Optimization of a Single-Switch Wireless Power Transfer Circuit Based on a Multi-Coil Array

Abstract

In response to the issue of large input current ripple and noise, which can cause current shocks and compromise the overall stability in single-tube wireless power transmission systems, a P^# type LCC-S compensation network and a multi-coil phase-shifting control method have been proposed to suppress input current ripple, improve input current waveform, reduce input current total harmonic distortion (THD), and ultimately enhance system efficiency and stability. Firstly, the working mode and waveform of the P^# type LCC-S compensation network are analyzed, and the calculation method for its parameters is provided. Secondly, the analytical relationship between input current, input voltage, coil mutual inductance, and load impedance of the multi-coil array is derived. Additionally, Fourier transform is used to analyze the input current composition, and the phase shift suppression method is employed to reduce the input current ripple. Finally, a test platform is constructed to verify the relevant experiments. The experimental results demonstrate that the input current ripple is significantly suppressed at the rated transmission power, and the system efficiency is improved to 88.2%, which validates the effectiveness of the proposed method.

1. Introduction

Wireless power transfer (WPT) technology enables energy to be transmitted through an air gap without physical contact [1,2,3,4,5]. Due to its advantages of safety, convenience, and flexibility, it is the best choice for charging, in place of cables [6,7,8]. Consequently, it has been widely used in the power supply of consumer electronics, electric cars, special machinery, and medical electronics [9,10].

In the research of wireless power transfer technology, the research on multi-coil parallel transmission is mostly based on full-bridge or half-bridge topology [11,12,13,14,15,16]. However, these topologies have some problems, such as complex peripheral circuits and the risk of short circuits on one arm of the inverter bridge [17,18,19,20,21]. In contrast, the single-switch resonant inverter circuit has the advantages of high reliability, simple control, and low cost, and it is easy to realize zero-voltage turn-on, but it has some disadvantages such as limited transmission power and large input current ripple. Therefore, by connecting multiple transmitters in parallel and controlling the angle of the input current of the system, the conducting ripple is suppressed and the transfer power is increased. It is an effective way to overcome the deficiency of a single-switch resonant inverter. Under the same transfer power, the control scheme of the system is simpler than the full-bridge topology. A master–slave phase parallel inverter topology with phase synchronization control is proposed by [22], but the auxiliary inverter is only used for tuning. In reference [23], a WPT system with input parallel and output series topology based on a full-bridge inverter is proposed, along with an efficiency optimization method. The efficiency of the single-switch LCC-S compensation network was optimized, resulting in an output power of 11 W and efficiency of 86.3% [24]. SiC MOSFET is used in wireless power transfer circuits based on a single-switch PP resonant inverter, which effectively improves the system efficiency, but the input current alignment of the system is not considered [25].

Due to the unique characteristics of the single-switch resonant inverter wireless power transfer system, the conventional LCC resonant topology cannot be directly applied. The compensation network of a single-switch resonant inverter transmitter typically features a P-type structure. The resonant frequency of PP-type and PS-type circuits is determined by the transmitter’s L_t, the receiver’s L_r, the mutual inductance M, and the load R_L [26].

LCC topology has the following advantages:

a.

The compensation network parameters can be adjusted to achieve constant voltage output for the system.

b.

The resonant frequency of the system is only related to the transmitter and receiver which are not affected by the change in mutual inductance or load, which will not be detuned easily when the system works.

c.

The LCC topology has a high-quality index of merit as a high-order network and a good filtering effect on high harmonics. The voltage gain is adjustable, and it requires a low input voltage level.

However, when the magnetic coupler shifts, the mutual inductance M changes, which can significantly alter the resonant frequency and ultimately impact the transmission power and efficiency of the WPT system. Additionally, P-type compensation networks have low voltage gains and a low figure of merit. At high input voltages, the filtering effect of the system is also poor. To summarize, the main contributions are as follows:

(1)

To improve the THD of the system’s input current, the working modes and parameters of different resonant circuits are analyzed, and the P^# type LCC-S compensation network is determined. We suggest a P^# type LCC-S compensation network suitable for single-switch resonant inverter, specifically for multi-coil single-switch wireless power transfer.

(2)

To improve the transmission power of the system, three coils are input in parallel to increase the transmission power of the system. Aiming at the topology of three-coil parallel input, Fourier expansion analysis is carried out to obtain the mathematical model of three-coil compensation network.

(3)

To suppress the ripple of the input current, the effective values of the fundamental and harmonic components are obtained through a frequency domain analysis of the input current. Meanwhile, the relationship between the input current of the coil and input voltage, coil mutual inductance and negative load impedance under the unbalanced coupling of three turns is deduced. In view of the topology of the three-coil parallel input, the input current ripple is suppressed using the method of phase shift control. The system efficiency is improved.

