Co-optimized recovery framework for damaged coupled power-water systems with temporal-spatial coordination and MT-SOPs

The resilience of modern coupled power-water (CPW) systems is challenged by various disruptions and risks. While the restoration and repair of individual systems are documented in the literature, their coordination in CPW recovery is rarely focused on. This work proposes a temporal-spatial coordinative method to improve CPW resilience by co-optimizing the recovery process comprising repair crew dispatch and adaptive service restoration. Firstly, a CPW model is developed based on physical mechanisms and component-level interdependencies. The model includes typical post-disruption features, like imbalanced three-phase power flows and pipe breakages. Secondly, a coordinated framework is designed for recovering damaged CPW, considering faulted components, available crew, and resources. The framework hierarchically comprises two stages. The first stage conducts absorption via components' operation and network topology adjustment. The second stage organizes the grouping and routing of repair crews, with further adjustments of absorption to exploit newly repaired components. In addition, multi-terminal soft open points (MT-SOPs) are applied to facilitate flexible power flow control and network reconfiguration of imbalanced power networks to augment the repair process. We also modeled the diverse correlated uncertainties and applied a sample-based optimization approach for timely and robust solutions. The proposed method is validated on a modified 36-node/33-bus CPW system, demonstrating a 32.51 % reduction in unsupplied loads compared to separate recovery. Additionally, incorporating MT-SOPs further reduces unsupplied loads by 16.94 % compared to traditional tie-lines. A large-scale evaluation on a 308-node/150-bus synthetic model further confirms the effectiveness of our framework in real-world CPW systems.