**3.3 Solar energy production** *Epaverage*

The average solar energy production *Epaverage* (kWh/year) follows Eq. (3).

$$Ep\_{average}(n, i, o) = \frac{\sum\_{1}^{n} G\_{average}(i, o) \times (\eta(n - 1) - \eta(n - 1).P) \times S \times PR}{n} \tag{3}$$

Where: *n*: 20 years

*Gaverage*(i,o): average global irradiation over a year depending on the tilt *i* and orientation o of the surface (kW/m<sup>2</sup> /year)

*η*: efficiency of a panel (%)

*P*: loss of yield of the panels over time (%)

*S*: total installed area (m<sup>2</sup> )

*PR*: performance ratio (%)

It is necessary to know the average irradiation over a year.

Solar irradiation is a radiometric quantity that measures the amount of solar energy received per unit area after considering atmospheric absorption and scattering. The measured value depends on the tilt of the sensor of the measuring device and its analysis spectrum. The irradiance will allow the calculation of the solar energy produced (kWh). This magnitude will depend, initially, on geographical locations, including the time of sunshine that will be different from one region to another (**Figure 7**), and the latitude, which will play on the path of the sun. For example, in Lille the irradiance for a horizontal surface is on average 1090 kWh/m2 /year, in Toulon 1612 kWh/m<sup>2</sup> /year, and in Limoges 1261 kWh/m<sup>2</sup> /year. The irradiance data come from the PVGIS software [9], which allows us to know the irradiance according to the geographical area in Europe and North Africa.

It will also vary according to the tilt and orientation of the surface. For example, in Limoges:

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


For Limoges, the most important irradiation is obtained for a tilt of 36°, full south with 1467 kWh/m2 /year on average (**Figure 8**).

Irradiation will also vary over time, daily (day/night, climatic variations) and monthly (seasonality) (**Figures 9** and **10**). Finally, it is never the same from one moment to another, from 1 day to another and from 1 year to another.

**Figure 9.** *Daily irradiation variation - 30° south in Limoges.*

**Figure 10.** *Monthly variation of irradiation - 30° South in Limoges.*

But the calculation of the solar production is not limited to the solar irradiation. It is necessary to know the characteristics of the panels with their yield, their loss over time and the total installed surface. Depending on the technologies and brands, all these parameters vary, ranging from a yield of 19–21% associated with loss of 0.25% per year to 0.55% per year depending on the panels (see **Table 3**).

The PR depends on the losses due to shading, wiring, inverters or microinverters, temperature and so on. According to the study [11], the average PR is 79% whether with microinverters or inverters regardless of the geographical area and the size of the installation. Variations in the PR are possible from 69–91%.

**Figure 11** shows the cumulative energy produced over 20 years as a function of the installed peak power. Depending on the panels presented in **Table 3**, the yield and its loss over time and the performance ratio (see **Table 4**), the energy produced will be more or less important. The two blue curves represent the maximum (meaning panels with the best performance ratio and yields) and the minimum (meaning panels with the worst performance ratio and yields) possible energy produced.

### **3.4 Feed-in tariffs Tvt**

For the calculation of the profitability, it is also necessary to know the feed-in price of the Tvt electricity, resold to a supplier. At least until September 2022, the feed-intariff, dictated by the CRE (Commission for the Regulation of Energy) in the total resale is 17.89 and 15.21 c€/kWh for installations below 3 and 9 kWp, respectively (**Table 5**). Over time, these feed-in tariffs have been decreasing every 6 months (**Figure 12**). For self-consumption with resale, the feed-in tariff is currently 10 c€/kWh for any installation below 9 kWp and has not changed since the beginning of self-consumption (**Figure 13**).

The feed-in tariff is fixed according to a 20-year locked-in contract with the supplier. It will not change over time for the individual once the contract is signed.

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



**Table 3.**

*The different characteristics of solar panels useful for profitability calculations [10].*

**Figure 11.**

*Extremum for the cumulative solar production over 20 years for an irradiation fixed at 1460 kWh/year (Limoges 30° south).*


#### **Table 4.**

*The different sources of variability of the solar production EPaverage.*

## **3.5 Energy tariff TH**

For self-consumption, the evolution of the price of electricity will have an impact on the profitability of the installation. In France, to summarize, it is possible to choose


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

#### **Table 5.**

*Data of the variables used for the profitability calculation. The example is for an installation in Limoges with panels arranged 30° south and average characteristics.*

**Figure 12.**

*Evolution of the electricity buy-back (orange curves) and of the state premium (blue curves) over the years for installations below 9 kWp in self-consumption.*

an off-peak/peak hour subscription or a basic subscription. The tariffs will be different according to the subscription and according to the time of the day with an off-peak/peak hour subscription.

According to the regulated tariffs of the CRE, the price of electricity has been increasing steadily for both subscriptions as shown in **Figure 14** with a much higher increase for off-peak hours than for peak hours.

**Figure 13.**

*Evolution of the electricity buy-back over the years for installations below 9 kWp in total resale. Until 2017, the blue and red curves are mixed.*

#### **Figure 14.**

*Evolution of regulated electricity tariffs in France according to the CRE for daytime (peak hours), nighttime (off-peak hours) and basic tariffs (same tariff all day).*

In self-consumption, it is preferable to choose off-peak hours HC – peak hours HP contract rather than the basic price because it is during the peak hours HP (most expensive rate) that the solar production will intervene.

The price of electricity is currently 0.1841 €/kWh in HP (between 6 h30 and 21 h30) and 0.1470 in off-peak (between 21 h30 and 6 h30). Please note that the off-peak/peak hours may vary slightly from one area to another.

In addition, for the last 10 years, the price of electricity has been rising steadily, generating an INFLA inflation of about 3%/year for the off-peak/peak hour rates (**Figure 14**).

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