, allowing islands to dynamically merge during both restoration and line repair processes. Considering the variable network topology during restoration, a novel radiality constraint is proposed to explicitly characterize the relationship between the states of lines and buses, reducing redundant islands and improving overall network resilience. Through case studies on multiple IEEE test systems and a practical 2121-bus network, the model demonstrates a 54% higher load restoration rate, and achieves full recovery 30% faster than fixed-island models. The capability of the proposed model is shown to maintain radial topology and the effectiveness for launching the multi-period restoration.