When a major outage occurs in a distribution system due to extreme events, service restoration (SR) strategies pick up critical loads after isolating the faults that have occurred. However, in extreme conditions, traditional SR strategies could pose potential security risks to restored services due to subsequent contingencies in succeeding events. To address this challenge, we propose a microgrid-based SR methodology that aims to enhance the preparedness of microgrids during unfolding extreme events. The proposed SR strategy comprises microgrid formation (MF) and sequential service restoration (SSR) steps. The MF makes the benefit of topology switching, generator allocation, and load demand response. Additionally, the uncertainty of line failure probability is considered, and a distributionally robust optimization model is proposed to maximize the expected load restoration with regard to the worst-case distribution of contingencies. Then, the SSR is formulated as a mixed-integer linear program model to yield proper load switching sequences and generation of power sources for sequentially restoring the outage system. The proposed SR measure enhances the system resilience by the proactive formation of microgrids, reducing the impact of cascading phenomenon when lines with high failure probability are tripped. The effectiveness of the proposed method is validated by numerical simulations.

Service restoration (SR) is essential to recovering distribution systems with outages when extreme weather conditions occur. However, the occurrence of long-duration extreme weather events may cause a restored system to become susceptible to subsequent random contingencies. To address this challenge, this paper proposes a microgrid-based SR approach for recovering critical loads in wind power penetrated distribution systems incorporating the impacts from subsequent random contingencies. A hybrid stochastic-robust optimization model is developed considering both the subsequent random contingencies that may occur and the uncertainty of wind power generation. The expected load shedding is minimized by locating mobile emergency generators, dynamically adjusting microgrid (MG) topologies, and dispatching power sources. To ensure the tractability of the optimization, the original problem is reformulated and decomposed into a master problem and several robust optimization subproblems based on the column-and- constraint generation approach. In addition, the master problem, which is in the format of stochastic optimization is solved by an improved progressive hedging algorithm to accelerate optimization. The proposed method is validated on the modified IEEE distribution systems and the simulation results show the effectiveness of the proposed SR method in reducing security violation risk and reducing the computational complexity.

This paper proposes a two-stage microgrid (MG) scheduling approach that considers the dynamic MG formation and the coordinated optimization of active and reactive powers to enhance the distribution system resilience after blackouts. It aims to dispatch multiple devices operating in different timescales to sectionalize the distribution system into self-supplied MGs and supply the critical loads continuously with reliable power. In the hour-ahead operation stage, switches, capacitor banks and energy storage charging/discharging decisions are optimized based on hour-ahead interval predictions of renewable energy generations and load demands. In the intra-hour operation stage, the output of distributed energy resources and static Var compensators are redispatched to compensate the hour-ahead operation decisions after the uncertainty realization. Compared with the existing methods, the proposed MG scheduling method can restore more critical loads and sustain secure operation under random renewable energy generation and load demand. In addition, to address uncertainties, the MG scheduling problem is modeled as a robust optimization model, which is decomposed into a master problem and a subproblem by adopting the column-and-constraint generation algorithm. Furthermore, the subproblem is reformulated via the disjunctive programming method to reduce the computational complexity. The effectiveness of the proposed method is verified on the modified IEEE test systems.

Mobile emergency generators (MEGs) are critical resources for distribution system restoration after disaster-induced outages. However, insufficient fuel storage can cause MEGs to cease operation, leading to secondary interruptions of restored services. To enhance supply resilience, we include fuel tank (FT) dispatch as part of the MEG-aid restoration strategy. An integrated sequential service restoration model is developed to optimize the spatiotemporal travel behavior of MEGs and FTs, restoration paths, and load pickup sequences in the distribution network. To account for uncertain distribution line faults and traffic congestion, a stochastic programming approach is used. The proposed method optimally prepositions MEGs and routes them to target locations to restore critical loads by gradually forming microgrids. Moreover, the FTs in the transportation network are scheduled to ensure adequate fuel for the uninterrupted and reliable operation of MEGs. The presence of both uncertainty and discreteness presents computational challenges to the stochastic mixed-integer programming model. Thus, a distributed algorithm that combines the progressive hedging and Frank-Wolfe methods is applied to enhance computational efficiency while ensuring global convergence. Simulation results showed the effectiveness of the proposed method in improving the reliability of restoration schemes and computational efficiency.

Microgrid formation (MF) is a core solution for increasing the resilience of distribution systems in extreme situations. However, a significant power imbalance at the MF onset will result in the violation of dynamic frequency constraints, especially in low-inertia wind power penetrated distribution systems (WPP-DSs). To ensure the secure MF after emergencies, this paper proposes a frequency constrained proactive scheduling method for WPP-DSs. The primary frequency response (PFR) model is proposed to describe the microgrid frequency dynamics after islanding, where wind turbines are deloaded to provide a primary reserve. Then the PFR model is incorporated into the scheduling model to ensure frequency security during MF process. The proposed method proactively dispatches controllable units to mitigate the power imbalance and to reserve power for frequency regulation. After emergencies, the primary reserve is released, and adaptive microgrids are securely formed to sustain critical services. The PFR model is formulated as algebraic differential equations (ADEs), which makes it difficult to solve the model directly. Thus, the PFR model is discretized into difference equations and further linearized to facilitate solution. Simulation results validate the merits of the proposed method in reducing the conservatism of proactive scheduling strategies and improving the microgrid security during MF process.