Optimizing market clearing in security-constrained DCOPF using α, β-CROWN

In power systems, the power flow equations are fundamental mathematical formulations that capture the physics of electricity across the network. These equations describe how power flows from generators to loads while accounting for network constraints such as line impedances, voltage limits, and generator capacities. This study proposes a simplified power flow model for transmission, Direct Current Optimal Power Flow (DCOPF), to optimize market clearance under N-1 contingency conditions. The mathematical model incorporates constraint violations as penalties in the objective function, allowing formulation within PyTorch, a widely used machine learning library, alongside α, β-CROWN, a state-of-the-art Neural Network Verification tool.