2. System Structure and Operation Process

2.1. The Circuit Model of Triple-Coil Single-Switch Resonant Inverter WPT System

The construction and dimensions of the three-coil WPT system are shown in Figure 1. The distance between the transmitter and the receiver is 50 mm. The length and width of the ferrite are 160 mm, and the thickness is 2 mm. The magnetic coupler is wound with 0.1 mm × 150 strand litz wire.

The circuit construction of the system is shown in Figure 2. V_dc is the input DC voltage of the single-switch resonant inverter; Q₁~Q₃ is the power MOSFET; L_f1~L_f3 is the transmitter compensation inductance; C_f1~C_f3 is the transmitter parallel compensation capacitor; L_t1~L_t3 is the transmitter; C_t1~C_t3 is the transmitter series compensation capacitor; L_f1~L_f3, C_f1~C_f3, C_t1~C_t3, and L_t1~L_t3, respectively, constitute the LCC compensation circuit at the transmitter; R_t1~R_t3 is the parasitic resistance of the transmitter; L_a1~L_a3 is the resonant inductor; C_a1~C_a3 is the resonant capacitor; M₁~M₃ is the mutual inductance between the magnetic coupler; L_r1~L_r3 is the receiver; R_r1~R_r3 is the parasitic resistance of the receiver; C_r1~C_r3 is the compensation capacitor of the receiver; D₁~D₃ is the rectifier; C_L1~C_L3 is the output filter capacitor; and R_L is the load resistance. I_in1~I_in3 is the input current of each inverter; i₁~i₃ is the compensation inductance current at the transmitter; i_t1~i_t3 is the excitation current of the transmitter; i_r1~i_r3 is the output current of the receiver; v_o1~v_o3 is the input voltage of the rectifier; I_L is the load current; and V_L is the load voltage.

2.2. Analysis of Circuit Model Operation Mode of Three Groups of Single-Switch Resonant Inverter WPT System

Because of the particularity of the single-switch resonant inverter, the conventional LCC resonant network cannot be directly applied. It is possible to add an additional LC resonance circuit at the transmitter for resonance, and the LCC compensation network is used as the compensation circuit, as shown in Figure 3a. So, the single-switch resonant inverter has the characteristics of an LCC compensation network. In addition, the LC resonant circuit also plays a role in adjusting the zero-voltage switching margin (ZVSM). However, the system input current of the traditional single-switch LCC compensation network is seriously distorted, as shown in Figure 4a.

Therefore, based on the traditional LCC compensation network, this paper proposes a P^# type LCC compensation network suitable for the single-switch resonant inverter, as shown in Figure 3b. The resonant capacitor C_a of this circuit is connected in parallel with the MOSFET to transfer the current oscillation at the input of the system to the ground, as shown in Figure 4b, which effectively improves the system input current waveform, reduces the THD of the system input current, and improves the system efficiency.

As shown in Figure 2, the compensation network can be divided into an LC resonance network and an LCC compensation network. For the convenience of analysis, it is assumed that all components in the circuit are ideal components. The system operating mode waveforms of different compensation networks are shown in Figure 4. V_gs is the driving voltage of the MOSFET. i_La is the resonant inductance current, i is the compensation inductance current at the transmitter, and V_ds is the voltage between the drain and source of the MOSFET.

As shown in Figure 4 and

Table 1. Modal analysis of the transmitter.

Mode	The Traditional LCC Compensation Network	P# Type LCC Compensation Network
Stage 1 [t0–t1]	At time t0, the MOSFET is turned on. The resonance capacitor Ca is equivalently short-circuited. The input current Iin gradually decreases and crosses zero at time t1.	It is the same as the operating mode [t0–t1] of the traditional LCC compensation network.
Stage 2 [t1–t2]	At time t1, the MOSFET is turned off, so the input current Iin rapidly drops to zero. The excitation current it of the transmitter continues to drop to zero.	At time t1, the MOSFET is turned off. The input current Iin starts to decrease. The excitation current it of the transmitter continues to drop to zero.
Stage 3 [t2–t3]	At time t2, the current it increases in reverse, and Vds reaches the maximum.	At time t2, the input current Iin in creases to the maximum. The excitation current it of the transmitter increases in reverse. Vds reaches the maximum.
Stage 4 [t3–t4]	At time t3, the input current Iin rapidly increases in reverse and then starts to decrease. The Vds voltage is zero, and the MOSFET enters the soft switching stage.	At time t3, the input current Iin de creases to zero in reverse. The Vds voltage is zero, and the MOSFET enters the soft switching stage.
Stage 5 [t4–t5]	At time t4, the MOSFET is turned on. The excitation current It of the transmitter reversely decreases to zero.	It is the same as the operating mode [t4–t5] of the traditional LCC compensation network.
Stage 6 [t5–t0]	At time t5, the input current Iin and the excitation current it of the transmitter increase in a positive direction.	It is the same as the operating mode [t5–t0] of the traditional LCC compensation network.

