AC transmission system planning choosing lines from a discrete set

Transmission system planning (TSP) is a difficult nonlinear optimization problem involving non-convex quadratic terms, as well as discrete variables. We extend prior results for linear relaxations, drawing on a preliminary notional model of the power grid for the State of Florida. Realistic line choices necessitate a binary formulation, which is at the same time substantially more expensive than the mixed-integer counterpart and more accurate. In many cases, our relaxation directly generates a feasible solution; where it does not, we apply a practical load-deflation heuristic to recover strong solutions.