## 2 Calculation Methodology of the PVCS Global Cost
### Maintenance Costs
#### 2.2.1 Replacement Cost  
The replacement cost corresponds to the expenses incurred for the renewal of components reaching the end of their life. Since the analysis period is 30 years, the aging of the concrete and steel infrastructure, or of the building on which the system is deposited, is not considered. The components to be replaced concern the PVCS energy chain, such as charging terminals, stationary batteries, and inverters. These elements must be replaced because their lifespan is shorter than the analysis period (30 years). At the end of this period, a new investment must be made by the owner of the PVCS. The cost quantified below corresponds to the redemption prices of the various components and includes the purchase and the installation of the material, excluding taxes. A lifespan of 30 years is considered for the PV panels. This lifespan is thus estimated because the manufacturer's warranty states that the efficiency of the panels will be greater than 80% of the initial efficiency after 25 years. The assumption was therefore made that the panels are generally still usable 5 years after the end of this warranty. Since the overall cost analysis period is 30 years, there will be no replacement cost for the PV panels. Inverter  
It is considered that one inverter is installed on the PVCS. An inverter has an average lifespan of 15 years [23]. As the analyzed period is 30 years, a replacement will be necessary for this component. The replacement number of the inverter \(r_{inv}\) can be calculated using Equation (13) according to the analysis period in years (\(q\) = 30 years) and the lifespan of the inverter \(q_{inv}\):  
\[r_{inv}=\frac{q}{q_{inv}}-1 \tag{13}\]  
Then, to obtain the replacement cost of the inverter \(C_{repl,inv}\), the following equation will be used:  
\[C_{repl,inv}=C_{repl,inv,un}\cdot P_{p}\cdot r_{inv} \tag{14}\]  
where \(C_{repl,inv,un}\) is the unit replacement cost of the inverter in \(\epsilon/\text{kWp}\) and \(P_{p}\) is the total installed power in kWp. \(C_{repl,inv,un}\) includes the purchase of materials and the manpower of the installation of the inverter. The replacement cost of the stationary storage installed on the PVCS is estimated in this section. With a lifespan \(q_{bat}\) of 10 years and during 30 years as the analysis period, two replacements will be necessary for the stationary batteries. The number of replacements \(r_{bat}\) of the batteries can be expressed using the equation below:  
\[r_{bat}=\frac{q}{q_{bat}}-1 \tag{15}\]  
To obtain the replacement cost of the battery, the following equation will be used:  
\[C_{repl,bat}=C_{repl,bat,un}\cdot C\cdot r_{bat} \tag{16}\]  
where \(C_{repl,bat,un}\) is the unit replacement cost of the lithium-ion battery in \(\upxi\)/kWh, including the purchase of materials and the manpower of the installation. In this section, the method used to calculate the cost of replacing the charging terminals installed on the PVCS is detailed. As a reminder, two types of charging terminals are considered: the fast terminals placed on the ground and delivering a maximum power of 22 kW, and the slow terminals, which are suspended on a wall or pole and deliver a maximum power of 2.3 kW. Since there is no information about the lifespan of the charging terminals (this technology is very recent), a change every 10 years is considered for both types of charging terminals. As the analysis period is 30 years, two replacements will be necessary for these components. This value can be calculated using Equation (17), where the lifespan of the charging terminal \(q_{ter}\) is 10 years:  
\[r_{ter}=\frac{q}{q_{ter}}-1 \tag{17}\]  
Then, to obtain the replacement cost of the charging terminals of 2.3 kW and 22 kW, the following equations will be used:  
\[\left\{ \begin{array}{l}C_{repl,ter,slow}=C_{ter,slow,un}\cdot N_{ter,slow} \cdot r_{ter}\\ C_{repl,ter,fast}=C_{ter,fast,un}\cdot N_{ter,fast}\cdot r_{ter}\end{array} \right.