, the status of a single period for two different LCC resonant topologies. As can be seen from Figure 4 and Figure 5, the operating difference of the two different compensation networks is only reflected in the input current. When the traditional LCC compensation network works, its input current I_in has large higher harmonics, and the process of phase shifting to suppress the fundamental and lower harmonics will cause the superposition of higher harmonics, so the LCC compensation network is not suitable for phase shifting to suppress the input current. However, the P^# type LCC compensation network eliminates the high-order harmonics in the input current I_in and reduces the THD of the input current, so it is suitable for the phase-shifting suppression of the input current.

2.3. Single-Switch LCC-S Circuit Model Analysis

The waveform of the input AC voltage U_in of the LCC compensation network in one cycle is shown in Figure 6a. The voltage U_La across the resonant inductor L_a is a periodic square wave voltage and a sine half wave voltage. According to the area equivalence rule, the U_in waveform can be equivalent to Figure 6b.

According to Figure 6b, the equivalent AC voltage is as follows

$$U_{\mathrm{in}}=\{\begin{array}{l}{V}_{\mathrm{dc} }\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}0\le t\le D+t_{\mathrm{ZVS}}\\ -V_{\mathrm{P}}\sin ({\omega }_{\mathrm{n}}t)\hspace{1em}D+t_{\mathrm{ZVS}}\le t\le T_{\mathrm{s}}\end{array}$$

(1)

According to the volt second balance of the inductance, the inductance voltage is zero in one cycle; the equation is

$$(D+t_{\mathrm{ZVS}})·V_{\mathrm{dc}}=\frac{V_{\mathrm{P}}}{\sqrt{2}}\left(1-D-t_{\mathrm{ZVS}}\right)$$

(2)

The peak value of equivalent input voltage $V_{\mathrm{P}}$ can be calculated as

$$V_{\mathrm{P}}=\sqrt{2}{V}_{\mathrm{dc}}\frac{(D+t_{\mathrm{ZVS}})}{\left(1-D-t_{\mathrm{ZVS}}\right)}$$

(3)

D is the duty ratio, and t_zvs is the soft switching margin.

The output impedance R_L1, R_L2, and R_L3 can be expressed as [25]

$$\{\begin{array}{c}{R}_{\mathrm{L}1}=\frac{8R_{\mathrm{L}}}{{\pi }^2}(\frac{V_{\mathrm{L}1}}{V_{\mathrm{L}}})\\ R_{\mathrm{L}2}=\frac{8R_{\mathrm{L}}}{{\pi }^2}(\frac{V_{\mathrm{L}2}}{V_{\mathrm{L}}})\\ R_{\mathrm{L}3}=\frac{8R_{\mathrm{L}}}{{\pi }^2}(\frac{V_{\mathrm{L}3}}{V_{\mathrm{L}}})\end{array}$$

(4)

Due to the good high-order filtering characteristics of the compensation network, the system can be analyzed by using the harmonic approximation method. The equivalent circuit of the system is shown in Figure 7. In order to simplify the analysis process, when the transmitter is far apart, the cross coupling between the transmitter on the same side can be ignored [23]. Theoretically, the number of coils can be expanded to N, and the ripple suppression will be better if the appropriate phase shift angle is found. However, in order to verify the effectiveness of this scheme, three groups of coils are used for theoretical analysis and experimental research.

According to Kirchhoff’s voltage law, the KCL and KVL equations of the LCC−S circuit model in Figure 7 are shown in Equation (5)

