*2.1. Power System*

Frequency regulation based on droop speed control can be divided into two consecutive control actions: frequency containment and frequency restoration. On the one hand, frequency containment (or primary frequency regulation), which is based on the governor control, adjusts the active power of the generation units to correct frequency variations. In fact, the frequency nadir is directly related with the generator's droop characteristic. In Spanish electric power system, primary regulation services act up to 30 s after a frequency disturbance [62]. On the other hand, frequency restoration (or secondary frequency regulation) refers to the AGC, adjusting the active power output of generation units to bring system frequency back to its rated value after the governor-based primary response.

An aggregated inertial model is commonly used to analyze frequency deviations in isolated power systems [63]. This modeling approach has been previously applied in El Hierro isolated power system (another isle of the Canarian archipelago) in [64]. Therefore, frequency deviations are the result of the imbalance between the power supplied by the generation units and the power demand:

$$f\frac{df}{dt} = \frac{1}{T\_{m,ther}(t)}(p\_{ther} + p\_w - p\_{dem} - D\_{net}\,\Delta f),\tag{1}$$

where *Tm*,*ther*(*t*) corresponds to the total mechanical inertia of thermal units depending on the number of generation operating units at each moment. Note that only thermal units provide inertia to the power system, since VSWTs are decoupled from the grid through power inverters.

When frequency disturbances are higher than certain limits, an under frequency load shedding scheme is activated to recover the grid frequency and fulfill certain frequency range requirements. In this work, a realistic load shedding scheme is included, consisting of the sequential and sudden disconnection of certain amount of load as established frequency thresholds are exceeded. The load shedding program can be found in [59].
