Co-Optimizing Substation Hardening and Transmission Expansion Against Earthquakes: A Decision-Dependent Probability Approach

In light of the rising frequency and impact of natural hazards on power systems, planning resilient network investments is becoming increasingly important. This task, however, needs, in addition to widely accepted investment options focused on installing new infrastructure, explicit recognition of investment propositions to harden existing infrastructure such as substations. Hardening networks is fundamentally challenging to incorporate in optimization problems since it affects outage probabilities. Therefore, we propose an optimization approach to determine optimal portfolios of resilient network investments, considering endogenous probabilities that change with hardening investment options. This decision-dependent-probability model finds the optimal network enhancements in a cost-benefit fashion, minimizing investment plus operational costs, including demand curtailments. The proposed model also considers distributed energy resources (DER), which can displace costly network investments. Additionally, the model takes into account the lack of fully accurate fragility curves; thus, outage probabilities are not only affected by hardening decisions but also by the inherent uncertainty associated with fragility modeling. This is a key concern in practical resilience assessment and is addressed in this work through a global-convergent exact algorithm. Case studies applied on earthquakes in Chile demonstrate the benefits of our proposed network planning approach.