Distributionally Robust Reliability Assessment for Transmission System Hardening Plan Under $N-k$ Security Criterion

Increasing the complexity of power transmission networks has led power systems to be more vulnerable to cascading failures. Thus, hardening and reliability assessment of such complex networks have become a must. In addition, the commonly used $N-1$ security criterion does not guarantee the reliability of the system against possible cascading failures. In this paper, given a hardening plan, we develop two models to evaluate the reliability of the power transmission system under $N-k$ security criterion. In the first model, we quantify the probability of no load-shedding in the system to assess the possibility of load curtailment. Then, to have a better insight of the amount of load-shed in the second model, we use the conditional value-at-risk as a risk measure to evaluate the reliability of the system. To perform reliability assessment, the information of contingency probabilities is required. However, such probability information is usually unknown and cannot be estimated precisely. Therefore, in this paper, we assume the probability of contingencies as unknown and ambiguous. Then, we construct an ambiguity set for the unknown probability distribution of contingencies. Our approaches are robust because they analyze the reliability of the transmission system with respect to the worst-case distribution in the ambiguity set. We formulate both models as bilevel programs and solve them using the Bender's decomposition technique. Finally, we conduct numerical experiments on 6-bus and IEEE 118-bus test systems to show the effectiveness of the proposed approaches.