On the Construction of Linear Approximations of Line Flow Constraints for AC Optimal Power Flow

The AC optimal power flow problem is a non-convex optimization problem that is difficult to solve quickly and reliably for large-scale grids. While various approximations have been proposed, they may lead to physically meaningless solutions. This paper presents a computationally efficient algorithm for constructing accurate linear approximations of line flow constraints. These approximations reduce the complexity of the optimization problem while ensuring that the solution is physically meaningful and has a high quality. The algorithm is based on an in-depth analysis of the feasible set of the line flow constraint. Numerical experiments are performed on ten large-scale systems using three nonlinear programming solvers. Obtained results indicate that the proposed formulation helps improve the solvers' reliability and reduce the computation time for hard large-scale problems. At the same time, the developed algorithm provides high quality approximations of the line flow constraints.