## 5 Methodology
### High-Voltage Battery Simulation Model  
The propulsion system for electric vehicles necessarily includes a power source system. Accordingly, this section introduces the applied high-voltage battery simulation model. The majority of electric vehicles manufactured in the present era continue to utilize lithium-ion battery packs [57]. The main reason for the use of this technology is that it is still the most readily available solution in the automotive industry. The accumulated expertise and knowledge derived from two decades to 25 years of prior consumer electronics utilization enables the effective and cost-efficient integration of lithium cells into vehicle systems [8]. The various cell layouts are typically arranged in systems with a voltage range from 400 to 800 volts. The specified voltage levels are sufficient to power a permanent magnet synchronous motor (PMSM) machine, a 12 V battery, and the remainder of the electronics over an extended period [58]. In the case of our particular vehicle, it is constructed on a 400 V system, yet its cell layout is completely different from the average battery design. Additionally, it was established based on a cell type that is distinct from the one used in the original design. In order to achieve optimal simulation results, we constructed a model of high-voltage batteries in vehicles. We applied battery packs with a generic battery model from the Simcape Toolset [59]. The input parameters of the battery block are those given in Table 2. The battery model currently in use does not incorporate the battery State of Health (SOH), which would be responsible for defining the maximum capacity of the battery [60,61]. Instead, assuming that we are referring to a vehicle that has not been driven much, for simplicity, we can determine the maximum available capacity in the current model without significant error, taking into account the data in the catalogue. The battery pack properties were validated through the examination of the open circuit voltage level of the pack and its capacity when connected to a 1000 W power consumer. Information about the battery is available on the Internet [62]. The I-Pace battery pack consists of a 1084p battery assembly layout. The vehicle is equipped with LGX N2.1 lithium-ion cells, as detailed in Table 2. The vehicle is equipped with 432 pcs of LGX N2.1 lithium-ion cells [63]. The characteristics of the simulated battery pack are illustrated in Figure 7.  
As illustrated in the diagram, if a 1000 W load is connected to the battery connectors, the battery can supply this load for approximately 90 h.  
\[t_{Battery}=\frac{E_{Battery}}{P_{Load}} \tag{16}\]  
\[t_{Battery}=\frac{90\text{ kWh}}{1000\text{ W}} \tag{17}\]  
\[t_{Battery}=90\text{ h} \tag{18}\] \begin{table}
\begin{tabular}{l l} \hline
**Battery Information** & **Data** \\ \hline Nominal voltage & 3.6 V \\ Maximal voltage & 4.2 V \\ Cut-off voltage (25–0 \({}^{\circ}\)C) & 2.75 V \\ Nominal capacity & 60 Ah \\ \hline \end{tabular}
\end{table} 
Table 2: LGX N2.1 Cell information The diagram demonstrates that the nominal voltage of the battery is 388 V, which is comparable to the value that can be derived from the cell data. \[Vcell_{nom}=3.6\;\mathrm{V} \tag{19}\]  
\[Vpack_{nom}=Vcell_{nom}*108 \tag{20}\]  
\[Vpack_{nom}=388.8\;\mathrm{V} \tag{21}\]  
By employing the aforementioned methodology, the maximum voltage of the pack can be determined:  
\[Vpack_{max}=453.6\;\mathrm{V} \tag{22}\]  
\[C_{pack}=C_{cell}*4 \tag{23}\]  
\[C_{pack}=60\;\mathrm{Ah}*4 \tag{24}\]  
\[C_{pack}=240\;\mathrm{Ah} \tag{25}\]  
By combining the capacity in ampere-hours (Ah) with the voltage, it is possible to calculate the energy in kilowatt-hours (kWh). \[E_{pack}=C_{pack}*V_{pack} \tag{26}\]  
\[E_{pack}=240\;\mathrm{Ah}*388.8\;\mathrm{V} \tag{27}\]  
\[Vcell_{nom}=3.6\;\mathrm{V} \tag{19}\]0  
The equations indicate the theoretical capacity of the battery pack based on the available data regarding the individual cells.