## 3 Control Strategy of HFL Three-Phase Four-Leg MC
### Hybrid Pulse Width Modulation Control Strategy of HFL Three-Phase Four-Leg MC  
After decoupling, the positive and negative inverters work in coordination according to the HPWM modulation strategy: When the positive inverter works, the eight unidirectional switches of the negative group inverter are all turned on, acting as a freewheeling circuit. On the contrary, the negative group works also has this relationship. Taking the A-phase bridge leg as an example, the control principle of the four-wire MC switch drive signal is given, the logic implementation circuit is designed.  
Firstly, the sawtooth wave \(u_{\rm ca}\) and the sinusoidal modulation wave \(u_{\rm sa}\) are compared to obtain two complementary sinusoidal pulse width modulation (SPWM) pulses. Then two high-frequency square waves \(u_{1}\), \(u_{2}\) with a duty cycle of 0.5 and complementary are used to logically combine with the SPWM pulse. Finally, four switch drive signals on the phase A bridge leg are obtained. The waveform diagram is shown in Figure 5. In the figure, the amplitude of sinusoidal modulation wave \(u_{\text{sa}}\) is 1, the amplitude of sawtooth wave \(u_{\text{ca}}\) is 0.8. \(u_{1}\) and \(u_{2}\) represent the positive and negative high-frequency square waves, respectively. \(u_{\text{S}ka}\) represents the four driving signals of the phase A bridge leg.  
Figure 5 shows the control principle waveform of HPWM control based on de-re-couple, and it is easy to understand the control strategy from the figure. Among them, the high-frequency transformer passes a bipolar high-frequency square wave signal, and it can be known that the transformer operating frequency and the switching frequency of high-frequency inverter bridge are still the same, so it can greatly reduce the size of the transformer and output filter links.  
\(u_{1}\), \(u_{\text{SPWM}}\) is defined as \"1\" with high level and \"0\" with low level using the following switching function:  
\[\begin{cases}\text{S}_{\text{S}ka}=1&\text{S}_{\text{S}ka}:\text{on}\\ \text{S}_{\text{S}ka}=0&\text{S}_{\text{S}ka}:\text{off}\end{cases}\quad k\in \{\text{p},\text{n}\}\quad\text{i}\in\{\text{u},\text{d}\} \tag{9}\]  
The control logic truth (shown in Table 1) is listed by the above control principle. The definitions of the symbols in Table 1 are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(u_{1}\) & \(u_{\text{SPWM}}\) & \(u_{\text{Spua}}\) & \(u_{\text{Snua}}\) & \(u_{\text{Spda}}\) & \(u_{\text{Snda}}\) \\ \hline
0 & 0 & 1 & 1 & 1 & 0 \\ \hline \end{tabular}
\end{table}
Table 1: Truth table of integration SPWM composite.  
Figure 5: Drive signal for switches of phase A.  
From Table 1, we can obtain the logic equation of four driving signals of the phase A bridge leg:  
\[\left\{\begin{array}{l}u_{\text{Spua}}=\overline{u_{1}}+u_{\text{SPWM}} \bullet u_{1}\\ u_{\text{Snua}}=u_{1}+\overline{u}_{\text{SPWM}}\bullet\overline{u_{1}}\\ u_{\text{Spda}}=\overline{u_{1}}+\overline{u}_{\text{SPWM}}\bullet\overline{u_{1}} \\ u_{\text{Snda}}=u_{1}+u_{\text{SPWM}}\bullet\overline{u_{1}}\end{array}\right. \tag{10}\]  
In addition, the three-phase high-frequency link matrix converter (HFLMC) is modulated in the control circuit by using an integrated HPWM modulation strategy in which the drive signal of the pre-stage high frequency inverter and the drive signal of the rear-stage MC are combined. Moreover, the HPWM control, itself, has an adaptive one-step commutation, which reduces the commutation difficulty and switching stress, ensuring safe operation of the system [23].  
Similarly, the driving signals of the B, C, and N-phase switches can also be obtained, thereby implementing the control of the four bridge leg of rear-stage MC.