Convex Polar Second-Order Taylor Approximation of AC Power Flows: A Unit Commitment Study

Modern mixed-integer quadratic solvers generally handle binary variables more efficiently than nonlinear mixed-integer solvers. This is relevant to the power system operation models as the unit commitment formulations typically contain a large number of binary variables. This paper investigates how to achieve the accuracy level close to the one of the exact nonlinear models, but by utilising convex models and solvers. The presented unit commitment model is based on a Taylor-series expansion where both the voltage magnitude and angle are quadratically constrained. To achieve high accuracy, the model takes advantage of the meshed transmission network structure that enables replacement of the quadratic inequality constraints that cause constraint relaxation errors with the linear equality constraints. Quadratic constraints to be replaced as well as the operating point parameters are determined based on the presolve. The first presented case study validates the model's accuracy and the convergence of the iterative algorithm, while the second is a non-iterative full unit commitment problem. Unit commitment results show superior accuracy and similar computation times to the existing quadratic formulations on one hand and faster computation times than the exact nonlinear polar formulation on the other.