# Economic Analysis of Potential Secondary Use of Batteries from Electric Vehicles
## 3 Economic Analysis
### Input Parameters for the Calculation and 2 nd Life Battery Pricing
In case that the secondary use of batteries is applied and batteries from EV are used, the question arises: how to properly price these batteries. The calculated price will be paid to the owner of the EV (or dealer), who will reduce the cost of purchasing a new battery. This analysis will work with a slightly modified procedure from the team of authors from the source [22], there is a basic formula for pricing the 2 nd battery life:  
\[c_{2 nd\ life}\ =\ c_{new}\cdot k_{health}\cdot k_{demand}, \tag{1}\]  
where \(c_{2 nd\ life}\) is the price for 1 kWh of the battery from the EV (USD/kWh), \(c_{new}\) is the price for 1 kWh of a new battery (USD/kWh), \(k_{health}\) is the coefficient of the 2 nd battery life status <0; 1> (-) and \(k_{demand}\) is the demand coefficient of used batteries <0; 1> (-) [22]. Coefficient \(k_{demand}\) captures the current market demand for used batteries, which cannot be reliably calculated. [PERSON] et al. (2012) set this coefficient at 0.75, which will be used in this analysis, and a sensitivity analysis will be performed at the end [22]. The 2 nd battery life factor can be calculated as follows:  
\[k_{health}\ =\ \frac{PVB_{2 nd\ life}}{PVB_{new}}, \tag{2}\]  
where \(PVB_{2 nd\ life}\) is the present value of the theoretically possible supplied energy of the selected battery from the EV (kWh) and \(PVB_{new}\) is the current value of the theoretically possible supplied energy of a new battery (kWh) [22]. The current values are calculated as follows:  
\[PVB_{x}\ =\ \sum_{i\ =\ 1}^{n}\frac{(1+v)^{i}}{(1+r)^{i}}\cdot x_{i}, \tag{3}\]  
where \(n\) is the life of the battery (year), \(i\) is a year, \(x_{i}\) is theoretically supplied energy per year (kWh), \(r\) is discount cash (%) and \(v\) is the annual increase in the price of electricity (%). To determine the price of the 2 nd life of the battery, it was necessary to enter the following technical and economic input parameters for the calculation model (see Table 5). Figure 3: Battery degradation depending on mileage [20,21]. According to Damodaran's cash flow valuation, this cash discount (r) was chosen in energy production at 7.2% [23]. The annual increase in the price of electricity (v) was set at 3.1% based on historical data. Next, it was necessary to enter the DoD and charging voltage, which the model used to calculate the total number of batteries CCs. The power dependence of the DoD and the charging voltage on the total number of batteries CCs is used. Due to the use of a lower charging voltage, the model corrected the available battery capacity. After dividing the total number of cycles by the number of days in the year, the battery life (n) was obtained. For direct calculation, the DoD was set at 40% and the charging voltage at 4.1 V to increase battery life. Other input parameters include mileage and average EV power consumption, which help determine the residual capacity and remaining CCs of the 2 nd battery life. Due to the lack of data, it was not easy to determine the dependence of battery degradation on mileage. Therefore, the battery capacity in EV was fixed at 43 kWh, which corresponds to the weighted average of EV sold in the EU until mid-2019, and the dependence of degradation on mileage was also determined for this value. The battery in an EV is limited by its size and weight, so car companies set DoD to higher values at the expense of life. The computational model works with DoD in EV at 80%. Based on all these values, it was possible to calculate the total EV consumption and the number of CCs used. By back-calculation using the power dependence, the model calculated the remaining cycles of the 2 nd battery life at a DoD of 40% and determined the amount of degradation of the capacity of the 2 nd life battery. Due to these values, it is possible to determine the theoretically delivered energy per year (\(x_{i}\)) for the battery from EV. For a new battery, \(x_{i}\) is only calculated by multiplying the total battery capacity (43 kWh), DoD and correcting the capacity due to a change in charging voltage.