## 5 Verification
### Verification Process
#### 5.2.2 Comparison of Control Schemes  
The superiority of the proposed VSM-based charging system is confirmed by comparing with the traditional control. Most noteworthy, the traditional control [19; 20] means that the charging system does not possess the power regulation capabilities consistent with SM and only implements the charging function. The parameters of the VSM and grid are set in Table 2.  
The proposed control and traditional control are applied to the off-board charger I, respectively. The variations of the two control methods on the frequency and voltage of the grid are contrasted when the power battery II joins in and drop out of services through off-board charger II and the reactive power of the AC interface fluctuates. To explain, for VSM-controlled off-board charger I, the rated capacity of the power battery I is 100 Ah, in order to make it work in a fast-charging mode, the charging \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Parameters** & **Values** \\ \hline \multirow{6}{*}{VSM control parameters} & The charging power reference of the power battery I, \(P_{\text{bat}}\)\({}^{\star}\) & 150 \(U_{\text{bat}}\) \\  & The reactive power reference of the rectifier, \(Q^{\star}\) & 0 Var \\ \cline{1-1}  & The active droop coefficient of the VSM, \(D_{\text{p}}\) & 0.00009 \\ \cline{1-1}  & The reactive droop coefficient of the VSM, \(D_{\text{q}}\) & 0.003 \\ \cline{1-1}  & The virtual Inertia of the VSM, \(J\) & 0.1 \\ \cline{1-1}  & The virtual damping of the VSM, \(D\) & 20 \\ \hline \multirow{6}{*}{Grid control parameters} & The active power reference of the grid, \(P_{\text{e}}\)\({}^{\star}\) & 200 \(\times\) 10\({}^{3}\) W \\ \cline{1-1}  & The reactive power reference of the grid, \(Q_{\text{e}}\)\({}^{\star}\) & 0 Var \\ \cline{1-1}  & The active droop coefficient of the grid, \(D_{\text{pg}}\) & 0.00002 \\ \cline{1-1}  & The reactive droop coefficient of the grid, \(D_{\text{qg}}\) & 0.003 \\ \cline{1-1}  & The virtual Inertia of the grid, \(J_{\text{g}}\) & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Control parameters of the VSM and grid. Figure 9: Primary regulation of VSM (**a**) Active power of the rectifier; (**b**) Frequency of VSM; (**c**) Reactive power of the rectifier; (**d**) Voltage amplitude of VSM. current reference is set to 1.5 times rated capacity, i.e., \(I_{\text{bat}}\)* = 1.5 | Capacity | =150 A, so \(P_{\text{bat}}\)* = \(I_{\text{bat}}\)* \(\times\) U\({}_{\text{bat}}\) = 150 U\({}_{\text{bat}}\). Based on the above situations and parameter settings, there are three simulation scenarios are considered:  
1. The simulation time is 4.5 s. The grid quickly charged the power battery I with a charging current of 150 A through an off-board charger I before 1.5 s.
2. Power battery II is connected to the grid through the off-board charger II at 1.5 s, but the battery II exits operation at 2.5 s. In this time range, the consumed active power of the off-board charger II is 60 kW. 3. 2 kVar reactive load at the AC interface is connected to the grid at 3.5 s.  
The simulation results are given in Figure 10, where the red line indicates the traditional control (Denoted by \(x_{1}\), \(x\) = a, b, c,..., h) and the blue line represents the proposed control (Denoted by \(x_{2}\), \(x\) = a, b, c,..., h). Figure 10: Cont. In the initial state, the grid rapidly charges the power battery I with 150 A charging current by the off-board charger I. When the power battery II is connected to the grid at 1.5 s and the reactive load is increased at 3.5 s, for traditional control, Figure 10a1,b1 show that the off-board charger I system does not partake in the active and reactive power regulation no matter how the loads change. In this case, the whole variations of power are entirely borne by the grid. As a result, the active power sent by the grid increases from 115 kW to 175 kW (as shown in Figure 10c1), which results in the decrease of 0.32 Hz in grid frequency (as indicated from Figure 10e1).