**2. Single-Phase QZSI**

## *2.1. Operation and Steady-State Analysis*

The topology of single-phase QZSI is shown in Figure 1. Due to the existence of the quasi-Z-source network and the shoot-through state, both of the power switches in a leg can be turned on at the same time, which is used to step up the voltage. During the shoot-through state, the diode turns <sup>o</sup>ff, the inverter bridge is short circuited, the DC link voltage is 0, and the inverter does not generate the

power to load. In the non-shoot-through state, the diode turns on, and the QZSI operates the same as a conventional voltage source inverter (VSI). In a switching period, the state-space model of QZSI can be obtained by using the state-space average method, as shown in (1), where *iL*1 , *iL*2 , *vC*1 , and *vC*2 are the current of inductors *L*1 and *L*2, the voltage of the capacitors is *C*1 and *C*2, *v*DC is the voltage of the DC source, *d* is the shoot-through duty cycle, and *iPN* is the DC link current, respectively.

**Figure 1.** Single-phase quasi-Z-source inverter (QZSI).

Figure 2 shows the conventional modulation strategy (CMS) for the single-phase QZSI using the unipolar modulation strategy; its modulation waveforms are two sinusoidal waves with a difference of 180◦. The CMS uses two straight lines *vp*, *vn* to generate the shoot-through duty cycle. When the triangular carrier is greater than *vp*, the switch *S*1 or *S*3 turns on, and when the carrier is smaller than *vn*, the switch *S*2 or *S*4 turns on. *VS*1 and *VS*2 show the switch state of the switch *S*1–*S*4 in the H-bridge, respectively.

$$\begin{cases} L\_1 \frac{di\_{l\_1}}{dt} = v\_{\rm DC} - (1 - d)v\_{\rm C\_1} + dv\_{\rm C\_2} \\ L\_2 \frac{di\_{l\_2}}{dt} = -(1 - d)v\_{\rm C\_2} + dv\_{\rm C\_1} \\ C\_1 \frac{dv\_{\rm C\_1}}{dt} = (1 - d)(i\_{L\_1} - i\_{\rm PN}) - d i\_{L\_2} \\ C\_2 \frac{dv\_{\rm C\_2}}{dt} = (1 - d)(i\_{L\_2} - i\_{\rm PN}) - d i\_{L\_1} \end{cases} \tag{1}$$

**Figure 2.** Conventional modulation strategy (CMS).

From (1), the DC components of the QZSI in the ideal case can be obtained as (2), where *D* is the average value of the shoot-through duty cycle *d*, *d* = *D* + ˆ *d*, ˆ *d* is the variation of *d*, *VC*1 and *VC*2 are the average voltage of capacitor *C*1 and *C*2, *IL*1 and *IL*2 are the average current of inductor *IL*1 and *IL*2 , *V*DC is the average voltage of dc source, and *IPN* is the average value of the DC link current, respectively.

$$\begin{cases} V\_{\mathbb{C}\_1} = \frac{1 - D}{1 - 2D} V\_{\text{DC}} \\ V\_{\mathbb{C}\_2} = \frac{D}{1 - 2D} V\_{\text{DC}} \\ I\_{\mathbb{L}\_1} = I\_{\mathbb{L}\_2} = \frac{1 - D}{1 - 2D} I\_{PN} \end{cases} \tag{2}$$

The average value of the DC link voltage during the non-shoot-through time interval is

$$V\_{\rm PN} = V\_{\rm C\_1} + V\_{\rm C\_2} = \frac{1}{1 - 2D} V\_{\rm DC} \tag{3}$$
