**4. Case Study—Results**

The VSWT adaptive control strategy proposed in this study is applied to the Gran Canaria power system. Gran Canaria Island belongs to Spanish Canarian archipelago, being thus an isolated power system. Its electrical generation has always been based on fossil fuels from two power plants: *Jinámar* and *Barranco de Tirijana* power plants. These power plants included diesel, steam, gas, and combined cycle units. However, in recent decades, the governmen<sup>t</sup> started to promote wind power plants' installation, doubling its capacity up to 180 MW since 2017. Table 1 lists each thermal unit capacity of the Gran Canaria power system.


**Table 1.** Gran Canaria thermal units power.

## *4.1. Scenarios under Consideration*

Thirty different generation mixes of supply-side programs are under study for different demands and wind power generation. The generation mix scenarios are taken from [59], where a unit commitment model was also included. Figure 7 presents the different supply-side energy schedule of each program. From these generation mix scenarios, two different imbalance conditions are defined: (i) the loss of the largest power plant and (ii) the loss of the second largest power plant. In this way, a total of sixty different scenarios are analyzed. Figure 8 summarizes the supply-side after the disconnection of the largest and second largest units. In addition, it also points out the percentage that represents the loss of each unit over the total system demand.

**Figure 7.** Generation mix scenarios under consideration.

**Figure 8.** Generation mix after disconnection (**a**) Largest power plant disconnection. (**b**) Second largest power plant disconnection.

#### *4.2. Decision Table Definition: Regression Analysis*

From the sixty scenarios presented in Section 4.1, the corresponding Δ*p* values are determined following Section 3. In this work, and according to the load shedding scheme presented in [59], *flim* = 49 Hz, *tlim* = 1 s and Δ*pinc* = 0.01 pu for the Gran Canaria island power system. A mathematical relationship between such Δ*p* and other variables of the power system need to be found. As aforementioned, [73] proposed to relate the power to be shed with the RoCoF by a linear and quadratic regression, with *R*<sup>2</sup> = 0.951 and *R*<sup>2</sup> = 0.969, respectively. However, both the linear regression and the quadratic regression of Δ*P* and RoCoF for this case study accounted for low values of *R*2: *R*<sup>2</sup> = 0.433 for linear regression and *R*<sup>2</sup> = 0.512 for quadratic regression. As a consequence, other variables are introduced in the proposed mathematical lineal regression. By also considering the electrical power of each thermal technology assigned in the scheduled program, the system synchronous inertia before the incident, and neglecting all those cases in which the estimated Δ*p* was Δ*p* = 0, the coefficient of determination increased to *R*<sup>2</sup> = 0.801 following Equation (4):

$$
\Delta P = -386.15 + 108.63 \cdot \text{RoCoF} - 1.32 \cdot P\_{\text{gas}} + 0.26 \cdot P\_{\text{dir}} + 0.65 \cdot P\_{\text{st}} - 0.42 \cdot P\_{\text{cc}} + 32.92 \cdot T\_{\text{m}} \tag{4}
$$

being Δ*P* in MW, RoCoF in Hz/s, *Pi* in MW (*i* stands for *gas*, *cc*, *die* and *st*), and *Tm* in s.

Comparing the results of Δ*P* obtained from the simulations and those estimated with Equation (4), two additional conditions were included:


Moreover, the maximum overproduction power Δ*P* of the wind power plant was considered as 20% over the installed capacity of the wind power plant, Δ*Pmax* = 0.2 · *Pw*.
