## 1 Introduction  
With the exhaustion of energy and the growing environmental problems, the demand for energy-saving and environmentally-friendly new vehicles has increased significantly. Electric vehicles are the products that emerged under this trend. The emergence of the electric vehicles has made great contributions to promoting the development of modern society and the progress of civilization. The power used for electric vehicles is rich in resources, easy to transmit, and environmentally friendly, which can effectively cope with energy and environmental problems [1]. The charging methods of electric vehicles are divided into wired charging and wireless charging. In most cases, the charging mode of electric vehicles is wired charging. However, in this way, there are safety hazards such as bare wires and plugs in the charging process. In some special circumstances, such as chemical exposure, mining, and other inflammable and explosive situations, the resulting electric spark is enough to cause a huge safety accident. In recent years, wireless charging, as a technology for transmitting power, could be done without any physical contact, and it has attracted people's attention. Compared to traditional wired power transmission, it has many advantages, such as high current isolation, high flexibility, and high reliability [2]. Inductive power transfer (IPT) technology is used for wireless power transfer of electric vehicles. In a loosely coupled IPT system, the inductive link needs to generate a strong magnetic field so that energy can be transmitted from the outside of the vehicle to the vehicle receiving end through the air gap [3]; this requires the power frequency AC to be raised to high-frequency AC. The conversion of electric energy necessarily requires the addition of power electronic converters. At present, the most common converter structure is a two-stage conversion structure; that is, an AC-DC-AC type structure, which generally involves a low-frequency ac-to-dc power conversion as well as a dc-to-high-frequency ac power conversion, requiring two or more power electronic converters in conjunction with a large and expensive dc-link capacitor and a bulky low-frequency input inductor [4; 5]. In order to solve the above situation, matrix converters have been used in recent years to replace two-stage converters for inductive power transfer (IPT) systems. As a direct AC-AC converter, the matrix converter has a simple and compact topology, bidirectional power flow capability, a high quality input current waveform, and an adjustable input power factor compared with conventional converters [6; 7; 8; 9; 10; 11]. In [12], a single-phase matrix converter is used to alternately control the opening and closing of the switching tube by a phase shift of a certain angle. The method is simple. However, the switch cannot be turned on or off at zero voltage or zero current, and the switching loss is large. The study in [13] used a three-phase matrix converter, which can only realize the soft-switching start of the switching tube. When the circuit is turned off, the current is not zero, and the switching loss is large. The space vector pulse width modulation (SVPWM) control strategy is used in [14; 15] to make the converter have good input and output characteristics, but the strategy control is more complicated and cannot achieve full range of soft switching operation. In [16], based on energy injection and free oscillation technology, the soft switching operation and high efficiency of the converter can be realized. However, this method requires precise control of the energy injection time and the direction of the detected current, the control is complicated, and the converter has only the ability to flow in one direction. The IPT system needs to reduce the volt-ampere capacity and improve the power transmission capability through the resonance compensation circuit [17; 18].