## 5 Drive System Simulation
### Simulation Results
As shown in Figure 14b, the motor's input power was determined by motor's speed demand and the load torque, and was the summation of the two inverters' output power. While inverter1's output power was controlled to follow \(P_{inv1}^{*}\), inverter2's output power was made to compensate the lacking power or absorb the redundant power. During some periods where inverter1's output power was more than motor's requirement, inverter2's output power was negative, meaning inverter2 was absorbing power. In other words, the primary power source was charging the secondary power source through the motor. We define the voltage vector distribution mode number to specify the status of voltage vector distribution. Relations between the mode number and the specific circumstances of voltage vector distribution are listed in Table 4. And the curve of voltage vector distribution mode number is shown in Figure 15. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Voltage Vector** & \multicolumn{2}{c}{**Mode**} \\
**Distribution Method** & **Specific Circumstance** & **Number** \\ \hline Low switching frequency method & The nth candidate vector is selected (the mode number indicates the ranking of selected vector in the sorted sequence) & \(1\)–\(7\) \\ \hline Accurate power & inverter1’s power following deviation \(D_{pinv1\_AF}\) equals to \(0\) & \(0\) \\ \cline{2-3} following method & inverter1’s power following deviation \(D_{pinv1\_AF}\) is not equal to \(0\) & \(-1\) \\ \hline Linear partition method & inverter1’s power following deviation \(D_{pinv1\_LP}\) is not equal to \(0\), & \(-2\) \\ \cline{2-3}  & but \(\overset{\rightarrow}{u_{s}^{*}}\) can be integrally synthesized & \(-3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Meanings of voltage vector distribution mode number. Figure 15: Curve of voltage vector distribution mode number. As shown in Figure 15, some values of the mode number never appeared, such as \(-4\), \(5\), \(6\), and \(7\). The absence of \(-4\) is because in this simulation, the amplitude of \(\overrightarrow{u_{s}^{*}}\) was not too high and the DC-bus voltages of the two power sources were enough, thus \(\overrightarrow{u_{s}^{*}}\) could always be integrally synthesized. In low switching frequency method, inverter1's output power values corresponding to the candidate voltage vectors ranked behind were not in the tolerance range of inverter1's power following. Thus the absence of \(5\), \(6\), \(7\) is mostly decided by this tolerance range. The narrower this range is, the fewer the candidate voltage vectors can be selected. The voltage vector distribution of inverter1 and inverter2 in static DQ plane are shown in Figure 15(a),b respectively, with a sampling step of \(0.002\) s. The curves of inverter switching frequency and inverter losses are shown in Figure 16(a),b respectively. From Figure 16 we can see, all the sampled voltage vectors, noted as \"\(\times\)\", were within the modulation range of the corresponding inverter, indicated by the dashed hexagon, as expected. However, the distribution characteristics of these voltage vectors are different between inverter1 and inverter2. In Figure 15(a), many sampled voltage vectors overlapped at the circled positions, which are the vertexes and the center of inverter1's hexagon, where the candidate voltage vectors of low switching frequency method are lying. That is because during most of the simulation time, the low switching frequency method was selected, which can be discovered from Figure 15. For this reason, the sampled voltage vectors of inverter1 appeared sparser than inverter2's shown in Figure 15(b), while their amount were actually the same. We can also discover that there was a certain amount of sampled voltage vectors on the boundary of inverter1's modulation range. That is because sometimes inverter1's output power was hard to stay in its tolerance range, on these occasions inverter1 had to generate the voltage vector with highest amplitude to make its output power closer to the tolerance range.