Design of WPT System Based on Interleaved Boost Converter

Abstract

With the improvement of technology, the demand for electrical power continues to deepen. Wireless Power Transfer (WPT) technology can transmit power without using physical media such as cables, and it has the advantages of electrical isolation, convenience, and safety. At present, the miniaturization of the secondary side is an emerging trend of WPT systems, which is analyzed in this paper. By introducing an interleaved boost converter in the front stage, the DC bus voltage of the primary side is increased, the loss of the primary side is reduced, and the system efficiency is improved. At the same time, the self-inductance of the primary and secondary sides of the loosely coupled transformer is designed to meet the stress requirements of passive devices and the realization of a closed-loop system. Finally, a WPT system with an input voltage of 100 V, an output voltage of 100 V and a transmission power of 500 W is built. The transmission distance of this system is 170 mm, with a lateral offset of 200 mm and a vertical offset of 100 mm. After the offset of the primary and secondary sides, the output voltage can be stabilized at 100 V, and the system efficiency can reach 90.1%, which proves the feasibility of the system efficiency improvement strategy and the effectiveness of the closed-loop control.

1. Introduction

At present, wired power transmission technology using a metal medium to transfer electric power has been widely used. However, the long working time of the transmission line may produce sparks, which will not only increase the line loss but also significantly reduce the safety. In order to solve the above difficulties, an isolated power transmission technology is being widely promoted, namely wireless power transmission technology [1,2]. Wireless power transmission technology can be applied in electric vehicles [3], underwater equipment charging [4], implantable medical treatment [5] and other occasions [6,7].

To expand the load lifetime and achieve better performance, the output voltage/current of a WPT system should be stable. Nevertheless, the misalignment between the transmitter (Tx) and receiver (Rx) has a great impact on output voltage/current. Hence, an effective closed-loop control scheme is essential. Three types of control strategies are commonly utilized in WPT systems. They are primary side control (PSC), secondary side control (SSC), and primary and secondary side control (PSSC), respectively [8,9,10]. In this study, PSC (SSC) refers to the control that both the sampling and control are implemented at the primary (secondary) side while PSSC refers to the control that the sampling and control are implemented at the secondary and primary sides, respectively. The response of PSC is fast, but the output accuracy is low. It is not suitable for scenarios where high output accuracy is required. The output accuracy of SSC is high, but it increases the volume and weight of the Rx. PSSC feeds the output voltage/current at the secondary back to the primary. Hence, the control accuracy is high. In addition, PSSC is suitable for applications where the primary space is large and the secondary space is small, for instance, electric vehicle wireless charging systems (EVWCSs). Therefore, this paper will focus on PSSC.

Variable frequency control at the primary and secondary sides can keep the output voltage/current constant, but it results in the loss of resonance and zero phase angle (ZPA) and introduces a large amount of reactive power increasing the stresses over the components [11]. Phase shift control of a WPT system using a full bridge inverter can maintain the resonance of the system, but the disadvantages of low inverter gain (defined as the ratio of the fundamental harmonic of the output voltage of the inverter to the DC input voltage of the inverter) and narrow adjustment range limit its utilization in practical systems [12]. To increase the inverter gain and widen the adjustment range, this paper replaces the full bridge inverter with an interleaved boost converter (IBC). A greater inverter gain indicates a higher output voltage of the inverter and smaller currents and losses in the primary. Moreover, the IBC can reduce the ripple of the DC input current. Consequently, the impact of the WPT system on the power grid is attenuated.

Misalignment tolerance is an important issue in electric vehicle wireless charging systems (EVWCSs) [13,14,15]. Optimizing compensation topologies and modifying magnetic couplers are two widely employed methods that can effectively improve the misalignment tolerance of WPT systems. However, optimizing compensation topologies may introduce additional resonant components and reduce system efficiency [4,5,16]. When the primary and secondary sides are offset, the duty ratio of the primary side interleaved boost is adjusted by the method of closed-loop control to realize the voltage regulation characteristic.