$$\left[\begin{array}{c}{\dot{U}}_{\mathrm{in}}\\ {\dot{U}}_{\mathrm{in}}\\ {\dot{U}}_{\mathrm{in}}\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\end{array}\right]=\left[\begin{array}{c}\begin{array}{c}j{\omega }_{\mathrm{n}}{\dot{I}}_1{L}_{\mathrm{f}1}+({\dot{I}}_1-{\dot{I}}_{\mathrm{t}1})/j{\omega }_{\mathrm{n}}{C}_{\mathrm{f}1}\\ j{\omega }_{\mathrm{n}}{\dot{I}}_2{L}_{\mathrm{f}2}+({\dot{I}}_2-{\dot{I}}_{\mathrm{t}2})/j{\omega }_{\mathrm{n}}{C}_{\mathrm{f}2}\\ j{\omega }_{\mathrm{n}}{\dot{I}}_3{L}_{\mathrm{f}3}+({\dot{I}}_3-{\dot{I}}_{\mathrm{t}3})/j{\omega }_{\mathrm{n}}{C}_{\mathrm{f}3}\\ {\dot{I}}_{\mathrm{t}1}/j{\omega }_{\mathrm{n}}{C}_{\mathrm{t}1}+j{\omega }_{\mathrm{n}}{\dot{I}}_{\mathrm{t}1}{L}_{\mathrm{t}1}+{\dot{I}}_{\mathrm{t}1}{R}_{\mathrm{t}1}-j{\omega }_{\mathrm{n}}{M}_1{\dot{I}}_{\mathrm{r}1}-({\dot{I}}_1-{\dot{I}}_{\mathrm{t}1})/j{\omega }_{\mathrm{n}}{C}_{\mathrm{f}1}\end{array}\\ {\dot{I}}_{\mathrm{r}1}/j{\omega }_{\mathrm{n}}{C}_{\mathrm{r}1}+j{\omega }_{\mathrm{n}}{\dot{I}}_{\mathrm{r}1}{L}_{\mathrm{r}1}+{\dot{I}}_{\mathrm{r}1}(R_{\mathrm{L}1}+R_{\mathrm{r}1})-j{\omega }_{\mathrm{n}}{M}_1{\dot{I}}_{\mathrm{t}1}\\ \begin{array}{c}{\dot{I}}_{\mathrm{t}2}/j{\omega }_{\mathrm{n}}{C}_{\mathrm{t}2}+j{\omega }_{\mathrm{n}}{\dot{I}}_{\mathrm{t}2}{L}_{\mathrm{t}2}+{\dot{I}}_{\mathrm{t}2}{R}_{\mathrm{t}2}-j{\omega }_{\mathrm{n}}{M}_2{\dot{I}}_{\mathrm{r}2}-({\dot{I}}_2-{\dot{I}}_{\mathrm{t}2})/j{\omega }_{\mathrm{n}}{C}_{\mathrm{f}2}\\ {\dot{I}}_{\mathrm{r}2}/j{\omega }_{\mathrm{n}}{C}_{\mathrm{r}2}+j{\omega }_{\mathrm{n}}{\dot{I}}_{\mathrm{r}2}{L}_{\mathrm{r}2}+{\dot{I}}_{\mathrm{r}2}(R_{\mathrm{L}2}+R_{\mathrm{r}2})-j{\omega }_{\mathrm{n}}{M}_2{\dot{I}}_{\mathrm{t}2}\\ {\dot{I}}_{\mathrm{t}3}/j{\omega }_{\mathrm{n}}{C}_{\mathrm{t}3}+j{\omega }_{\mathrm{n}}{\dot{I}}_{\mathrm{t}3}{L}_{\mathrm{t}3}+{\dot{I}}_{\mathrm{t}3}{R}_{\mathrm{t}3}-j{\omega }_{\mathrm{n}}{M}_3{\dot{I}}_{\mathrm{r}3}-({\dot{I}}_3-{\dot{I}}_{\mathrm{t}3})/j{\omega }_{\mathrm{n}}{C}_{\mathrm{f}3}\\ {\dot{I}}_{\mathrm{r}3}/j{\omega }_{\mathrm{n}}{C}_{\mathrm{r}3}+j{\omega }_{\mathrm{n}}{\dot{I}}_{\mathrm{r}3}{L}_{\mathrm{r}3}+{\dot{I}}_{\mathrm{r}3}(R_{\mathrm{L}3}+R_{\mathrm{r}3})-j{\omega }_{\mathrm{n}}{M}_3{\dot{I}}_{\mathrm{t}3}\end{array}\end{array}\right]$$

(5)

According to the operating characteristics of LCC, when the system resonates, the input impedance Z_in is pure resistance; when the imaginary part is zero, there is the following relationship [22].

$$L_{\mathrm{fi}}{C}_{\mathrm{fi}}=L_{\mathrm{ri}}{C}_{\mathrm{ri}}=\left(L_{\mathrm{ti}}-L_{\mathrm{fi}}\right)C_{\mathrm{ti}}=\frac{1}{{\omega }_{\mathrm{n}}^2}\hspace{1em}(i=1,2,3)$$

(6)

By substituting Equation (6) into (5), the corresponding currents in both sides can be derived as

