**1. Introduction**

Wireless power transfer has been desired since the proposition made by Nikola Tesla about 100 years ago [1]. Due to the recent progress in power electronics technology and advancements in WPT techniques, it is realized that implementing a WPT system is now economical and can be used as a commercial product [2]. Compared to the plug-in charging system, WPT is simpler, reliable, and user-friendly [3]. Companies like Qualcomm, Witricity, and Evatran have developed many commercial products that can be charged wirelessly with good efficiency. Due to such developments, WPT can be used in many industrial applications [4] and in our daily life such as wireless charging of smartphones [5], electric vehicles [6,7], and biomedical implants [8–10].

According to the operating principles, WPT can be broadly divided into four categories, i.e., capacitive wireless power transfer (CWPT), electromagnetic radiation (EMR), acoustic wireless power transfer (AWPT), and resonant inductive power transfer (RIPT) [11,12]. In CWPT, the power is transferred using capacitor plates instead of coils. CWPT is simpler and can be used for both high voltage and low current, but the efficiency decreases when the air-gap between the transmitter and receiver plate increases [13]. In EMR, the power is transferred using microwaves. Although using this operating principle, WPT can achieve long-distance power transfer, this mode has much lower efficiency and has many health hazards due to high power radiation [14]. In optical wireless power transfer (OWPT), which is considered as a subclass of EMR, the same principles for power transfer are used, but the wavelengths are in the visible spectrum [15,16]. At the transmitting side, lasers are used to convert the electrical signal into the optical signal, and at the receiving side, photovoltaic diodes convert the optical signal back into an electrical signal. The advantage of EMR and OWPT techniques is that both techniques have high capability for power beaming. However, due to the conversion steps, almost 40 to 50% of the energy is lost [15]. In AWPT, the power is transferred by propagating energy in the form of sound or vibration waves. At the transmitting side, the electrical signals are converted into pressure waves by a transducer. The waves propagate through a medium and then are collected by the receiving side transducer, which converts it back into electrical signals. The benefit of AWPT is that it can achieve higher power beam directivity than electromagnetic transmitter of the same size and the power is transferred omnidirectional which reduces the losses such as coil misalignment but the power transfer capability and efficiency of the AWPT is very less compared to other WPT systems [12,17,18]. In RIPT, the power transfer takes place between a transmitter coil and a receiver coil using electromagnetic induction. A typical RIPT WPT system is shown in Figure 1, which consists of:


**Figure 1.** Typical RIPT WPT system.

To transfer the power from the transmitter coil to the receiver coil, the DC power is converted into high-frequency (HF) AC power through an inverter. To cancel out the leakage inductance, improve the system's efficiency, and lower the reactive power transfer in the WPT system, compensation networks are required on both the transmitting and receiving sides. The compensation network on the transmitting side eliminates the phase difference between the voltage and current, which minimizes the reactive power transfer, while on the receiving side, it maximizes the power transfer by improving the efficiency [19,20]. The required system characteristics, i.e., constant voltage or constant current, can also be achieved using suitable compensation networks. Based on the output characteristics, the compensation networks can be broadly divided into four different categories, i.e., series-series (SS), series-parallel (SP), parallel-parallel (PP), and parallel-series (PS) [21]. The equivalent circuit diagrams of these topologies are shown in Figure 2. In PP and PS, the transmitter coil does not transfer power in the absence of the receiver coil, protecting the source. Although it is a safe power transfer, during the misalignment of both coils, the topology cannot transfer high power [22]. The SP topology can transfer high power with constant output voltage, but it depends on the load variation, and the voltage gain is too high [23]. The SS topology is the most commonly used technique as the value of the capacitor is independent of the mutual inductance and load resistance [24]. In the SS topology, the resonant frequency is independent of the coupling coefficient and load conditions. This independence is very important as the coupling coefficient varies with misalignments between the coils, and when charging, the resistance of the battery changes. The problem with using the SS topology is that the output current has an inverse relationship with the duty cycle of the DC-DC converter due to which traditional control methods cannot be used. To solve the problem of this inverse relation, the LCC-S compensation topology was introduced in [25], which can achieve adjustable constant voltage at the input of the DC-DC converter.

**Figure 2.** Basic compensation networks (**a**) series-series, (**b**) parallel-series, (**c**) series-parallel, and (**d**) parallel-parallel.

The primary objective of the WPT system is to transfer the energy from the transmitter to charge the energy storage device, i.e., battery, ultra-capacitor, etc. For the simplification of the WPT system design, the energy storage device is considered as a variable load. Furthermore, based on the compensation topology, the WPT system efficiency varies with the load, i.e., the system can achieve the maximum efficiency at a particular resistance value [26]. The objective is to keep the system efficiency high regardless of the load variations. A common approach to solve this issue is to implement a DC-DC converter after the rectifier circuit, which adjust its input resistance by altering the duty cycle of the switch. According to the mentioned approach, researchers have implemented different DC-DC converters such as buck and boost converters [26,27]. By controlling the duty cycle, the input resistance of the buck and boost converter can be altered in the range of *RL* → +∞ and 0 → *RL*, respectively [28]. Conventionally, proportional–integral–derivative (PID) control is the method used to adjust the duty cycle of the DC-DC converter [26,29]. However, due to the linear nature of the PID control, the regulation is limited to a small region. To overcome the shortcomings of PID, the author in [30] proposed a sliding mode control (SMC) for the secondary side DC-DC converter. Due to the non-linear nature of SMC, compared to PID, it is not limited to a small region, but still under the load variations, it exhibits overshoots and has chattering at the equilibrium point. A super-twisting differentiator based high order sliding mode controller (HOSM+STD) was presented in [31]. Compared to the SMC, HOSM+STD has a quicker response during the transition phase, but the controller depends on an optimizing factor "*β*", which needed to be adjusted for different voltage levels. Otherwise, the response time of the controller will be slow.

Based on the mentioned research work, the LCC-S compensation network based WPT system with a secondary side buck converter is presented in this paper. To control the duty cycle of the buck converter, the discrete fast terminal sliding mode controller (DFTSMC) is proposed to overcome the shortcomings of the SMC. An ultra-capacitor (UC) is connected as the system load, the resistance of which will vary during the charging process. The objective of the paper is to control the duty ratio of the buck converter to maintain the maximum system efficiency during the charging process. Based on the charging requirements of the UC, an efficient control strategy is adopted to ensure that the UC is charged with maximum efficiency. The LCC-S compensation topology is implemented to ensure constant output voltage at the input of the buck converter during the variations in its duty cycle. Depending on the system requirements, the DFTSMC controller regulates the output current or output power under the variations in the connected load.

The paper is structured as follows. Section 2 presents the design and analysis of LCC-S compensation for the WPT system. The relationship of the system efficiency with respect to output load is derived and then transferred to the relationship between the output power and efficiency. The UC charging strategy and the design of the DFTSMC for the buck converter are presented in Section 3. The simulation results of the proposed system and the comparison with other control schemes are discussed in Section 4. Section 5 presents the experimental validation of the proposed system, and Section 6 concludes the paper.