The remainder of this paper is organized as follows. Section 2 analyzes the working principles of the WPT system, especially the input and output characteristics of the IBC. Section 3 focuses on the system modeling and closed-loop control strategy. Section 4 introduces the proposed parameter design method in detail. To verify the correctness of the theoretical analysis and the advantages of the proposed system, a prototype whose output power is 500 W was built in Section 5. Section 6 draws some conclusions.

The main electrical and physical parameters of the system are shown in

Table 1. Main electrical and physical parameters of the prototype.

Parameters	Symbol	Parameters	Symbol
Operation Frequency f0	f0	Dead time angle	θdead
Input Voltage	Uin	Output voltage of the IBC	UAB
Output Voltage	UO	RMS value of UAB	UAB1
Transmission Power	PN	duty cycle of the IBC	D
Self-inductance of primary coil	LP	Value of primary capacitor	C1
Self-inductance of secondary coil	LS	Value of secondary capacitor	C2
RMS current value of primary coil	ILP	Relative voltage gain	G0
RMS current value of secondary coil	ILS	Input impedance	Zin
Peak value of the voltage of C1	UC1	Input impedance angle	θin
Peak value of the voltage of C2	UC2	Copper losses	Ploss
Equivalent impedance of element	Xi	Disturbance coefficient	α/β

.

2. Circuit Analysis

2.1. System Introduction

Figure 1 is the schematic diagram of the proposed WPT system. U_in is the DC input voltage. Q₁~Q₄ are four high-frequency MOSFETs, and C_in is a voltage regulator capacitor. L₁ and L₂ are two interleaved parallel inductors used to boost the voltage on the DC bus. Q₁~Q₄, L₁ and L₂ constitute the DC/AC converter of the front stage. The converter can be regarded as consisting of an interleaved boost converter and a full-bridge inverter. C₁ and C₂ are the compensation capacitors of the primary and secondary sides, L_P and L_S are the self-inductances of the primary and secondary sides of the loosely coupled transformer, and M is the mutual inductance of the primary and secondary sides. D₁~D₄ are four rectifier diodes, C_F is a filter capacitor, and R is a resistive load.

2.2. Output Gain Analysis

When the duty cycle of the interleaved boost circuit is different, that is (a) D ≤ 0.5 and (b) D > 0.5, the output voltage waveform is shown in Figure 2. G(Q_X) is the driving signal of the switch tube Q_X.

According to Figure 2, the dead time angle of the output voltage U_AB can be expressed as:

$${\theta }_{\mathrm{dead}}=\left\{\begin{array}{cc}\mathsf{\pi }-2\mathsf{\pi }D& \left(D<0.5\right)\\ 0& \left(D=0.5\right)\\ 2\mathsf{\pi }D-\mathsf{\pi }& \left(D>0.5\right)\end{array}\right.$$

(1)

From the waveform in Figure 2 and Formula (1), the relationship between the fundamental RMS value of the output voltage of the interleaved boost converter and the parameters of the circuit can be obtained:

$$U_{\mathrm{AB}1}=\frac{2\sqrt{2}{U}_{\mathrm{in}}}{\mathsf{\pi }\left(1-D\right)}\cos \left(\mathsf{\pi }D-\frac{\mathsf{\pi }}{2}\right)$$

(2)

According to the controlled source equivalent model of the loosely coupled transformer, the equivalent model of the WPT system can be obtained. When the compensation capacitance and self-inductance of the primary side resonate in series, the expression of the RMS current value I_LS of the secondary side can be deduced:

$$I_{\mathrm{LS}}=-\frac{2\sqrt{2}{U}_{\mathrm{in}}}{\mathrm{j}\omega M\mathsf{\pi }(1-D)}\cos \left(\mathsf{\pi }D-\frac{\mathsf{\pi }}{2}\right)$$

(3)

From this, the expression of the output voltage can be deduced as:

$$U_{\mathrm{O}}=\frac{8R{U}_{\mathrm{in}}}{\omega k\sqrt{L_{\mathrm{P}}{L}_{\mathrm{S}}}{\mathsf{\pi }}^2(1-D)}\cos \left(\mathsf{\pi }D-\frac{\mathsf{\pi }}{2}\right)$$

(4)

