Risk-Averse Decision-Dependent Distributionally Robust Optimization for the Resilient Cyber-Physical Distribution System Against Contingencies

The cyber-physical deep coupling brings the distribution system the possibility of superposition vulnerability on cyber and physical spaces, which will potentially raise the unobservability and uncontrollability issues of the system, readily causing power outages during contingencies. To tackle this challenge, this paper proposes a resilience-oriented design for the cyber-physical distribution system based on a risk-averse decision-dependent distributionally robust optimization (DD-DRO) model. Firstly, observable and controllable intentional islands, as a promising way, are formed against contingencies by remote-controlled switch deployment, wireless communication configuration, and local controller activation. To this end, the cyber-physical coupling mechanism is investigated by hybrid wired/wireless communication modeling and fault propagation modeling, ensuring the cyber system’s observation and control. Secondly, reinforcement measures are adopted to mitigate the risk of uncertain contingencies, however, triggering decision-dependent uncertainty. To handle this uncertainty, the adaptive moment information method is developed to construct an N-k decision-dependent ambiguity set. Therefore, the proposed DD-DRO model is formulated and then recast to a mixed-integer linear programming problem by linearization techniques, which is solved by a customized nested column-and-constraint generation algorithm. Finally, numerical results on the modified IEEE 33-bus and IEEE 69-bus test systems demonstrate the effectiveness of the proposed model and method.