The transition to green energy is reshaping the energy landscape, marked by increased integration of renewable energy sources, distributed resources, and the electrification of other energy sectors. These changes challenge grid security, particularly regarding the N-1 security criterion, a crucial factor in preventing blackouts. Furthermore, climate change is contributing to the growing frequency of extreme weather events, which constitute the second major cause of blackouts. As grid complexity keeps on increasing, the need for N-k security, where k lines fail simultaneously, and increased resilience against extreme weather events is becoming increasingly evident. This necessitates studying the security constrained optimal power flow (SCOPF) problem considering multiple line outages (N-k). Current methods exhibit poor scalability as k increases. In response to the challenge of limited scalability, this thesis proposes a constraint-driven machine learning approach to approximate N-k SCOPFs.

The proposed approach relies on the linearized direct current optimal power flow. The approach utilizes a neural network to map power system loads to generator setpoints. A feasibility restoration layer is employed to restore base case infeasible predictions. By incorporating line outage distribution factors (LODFs), all post-contingency flows are computed. The loss function utilized to train the neural network draws inspiration from the penalty function method. Lastly, a copula analysis computes joint outage probabilities for k \textgreater 1 enabling a probabilistic security assessment. The first academic contribution of this thesis is the development of a constraint-driven approach to approximate N-k SCOPFs considering all contingencies using LODFs. The second academic contribution is the formulation of a N-k risk based security criterion, providing an alternative to the current deterministic N-1 security criterion.

The approach shows promise in its ability to scale effectively to N-k contingencies. Using LODFs, the approach effectively computes all post-contingency flows for up to k = 3. Moreover, case studies show the constraint-driven approach's effectiveness in identifying violating post-contingency cases, with up to 173$\times$ speedups and close to optimal dispatch costs. However, the consideration of N-k contingencies holds combinatorial complexity, and more efficient methods need to be developed for the computation and storage of all LODFs, and for the computation of all post-contingency flows. Additionally, the proposed constraint-driven approach can not enforce any post-contingency constraints, necessitating post-contingency feasibility checks when security against specific contingencies is required. Next, by incorporating probabilities, the approach shows promise in improving power systems security and resilience, but further research is necessary.

In this thesis, only line outages are considered. In the future, the approach could be modified to additionally account for other equipment outages (e.g. generator outages). Furthermore, future research could investigate the adoption of this approach in corrective control settings, where it is employed in the restorative phase of a contingency event. Another suggestion is centered around the incorporation of graph neural networks in the proposed approach, which could provide a more scalable alternative to fully connected linear neural networks. Furthermore, more scalable methodologies could be explored to construct the matrix containing all LODFs, and a more scalable methodology for computing all post-contingency flows could be developed. Finally, future work could investigate how to utilize the proposed approach under varying conditions like network topology changes or changing outage probabilities.