3. Efficiency Improvement Strategy Analysis

In this section, through the quantitative analysis of the copper loss of the primary and secondary sides of the secondary side miniaturized wireless charging system, the strategy for improving the system efficiency and the reasonable value of the boost ratio are obtained. For the convenience of analysis, the relative voltage gain G₀ is defined as:

$$G_0=\frac{1}{1-D}\cos \left(\mathsf{\pi }D-\frac{\mathsf{\pi }}{2}\right)$$

(5)

Assuming that the resistances on the primary and secondary coils of the loosely coupled transformer are R_LP and R_LS, respectively, the copper loss on the primary and secondary sides before the pre-stage boost conversion can be expressed as:

$$P_{\mathrm{loss}}=I_{\mathrm{LP}}{}^2{R}_{\mathrm{LP}}+I_{\mathrm{LS}}{}^2{R}_{\mathrm{LS}}$$

(6)

When the interleaved boost converter is used for boost conversion in the front stage, the fundamental RMS value of the output voltage after the inverter is increased by G₀ times, and the primary current is reduced by G₀ times:

$$I_{\mathrm{LP}}{}^{\prime }=\frac{1}{G_0}{I}_{\mathrm{LP}}$$

(7)

According to Formula (4), before and after the boost conversion, in order to keep the output voltage unchanged, the self-inductance of the primary and secondary sides needs to be increased, so the self-inductance relationship before and after the conversion is:

$$\sqrt{L_{\mathrm{P}}{}^{\prime }{L}_{\mathrm{S}}{}^{\prime }}=G_0\sqrt{L_{\mathrm{P}}{L}_{\mathrm{S}}}$$

(8)

For the convenience of analysis, let the self-inductance of the primary side increase to a times the original, and the self-inductance of the secondary side increase to b times the original. Then the relationship between the two is:

$$b=\frac{G_0{}^2}{a}$$

(9)

The square of the number of turns on the primary and secondary sides is proportional to the self-inductance value, and the parasitic resistance on the primary and secondary coils is proportional to the number of turns, so the square of the parasitic resistance on the coil is proportional to the self-inductance value. After the boost conversion, the parasitic resistance of the primary and secondary sides can be expressed as:

$$\left\{\begin{array}{l}{R}_{\mathrm{LP}}{}^{\prime }=\sqrt{a}{R}_{\mathrm{LP}}\\ R_{\mathrm{LS}}{}^{\prime }=\sqrt{b}{R}_{\mathrm{LS}}=\frac{G_0}{\sqrt{a}}{R}_{\mathrm{LS}}\end{array}\right.$$

(10)

At this time, the copper loss of the primary and secondary sides of the loosely coupled transformer is:

$$\begin{array}{cc}{P}_{\mathrm{loss}}{}^{\prime }& =I_{\mathrm{LP}}{{}^{\prime }}^2{R}_{\mathrm{LP}}{}^{\prime }+I_{\mathrm{LS}}{{}^{\prime }}^2{R}_{\mathrm{LS}}{}^{\prime }\hfill \\ & ={\left(\frac{1}{G_0}{I}_{\mathrm{LP}}\right)}^2\sqrt{a}{R}_{\mathrm{LP}}+I_{\mathrm{LS}}{}^2\frac{G_0}{\sqrt{a}}{R}_{\mathrm{LS}}\hfill \end{array}$$

(11)

According to Equations (6) and (11), the reduction in the primary and secondary side copper losses before and after the boost conversion is:

$$\begin{array}{cc}\Delta P_{\mathrm{loss}}& =P_{\mathrm{loss}}-P_{\mathrm{loss}}{}^{\prime }\hfill \\ & =\left(1-\frac{\sqrt{a}}{G_0{}^2}\right)I_{\mathrm{LP}}{}^2{R}_{\mathrm{LP}}+\left(1-\frac{G_0}{\sqrt{a}}\right)I_{\mathrm{LS}}{}^2{R}_{\mathrm{LS}}\hfill \\ & =\left(1-\frac{\sqrt{a}}{G_0{}^2}\right)P_{\mathrm{loss}-\mathrm{pri}}+\left(1-\frac{G_0}{\sqrt{a}}\right)P_{\mathrm{loss}-\sec }\hfill \end{array}$$

(12)

In the above formula, P_loss-pri and P_loss-sec represent the losses of the primary and secondary sides, respectively. In the traditional wireless power transmission system, the voltage levels of the input and output voltages are generally the same. When using the S/S compensation, the currents on the primary and secondary sides are generally the same. In the miniaturized WPT system on the secondary side, the parasitic resistance on the primary coil is greater than the secondary side, so the primary side loss is greater than the secondary side loss. Figure 3 shows the relationship between the loss reduction and the primary and secondary side losses under different relative voltage gains. The abscissa of the region is greater than 1 in this paper, that is, P_loss-pri > P_loss-sec.

