Long Solution Times or Low Solution Quality: On Trade-Offs in Choosing a Power Flow Formulation for the Optimal Power Shutoff Problem

The Optimal Power Shutoff (OPS) problem is an optimization problem that makes power line de-energization decisions to reduce the risk of igniting a wildfire, while minimizing the load shed of customers. This problem, with DC linear power flow equations, has been used in many studies in recent years. However, using linear approximations for power flow when making decisions on the network topology is known to cause challenges with AC feasibility of the resulting network, as studied in the related contexts of optimal transmission switching or grid restoration planning. This paper explores the accuracy of the DC-OPS formulation and the ability to recover an AC feasible power flow solution after de-energization decisions are made. We also extend the OPS problem to include variants with the AC, Second-Order-Cone, and Network-Flow power flow equations, and compare them to the DC approximation with respect to solution quality and time. The results highlight that the DC approximation overestimates the amount of load that can be served, leading to poor de-energization decisions. The AC and SOC-based formulations are better, but prohibitively slow to solve for even modestly sized networks thus demonstrating the need for new solution methods with better trade-offs between computational time and solution quality.