Reliable and resilient network design with distributionally robust optimization

Abstract

Transmission expansion models, so far, have not recognized properly the limited data and knowledge associated with the underlying process behind the realization of system contingencies. Therefore, investment in new transmission assets has traditionally been decided by models that either overlook the likelihood of different system outages, or assume perfect knowledge on their probability distribution, which can lead to non-optimal decisions. In this context, this work contributes with the development of two models. The first one proposes a distributionally robust approach to network security in order to acknowledge the ambiguity on reliability information, and analyzes the contribution that distributed energy resources (DER) can make to network security, potentially releasing latent capacity of existing transmission assets. To do so, a two-stage optimization model is developed, where the first stage determines the transmission expansion plan and the scheduling of post-contingency services, while the second one minimizes the expected cost of corrective actions. The second model is a two-stage mathematical program that determines the optimal portfolio of resilience enhancing strategies to harden the grid against earthquakes, considering the costs of investment, operation, and the costs of different contingency scenarios the system can undergo. To deal with the limited information regarding outage likelihoods during earthquakes, it minimizes against the worst-case probability distribution within an ambiguity set. However, since it is of great importance to assess the benefits of substation hardening, this ambiguity set depends on the decision taken. Through a number of quantitative assessments obtained by running the first model, this work demonstrates both the benefits of security services provided by DER, and the advantages of the proposed distributionally robust approach against alternative n-1 security and fixed probabilities (stochastic) solutions. Showing that, while the n -1 approach significantly undermines the value of DER in displacing network capacity, the fixed probabilities counterpart is too optimistic. Through the second model, we show that it is critical to consider the possibility of investing on substation hardening in order to determine the optimal array of measures to hedge the system against earthquakes, and that overlooking them may yield to unnecessary investments on new network infrastructure.