When the multiple of the primary side self-inductance increases a ≥ 2, the ordinates are all greater than 0, which also proves that increasing the primary side DC bus voltage can reduce the loss on the coil and effectively improve the efficiency of the system. It can be seen from Figure 3a,b that when the relative voltage gain is different, the trend of the curve is also different. In order to ensure that the ordinate of the image is greater than 0 under the condition that a takes different values, that is, the efficiency is improved, G₀ The value of is generally around 2.

In this paper, the input impedance angle of the system is analyzed to make it inductive, so as to create a condition for the realization of ZVS. The equivalent circuit of the proposed WPT system is shown in Figure 4.

In the resonant state, the equivalent impedance of the resonant elements are X₁^* and X₂^*

$$\left\{\begin{array}{c}{X}_1^{*}=\omega L_{\mathrm{P}}=\frac{1}{\omega C_1^{*}}\\ X_2^{*}=\omega L_{\mathrm{S}}=\frac{1}{\omega C_{{}_2}^{*}}\end{array}\right.$$

(13)

α and β are the disturbance coefficient. Equation (14) shows the relationship between the equivalent impedance and the disturbance coefficient, where C₁ and C₂ are the actual values, and X₁ and X₂ are the actual impedance.

$$\left\{\begin{array}{c}{X}_1=\frac{1}{\omega C_1}=\alpha X_1^{*}\\ X_2=\frac{1}{\omega C_2}=\beta X_2^{*}\end{array}\right.$$

(14)

Then, the expression of input impedance Z_in can be obtained.

$$Z_{\mathrm{in}}=\frac{{\omega }^2{M}^2{R}_{\mathrm{E}}+\mathrm{j}\left[-{\omega }^2{M}^2{X}_2(1-\beta )+X_1(1-\alpha )R_{\mathrm{E}}{}^2+X_1{X}_2{}^2(1-\alpha ){(1-\beta )}^2\right]}{R_{\mathrm{E}}{}^2+X_2{}^2{(1-\beta )}^2}$$

(15)

According to Equation (15), input impedance angle θ_in can be described as:

$${\theta }_{\mathrm{in}}=\arctan \left(\frac{X_1(1-\alpha )R_{\mathrm{E}}{}^2+X_2(1-\beta )\left[X_1{X}_2(1-\alpha )(1-\beta )-{\omega }^2{M}^2\right]}{{\omega }^2{M}^2{R}_{\mathrm{E}}}\right)$$

(16)

According to the above formula, the input impedance angle θ_in can be turned into inductive to realize ZVS.

Figure 5 shows the block diagram of the proposed closed-loop control system, where G_c(s), G_M(s), G_p(s), G_delay(s), and H(s) are the transfer functions of the compensator, PWM modulator, WPT system, wireless communication delay, and voltage sampling, respectively.

4. Stress Analysis and Parameter Design

The stress of passive components includes voltage stress and current stress. Excessive voltage stress is not conducive to the selection of compensation capacitors and the safe operation of the system. Excessive current stress and large loss on the coils are not conducive to the improvement of system efficiency. When the winding area of a loosely coupled transformer is fixed, the coupling coefficient between the primary and secondary sides generally does not change. Through simulation analysis, the coupling coefficient before and after the offset of the loosely coupled transformer in this paper changes from 0.10686 to 0.0778. Next, this paper designs the self-inductance of the primary and secondary sides according to the voltage stress and current stress. Since the system is a WPT system with a miniaturized secondary side, the optimization range of primary side self-inductance is 500–1500 μH. The optimization range of the secondary side self-inductance value is 100–500 μH. The relationship between the primary side current I_LP and other circuit parameters can be obtained as follows:

$$I_{\mathrm{LP}}=\frac{2\sqrt{2}}{\mathrm{j}\omega k\mathsf{\pi }\sqrt{L_{\mathrm{P}}{L}_{\mathrm{S}}}}{U}_{\mathrm{O}}$$

