# Hybrid Modulation Strategy to Eliminate Current Distortion for PV Grid-Tied H6 Inverter
## 2 H6 Grid-Tied Inverter Operation  
Previously a unipolar modulation technique for the H6 inverter, which has good performance as regards common mode leakage current, was reported in [11]. Here we refer to this as modulation mode I (MMI). Figure 1a displays the H6 grid-tied inverter topology [14] and the detailed operation of this modulation mode I is shown in Figure 1b. \(E\) represents the DC voltage which is regulated by the pre-boost converter from the PV generators, \(V_{ab}\) is the terminal voltage of the inverter, \(V_{ac}\) is the grid voltage, \(i_{L}\) is the grid-tied current, \(L_{1}\), \(L_{2}\) represents the grid-tied inductor \(L=L_{1}+L_{2}\), D\({}_{1}\) and D\({}_{2}\) are the freewheel diodes, S\({}_{1}\)-S\({}_{6}\) are the switches, and G\({}_{1}\)-G\({}_{6}\) are the corresponding gate driving signals for the switches. Figure 2a-d shows the current path in the converter for different conditions. Figure 2a,b shown the operation for positive voltage and current and Figure 2c,d for negative voltage and current. When the grid voltage is in the positive half cycle, S2, S3, and S6 are off, and S5 stays on. S1 and S4 switch on and off at high frequency with SPWM (sinusoidal pulse width modulation) control. When S1, S4 are turned on, see Figure 2a, the inductor is charging and the bridge output \(V_{ab}=+E\). When S1 and S4 are turned off, see Figure 2b, the inductor current freewheels through D1 and S5 resulting in the bridge output voltage \(V_{ab}=0\). When the grid voltage is in the negative half cycle, S1, S4, and S5 are turned off, while S6 maintains remains on. S2 and S3 now switch on and off at high frequency using SPWM control. When S1 and S4 are turned on, see Figure 2c, the inductor is charging and the bridge output \(V_{ab}=-E\). When S2 and S3 are turned off, see Figure 2d, the inductor current freewheels through diode D\({}_{2}\) and S\({}_{6}\) and the bridge output \(V_{ab}=0\). Figure 1: Structure of H6 and modulation mode I. (**a**) H6 grid-tied inverter topology, (**b**) modulation mode I (MMI). Figure 2: Switching states for modulation mode I. (**a**) Switch state 1, \(i_{L}>0\), S1 S4 S5 on, (**b**) switch state 2, \(i_{L}>0\), S1 S4 off, S5 on, (**c**) switch state 3, \(i_{L}<0\), S2 S3 S6 on, (**d**) switch state 4, \(i_{L}<0\), S2 S3 off, S6 on. Although MMI can eliminate common mode leakage current, we show below that it has a problem with grid current distortion under reactive power output. The output voltage of a grid-tied inverter is clamped to the grid voltage and therefore can only regulate the active and reactive current by controlling the phase and amplitude of the grid-tied current. Thus, for reactive power output, there is necessarily a phase shift between inverter terminal voltage and current, the phasor relationship for which is illustrated in Figure 3.  
Here \(V_{ac}\) represents the grid voltage phasor, \(V_{L}\) represents the inductor voltage phasor, \(V_{ab}\) represents the bridge output voltage phasor, \(I_{L}\) represents the current phasor (inductor current) of the grid-tied inverter. Based on the vector relationship, the phase angle difference between the inverter terminal voltage, \(V_{ab}\) and its current \(I_{L}\) for a non-unity power factor (\(\cos(\theta)\)), is given by  
\[\Delta\varphi=\arctan\left[V_{L}\cos(\theta)/(V_{ac}-V_{L}\sin(\theta))\right] -\theta \tag{1}\]  
Note that, even for the unity power factor at (\(\theta=0^{\circ}\)), \(\Delta\varphi\) is not equal to zero. For the H6 inverter under MMI, if the terminal voltage is positive and the current is negative and we continue to operate as in Figure 2a,b (turning on S5), the current cannot freewheel through D1 as normal when S1 and S4 are off, but rather flows through the parallel diodes of S1 and S4, so that the instantaneous terminal voltage is not 0 at this point, which from a control perspective means a loss of control, with resulting current distortion in this region.