Fair and Reliable Reconnections for Temporary Disruptions in Electric Distribution Networks

Increasing reliability and reducing disruptions in supply networks are of increasing importance; for example, power outages in electricity distribution networks cost $35–$50 billion annually in the United States. Motivated by the operational constraints of such networks and their rapid adoption of decentralized paradigms and self-healing components, we introduce the minimum reconnection time (MRT) problem, which models reliability metrics such as the System Average Interruption Duration Index (SAIDI). MRT seeks to reduce outage time after network disruptions by programming reconnection times of different edges (i.e., switches), ensuring that the operating network is acyclic. We show that MRT is NP-hard and is a special case of the well-known (weighted) minimum sum set cover (MSSC) problem. We develop the theory of kernel-based randomized rounding approaches to give a tight polynomial-time approximation for MSSC, improving the state-of-the-art approximation factor for these instances. Further, motivated by the reliability incentive structure for utility companies and operational energy losses in distribution networks, we study minimizing energy losses and reliability metrics such as SAIDI and reconnection times simultaneously. Optimizing for any single objective at a time can create unfair duration of expected outage for industrial and residential areas. We, therefore, propose local search over spanning trees to balance these multiple objectives. We computationally validate our reconfiguration methods on the National Renewable Energy Laboratory Synthetic Models for Advanced, Realistic Testing: Distribution Systems and Scenarios Greensboro synthetic network and show that this improves equity by a factor of four across industrial and residential areas.