In this paper, 2 quasi-Z-source matrix converters (qZSMCs) namely quasi-Zsource MC with discontinuous input current (qZSMC-I) and quasi-Z-source MC with continuous input current (qZSMC-II) are studied, and their dynamic characteristics are fully investigated. First, their small-signal models in space domain are obtained by state-space averaging method, providing an insight into their dynamic characteristics and their constraints. Their transfer functions are further calculated whereby they are analyzed to see how variations of passive elements and shoot-through duty ratio affect the locations of transfer functions' poles and zeros, and their transient responses. The results together with a frequency domain analysis based on Bode plot are then used to render an in-depth guide to choose proper passive elements for each Z-source MC. Further, they are compared with each other by means of simulation results while being used as grid interfaces of a permanent-magnet synchronous generator-wind energy conversion system. A control system is also designed for each Wind energy conversion system to enhance its low voltage ride-through capability.KEYWORDS frequency domain analysis, matrix converter (MC), permanent-magnet synchronous generator (PMSG), quasi-Z-source matrix converter (qZSMC), small signal model, wind energy conversion system (WECS) WECSs in high, medium, and low power levels. In Amei et al, 6 a simple low-cost configuration integrating a diode rectifier, a boost chopper, and a voltage source inverter (VSI) was proposed for low power levels (LPLs). The duty ratio's optimal value for capturing the maximum power from the wind was theoretically determined by differentiating the characteristic equation of generating power with respect to duty ratio of the boost chopper. Two-level back-to-back VSIs are also proposed in Li et al 7 and Yi et al 8 and Chinchilla et al 9 for LPLs. Replacing the generator-side 6-switch 2-level converter with Vienna rectifier has been proposed by Hao et al, 10 where a rigorous mathematical analysis has been performed, and it was shown that the proposed configuration is advantageous with respect to energy efficiency compared to 2-level back-to-back VSIs. In Rajaei et al, 11 system integration of Vienna rectifier and 3-level neutral-point clamped (NPC) inverter has been proposed as a power conditioner for the PMSG-based WECS. A vector control of the inverter which was capable of regulating power factor to any desired value was proposed. The results shows that the efficiency of the proposed WECS can be enhanced compared to WECS using back-to-back VSIs. An hybrid back-to-back topology composed of 2 series connected 3-phase voltage source converters (VSC) at the generator side, and a 3-level NPC converter at the grid side, was proposed by Durán 12 to achieve such promising features as improved power quality, increased efficiency, easier grid code compliance, and smaller cables. A grid interface integrating diode rectifier, 3-level boost (TLB) converter, and NPC inverter for HPLs is addressed by...