**5. Conclusions**

Due to the massive penetration of VSWTs, their contribution to frequency regulation has become a need. As isolated power systems have low synchronous inertia, VSWTs frequency control is even more required. Even though different control strategies for VSWTs have been proposed in the last decade, they usually imply important drawbacks in terms of efficiency, economic profits, and/or equipment wear. As a result, with the aim of reducing the mechanical stress of VSWTs providing frequency response, an adaptive control strategy is proposed in this work. Our approach is based on estimating the minimum overproduction power provided by VSWTs following a linear regression estimation. In this way, such overproduction power depends on some grid parameters (i.e., RoCoF, synchronous inertia, and assigned power of thermal units before the incident). The proposed controller is compared to a conventional fast power reserve strategy. The Gran Canaria isolated power system (Spain) is considered as case study, analyzing sixty representative imbalance scenarios. Results show that similar values for the power shed with the load shedding program are obtained with the two approaches. However, the new adaptive control reduces the VSWTs maximum torque variations and the speed variations (23% and 5% on average, respectively), in comparison to the conventional VSWTs frequency control strategy. This is due to the smoother transition from overproduction to recovery periods, which reduces the electrical and mechanical VSWT efforts. In addition, in 57% of the imbalance scenarios under consideration, VSWTs are not required to participate in frequency response. Thus, both electrical power and rotational speed are kept as constants (subsequently maintaining the torque). As a result, a longer life span is expected for the VSWTs electrical and mechanical components.

**Author Contributions:** Conceptualization, J.I.S.; Data curation, A.F.-G.; Formal analysis, G.M.-L.; Investigation, A.F.-G.; Methodology, J.I.S.; Resources, A.F.-G. and G.M.-L.; Software, A.F.-G.; Supervision, Á.M.-G. and J.I.S.; Validation, G.M.-L. and J.I.S.; Visualization, Á.M.-G.; Writing—original draft, A.F.-G. and G.M.-L.; Writing—review and editing, A.M.-G. and J.I.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partially supported by 'Ministerio de Educación, Cultura y Deporte' of Spain (ref. FPU16/04282) and by 'Ministerio de Economía y Competitividad', under the project "Value of pumped-hydro energy storage in isolated power systems with high wind power penetration" of the National Plan for Scientific and Technical Research and Innovation 2013–2016, gran<sup>t</sup> number ENE2016-77951-R.

**Conflicts of Interest:** The authors declare no conflict of interest.
