## 5 Verification
### Verification Process  
#### 5.2.1 Verification of the Basic Functionalities of the Proposed VSM Control  
For VSM-controlled off-board charger system, its inertia and damping characteristics as well as primary regulation abilities are required to be proved, whose validation results are in the following subsections. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Parameters** & **Values** \\ \hline \multirow{2}{*}{Filter parameters} & The series inductance of the filter, \(L\) & 3 mH \\  & The series resistance of the filter, \(R\) & 0.5 \(\Omega\) \\  & The parallel capacitance of the filter, \(C\) & 10 \(\mu\)F \\ \hline \multirow{4}{*}{LLC converter parameters} & DC side capacitance, \(C\) & 1900 \(\mu\)F \\  & Resonant inductor, \(L_{\mathrm{r}}\) & 0.06 nF \\ \cline{1-1}  & Resonant capacitor, \(\mathrm{C_{r}}\) & 34 \(\mu\)F \\ \cline{1-1}  & Excitation inductance, \(L_{\mathrm{m}}\) & 0.24 nH \\ \cline{1-1}  & Transformer ratio, \(T\) & 1.4 \\ \hline \multirow{2}{*}{Power battery parameters} & Nominal voltage & 400 V \\  & Rated capacity & 100 Ah \\ \hline \multirow{4}{*}{System parameters} & Reference value of DC voltage, \(U_{\mathrm{dc-ref}}\) & 800 V \\ \cline{1-1}  & Resonant frequency & 35 kHz \\ \cline{1-1}  & Rated frequency & 50 Hz \\ \cline{1-1}  & AC phase voltage effective value & 220 V \\ \cline{1-1}  & Rectifier switching frequency & 10 kHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 7: Simulation model structure diagram. (1) Verification of the Inertia and Damping Characteristics  
Taking the off-board charger I as an example in Figure 7, three typical values of the inertia and damping are selected separately to observe the effects of different inertia and damping on the active power of the rectifier, which are \(J\) = 0.05, 1, 1.5 and \(D\) = 12, 20, 30, respectively. In the initial state, the grid sends power to the power battery I and the power battery II. Power battery II is out of service at 1 s. Figure 8 shows the waveforms of the rectifier's active power varying with the inertia \(J\) and the damping \(D\). First, it is evident from Figure 8 that the proposed VSM introduces the inertia and damping characteristics of the synchronous motor into the control of the off-board charger in the transient process. Next, active power of the rectifier increases 8.4 kW to 10 kW due to the abrupt exit of the power battery II. For inertia, it can be observed from Figure 8a that it can restrain the sudden power change, but with the increase of inertia, dynamic response of the system slows down. Moreover, compared with \(J\) = 0.05, the active power starts to oscillate when \(J\) = 1, and oscillation amplitude of \(J\) = 1.5 is greater than \(J\) = 1. For damping, it can be noticed in Figure 8b that damping suppresses oscillations, where oscillation amplitude decrease in order with the increase of damping \(D\), but overdamping will make the system take longer to reach steady state. Therefore, the abovementioned inertia and damping effects are consistent with the dynamic characteristics of the synchronous motor, and choosing the appropriate inertia and damping is of great significance to enhance the stability of the charging system. (2) Verification of Primary Regulation  
Similarly, regarding the off-board charger I in Figure 7 as a focus point, we verify the primary regulation of VSM whose simulation results are depicted in Figure 9. The simulation scenario is set as follows:  
1. Before 1.5 s, the power grid supplies power to 1 kVar reactive load, power battery I and power battery II. 2. Off-board charger II is out of operation at 1.5 s and connects to the power grid again at 2.5 s.
3. 1 kVar reactive load at the AC interface exits operation at 3.5 s.  
It is worth noting that when the active power and reactive power fluctuates, the adjustment ratio of the grid and off-board charger I is set to 1:1. In addition, the active power of the off-board charger II is set to 30 kW.