*3.1. Sensitivity Analysis*

It is mandatory to check if the methodology here proposed would give stable results in case of the variation of the relevant variables considered in the calculations. The technical characteristics of the facilities, as well as the performance parameters of the equipment, are quite steady and will be under control with adequate maintenance. The more relevant variations can arise from (i) deviations or errors in the evaluation of the solar and wind resource at the location or the use of non-optimised facilities (i.e., tilt or azimuth angles of the PV facility different from the ideal) and (ii) different power capacity of the facilities. In this way, to determine the robustness of the methodology two sensitivity analyses were carried out with respect to those variables.

#### 3.1.1. Sensitivity Related to Errors in the Resource Valuation

To evaluate the variations in the valuation of the resource produced by errors, spatial smoothing effector the installation of the facilities (non-optimisation), the electricity generated is calculated by means of a modification of the Formulas (9) and (10) to include the multiplying factors *fpv* and *fw* to simulate the variation of the solar irradiance and wind resource. The methodology was applied for a wide variation range of the multiplying factors between 0.7 to 1.3 which represents a variation of ±30% in the renewable resources.

$$E\_{\rm x}^{\rm pv}(f\_{\rm pv}) = f\_{\rm pv} \cdot G\_{\rm x'} A \cdot \rm P \cdot P \cdot \eta \cdot \left[1 + \alpha (T\_{\rm x} - 293)\right] \tag{12}$$

$$E\_x^w(f\_{\rm tr}) = \rho \cdot \frac{P\_x(f\_{\rm tr})}{\rho\_{\rm std}} \cdot t \tag{13}$$

The variation of ε*PV*+*<sup>W</sup>* with the multiplication factors is illustrated in the Figure 14. As it can be shown, the methodology is robust because:


**Figure 14.** Variation of ε*PV*+*<sup>W</sup>* with the multiplication factors *fpv* and *fw*. (M1, M2 and M3 represent the results obtained by means of application of the normalisation methods 1, 2 and 3, respectively).

3.1.2. Sensitivity Related to the Power Capacity of the Facilities

We applied the methodology considering generation patterns of a PV+W hybrid facility with twice the power capacity of the facility previously considered to evaluate the potential variations in the results produced by changes on the installed power capacity of the wind and PV facilities. The solar panel and VAWT used now have the following characteristics:

1. A commercial solar panel manufactured with multi-crystalline silicon cells and an efficiency η of 17.5%. The rest of the solar panel characteristics are shown in the Table 9.


**Table 9.** Solar panel characteristics [85].

2. For the wind facility, a vertical-axis wind turbine generator was selected with a nameplate power capacity of 6 kW (similar to the PV facility capacity). Figure 15 shows the VAWT power curve for standard density (ρstd = 1.225 kg/cm2).

**Figure 15.** Power curve for the standard air density ρstd = 1.225 kg/cm2. Source [86].

Figure 16 illustrates the comparison of the matching factor for PV+W hybrid plants ε*PV*+*<sup>W</sup>* versus PV ε*PV* obtained for facilities with a power capacity of 3.6 kW and 6 kW. In a global context, the adaptation obtained for the 6 kW facility is 19% higher for the method 1, 15% higher for the method 2 and 13% for the method 3. When it is compared with the 3.6 kW, the improvement of the 6 kW facility is higher in all the climate areas.

**Figure 16.** Improvement of the matching factor: ε*pv*+*<sup>w</sup>* (hybrid) over ε*pv* (PV) facilities for different installed power capacity.

The matching factor for the PV+W hybrid ε*PV*+*<sup>W</sup>* versus wind facilities ε*<sup>W</sup>* obtained for the facilities of 3.6 kW and 6 kW is compared in Figure 17. As was obtained for the 3.6 kW facility, the improvement of the matching factor obtained for the 6 kW facility is better when it is compared with the wind facility than when it is compared with the PV facility. The improvement now reaches 32% for method 1, 28% for method 2 and 27% for method 3. The values maintain quite similar ranges in all the climate areas.

The variation of ε*PV*+*<sup>W</sup>* with the multiplication factors introduced in the Chapter 3.1.1. for the 6 kW PV+W hybrid facility is illustrated in the Figure 18. As it can be shown, for the new capacity the methodology also presents a robust performance because the results hardly vary with changes of

the irradiation for the three normalisation methods. Once again, the effect of variations in the wind resource is quite limited.

**Figure 17.** Improvement of the matching factor: ε*pv*+*<sup>w</sup>* (hybrid) over ε*<sup>w</sup>* (wind) facilities for different installed power capacity.

**Figure 18.** Variation of ε*PV*+*<sup>W</sup>* with the multiplication factors *fpv* and *fw*. in a 6 kW power capacity facility (M1, M2 and M3 represent the results obtained by means of application of the normalisation methods 1, 2 and 3, respectively).