$$\{\begin{array}{ccc}{\dot{I}}_1=\frac{{\dot{U}}_{\mathrm{in}}}{{\omega }_{\mathrm{n}}^2{L}_{\mathrm{f}1}^2}(R_{\mathrm{t}1}+\frac{{\omega }_{\mathrm{n}}^2{M}_1^2}{R_{\mathrm{r}1}+R_{\mathrm{L}1}})& {\dot{I}}_{\mathrm{t}1}=\frac{{\dot{U}}_{\mathrm{in}}}{j{\omega }_{\mathrm{n}}{L}_{\mathrm{f}1}}& {\dot{I}}_{\mathrm{r}1}=\frac{M_1{\dot{U}}_{\mathrm{in}}}{L_{\mathrm{f}1}(R_{\mathrm{L}1}+R_{\mathrm{r}1})}\\ {\dot{I}}_2=\frac{{\dot{U}}_{\mathrm{in}}}{{\omega }_{\mathrm{n}}^2{L}_{\mathrm{f}2}^2}(R_{\mathrm{t}2}+\frac{{\omega }_{\mathrm{n}}^2{M}_2^2}{R_{\mathrm{r}2}+R_{\mathrm{L}2}})& {\dot{I}}_{\mathrm{t}2}=\frac{{\dot{U}}_{\mathrm{in}}}{j{\omega }_{\mathrm{n}}{L}_{\mathrm{f}2}}& {\dot{I}}_{\mathrm{r}2}=\frac{M_2{\dot{U}}_{\mathrm{in}}}{L_{\mathrm{f}2}(R_{\mathrm{L}2}+R_{\mathrm{r}2})}\\ {\dot{I}}_3=\frac{{\dot{U}}_{\mathrm{in}}}{{\omega }_{\mathrm{n}}^2{L}_{\mathrm{f}3}^2}(R_{\mathrm{t}3}+\frac{{\omega }_{\mathrm{n}}^2{M}_3^2}{R_{\mathrm{r}3}+R_{\mathrm{L}3}})& {\dot{I}}_{\mathrm{t}3}=\frac{{\dot{U}}_{\mathrm{in}}}{j{\omega }_{\mathrm{n}}{L}_{\mathrm{f}3}}& {\dot{I}}_{\mathrm{r}3}=\frac{M_3{\dot{U}}_{\mathrm{in}}}{L_{\mathrm{f}3}(R_{\mathrm{L}3}+R_{\mathrm{r}3})}\end{array}$$

(7)

From Equation (7), the rectifier input voltage of each subsystem is ${\dot{V}}_{\mathrm{o}1}$, ${\dot{V}}_{\mathrm{o}2}$ and ${\dot{V}}_{\mathrm{o}3}$.

$$\{\begin{array}{c}{\dot{V}}_{\mathrm{o}1}={\dot{I}}_{\mathrm{r}1}{R}_{\mathrm{L}1}=\frac{M_1{\dot{U}}_{\mathrm{in}}{R}_{\mathrm{L}1}}{L_{\mathrm{f}1}(R_{\mathrm{L}1}+R_{\mathrm{r}1})}\\ {\dot{V}}_{\mathrm{o}2}={\dot{I}}_{\mathrm{r}2}{R}_{\mathrm{L}2}=\frac{M_2{\dot{U}}_{\mathrm{in}}{R}_{\mathrm{L}2}}{L_{\mathrm{f}2}(R_{\mathrm{L}2}+R_{\mathrm{r}2})}\\ {\dot{V}}_{\mathrm{o}3}={\dot{I}}_{\mathrm{r}3}{R}_{\mathrm{L}3}=\frac{M_3{\dot{U}}_{\mathrm{in}}{R}_{\mathrm{L}3}}{L_{\mathrm{f}3}(R_{\mathrm{L}3}+R_{\mathrm{r}3})}\end{array}$$

(8)

According to Equation (8), the dc output voltage V_L1, V_L2, and V_L3 can be expressed as

$$\{\begin{array}{c}{V}_{\mathrm{L}1}=\frac{\pi {\dot{V}}_{\mathrm{o}1}}{2\sqrt{2}}=\frac{\pi M_1{\dot{U}}_{\mathrm{in}}{R}_{\mathrm{L}1}}{2\sqrt{2}{L}_{\mathrm{f}1}(R_{\mathrm{L}1}+R_{\mathrm{r}1})}\\ V_{\mathrm{L}2}=\frac{\pi {\dot{V}}_{\mathrm{o}2}}{2\sqrt{2}}=\frac{\pi M_2{\dot{U}}_{\mathrm{in}}{R}_{\mathrm{L}2}}{2\sqrt{2}{L}_{\mathrm{f}2}(R_{\mathrm{L}2}+R_{\mathrm{r}2})}\\ V_{\mathrm{L}3}=\frac{\pi {\dot{V}}_{\mathrm{o}3}}{2\sqrt{2}}=\frac{\pi M_3{\dot{U}}_{\mathrm{in}}{R}_{\mathrm{L}3}}{2\sqrt{2}{L}_{\mathrm{f}3}(R_{\mathrm{L}3}+R_{\mathrm{r}3})}\end{array}$$

(9)

According to Equations (4) and (7), the mutual inductance M₁, M₂, and M₃ between coils is as follows

$$\{\begin{array}{c}{M}_1=\frac{\sqrt{2}\pi L_{\mathrm{f}1}(V_{\mathrm{L}1}+I_{\mathrm{L}1}{R}_{\mathrm{r}1})}{U_{\mathrm{in}}}\\ M_2=\frac{\sqrt{2}\pi L_{\mathrm{f}2}(V_{\mathrm{L}2}+I_{\mathrm{L}2}{R}_{\mathrm{r}2})}{U_{\mathrm{in}}}\\ M_3=\frac{\sqrt{2}\pi L_{\mathrm{f}3}(V_{\mathrm{L}3}+I_{\mathrm{L}3}{R}_{\mathrm{r}3})}{U_{\mathrm{in}}}\end{array}$$

