## 3 Control Strategy  
### Matrix Converter  
According to the circuit topology characteristics shown in Figure 1, the matrix converter can be converted into common converters for analysis by de-re-coupling. Therefore, modulation and control strategies widely used in conventional single-phase switching converters can be applied to matrix converters, making the analysis and control of bidirectional switching circuits simpler. In this paper, based on the de-re-coupling method, a de-re-coupling vector modulation strategy suitable for direct three-phase AC-AC matrix converter is proposed. The proposed strategy also needs to be processed by \"two-step\" de-coupling and re-coupling. Firstly, direct three-phase AC-AC matrix converter is processed by the \"de-coupling\" idea, and the original topology is presented as a form of a positive six-switch converter and a reverse six-switch converter as shown in Figure 2. When the positive converter is operated, the forward current flows through the anti-parallel diodes of the reverse  
Figure 1: Electric vehicle wireless charging system based on direct three-phase AC–AC matrix converter.  
converter switches, and the switch tubes corresponding to the reverse converter are all turned off. When the reverse converter is operated, the reverse current flows through the anti-parallel diodes of the positive converter switches, and the switch tubes corresponding to the positive converter are all turned off.  
Secondly, the \"re-coupling\" work focuses on generating drive pulses for each switching device in the \"de-coupling\" circuit through logical combination and transformation. The research object of this paper is the voltage type matrix converter. For this reason, the control mode of Figure 3 is selected in the driving mode of the bidirectional switch (taking a single bridge arm as an example); that is, two switching tubes are respectively applied with different driving, and are separately controlled. \(S_{amax}\) and \(S_{amin}\) are the driving signals of the A-phase arm; and the polarity selection signal \(V_{u}\) and the polarity selection signal \(V_{n}\) are complementary high-frequency square waves with a duty ratio of 50%, and the frequency is the same as the switching frequency. In the first half of the polarity selection's high-frequency square wave signal, the matrix converter outputs a positive voltage, which is equivalent to turning off the reverse converter and driving the positive converter. In the latter half of the period, when the polarity selects the high-frequency square wave signal, the matrix converter outputs a negative voltage, which is equivalent to turning off the positive converter and driving the reverse converter. Thereby, the matrix converter output can be realized as a high-frequency alternating voltage in one high-frequency period.  
In Figure 4, taking the ab phase voltage as an example, the output voltage \(v_{s}\) of the matrix converter is synthesized by the polarity selection signals \(v_{u}\), \(v_{n}\).  
Figure 3: The re-coupling logic of the A phase drive signal.  
Figure 2: De-coupling diagram of direct three-phase AC–AC matrix converter.  
As shown in Table 1, the three-phase AC-AC matrix converter has twelve operating states throughout the cycle, which are determined based on the polarity selection signal and the relative order of the three-phase input voltages.  
\[\begin{array}{l}S_{n1}=S_{ab}\cdot\overline{S_{ca}}\cdot(\overline{S_{p}}\cdot S _{f}+S_{p}\cdot S_{v})\\ S_{p1}=\overline{S_{ab}}\cdot S_{ca}\cdot(S_{p}\cdot S_{f}+\overline{S_{p}}\cdot S _{v})\end{array} \tag{1}\]  
The logic signal of switch \(S_{1}\) of the converter can be obtained from Table 1 as shown in Equation (1), where the variables are defined as \(S_{ab}\): \(u_{a}>u_{b}\), \(S_{bc}\): \(u_{b}>u_{c}\), \(S_{ca}\): \(u_{c}>u_{a}\), \(S_{u}\): \(V_{u}>0\), \(S_{f}\): forward power transfer mode, \(S_{v}\): reverse power transfer mode. The logic signals of other switches (\(S_{2}\)-\(S_{6}\)) are similar to Equation (1).