Radiality constraints are involved in both distribution system restoration and reconfiguration problems. However, a set of widely used radiality constraints, i.e., the spanning tree (ST) constraints, has its limitations which have not been well recognized. In this letter, the limitation of the ST constraints is analyzed and an effective set of constraints, referred to as the single-commodity flow constraints, is presented. Furthermore, a combined set of constraints is proposed and case studies indicate that the combined constraints can gain computational efficiency in the reconfiguration problem. Recommendations on the use of radiality constraints are also provided.

After major outages, local power sources, including mobile power sources (MPSs), can be coordinated to serve critical loads in distribution systems (DSs). Repair crews (RCs) are sent to repair faulted components. Both mobile emergency resources, i.e., MPSs and RCs, need to travel through the transportation system (TS) before they reach the destination for service. However, traffic congestion may happen after natural disasters and impact the dispatch of MPSs and RCs. Therefore, the dynamic traffic state in the TS should be considered for efficient dispatch of mobile emergency resources. This paper proposes a framework to determine critical load restoration strategy for the DS, considering the dispatch strategy of MPSs and RCs in the TS. The cell transmission model (CTM) is used to formulate the weighted dynamic traffic assignment problem (WDTA) in the TS as a linear program (LP), aiming at minimizing the total prioritized travel time of MPSs and RCs. For the DS, the multi-period critical load restoration problem (CLR-DS) is formulated as a mixed-integer linear program (MILP) to maximize the cumulated service time to critical loads. Unbalanced three-phase power flow and time-varying topological constraints are considered. Case studies validate the effectiveness of the proposed method.

In this paper, an optimal energy storage sizing method is proposed for networked microgrids (NMGs) considering reliability and resilience enhancement. A bi-level optimization model for energy storage sizing is developed. The upper-level model is focused on the optimal energy storage sizing problem, aiming at maximizing annual profit. The lower-level problem is aimed at operation optimization for profit maximization under multiple operating scenarios, i.e., normal operation, typical fault, and extreme fault scenarios. The bi-level model is converted into a mixed-integer linear program (MILP), which can be solved by off-the-shelf optimization solvers such as CPLEX. For comparison, the optimal energy storage size schemes are obtained for NMGs and non-networked microgrids (NNMGs), respectively. The results indicate that the required energy storage size can be reduced while the operating profit is improved by interconnecting microgrids (MGs). The results also indicate that the energy interaction in NMGs enables the enhancement of both reliability and resilience during grid outages.

A major outage in the electricity distribution system may affect the operation of water and natural gas supply systems, leading to an interruption of multiple services to critical customers. Therefore, enhancing resilience of critical infrastructures requires joint efforts of multiple sectors. In this paper, a distribution system service restoration method considering the electricity-water-gas interdependency is proposed. The objective is to provide electricity, water, and natural gas supplies to critical customers in the desired ratio according to their needs after an extreme event. The operational constraints of electricity, water, and natural gas networks are considered. The characteristics of electricity-driven coupling components, including water pumps and gas compressors, are also modeled. Relaxation techniques are applied to nonconvex constraints posed by physical laws of those networks. Consequently, the restoration problem is formulated as a mixed-integer second-order cone program, which can readily be solved by the off-the-shelf solvers. The proposed method is validated by numerical simulations on electricity-water-gas integrated systems, developed based on benchmark models of the subsystems. The results indicate that considering the interdependency refines the allocation of limited generation resources and demonstrate the exactness of the proposed convex relaxation.

High voltage transmission lines, especially high-voltage direct-current (HVDC) lines, have been built around the world linking the populated load centers with major green energy resources at a far distance or offshore. Any major faults on these long-distance point-to-point connections may lead to large power unbalances and cause frequency security problems in the regional grid at the energy receiving end. In this work, an emergence frequency control strategy is proposed, utilizing available frequency response resources at the receiving end, including synchronous generators, local wind farms, battery-based energy storage systems, pumped hydro storages, etc. First, a system frequency response model consisting of multiple resources is formulated, including the secondary frequency drop caused by wind farms. Then, the order of the model is reduced to derive the analytical expressions of the frequency nadirs and the quasi-steady-state frequency. Finally, the emergency frequency control decision method is proposed with the consideration of the system frequency security constraints. The proposed strategy is studied and analyzed with simulations on a generalized model of Huadong regional grid in eastern China.