In recent years, large investments have been made in wind power, and this trend is expected to continue in the coming decades. Integrating more wind power in the production mix offers great opportunities for the society, such as reducing greenhouse gas emissions and the dependence on foreign fuel. Large wind power penetration does, however, require changes in the way power systems are planned and operated. The power transfers across the electrical grid are determined by the load and the production. A secure operation of power systems requires that these power transfers stay within certain limits. Frequency control schemes are crucial for ensuring the balance between the electric demand and the production. They enable system operators to re-dispatch the production (for example via the activation of balancing bids) during real-time operations to follow the load variations. With wind power, these frequency control schemes must not only meet the variations of the load but also those of the wind. An optimal use of the frequency control reserves would allow system operators to operate the system in the most cost effective and secure manner, that is, using the cheapest available resources while taking into account the stability limits of the system and the uncertainty. With no wind power, the load is the main source of uncertainty, and it can be forecasted accurately. This enables system operators to dispatch the generation in the most cost-effective way to meet the load while keeping the system within its stability limits. Adding wind power to power systems, on the other hand, introduces a new source of uncertainty on the production side, which is more difficult to forecast. The tools used today for computing the stability limits and operating the system do not consider the whole range of possible future load and wind power production levels, but only pick a few likely values in this range. In this work, we propose a new approach which accounts for the whole uncertainty in the load and wind power, and gives the optimal re-dispatch which ensures a given level of system security given this uncertainty. The approach is a so-called Stochastic Optimal Power Flow (S-OPF) formulation, developed in the scope of this project for the optimal activation of balancing bids. It is a nonlinear optimization problem with one probabilitistic constraint ensuring a certain level of system security -- computed as the probability that the system stays within its stability limits -- and whose objective function is the minimization of the generation re-dispatch. Compared to what is done today, the S-OPF formulation enables system operators to consider the uncertainty when making decisions. An approximation of the proposed S-OPF formulation is developed to render the problem tractable. In particular, the stability boundary, defined as the set of stability limits, is approximated by second-order approximations. The accuracy of these second-order approximations are analyzed in the IEEE 9 bus system by computing the distance between the actual boundary and its approximation. The S-OPF problem is then solved in the IEEE 39 bus system using the approximated stability boundaries. Monte Carlo simulations are run in order to assess the accuracy of the approximation and check whether the optimal solution of the approximation does ensure the specified level of system security. / <p>QC 20121121</p>