**1. Introduction**

The single-phase quasi-Z-source inverter (QZSI) consists of two modules, a quasi-Z-source network, and an H-bridge, and the quasi-Z-source network includes two inductors, two capacitors, and a diode [1]. Different from traditional two-stage inverters, the QZSI reduces the number of active devices, has no dead time, and can realize DC-DC and DC-AC by its unique impedance network and shoot-through modulation method [2,3]. Currently, the QZSI has been widely studied and applied in photovoltaic power generation, AC speed regulation, electric vehicles, and as a module in cascaded multilevel inverters [4–7].

For the single-phase inverter system, the double-frequency (2ω) power flows between the DC side, and the AC side causes 2ω ripples of capacitor and DC link voltage, 2ω ripples of inductor and DC link current. These 2ω ripples will cause the temperature of passive devices and the DC source to increase, which seriously affects their working life, distort the output voltage of the inverter, and the low frequency current ripple components in the DC side will affect the maximum power point tracking (MPPT) and reduce the efficiency of the photovoltaic system [8–14]. Therefore, it is necessary to suppress the 2ω ripple in the DC side. The simplest method to reduce the ripple is to increase the value of the quasi-Z-source network to buffer 2ω power in a large capacitor or inductor [8]. In [9], a parameter design method with a dynamic photovoltaic-panel and terminal capacitors for the single-phase quasi-Z-source photovoltaic inverter was proposed to reduce the 2ω ripple. However, these methods will not only lead to large volume, large weight and high cost, but also reduce reliability and efficiency due to the large value of capacitors and inductors in the quasi-Z-source network. In [10], a comprehensive model and an asymmetric quasi-Z-source network design method for a single-phase energy-stored quasi-Z-source-based photovoltaic inverter system were proposed to reduce the 2ω ripple.

The active power filter (APF) technology is usually applied to the ripple suppression for QZSI. In [11], an active-filter-integrated single-phase QZSI was proposed: The APF consists of an extra switch leg and a second-order filter; the 2ω pulsating power of the AC load is transferred to the filter and the extra leg; the capacitor voltage and the inductor current in the DC side will no longer have the 2ω ripple component with this method, but an extra circuit means a higher cost and more complicated control. In [12,13], 2ω ripple control strategies were proposed based on feed-back control. In [12], a low-pass filter was used to obtain the 2ω ripple of the inductor current in the DC side by extracting its DC component, which is used to generate a small variation of the shoot-through duty cycle, and Reference [13] regards the 2ω voltage ripple of the DC source as the feed-back signal. Reference [14] proposes a 2ω ripple suppression method based on feed-forward control: The feed-forward signal is obtained by a ripple observer, which can observe the 2ω current of the DC link by detecting the output current of the inverter. References [12–14] can realize the suppression of the 2ω ripple without an extra active filter circuit; we can call it virtual APF technology. However, they still need filters or sensors to detect the 2ω ripple components, which will increase the cost. Therefore, the relationship between the variation of the shoot-through duty cycle and the 2ω ripple in the DC side, and realizing the suppression of the 2ω ripple with less hardware, needs further study.

Reducing the modulation ratio of QZSI can effectively reduce the ripple content in the DC side; however, with the decrease of the modulation ratio and the increase of the shoot-through duty cycle, the harmonic distortion value of the inverter output voltage and the loss of switching devices will increase [15]. Some new modified modulation strategies have been addressed. In [16], a modified modulation strategy was proposed, which was different from the traditional modulation strategy; the shoot-through control lines are modified to a line with a 2ω component. Reference [17] proposes a novel dual switching frequency modulation that combines low-frequency sinusoidal pulse width modulation (SPWM) and high-frequency pulse width modulation (PWM) to remove the interdependence between the shoot-through duty cycle and the inverter modulation index. Reference [18] proposes two new space vector modulation strategies to reduce the inductor current ripple based on the principle of the volt-second balance, which can divide shoot-through times in real time. Reference [19] proposes a PWM strategy with a minimum inductor current ripple; the shoot-through time interval of three phase legs are designed according to the active state and 0 state time. In [20], a finite-control-set model-predictive control algorithm for a quasi-Z-source four-leg inverter based on the discrete time model and a predictive controller was proposed to minimize the 2ω ripple in the DC side. Reference [21] proposed a model-based current control approach based on the inherent relationship between the ripple component inductor and capacitor voltages in the DC side. This approach can reduce the DC side inductor current ripple with active damping and constant virtual time for single-phase grid-tied QZSI with an LCL filter.

This paper mainly focuses on the suppression of the 2ω current ripple of inductors and proposes a new modulation strategy based on ripple vector cancellation. In the modulation strategy, the compensated 2ω variation of the shoot-through duty cycle with a specific amplitude and phase angle is obtained to cancel the 2ω current ripple of inductors. Section 2 focuses on the operation analysis, ripple transmission, and generation mechanism of single-phase QZSI. Section 3 presents the proposed modulation strategy. Simulation and experimental studies are discussed in Section 4. Finally, conclusions are given in Section 5.