(10)

Therefore, the voltage gains G₁, G₂, and G₃ of each subsystem are as follows

$$\{\begin{array}{c}{G}_1=\frac{\sqrt{2}{M}_1{R}_{\mathrm{L}1}}{2\pi L_{\mathrm{f}1}(R_{\mathrm{L}1}+R_{\mathrm{r}1})}\\ G_2=\frac{\sqrt{2}{M}_2{R}_{\mathrm{L}2}}{2\pi L_{\mathrm{f}2}(R_{\mathrm{L}2}+R_{\mathrm{r}2})}\\ G_3=\frac{\sqrt{2}{M}_3{R}_{\mathrm{L}3}}{2\pi L_{\mathrm{f}3}(R_{\mathrm{L}3}+R_{\mathrm{r}3})}\end{array}$$

(11)

It can be seen from Equation (11) that the voltage gain G is related to the compensation inductance L_f, the mutual inductance M, the equivalent load, and the parasitic resistance of the receiver. Therefore, we can reduce the compensation inductance L_f and increase the voltage gain to reduce the input voltage level.

2.4. Single-Switch LCC-S Circuit Model Parameter Design of Resonance Inductance and Capacitance L_a and C_a

In order to realize soft switching, according to the design principle of a class E power amplifier, the input resonance frequency f_in between the resonance inductance L_a and the resonance capacitance C_a should be slightly lower than 1.5 times the switching frequency f, as follows [18,19]

$$\frac{1}{\sqrt{L_{\mathrm{a}}{C}_{\mathrm{a}}}}=3\pi f_{}$$

(12)

The resonance capacitance C_a is selected as

$$C_{\mathrm{a}}=\frac{\pi }{11.2f_{{}_{\mathrm{in}}}{R}_{\mathrm{L}}}$$

(13)

The resonance inductance L_a is selected as

$$L_{\mathrm{a}}=\frac{31.36}{{\pi }^4}{C}_{\mathrm{a}}{R}_{{}_{\mathrm{L}}}^2$$

(14)

According to the above parameters, the voltage waveform at both ends of the switch tube is obtained as shown in Figure 8.

3. System Structure and Phase-Shifting Control

3.1. Ripple Suppression of Input Current

According to Equation (7), the input currents I_in1, I_in2, and I_in3 of each phase subsystem can be expressed as

$$\{\begin{array}{c}{I}_{\mathrm{in}1}=(\frac{U_{\mathrm{in}}}{{\omega }_{\mathrm{n}}^2{L}_{\mathrm{f}1}^2}(R_{\mathrm{t}1}+\frac{{\omega }_{\mathrm{n}}^2{M}_1^2}{R_{\mathrm{r}1}+R_{\mathrm{L}1}})+\frac{U_{\mathrm{in}}}{j{\omega }_{\mathrm{n}}{L}_{\mathrm{a}1}})\\ I_{\mathrm{in}2}=(\frac{U_{\mathrm{in}}}{{\omega }_{\mathrm{n}}^2{L}_{\mathrm{f}2}^2}(R_{\mathrm{t}2}+\frac{{\omega }_{\mathrm{n}}^2{M}_2^2}{R_{\mathrm{r}2}+R_{\mathrm{L}2}})+\frac{U_{\mathrm{in}}}{j{\omega }_{\mathrm{n}}{L}_{\mathrm{a}2}})\\ I_{\mathrm{in}3}=(\frac{U_{\mathrm{in}}}{{\omega }_{\mathrm{n}}^2{L}_{\mathrm{f}3}^2}(R_{\mathrm{t}3}+\frac{{\omega }_{\mathrm{n}}^2{M}_3^2}{R_{\mathrm{r}3}+R_{\mathrm{L}3}})+\frac{U_{\mathrm{in}}}{j{\omega }_{\mathrm{n}}{L}_{\mathrm{a}3}})\end{array}$$

(15)

Fourier decomposition of input current $I_{\mathrm{in}}(t)$

$$I_{\mathrm{in}}(t)=a_0+a_1\cos {\omega }_{\mathrm{n}}t+b_1\sin {\omega }_{\mathrm{n}}t+{\displaystyle \sum _{k=2}^{\infty }(a_{\mathrm{k}}\cos k{\omega }_{\mathrm{n}}t+b_{\mathrm{k}}\sin k{\omega }_{\mathrm{n}}t)}$$

(16)

