**5. Conclusions**

This article presents a developed detailed mathematical approach to study and perform sensitivity studies for the capability of different technologies to provide FCP in different grid conditions. This method allows design of the droop for different technology providing FCP in a power system operating within certain range of inertia. The proposed mathematical approach has been validated on simulated CE network.

Several simulations and comparative studies between FCR provision from conventional generators and WTs have been performed and analyzed in a generic power system with large penetration of WTs in order to study the impacts of droop settings and system inertia. The proposed analytical approach provides a feasible range of droop settings for different values of system inertia.

The results show that providing FCP can become challenging for large disturbances, especially in low inertia systems. The availability of adequate volume of FCR is necessary but not sufficient condition for frequency stability. It has also been observed that time to reach peak response is independent of the size of the disturbance. Furthermore, it has been noticed that the system frequency oscillates

sinusoidally with an exponential decay following a large disturbance and that the exponential decay depends on attenuation and damping ratio. Attenuation and damping ratio are independent of size of disturbance and dependent on inertia constant and droop.

The results of this work can be used as a starting base for additional sensitivities studies such as ramp rates and measurement delays and studying future power system scenarios, when the technologies become more flexible.

**Author Contributions:** Conceptualization, K.D.; Formal analysis, K.D.; Investigation, K.D.; Methodology, K.D.; Resources, K.D. and M.A.; Supervision, M.A., A.D.H. and P.E.S.; Writing—original draft, K.D.; Writing—review & editing, A.D.H. and P.E.S.

**Funding:** This research received no external funding.

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