**3.6 Self-consumption rate** *τself*

The self-consumption rate is the proportion of energy directly consumed on site. This parameter is only useful for calculating the profitability in self-consumption.

The annual self-consumption rate *τself* follows Eq. (4).

$$\tau\_{\text{self}}(i, o) = \frac{\text{Production} \,\text{consumed} \,\text{site}}{\text{Total production}} = 1 - \frac{\text{Surplus}(i, o)}{\text{Total production}(i, o)} \tag{4}$$

Where

$$Total production(i, o) = Epaverage(i, o)\tag{5}$$

$$Surplus(i, o) = \sum\_{1 \le i \le r} (Ep(i, o) - consumption) \tag{6}$$

The surplus being the moment when the production is higher than the consumption (Eq. 6).

For the calculation of surplus, it is necessary to know the consumption and production or by substitution the irradiation (Eq. 5), at an identical time scale and the shortest possible time to have a rate of self-consumption as realistic and accurate as possible.

To try to take at best the consumption variabilities, the Linky communicating meter will allow to recover the consumption data and thus the load curves by semihourly steps. For the example of the profitability calculation of this article, the load curve recovered is for an all-electric household (water heater, electric heating) of four people and 100 m<sup>2</sup> , in the countryside near Limoges, for the year 2019 with an average consumption of 15,000 kWh/year. The load curves are in red in **Figures 15**–**17**. Note that, for all other houses, the load curve will be completely different because it depends on the household appliances, the heating system, the insulation, the surface, the number of people, the habits of each person and so on.

#### **Figure 15.**

*Solar production for a 3 kWp installation at 30° south in 2019 in Limoges (yellow curve) and load curve in 2019 for a house of four people, all electric, in Limoges (red curve). The green curve represents the annual average of production over the year 2019.*

#### **Figure 16.**

*Zoom-in January solar energy for 2.84 kWp 30° South in Limoges in 2019 and load curve 2019 for a house of four persons, all electric, in Limoges.*

#### **Figure 17.**

*Zoom-in July solar energy for 2.84 kWp 30° south in Limoges in 2019 and load curve 2019 for a house of four persons, all electric, in Limoges.*

For the production variability, PVGIS [9] will give the irradiance for any location, tilt and orientation in Europe and North Africa following the calculation methods detailed in [12–15]. The SARAH [16] and ERA5 [17] data give irradiances in hourly steps from 2005 to 2020. To reduce the hourly step to a semi-hourly step, the values of SARAH (satellite passage at 00:00–1:00 - … ) and ERA5 (satellite passage at 00:30– 1:30 - … ) have been switched for the year 2019. The production curve for 3 kWp 30° south in Limoges is represented by the curves in yellow in **Figures 15**–**17**.

Moreover, the rate of self-consumption will vary according to the layout of the installation. Indeed, the surplus will be less important if the production is less and better adapted to the consumption curve. For example, the self-consumption rate is *What is the Profitability of a Photovoltaic Installation in France for an Individual? DOI: http://dx.doi.org/10.5772/intechopen.109859*

more important if the panels are oriented east rather than south (**Figure 18**) or if the installation is in a less sunny geographical area (**Figure 19**). Be careful that a higher self-consumption rate does not necessarily mean a higher yield (**Figure 20**).

#### **Figure 18.**

*Self-consumption rate according to the installed power according to different tilts (30° and 60°) and orientations (south or east) for the city of Limoges and for a typical consumption of a house of 100 m2 for 4 persons with electric heating.*

#### **Figure 19.**

*Self-consumption rate according to the installed power for different cities (Limoges, Lille and Toulon) for installations inclined at 30° and oriented south and for a typical consumption of a house of 100 m<sup>2</sup> of 4 persons with electric heating.*

**Figure 20.**

*Self-consumption rate according to the installed power separated in two seasons, summer (from April to September) and winter (from October to March), for the city of Limoges and for a typical consumption of a house of 100 m<sup>2</sup> for four persons with electric heating.*
