Optimally Linearizing Power Flow Equations for Improved Power System Dispatch

Abstract: Managing power grids with the increasing presence of variable renewable energy-based (distributed) generation involves solving high-dimensional optimization tasks at short intervals. Linearizing the AC power flow (PF) constraints is a standard practice to ease the computational burden at the cost of hopefully acceptable inaccuracies. However, the design of these PF linearizations has traditionally been agnostic of the use case. Towards bridging the linearization-application gap, we first model the complete operational sequence needed to implement optimal power flow (OPF) decisions on power systems and characterize the effect of PF linearization on the resulting steady-state system operation. We then propose a novel formulation for obtaining optimal PF constraint linearizations to harness desirable system-operation attributes such as low generation cost and engineering-limit violations. To pursue the optimal PF linearization, we develop a gradient-based approach backed by sensitivity analysis of optimization routines and AC PF equations. Numerical tests on the IEEE 39-bus system demonstrate the capabilities of our approach in traversing the cost-optimality vs operational feasibility trade-off inherent to OPF approximations.