**2. Methodology**

Our work aims to analyse if the generation patterns of PV+W hybrid facilities match better with the demand profiles than if the facilities were considered separately. We will not determine what would be the absolute coverage of electricity that the facilities could provide to the whole electric demand. This approach is like evaluating to what extent the generation and demand curves have the same "shape".

We propose the evaluation of the adaptation level by the determination of the matching factor (ε). It will be calculated as the average quadratic error between the electric generation patterns and the demand profiles, previously normalised and particularised for every single location under study, as will be detailed below. In this way, ε would be zero when the adjustment is perfect; it means, when the generation and demand curves have the same shape, and ε would rise to one when the di fference becomes higher. The proposed methodology to calculate ε is illustrated in Figure 2.

**Figure 2.** Methodology for obtaining the matching factor (ε) at a single location.

The calculation starts with the collection of hourly climate data representative of an average year in every single location included in the analysis. The data collected have been pressure p, temperature T, wind speed v and irradiation G. To generalise the results, it is essential to count on climatologic data for multiple locations spread around the Earth. With this data, together with the dimensioning and

characterisation of a PV+W hybrid facility, we obtain yearly patterns of the foreseen generation for every type of facility *Epvx* , *Epx* y *Epv*+*<sup>w</sup> x* .

Second, electricity demand profiles are required. To select the appropriate load profiles to be utilised in the calculation of the matching factor, it is required to quantify to what extent the hybrid facilities' generation would contribute to the country-level aggregated load. With this aim, first we have done a rough estimation of the amount of electricity that could be generated by hybrid facilities placed in an urban environment (buildings) in a scenario of high penetration, and, second, we have calculated the aggregated demand coverage on hourly basis. The hourly aggregated demand coverage was calculated by using Equation (1):

$$\text{Hourly agregated demand coverage} = \frac{\text{NB} \times \text{AB} \times \text{CF} \times \text{AHIC}}{\text{RHAD}} \tag{1}$$

where:


To have an estimate in different scenarios, the calculation of the hourly aggregated demand coverage was done for two regions (Europe and the United States) and a European country (Spain) Table 2 shows the specifics of each region or country considered in the calculations.


**Table 2.** Region and country specifics for hourly aggregated demand coverage calculation.

Table 3 shows the hourly aggregate demand coverage of the hybrid facilities for different values of (i) *AHIC* and (ii) *AB*. To obtain conservative values, it was set up 50% of *CF* and limits of 15% for *AB* and 10 kW for the *AHIC*. The results show that shares around 10% of hourly aggregated demand coverage could be reached with moderated values of *AB* and *AHIC*. The hourly coverage might reach levels over 20% in more optimistic scenarios.

**Table 3.** Hourly aggregated demand coverage.


The level of coverage obtained should be considered in the managemen<sup>t</sup> of ancillary services and market operations. Based on the above, aggregated load profiles have been selected in the calculation of the matching factor.

The demand evolution presents a high dependency on the climate, the distribution of the working days and the consumer´s habits. One of the objectives of this study is to obtain results applicable globally. Hence, we have utilised multiple profiles to characterise the electricity consumption everywhere. The methodology here proposed includes the determination of 16 different hourly demand curve profiles, as shown in Table 4, distinguishing between (i) the Northern or Southern hemisphere, (ii) the year season and (iii) weekdays and weekends (bank holidays are included in the weekend day category). Based on the above, the demand profiles used in the calculation for every location will be the eight corresponding to the hemisphere where the location is placed.


**Table 4.** Hourly demand profiles.

As has been discussed before, our methodology is applied to quantify the adaptation degree of the generation to the aggregate demand (i.e., for a country) and not only to local demand where the facility is placed (household, garage, shopping centre, etc.). However, the absolute generation level of every facility, even the aggregation of a high number of them cannot be compared to the global, regional or national demand. We are, therefore, obliged to include in the methodology a mechanism to eliminate the scale effect from ε calculation. The way we propose here is to determine normalised patterns for both generation and demand profiles as follows:

	- • Method 1: By adding the individual PV and W (wind) normalised profiles:

$$
\epsilon\_x^{pv+w} = \epsilon\_x^{pv} + \epsilon\_x^w \tag{2}
$$

• Method 2: By dividing every hourly data into the maximum value of both facilities.

$$\epsilon\_{\mathbf{x}}^{\text{pv}+\text{uv}} = \frac{E\_{\mathbf{x}}^{\text{pv}+\text{uv}}}{\max\{E\_{\mathbf{x}}^{\text{pv}}, E\_{\mathbf{x}}^{\text{uv}}\}} \tag{3}$$

• Method 3: By dividing every hourly data into the daily maximum value of the hybrid facility.

$$\epsilon\_x^{pv+w} = \frac{E\_x^{pv+w}}{\max\{E\_x^{pv+w}\}} \tag{4}$$

These three methods to normalise the values of the hourly hybrid generation profiles do not pretend to have a physical sense by themselves. Our methodology is oriented to find out how the matching factor ε changes when the PV and wind facilities are considered together in a hybrid plant. With this aim, what is relevant to quantify this change is to evaluate it by using the results obtained with the same normalisation method.

Figure 3 shows, as an example, the normalised curves for one day in the period under analysis, where it can be seen:


**Figure 3.** One-day-example of the normalised generation and load profile evolution.

Once the normalised hourly patterns are determined, ε is calculated for every single location by following the next steps:


$$
\epsilon^i\_{\mathbf{x}, \mathbf{y}, D} = \frac{\sum\_{n^i\_{\mathbf{x}, \mathbf{y}}} \left[ l\_{\mathbf{x}, \mathbf{y}, D} - \epsilon^i\_{\mathbf{x}, \mathbf{y}} \right]^2}{n^i\_{\mathbf{x}, \mathbf{y}}} \tag{5}
$$

$$\varepsilon\_{x,y,E}^{i} = \frac{\sum\_{n\_{x,y}^{i}} \left[ l\_{x,y,E} - \varepsilon\_{x,y}^{i} \right]^2}{n\_{x,y}^{i}} \tag{6}$$

$$
\varepsilon\_{x,y}^i = \frac{5\left.\varepsilon\_{x,y,D}^i + 2\left.\varepsilon\_{x,y,E}^i\right|}{7} \tag{7}
$$

where:

• ε*i <sup>x</sup>*,*y*,*D* and <sup>ε</sup>*ix*,*y*,*<sup>E</sup>* are the matching factors in weekdays *D* and weekend days *E*, respectively, for the facility type *i*, placed at the location *x*, during the season *y*.

• *<sup>n</sup>ix*,*<sup>y</sup>* is the number of hours in the season *y* at the location *x*.


$$
\varepsilon^i\_x = \overline{\varepsilon^i\_{xy}} = \frac{\varepsilon^i\_{x,S} + \varepsilon^i\_{x,II} + \varepsilon^i\_{x,A} + \varepsilon^i\_{x,W}}{4} \tag{8}
$$
