# FPGA-Based Frequency Tracking Strategy with High-Accuracy for Wireless Power Transmission Systems
## 1 Introduction  
Wireless power transmission (WPT) technology is a power transmission mode that can transfer power to electric equipment without any tangible media contact. Due to its non-contact, safety, and flexibility advantages, WPT technology is often widely used in new energy electric vehicles, aerospace, smart homes, medical equipment, and other fields [1; 2; 3; 4; 5; 6]. When the wireless power transmission system is under a resonating state, the transmission efficiency of electric energy is the highest. In practical work, the WPT system is a complex nonlinear system The stability of the system will be affected by multiple parameters, and a change in parameters will lead to the phenomenon of frequency detuning, which will lower the transmission efficiency of the system [7; 8; 9]. The literature [10; 11; 12] shows that frequency splitting will occur when the system works under over-coupling conditions, which will interfere with frequency-tracking technology and affect output power and transmission efficiency. In order to avoid system detuning and improve transmission power and efficiency, there are mainly two methods: automatic tuning technology and frequency-tracking technology. Automatic tuning technology solves the problem of frequency detuning by automatically matching new compensation capacitors [13; 14] with inductors [15; 16]. This method regulates the operating frequency discontinuously and with low accuracy. Frequency-tracking technology tracks the resonating frequency by adjusting the switching frequency of the inverter circuit. This method has become a hot research model because of its fast response and high regulation accuracy. In [17], an analogue phase-locked loop (PLL) was used to achieve frequency tracking. However, the analogue PLL circuit design is complex, the anti-noise performance is poor, and the phase lock range is narrow. Another study [18] proposed a frequency-tracking strategy for low-frequency WPT systems, which can improve transmission efficiency by varying the pulse width modulation frequency (PWM) and does not require communication between the transmitter and receiver. The authors of [19] proposed a natural frequency-tracking method by tracking the natural damping frequency of the resonating circuit, which can eliminate the detuning effect caused by static and transient changes in the system. However, this control is unstable, and there is always an error between the natural damping frequency and the resonating frequency. In [20], a frequency-tracking method using a PLL under coil offset conditions is presented, which has a phase difference between the load current at the receiver side and the inverter output voltage at the transmitter side for tracking and continuously reducing. Further, the study in [21] adopts a detuning control strategy of differential PLL to track the system's resonating frequency, reducing the WPT system's power fluctuation. The system works at a reasonable detuning rate by controlling the angle difference and realizes zero-voltage switching (ZVS). Other studies [22; 23] adopted a frequency-tracking control method based on the maximum received voltage, which monitors the voltage at the receiver and adjusts the transmitter source frequency based on the voltage's feedback information. However, this frequency-tracking method has poor accuracy and does not consider the system ZVS. In [24], a hybrid control method was proposed based on PLL frequency tracking control and dynamic compensation tuning. The system keeps frequency splitting from occurring by changing the capacitance. The operating frequency of the inverter circuit is the resonating frequency by precise tuning through frequency tracking. It is difficult to achieve continuous adjustment of capacitor parameters with this method, it has poor regulation accuracy and does not achieve ZVS, and the inverter output voltage spikes. The study in [25] achieved a resonating state that can follow frequency splitting by tracking the current at the receiver side.