**4. Results**

Starting from Eqs. (1) and (2) for total resale and self-consumption, respectively, as well as Eq. (3) for the average energy produced, the values of each variable are shown in **Table 5** and will be used for an example of profitability curve.

The values of the variables are chosen for a specific case, but they are adjustable according to the many parameters exposed in part III. The example here is for an installation in Limoges with panels placed 30° south and average characteristics of what is currently found. For self-consumption, the load curve is recovered for an allelectric household (water heater, heating) of four people and 100 m<sup>2</sup> , in the countryside near Limoges, for the year 2019 consuming an average of 15,000 kWh/year.

For any installed power from 1 to 9 kWp under the conditions of an irradiation of 1460 kWh/m<sup>2</sup> /year, self-consumption is more profitable, ranging from a gain over 20 years of 2500€ for 1 kWp to 14,500€ for 9 kWp. On the other hand, in the total resale of the installations, lower than 1 kWp is not profitable but can still generate gains of 11,500€ for 9 kWp (**Figure 21**). Consequently, the year from which the installation is amortized arrives well before (**Figure 22**) for self-consumption, approximately 12 years for any installed power against 15–16 years for the total resale on small installation and being able to go down to 12 years for a 9 kWp. On the other hand, the range of profitability for the same irradiation is large according to the variables. The curves of the extremes were obtained by starting from **Figures 4**, **6** and **11**. In the most pessimistic case, after 20 years of the contract, the installation will still not be amortized whatever the installed power and the typology of installation.

In addition, to compare the gain from solar production to a *Pfinancial* investment over several years, Eq. (7) is used.

*What is the Profitability of a Photovoltaic Installation in France for an Individual? DOI: http://dx.doi.org/10.5772/intechopen.109859*

#### **Figure 21.**

*Comparison of the gains reported by an installation after 20 years of the contract for different installed powers for total resale and self-consumption in Limoges disposed 30° south according to the average variables and their extremums.*

#### **Figure 22.**

*Comparison of the years from which the photovoltaic installation becomes beneficial for different installed powers for the total resale and self-consumption in Limoges disposed 30° south according to the average variables and their extremums.*

$$P\_{final} = \left[ \left( \frac{Gain(n, i, o) + ID}{ID} \right) \middle| \frac{1}{n} - 1 \right] \times 100 \tag{7}$$

The financial investment *Pfinancial* shows the interest rate that the initial investment would yield if it had been put in the form of an investment in percentage per year during the 20 years of the contract.

Contrary to the gain, for self-consumption, a small installation corresponds to a more interesting financial investment that can go in our example to an equivalent investment of 3% per year for 20 years for the individual (red curve in **Figure 23**). On the other hand, for total resale (blue curve in **Figure 23**), the larger the installation, the more interesting the investment becomes over 20 years.

**Figures 24**–**26** show, respectively, the 3 criteria of profitability (earnings, year of amortization and interest rate) for installations of 3 and 9 kWp in the total resale by starting again from the criteria of **Table 5**.

These curves allow us to show that the profitability in the total resale is more important for big installations and for higher irradiations, depending as well on the geographical zone or on the orientation and tilt of the installation. Examples of profitability have been placed according to geographical areas well exposed (Toulon and Lille) and according to orientations (east and south) and tilts (30° and 60°) of the different panels.

For self-consumption, **Figures 27**–**29** show the profitability according to the same three criteria (earnings, year of amortization and interest rate) as before for a 9 kWp photovoltaic installation. The higher the average irradiation over a year and the higher the self-consumption rate, the higher the profitability.

In the figures, different points have been placed corresponding to different geographical areas (Limoges, Lille or Toulon), orientations (south or east) and tilts (30° or 60°) of the panels and the consumption of the house according to an electric heating or not by making the hypothesis that the rate of self-consumption of a house

#### **Figure 23.**

*Comparison of the interest rates that an installation would earn after 20 years of the contract for different installed powers for the total resale and self-consumption in Limoges located at 30° south.*

*What is the Profitability of a Photovoltaic Installation in France for an Individual? DOI: http://dx.doi.org/10.5772/intechopen.109859*

#### **Figure 24.**

*Comparison of the gains reported after 20 years of the contract for installations of 3 and 9 kWp according to different irradiances corresponding to installations with different orientations, tilts, and geographical areas for total resale.*

#### **Figure 25.**

*Comparison of the years from which the photovoltaic installation becomes beneficial for installations of 3 and 9 kWp according to different irradiances corresponding to installations with different orientations, tilts and geographical areas for the total resale.*

#### **Figure 26.**

*Comparison of the interest rates that an installation would earn after 20 years of the contract for installations of 3 and 9 kWp according to different irradiances corresponding to installations with different orientations, tilts and geographical areas for the total resale.*

without electric heating was the same in the year as the rate of self-consumption of the summer part (**Figure 20**).

For example, an installation in self-consumption of 9 kWp, located in Limoges (center of France), inclined 30° and oriented south with a consumption of 15,000 kWh/year (a house with electric heating) corresponds to an average irradiation of 1460 *kWh/year and a rate of self-consumption of 30*.*8%. In this situation*, *the gain after 20 years* will be 14,250 €, allowing to make the installation profitable after 11 years and corresponding to an investment of about 2.63% per year over 20 years. For the same installation but with a consumption not using electric heating, the irradiation is the same, but the rate of self-consumption becomes weaker, of 21.3%. Thus, the profitability will be less because the gain will be 11,370 €, allowing us to make the installation profitable after 12 years and corresponding to an investment of about 2.09% per year over 20 years.

Also, the fact that the orientation and the tilt of the panels differ from the optimum (30° south) increases the rate of self-consumption but decreases the irradiation, not allowing us to have a more important profitability, quite the contrary.
