## 3 Model Details  
### 1D Model Validation  
The study of the VCD is based on a four-cylinder gasoline engine of a SAIC Motor with a double variable valve train (DVVT), and the main parameters of the prototype engine are listed in Table 1.  
The 1D prototype engine model is constructed and calibrated using experimental data in GT-Power. In the simulation model, the WoschniGT model is adopted to simulate the heat transfer processes, and the formula is shown as below:  
\[h_{c}=3.26B^{-0.2}p^{0.8}T^{-0.55}w^{0.8} \tag{1}\]  
Figure 6: The schematic of the valve strategy based on exhaust gas trapping.  
where \(h_{c}\) is the heat transfer coefficient, \(B\) is the bore of cylinder, \(p\) is the instantaneous cylinder pressure, \(T\) is the mean cylinder gas temperature, and \(w\) is the average cylinder gas velocity. The engine friction is calculated using the Chen-Flynn engine friction model, as shown in Equation (2).  
\[\textit{FMEP}=\textit{FMEP}_{\textit{Const}}+\textit{AP}_{\textit{Cyl.max}}+ \textit{Bc}_{p,m}+\textit{Cc}^{2}_{p,m} \tag{2}\]  
where \(\textit{FMEP}_{\textit{Const}}\) is the constant part of FMEP, \(A\) is the peak cylinder pressure factor, \(B\) is the mean piston speed factor, \(C\) is the mean piston speed squared factor, \(P_{\textit{Cyl.max}}\) is the maximum cylinder pressure, and \(c_{p,m}\) is the mean piston speed. The accuracy of the model under full load condition is validated through the experiments of the prototype engine, as shown in Figure 7. Data analyses demonstrate that the prediction error of the model is less than 5% under full load condition. In a GT-Power environment, heat transfer losses and friction losses are calculated based on every cylinder pressure. The heat transfer losses and friction losses are the sum of each cylinder's contributions. For the VCD operation, heat transfer losses and friction losses are reduced compared to normal engine operation due to the lower pressure of some inactive cylinders. Therefore, the WoschniGT model and the Chen-Flynn friction model are feasible for the VCD engine model.  
In this study, VCD is mainly discussed at 1200 rpm and 1600 rpm, and the comparisons of the BMEP and the brake specific fuel consumption (BSFC) between the simulation results and the experiment results are presented in Figure 8. The errors of BMEP and BSFC are also less than 5%. Therefore, the target engine model can be established based on the simulated prototype engine with high accuracy in the prediction of engine performances. In order to analyze VCD performances with the EMIV, the 1D model with the EMIV is established in GT-Power by replacing the valve train of prototype engine model with the template ValveSolSignalConn controlled via a logic signal (0 or 1), as shown in Figure 9. The valve will start opening or closing when the control signal switches between 0 and 1, which provides a method to simulate VCD performances with the EMIV.  
\begin{table}
\begin{tabular}{c c} \hline Engine type & L4 \\ Displacement & 1.8 L \\ Valve train & DVVT \\ Number of valves & 4 per cylinder \\ Stroke/Bore & 89.3 mm/80 mm \\ Connecting rod length & 133.1 mm \\ Compression ratio & 10.5 \\ Rated power & 95.7 kW @ 6000 r/min \\ Rated torque & 171.3 N\(\cdot\)m @ 4500 r/min \\ \hline \end{tabular}
\end{table}
Table 1: Engine specifications.  
Figure 7: Comparisons of simulations and experiments under full load condition.