This paper deals with the problem of reserve scheduling for power systems with wind power generation, and proposes a new set-up that incorporates an AC Optimal Power Flow (AC OPF) formulation. The AC OPF problem is nonconvex and in general hard to solve. Here we propose an approach building on convex relaxations of the AC OPF problems and discuss a modification that we believe has certain advantages when combined with the reserve scheduling formulation. Numerical simulations suggest that the proposed relaxation technique results in a feasible solution for the exact problem. Using the proposed modification of the AC OPF problem, we focus on systems with uncertain generation and formulate a chance constrained optimization problem to determine the minimum cost of production and reserves. Due to the complex structure of the resulting problem, we use a heuristic procedure to solve it numerically. This is achieved following a sampling based methodology. The proposed algorithm is applied to the IEEE-30 bus network and is compared against its DC power flow counterpart by means of Monte Carlo simulations.