The $a_0$, $a_1$, and $b_1$ can be expressed as

$$\{\begin{array}{l}{a}_0=\frac{2}{T_{\mathrm{s}}}{\displaystyle {\int }_0^{T_{\mathrm{s}}}{V}_{{}_{\mathrm{P}}}\sin {\omega }_{1}tdt}=\frac{2V_{{}_{\mathrm{P}}}}{T_{\mathrm{s}}{\omega }_1}\\ a_1=\frac{2}{T_{\mathrm{s}}}{\displaystyle {\int }_0^{T_{\mathrm{s}}}{V}_{{}_{\mathrm{P}}}\sin {\omega }_{1}t\cos {\omega }_{\mathrm{n}}tdt}=\frac{2V_{{}_{\mathrm{P}}}{\omega }_1(\cos {\omega }_{\mathrm{n}}{T}_{\mathrm{s}}+1)}{T_{\mathrm{s}}({\omega }_1^2-{\omega }_{\mathrm{n}}^2)}\\ b_1=\frac{2}{T_{\mathrm{s}}}{\displaystyle {\int }_0^{T_{\mathrm{s}}}{V}_{{}_{\mathrm{P}}}\sin {\omega }_{1}t\sin {\omega }_{\mathrm{n}}tdt}=\frac{2V_{{}_{\mathrm{P}}}{\omega }_1}{T_{\mathrm{s}}({\omega }_1^2-{\omega }_{\mathrm{n}}^2)}\sin {\omega }_1{T}_{\mathrm{s}}\end{array}$$

(17)

The fundamental waves I_in1, I_in2, and I_in3 and harmonics of the input currents I_in1, I_in2, and I_in3 of each subsystem can be obtained according to Equation (16), and the fundamental waves can be phase-shifted and suppressed according to the vector analysis shown in Equation (18).

$$\{\begin{array}{c}{\dot{I}}_{\mathrm{in}1}=-({\dot{I}}_{\mathrm{in}2}\times \cos \alpha +{\dot{I}}_{\mathrm{in}3}\times \cos \beta )\\ {\dot{I}}_{\mathrm{in}2}\times \sin \alpha =-({\dot{I}}_{\mathrm{in}3}\times \sin \beta )\end{array}$$

(18)

If the phase shift angle of subsystem 1 is zero, α and β are the phase shift angles of subsystem 2 and subsystem 3.

According to Equation (17), taking the input voltage of 25 V, the load of 10 Ω, the switching frequency of 100 kHz, and the balanced coupling of three coils as an example, the harmonic content of the input current I_in(t) after Fourier decomposition before and after phase shifting is shown in Figure 9a,b. The black curve in Figure 9a is the input current waveform before phase shifting; it can be decomposed into a DC component, fundamental wave, and superposition of harmonics with Fourier. DC in Figure 9a,b represents the DC component. I–V in Figure 9 represents the DC component fundamental wave and harmonics, respectively. Figure 9a shows that the input current has a large harmonic content and a large fundamental effective value before phase shifting. Figure 9b shows that the input current has a small harmonic content and a small fundamental effective value after phase shifting.

3.2. System Structure

The system structure diagram is shown in Figure 10. During the transmission process, by adjusting the phase shift conduction angle of the coils α and β, the total current output of the DC source is controlled so that the ripple of the total current is minimized, and the efficiency of the whole machine is higher.

In the actual system, a single-switch wireless power transfer subsystem is selected as the reference, and its conduction angle is 0°, so the remaining two control degrees of freedom α and β can be obtained according to Equation (18).

4. Verification of Simulation and Experimental Results

4.1. Verification of Simulation Results

The three-coil parallel transmission simulation model was built using MATLAB/Simulink software, and the parameters are shown in

Table 2. Prototype parameters of single-switch WPT system.

Vdc	f	La	Ca	Lf	Cf	Ct
25 V	100 kHz	6 μH	187 nF	60 μH	42.2 nF	77.5 nF
Lt	M	Cr	Lr	Rt	Rr	RL
97.7 μH	46.4 μH	28.2 nF	90.5 μH	350 mΩ	330 mΩ	10 Ω

. The switching frequency of the system was 100 kHz, and the duty ratio of the switch tube was set to 0.5.

4.1.1. Verification of Subsystem Balanced Coupling Simulation Results

In order to verify the advantages of P^# type single-switch resonant inverter structure, the parameters of traditional and P^# type LCC compensation topologies were set to be the same. In the case of the balanced coupling of the system, the input current I_in before and after the phase shift of the traditional single-switch resonant inverter LCC compensation network is shown in Figure 11. When the subsystem adopted the traditional control strategy of simultaneous conduction, the input current was distorted seriously. The THD was 47.1%, the DC component was 7.5 A, and the fundamental wave effective value was 7.7 A. When the subsystem adopted the conduction mode of sequential phase shift of 120°, the current amplitude was greatly reduced, but the current distortion was more serious. The THD was 61.1%. At this time, the DC component was 7.4 A, and the fundamental wave effective value was 1.9 A.

