This paper deals with control of variable speed wind turbines, which provide frequency support through temporary overproduction. In particular, it determines the optimal profile of power extraction among multiple generators in order to minimize the total loss of efficiency, while allowing for a prescribed increase in generation. Starting with the simplifying assumption of unconstrained generated/supplied power for the single turbine, the scheduling is characterized as the solution of an optimal control problem. On the basis of this result, a heuristic control strategy is proposed for the case of turbines with limited power output, investigating under which conditions this choice achieves optimality. Using a similar approach, the problem of energy recovery is also considered, calculating the optimal power profiles that bring back the turbines to their working point of maximum efficiency after having provided frequency response.
De Paola, A., Angeli, D., & Strbac, G. (2016). Scheduling of Wind Farms for Optimal Frequency Response and Energy Recovery. IEEE Transactions on Control Systems Technology, 24(5), 1764-1778. https://doi.org/10.1109/TCST.2016.2514839