**3. Methods of calculation**

The profitability of a photovoltaic installation for the total resale follows Eq. (1):

$$Gain(n, i, o) = Ep\_{average}(n, i, o) \times Tvt - ID - \sum\_{n=1}^{20} ((IA)(n - 1) \times [1 + in]la2) \tag{1}$$

Where

*n*: the number of years, which is 20 years (time of the energy buy-back contract) *i*: tilt of the panels

*o*: orientation of the panels

*Ep*average: average energy produced over a year, starting from an average irradiation

*Tvt*: buy-back price of electricity in €/kWh

*ID*: initial investment in €.

*IA*: annual investment in €/year

**Figure 2.** *Self-consumption.*

*Infla2*: inflation of the annual investment price

The profitability of a photovoltaic installation for self-consumption differs slightly and follows Eq. (2):

$$\begin{split} Gain(n,i,o) &= \sum\_{n=1}^{20} \left( \tau\_{como} \times Ep\_{average}(n-1,i,o) \times THP(n-1) \times [1+in]la \right) \\ &+ \sum\_{n=1}^{20} \left( (1-\tau\_{como}) \times Ep\_{average}(n-1,i,o) \times Tvt \right) \\ &- \sum\_{n=1}^{20} ((IA)(n-1) \times [1+in]la 2)) - ID \end{split} \tag{2}$$

Where

*n*: the number of years, which is 20 years (time of the energy buy-back contract) *i*: tilt of the panels

*o*: orientation of the panels

*Epaverage*: average energy produced over a year starting from an average irradiation τself: self-consumption rate

*THP*: peak hour tariff in €/kWh

*Tvt*: feed-in tariff in €/kWh

*ID*: initial investment in €.

*IA*: annual investment in €/year

*Infla*: inflation of electricity

*Infla2*: Inflation of the annual investment price

The different parameters of the profitability calculation are explained in the following sections.

## **3.1 Initial investment ID**

The material selected for the realization of a photovoltaic project is essential. It must have the best quality/price ratio, guaranteeing an optimal yield for at least 20 years.

To sell the electricity to a supplier, it is mandatory that the installation is carried out by a certified company.

The installation will vary depending on the installers, the material, and the geographical area and follows a price range according to the following equations (see **Figure 3**):

Low range: 2.25-0.06\*kWp €/Wp

High range: 3.29-0.13\*kWp €/Wp

The price of the installation includes the solar panels, the inverters (inverters or micro-inverters), the decoupling relays, the cables, the protection boxes, the fixing kits, the transport, the labour, the security of the building site and the administrative procedures [6].

For example, an installation of 3 kWp of panels will cost the private individual with the installation by an approved installer and the price of the material between 6200 and 8700 €.

For the total resale, the connection fees of Enedis (Electricity Distribution System Operator) will be added. Prices vary according to the place of residence and the difficulty of connection. With a Linky meter, it is between 400 and 800 € and with the old meters between 1000 and 1400 €.

On the other hand, for self-consumption, mainly with resale of surplus, state bonuses are possible, ranging from 380 to 280 €/kWp depending on the power installed. *What is the Profitability of a Photovoltaic Installation in France for an Individual? DOI: http://dx.doi.org/10.5772/intechopen.109859*

#### **Figure 3.**

*High and low range of a photovoltaic installation in €/Wp according to the installed power in kWp in France.*


#### **Table 1.**

*The different sources of initial investment to be considered for the profitability calculation.*

#### All the initial investments are summarized in **Table 1**.

The price range of the initial investment as a function of the installed power, between the 2 blue curves (maximum and minimum investment possible according to **Table 1**) for the total resale or between the 2 red curves for self-consumption, is presented in **Figure 4**. The initial investment is more advantageous in selfconsumption because there is no need for connection to the grid and there is also a premium from the state.

#### **3.2 Annual investment IA**

In addition to the initial investment, there are annual charges.

There is the "tariff for the use of public electricity networks," or TURPE in French, created in 2000 to remunerate the electricity transmission network, Enedis and the local distribution companies [7]. It is currently 35.45 € including taxes/year for the total resale and 8.86 € including taxes/year for self-consumption with surplus resale (**Figure 5**). Since 2017, TURPE has changed very little over time and is cheaper for self-consumption.

**Figure 4.**

*Extremum for a starting investment ID for the total resale (blue curves) and self-consumption (red curves).*

The maintenance of the installation (panels, inverters) can also be a source of expense, but it is generally carried out by the individual himself for small installations.

It can also have an overpricing of the home insurance; this data depends on the insurance of each, the contract closures, and so on.

These annual fees are re-evaluated every year, resulting in INFLA2 inflation. Since the beginning of self-consumption in France, the TURPE for PV has not increased (**Figure 5**). As the maintenance and insurance tariffs are variable to the situation, it is considered here that the annual investment inflation INFLA2 is 0%.

The total annual investments are summarized in **Table 2**.

The price range for both full resale and self-consumption is shown in **Figure 6**. The blue curves represent the maximum and minimum price to be considered for the annual investment in the total resale and the red curves for self-consumption

**Figure 5.**

*Evolution of TURPE over the years, for the total resale (blue curves) and self-consumption (red curves).*

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


#### **Table 2.**

*The different sources of annual investment to be considered for the profitability calculation.*

#### **Figure 6.**

*Extremum for the cumulative annual investment IA over 20 years for total resale (blue curves) and selfconsumption (red curves).*

according to the possible variations in the TURPE, the price of insurance and maintenance. Taking the extremes, the price of the annual investment is one time cheaper in self-consumption due to the TURPE.