When the input current I_in of the P^# type single-switch resonant inverter LCC compensation network subsystem was simultaneously turned on, as shown in Figure 12, the THD was 32.8%, the DC component was 7.4 A, and the fundamental wave effective value was 11.4 A. The current waveform of the subsystem was smooth after the 120° phase shift in turn. The THD value decreased significantly to only 6.1%, the DC component was 7.4 A, and the fundamental wave effective value decreased to 0.68 A.

4.1.2. Verification of Simulation Results of Unbalanced Coupling of Subsystems

In order to verify the universality and effectiveness of the proposed phase shift ripple suppression method, the coupling coefficients of the P^# type single-switch resonant inverter subsystem were set to M₁ = 50 μH, M₂ = 46.4 μH and M₃ = 42 μH, respectively. According to Equation (18), the optimal phase shifting angles of the input currents I_in1, I_in2, and I_in3 are 0°, 125.7°, and 239.7°, respectively. The input current I_in is shown in Figure 13. When all subsystems were turned on at the same time, the THD of the input current was 32.9%, the DC component was 7.4 A, and the fundamental effective value was 11.2 A. After the phase shift was turned on, the THD value of the input current decreased greatly to only 9.7%, the DC component was 7.5 A, and the effective value of the fundamental wave was only 0.66 A.

4.2. Verification and Analysis of Experimental Results

In order to further verify the feasibility of the method proposed in this paper, an experimental platform was built, as shown in Figure 14.

The main parameters were consistent with the simulation parameters. The controller was STM32F407ZGT6, the drive circuit was UCC27511, and the switch of the P^# single-switch resonant inverter was B33N60E power MOSFET. The number of turns of the transmitting and receiving coils was 24 and the diameter was 160 mm. At the same time, a 2 mm thick ferrite was laid on the bottom of the coil to improve the coupling coefficient and shield magnetic leakage. The distance between the transmitter and the receiver was 50 mm.

Figure 15 is a soft switching waveform of the switch tube of the inverter 1. When the driving signal V_gs of the switch changed from the low level at time t₁ to the high level at time t₂, the drain source voltage V_ds of the switch fell to zero, which indicates that the switch realized zero-voltage turn-on.

Figure 16 shows waveforms of the input voltage V_o and the input current I_r of the rectifier 1. The RMS of the input voltage V_o was 21.8 V and the RMS of the input current I_r was 2.46 A.

Figure 17 is a comparison of the input current I_in of the traditional single-switch resonant inverter and the P^# type single-switch resonant inverter LCC compensation topology. Through comparison and analysis, it can be seen that the distortion of the input current I_in of the traditional single-switch resonant inverter was reduced due to the clamping effect of the power supply, but the input current of the P^# type LCC compensation topology was smoother.

Figure 18 is a comparison of input current waveforms before and after parallel phase shifting based on the P^# type single-switch resonant inverter subsystem under the transmission distance of 50 mm. The input current ripple before phase shifting of the system was large, with a peak-to-peak value of 8.5 A. The input current peak-to-peak value of the subsystem was 2.76 A after phase shifting of 0°, 123.7°, and 241.5°, which greatly reduced the input current ripple and made the input current waveform more stable.

Figure 19 is the input current waveform before and after parallel phase shifting based on the P^# type single-switch resonant inverter subsystem when the transmission distance is 40 mm, 50 mm, and 60 mm, respectively. The peak-to-peak value of the input current before phase shifting of the system was 6.98 A; the peak-to-peak value of the input current of the system was 1.6 A after the subsystem was shifted by 0°, 88.7°, and 251.4°, respectively. It shows that the proposed method also has good anti-offset control performance in the case of asymmetric system parameters.

Figure 20 shows the efficiency changes before and after the phase shift of the three coils in parallel by comparing the input voltage of 5–30 V and the load of 5–30 Ω. With the increasing input voltage, when the input voltage was greater than 8 V, the effect after the phase shift was gradually better than that without the phase shift. When the input voltage was 30 V and the load was 15 Ω, the pre-phase-shift efficiency was 84.3% and the post-phase-shift efficiency was 88.2%, an increase of 3.9 percentage points. The fundamental reason is that the proposed control method can effectively improve the input current ripple and improve the system efficiency.

5. Conclusions

This paper proposes a novel P^# type LCC-S compensation network for the single-switch wireless power transfer system of electric-powered vehicles. The proposed method was used to phase shift the ripple to reduce the ripple of the input current and improve the efficiency of the system. Finally, simulation and experimental verification were carried out, which proved the validity and feasibility of this method. The following key conclusions can be drawn:

(1)

Connecting the resonant capacitor C_a in parallel with the switch tube can effectively improve the input current waveform and reduce the THD of the input current.

(2)

By controlling the phase shift of the excitation current of the multi-coils, the input current ripple can be effectively eliminated, so that the input current becomes stable and the system efficiency can be improved.

(3)

When the input voltage was 30 V and the rated power was 150 W, the efficiency of the system increased from 84.3% to 88.2%. It increased by 3.9 percentage points.