(17)

According to Equation (17), the contour image of the change of the primary side current with self-inductance when the primary and secondary sides are aligned and offset to the farthest distance (i.e., the coupling coefficient is reduced to the lowest value) can be drawn, as shown in Figure 6. In order to reduce the loss, the value of primary side current is generally less than 5 A. When the primary and secondary sides are offset, the current of the primary side increases significantly. In order to integrate the two situations before and after the offset, the 5 A contour line after the offset is retained, that is, the purple curve in Figure 6b. The secondary side current has nothing to do with the self-inductance of the primary and secondary sides, and the RMS is 5.55 A. In a WPT system with a miniaturized secondary side, the parasitic resistance of the secondary side coil is generally small, so the current value is within a reasonable range.

In this paper, the voltage stress at both ends of the compensation capacitor on the primary and secondary sides is analyzed. The peak value of the voltage U_C1 of the compensation capacitor C₁ is:

$$U_{\mathrm{C}1}=\frac{4L_{\mathrm{P}}{U}_{\mathrm{O}}}{k\mathsf{\pi }\sqrt{L_{\mathrm{P}}{L}_{\mathrm{S}}}}$$

(18)

According to Formula (18), the change of U_C1 with the self-inductance of the primary and secondary sides before and after the offset can be drawn, as shown in Figure 7. When the primary and secondary sides are offset, the voltage across C₁ increases significantly. In order to synthesize the two situations before and after the offset, the 4 kV contour line after the offset is retained in this paper, the voltage across C₁ is less than 4 kV.

The relationship between the voltage U_C2 on the compensation capacitor C₂ and the parameters in the circuit is:

$$U_{\mathrm{C}2}=\sqrt{2}\mathrm{j}\omega L_{\mathrm{S}}{I}_{\mathrm{LS}}$$

(19)

Similarly, the change of U_C2 with the self-inductance of the primary and secondary edges can be drawn, as shown in Figure 8. According to Equation (19), U_C2 is only related to the primary edge self-inductance L_S. In the secondary side-miniaturized WPT system, the secondary side self-inductance is relatively small, so the impedance of the secondary side compensation capacitor is small, and the limit of U_C2 can be appropriately reduced. In this paper, the limit of U_C2 is 1.5 kV. Through the stress limit of passive devices, the stress limit area surrounded by three stress contours can be obtained.

Since the WPT system proposed in this paper is a closed-loop control system, in addition to the stress of passive components, the possibility of closed-loop system implementation should also be considered when designing parameters. According to Equations (4) and (5), the relationship between the relative voltage gain and the self-inductance of the primary and secondary sides can be obtained as:

$$G_0=\frac{\omega k{\mathsf{\pi }}^2{U}_{\mathrm{O}}\sqrt{L_{\mathrm{P}}{L}_{\mathrm{S}}}}{8R{U}_{\mathrm{in}}}$$

(20)

According to Figure 2, it can be found that when the duty cycle is around 0.5, that is, when the relative voltage gain G₀ is around 2, the smaller the dead zone of the output voltage of the interleaved boost converter, the better the overall performance. According to the analysis of system efficiency improvement in Section 2, when G₀ is around 2, the system efficiency improvement can also be guaranteed. According to Equation (20), the contour diagram of the relative voltage gain and the self-inductance of the primary and secondary sides can be drawn before and after the offset, as shown in Figure 9. When the self-inductance of the primary and secondary sides is within the black circle, the stress limit of the passive devices is satisfied, and the relative voltage gain is maintained at around 2. From the result of the simulation, the final value of the primary and secondary side self-inductance is at point A, where the primary side self-inductance L_P is 1177 μH, and the secondary side self-inductance L_S is 282 μH.

