Secure and reliable operation is one of the main challenges in restructured power systems. Wind energy has been gaining increasing global attention as a clean and economic energy source, despite the operational challenges its intermittency brings. In this study, we present a formulation for electricity and reserve market clearance in the presence of wind farms. Uncertainties associated with generation and line outages are modeled as different system scenarios. The formulation incorporates the cost of different scenarios in a two-stage short-term (24-hours) clearing process, also considering different types of reserve. The model is then linearized in order to be compatible with standard mixed-integer linear programming solvers, aiming at solving the security constrained unit-commitment problem using as few variables and optimization constraints as possible. As shown, this will expedite the solution of the optimization problem. The model is validated by testing it on a case study based on the IEEE RTS1, for which results are presented and discussed.