Stochastic Planning for Power Distribution System Resilience Enhancement Against Earthquakes Considering Mobile Energy Resources

Earthquakes, which are high-impact low-probability extreme events, can cause severe damage to electrical infrastructure. This article studies the stochastic planning of resilient power distribution systems (PDSs) against earthquakes. Specifically, the portfolio of resilient measures including hardening distribution lines (DLs), and investing Mobile Emergency Generators (MEGs) and Mobile Energy Storage Systems (MESSs) are investigated in a stochastic environment. A stochastic spatial seismic damage model is developed to geographically characterize the random damages of earthquakes. Based on the stochastic model, the PDS planning problem is formulated as a risk-averse two-stage stochastic bi-level programming problem. The upper-level minimizes the total investment cost and the expected interruption cost. The lower-level minimizes the expected loss of load through MEG and MESS coordination, including co-allocation and energy exchange. To solve this problem, a scenario aggregation method based on graph theory and community detection is proposed to reduce the size of scenario set, and an endogenous uncertainty relaxation method is developed to address the DL hardening decision-dependent uncertainty. Then, the PDS planning problem with minmax form is reformulated into a standard bi-level programming problem with minmin form. A decomposition method is also proposed to break up the problem into two separate sub-problems to speed up the computation. The effectiveness of the proposed PDS planning strategy against earthquakes is evaluated through case studies based on the IEEE 37-Node Test Feeder and the IEEE 123-Node Test Feeder.