# Modeling and Control Simulation of Power Converters in Automotive Applications
## 3 Technical Specifications and Components: Sizing and Selection  
In this section, the rationale employed for selecting the values of passive and active circuit components is presented, referencing the design specifications for an onboard charger (OBC) device for electric vehicles. In this study, reference is made to the commercial solution presented by Infineon [82], and for completeness, the specific operational techniques are detailed. The technical specifications of the active rectifier are outlined in Table 1, while Table 2 provides the characteristics of the DC/DC converter. The first step is to size the circuit components of the LCL filter input to the active rectifier. For such a filter, its main objective involves attenuating high-frequency harmonics with respect to the mains frequency; it aims to meet the specifications for current ripple at the input of the controlled rectifier (the part consists of the active switching components). The maximum value of the filter capacitance can be derived by Equation (5). Figure 11: From the internal layers of the devices to the Foster model. Figure 10: Schematic illustration of the phase shifting control for the selected DC/DC converter. The value must take into account the reactive power \(Q_{max}\) associated with a desired power factor value \(PF\), as well as take into account the value of the AC supply voltage \(V_{g}\) (rms) and the supply frequency \(f_{g}\). \[C_{f,max}=\frac{Q_{max}}{2\pi{f_{g}}{V_{g}}^{2}}=\frac{tan[arc(cos(1-PF))]P_{in }}{2\pi{f_{g}}{V_{g}}^{2}}\cong 1.1\;\mathrm{mF} \tag{5}\]  
Ensuring that the resonant frequency of the LCL filter meets the constraint in Equation (6), it must necessarily be much higher than the supply frequency, and much lower than the switching frequency of the rectifier stage. \[f_{g}<<f_{LCL}<<f_{sw}\]  
\[f_{LCL}^{lower}=10f_{g}=500\;\mathrm{Hz}\;\;\longrightarrow f_{LCL}=\frac{f_{ LCL}^{lower}+f_{LCL}^{upper}}{2}\cong 5\;\mathrm{kHz} \tag{6}\]  
\[f_{LCL}^{upper}=f_{sw}/10=10\;\mathrm{kHz}\]  
From the circuit analysis, it is possible to derive the expression of the filter resonant frequency as an explicit function of the circuit components, and derive the value of the series inductance of the LCL filter, as in Equation (7). \[f_{LCL}=\frac{1}{\sqrt{2\pi{L_{f}}{C_{f}}}}\longrightarrow L_{f,min}=\frac{1} {2\pi{C_{f,max}}f_{LCL}^{2}}\cong 5.8\;\mathrm{\mu H} \tag{7}\] \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Specifications** \\ \hline \multirow{4}{*}{Input} & Single Phase \\  & Voltage: 90–265\(V_{rms}\) \\  & AC frequency: \(f_{g}=50\)–60 Hz \\  & Current: 32\(A_{rms}\)@240 V \\  & Power Factor: \(\geq\)0.99 \\ \hline \multirow{4}{*}{Output} & PFC output: 400\(V_{dc}\) (typical) \\  & Max output power: 7.4 kW@400\(V_{dc}\) \\  & peak efficiency: \(\eta_{max}=0.985\) \\ \hline \multirow{4}{*}{Performance} & PFC stage for HV Lion Battery OBC \\  & switching frequency: \(f_{sw}=120\;\mathrm{kHz}\) \\  & isolation: reinforced \\  & input AC sensing \\  & PFC output voltage sensing \\ \hline \multirow{4}{*}{Protection} & over-temperature protection \\  & short-circuit-protection \\ \cline{1-1}  & over-current protection \\ \cline{1-1}  & under-voltage protection \\ \cline{1-1}  & over-voltage protection \\ \hline \end{tabular}
\end{table} 
Table 1: Active rectifier key specifications. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Specifications** \\ \hline Prim. voltage & 400–450\(V_{dc}\) \\ Sec. voltage & 250–450\(V_{dc}\) \\ Power rating forward & 7.4 kW \\ Output current & 20 A \\ Efficiency & \(\eta_{max}=0.98\) \\ Switching frequency & \(f_{sw}\in[200;800]\;\mathrm{kHz}\) \\  & resonance at \(f_{res}=500\;\mathrm{kHz}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Dual Active Bridge Key Specifications. The relationships reported above are obviously useful as guidelines for choosing the values of the components, but on their own, they do not represent systematic and reliable procedures.