# Concept for Generating Energy Demand in Electric Vehicles with a Model Based Approach
## 4 Simulation and Model Environment
### Vehicle Model
#### 4.1.1 Battery Model  
Since the energy storage model is the main objective for the simulation and measurement of energy consumption, the focus in this paper is placed on the energy storage model for clarity reasons. The description of the other subsystems are modeled according to [22; 23]. To model the lithium-ion cell, an equivalent circuit--or Thevenin-based model--is used in Figure 3. The proposed model consists of a resistor \(R_{0}\), which represents the internal resistance of the lithium-ion cell, and two RC connections of \(R_{1}\), \(C_{1}\), \(R_{2}\) and \(C_{2}\), which represent the transient voltage response \(V_{t}\) of the cell. The model again considers the rate capacitance effect, where the usable capacity varies depending on the current supplied by the cell, as described in [24].The state of charge is calculated using the usable \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Value** & **Unit** \\ \hline
**Curb Mass** & 1195 & kg \\
**Engine Power** & 125 & kW \\
**Max. Torque** & 250 & Nm \\
**Max. Velocity** & 150 & km/h \\
**Length** & 3999 & mm \\
**Width** & 1775 & mm \\
**Height** & 1579 & mm \\
**No. of Electric Motors** & 1 & - \\
**Capacity of Battery** & 61 & Ah \\
**Voltage** & 360 & V \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the modelled BMW i3. Figure 2: Structure of subsystems used for the virtual vehicle model. The five main subsystems are: the main body, the drivetrain, the steering system, the brakes and the suspension. capacity values; therefore, the parameters of this model depend on the state of charge and current [25]. An accuracy analysis in [27] showed that the second RC circuit has the greatest influence on the accuracy and the smallest root-mean-square percentage error (RMSPE) and maximum percentage error (MPE), respectively. With each additional RC circuit, the battery model becomes more accurate, but the rate decreases progressively. Figure 4 shows this correlation. According to _[PERSON]'s_ voltage law, Equation (1) can be derived from the equivalent circuit model described in Figure 3. This equation thus also forms the basis of the lithium-ion cell model introduced here. \[V_{t}=OCV-V_{1}-V_{2}-V_{0} \tag{1}\]  
The usable capacity of a lithium-ion cell can vary depending on the current value at which it is discharged or charged [25]. Equation (2), known as the _Peukert equation_, applies to determine the usable capacity [28]. \[Q_{0}=(\frac{I_{BT}}{I_{BT,rated}})^{1-n}*Q_{0,rated} \tag{2}\]  
\(Q_{0}\) describes the usable capacity, \(I_{BT}\), in A, the current at which the cell discharges, \(Q_{0,rated}\) the nominal capacity of the cell, which is discharged with a current value \(I_{BT,rated}\) and \(n\) [h], the Peukert exponent, which for lithium-ion batteries have a value of 1.05 [28]. The method to determine the state of charge of the battery used in this project is the Coulomb counting method, which is described by Equation (3). This method allows the  
Figure 4: Relationship between RMSPE/MPE and the number of RC circuits based on [27]. Figure 3: The equivalent circuit the battery model based on [26]. calculation of the current state of charge \(SoC\) of a lithium-ion cell as a function of the current value \(I_{BT}\), the usable capacity \(Q_{0}\), and the previous state of charge \(SoC_{init}\) of the cell. \[SoC=SoC_{init}-\int\frac{I_{BT}}{Q_{0}*3600}dt \tag{3}\]  
When the values of \(R_{1}\), \(R_{2}\), \(C_{1}\) and \(C_{2}\) have been determined for different current values and states of charge, the voltages in each of the electrical components are determined. Therefore, the RC parallel connection is analyzed by using the _s-domain_, according to [25; 29]. Equation (4) is obtained by doing this. To do this, we proceed according to [25; 29], where, using the _s-domain_ to analyze the RC parallel connection, Equation (4) is obtained. Therefore, Equation (4) is obtained by analyzing the RC parallel connection using the _s-domain_.