Abstract-In several countries, the wind power penetration increased tremendously in the last years. As the current wind turbines do not participate in frequency control nor reserve provision, this may compromise the proper functioning of the primary control and the provision of power reserves. If no actions are taken, increasing levels of wind penetration may result in serious problems concerning the stable operation of the power system. This paper focuses on the provision of power reserves by wind turbines. For this service, the constant power control strategy is chosen as control strategy, as it gives a constant power output and has the ability to provide power reserves. In this way, the wind turbine behaves more like a conventional power plant. The choice of the power reference value is crucial as it determines whether or not a stable operation of the wind turbine is possible and power reserves can be provided. In this paper, an algorithm is proposed to obtain the range of possible reference values. By means of simulations, the optimal reference value to provide power reserves with a single wind turbine is obtained. Also, reserve provision in a wind farm is investigated. It is shown that the provision of power reserves with wind turbines using the constant power strategy is possible, especially in wind farms.