We formulate mixed-integer conic approximations to AC transmission system planning. The first applies lift-and-project relaxations to a nonconvex model built around a semidefinite power flow relaxation. We then employ a quadratically constrained approximation to the DistFlow equations in constructing a second-order cone model that is convex without relaxation. We solve mixed integer linear and second-order cone programs using commercial software and assess their performance on two benchmark problems. As with DC power flow models and linear AC relaxations, the new models usually produce solutions which are infeasible under the original constraints. However, they are nearer to feasibility, and therefore represent stronger alternatives.