Two-Layer Collaborative Optimization for Multi-Period Fault Recovery in Active Distribution Networks with Fast Decomposition

Abstract

With the increasing integration of distributed generation, energy storage, and flexible loads, active distribution networks have gained multiple fault-recovery options, including network reconfiguration, islanded operation, and coordinated source–load regulation. However, existing studies often lack an effective link between system-level restoration decisions and resource-level execution. To address this issue, this paper proposes a two-layer collaborative optimization method for multi-period fault recovery with fast decomposition. The upper layer develops a multi-period restoration model that jointly optimizes network reconfiguration, load restoration targets, and fault repair sequences, with the objectives of minimizing load loss and recovery cost while maximizing continuous power-supply duration. The model incorporates load priorities, switch operations, distributed generation, energy-storage states, flexible-load response, main-grid support, and inter-period coupling constraints. Based on the restoration targets generated by the upper layer, the lower layer applies a fast sort-and-fill decomposition strategy to allocate regulation demands among photovoltaic generation, wind power, energy storage systems, flexible loads, and main-grid support, thereby forming a closed-loop coordination mechanism between restoration planning and resource execution. The proposed method is validated on a modified IEEE 33-bus active distribution network under multi-period fault scenarios. Results show that the load restoration rate is 88.78% in Period 1 and reaches 100% from Period 2 onward. Compared with static restoration, unserved energy decreases from 4.6896 MWh to 0.3113 MWh, while restored energy increases from 8.2505 MWh to 12.6288 MWh. Over 1000 randomized feasible operating points, the maximum absolute objective gap between the proposed sort-and-fill procedure and direct LP re-optimization is 7.55×10−14%, and the maximum power-balance error is 2.73×10−12 kW. These results demonstrate that the proposed method improves restoration effectiveness while reproducing the exact lower-layer LP solution within numerical precision.