Supply restoration from outages is essential for improving the reliability of active distribution networks (ADNs) after fault isolation. Soft open point (SOP) can adjust the power flow among feeders and provide voltage support for power outage areas. Considering the sequential coordination of switching operation and SOP control mode selection, a multi-stage supply restoration method with SOPs is proposed for ADNs. First, the sequential energization is formulated, in which the impact of SOP control mode on restoration sequence is analyzed. By providing voltage support, the coordination of SOPs will rapidly energize the outage area and improve the voltage profile. Then, a multi-stage restoration model with SOPs is proposed, in which reconfiguration of switches and control mode selection of SOPs are coordinated in sequence to maximize the load recovery level of ADNs. Through the switching action-time mapping, secure operation is ensured during the entire supply restoration process. Finally, the effectiveness of the proposed method is validated on a modified IEEE 33-node distribution system and practical distribution networks with four-terminal SOP. Results show that the proposed method can fully exploit the potential benefits of SOPs and effectively enhance the load recovery level of ADNs.

断电恢复供电对于提高故障隔离后有源配电网络 (ADN) 的可靠性至关重要。软开放点（SOP）可以调节馈线之间的潮流，为停电区域提供电压支持。考虑到开关操作和SOP控制模式选择的顺序协调，提出了一种带有SOP的ADN多级电源恢复方法。首先，制定了顺序通电，其中分析了SOP控制方式对恢复顺序的影响。通过提供电压支持，SOP 的协调将迅速激活停电区域并改善电压分布。然后，提出了具有 SOP 的多阶段恢复模型，其中开关的重新配置和SOP的控制模式选择依次协调，以最大限度地提高ADN的负载恢复水平。通过切换动作时间映射，保障整个供电恢复过程的安全运行。最后，在改进的 IEEE 33 节点配电系统和具有四端 SOP 的实际配电网络上验证了所提出方法的有效性。结果表明，所提出的方法可以充分发挥SOPs的潜在优势，有效提高ADNs的负载恢复水平。该方法的有效性在改进的 IEEE 33 节点配电系统和具有四端 SOP 的实际配电网络上得到验证。结果表明，所提出的方法可以充分发挥SOPs的潜在优势，有效提高ADNs的负载恢复水平。该方法的有效性在改进的 IEEE 33 节点配电系统和具有四端 SOP 的实际配电网络上得到验证。结果表明，所提出的方法可以充分发挥SOPs的潜在优势，有效提高ADNs的负载恢复水平。