Second-Order-Cone Formulations of Power Flow for Topology Optimization

Optimization problems that involve topology optimization in scenarios with large scale outages, such as post-disaster restoration or public safety power shutoff planning, are very challenging to solve. Using simple power flow representations such as DC power flow or network flow models results in low quality solutions which requires significantly higher-than-predicted load shed to become AC feasible. Recent work has shown that formulations based on the Second Order Cone (SOC) power flow formulation find very high quality solutions with low load shed, but the computational burden of these formulations remains a significant challenge. With the aim of reducing computational time while maintaining high solution quality, this work explores formulations which replace the conic constraints with a small number of linear cuts. The goal of this approach is not to find an exact power flow solution, but rather to identify good binary decisions, where the power flow can be resolved after the binary variables are fixed. We find that a simple reformulation of the Second Order Cone Optimal Power Shutoff problem can greatly improve the solution speed, but that a full linearization of the SOC voltage cone equation results in an overestimation of the amount of power that can be delivered to loads.