【目的】在配电网因极端故障引发大范围停电时，为实现高效供电恢复并保证输电网运行安全，输配电网协同恢复至关重要。然而，输配电网隶属不同调度主体，跨层级间难以实现运行数据完全共享。为此，提出一种基于边界安全域刻画的输配电网协同分布式供电恢复方法。【方法】提出一种结合伞约束辨识预处理的改进傅里叶-莫茨金算法，利用伞约束辨识提取输电网有效约束，并通过隐式优化策略动态剔除消元过程中的冗余项，从而抑制约束规模爆炸，有效获取输电网边界功率的低维等值域，即边界安全域。提出一种考虑边界安全域的输配电网分布式协同恢复策略，该策略将边界安全域通过欧几里得投影嵌入交替方向乘子法迭代框架，实现输配电网协同供电恢复模型的分布式计算。【结果】仿真结果表明，所提安全域刻画兼顾计算精度与速度，在供电恢复效果上，所提分布式策略实现了失电区域最大化复电，且总成本与集中式全局最优解的偏差仅为0.01%。【结论】所提结合伞约束辨识预处理的改进投影算法在保证刻画精度的同时，显著降低了安全域刻画的计算复杂度，有效提升了求解效率。所提输配电网分布式供电恢复策略在保证隐私的前提下，可求得接近全局最优的复电方案。

[Objective] In distribution networks where large-scale blackouts are caused by extreme faults, coordinated restoration of transmission and distribution networks is considered essential for achieving efficient power supply restoration while ensuring the operational security of the transmission network. However, since the transmission and distribution networks are operated by different dispatch entities, complete sharing of operational data across hierarchies is difficult to be achieved. For this purpose, a coordinated distributed service restoration method for transmission and distribution networks based on boundary security region characterization is proposed. [Methods] An improved Fourier-Motzkin algorithm is proposed, which incorporates umbrella constraint identification as a pre-processing step. This approach utilizes umbrella constraint identification to extract effective constraints for the transmission network and employs an implicit optimization strategy to dynamically eliminate redundant terms during the elimination process, thereby mitigating the explosion of constraint size and effectively obtaining the low-dimensional level set of boundary power for the transmission network, that is the boundary security region. A distributed collaborative restoration strategy for transmission and distribution networks that takes the boundary security region into account is proposed. This strategy embeds the boundary security region into the iterative framework of the alternating direction method of multipliers via euclidean projection, thereby enabling distributed computation of the collaborative service restoration model for transmission and distribution networks. [Results] Simulation results indicate that the proposed security region characterization strikes a balance between computational accuracy and speed. In terms of service restoration performance, the proposed distributed strategy achieves maximum service restoration in the outages area, with the total cost deviating from the centralized global optimal solution by only 0.01%. [Conclusions] The improved projection algorithm combined with umbrella-constraint identification preprocessing significantly reduces the computational complexity of security region characterization while maintaining high accuracy, thereby effectively enhancing efficiency. Furthermore, under the premise of privacy preservation, a restoration scheme close to the global optimum can be obtained by the proposed distributed service restoration strategy for transmission and distribution networks.