5. Results and Discussion

According to the previous theoretical analysis, this paper builds a 500 W wireless power transmission experimental prototype, as shown in Figure 10. The photograph of the experimental setup is as follows. The prototype is comprised of ten modules:

(1)

a dc voltage source for the power circuit;

(2)

a dc voltage source for the driver and controller;

(3)

a boost inverter;

(4)

a primary compensation capacitor;

(5)

a transmitter;

(6)

a receiver;

(7)

a secondary compensation capacitor;

(8)

a full-bridge rectifier and a sampling circuit;

(9)

a resistive load;

(10)

two Bluetooth modules surrounded by yellow dashed circles.

The electrical and physical parameters of the system are shown in

Table 2. Main electrical and physical parameters of the prototype.

Parameters	Value	Parameters	Value
Operation Frequency f0	85 kHz	Transmission Distance	170 mm
Input Voltage Uin	100 V	Lateral Offset Distance	200 mm
Output Voltage UO	100 V	Vertical Offset Distance	100 mm
Transmission Power PN	500 W	Rated Load R	20 Ω
Self-inductance of primary coil LP	1090.4 μH	Value of capacitor C1	3.215 nF
Self-inductance of secondary coil LS	258.9 μH	Value of capacitor C2	13.54 nF

.

The voltage and current waveforms at each node of the system are shown in Figure 11 in the face-to-face situation. At this time, the output voltage is 100 V, the input power is 555 W, the output power is 500 W, and the system efficiency can reach 90.1%. At this time, the dead time of the interleaved boost converter is 0.37 μs, the duty cycle is 0.5157, and the bus voltage is boosted to 206 V. When the primary and secondary sides are laterally offset by 200 mm, the output waveform is similar to that when the primary and secondary sides are aligned. At this time, the output voltage is 99.8 V, the input power is 578 W, the output power is 498 W, and the system efficiency can reach 86.2%. At this time, the dead time of the interleaved boost converter is 0.64 μs, the duty cycle is 0.4728, and the bus voltage is boosted to 185 V. When the primary and secondary sides are offset by 100 mm longitudinally, the output waveform is similar to that when the primary and secondary sides are offset by 200 mm in the lateral direction. At this time, the output voltage is 100 V, the input power is 575 W, the output power is 500 W, and the system efficiency can reach 87%. At this time, the dead time of the interleaved boost converter is 0.67 μs, the duty cycle is 0.4715, and the bus voltage is boosted to 183 V.

Figure 12 shows the dynamic response waveform of the system. When the input voltage changes from 90 V to 120 V when the original and auxiliary sides are facing each other, the output voltage of the system remains unchanged, and the adjustment time is 62 ms. The dynamic performance of the system is excellent, which verifies the effectiveness of the closed-loop system.

The experimental waveforms in different phase-shifted conditions are as shown in Figure 13. The duty cycle of parallel boost is 0.516, 0.473 and 0.471, respectively. As can be seen from the figure, ZVS is realized in different phase-shifted conditions.

The power transfer efficiency (PTE) and output voltage curves according to the offset condition are given as shown in Figure 14.

In the whole operating area, the output voltage is stable which only fluctuates by 0.2%. The accuracy of the closed-loop control is demonstrated. PTE decreases when X- and Y-direction misalignments are increased. However, the minimum PTE is as high as 86.2% even if the X-direction misalignment is 200 mm. More importantly, such an efficiency is achieved in the case that the employed ferrite is reduced by 41% and the power transfer distance is as long as 170 mm.

6. Conclusions

In this paper, a WPT system based on an interleaved boost converter was proposed. When the primary and secondary sides were offset and the input voltage was disturbed, the output voltage could keep constant by adjusting the duty ratio of the interleaved boost converter on the front stage. In a miniaturized WPT system of the secondary side, increasing the DC bus voltage of the primary side could reduce the copper loss of the loosely coupled transformer. In this paper, the stress of passive devices was analyzed, and the self-inductance of the primary and secondary sides was reasonably designed so that the stress after the system offset was within a reasonable range, and the duty cycle of interleaved boost converter fluctuated around 0.5. In order to verify the theoretical analysis, a 500 W prototype with a maximum efficiency of 90.1% was built. When the primary and secondary sides were offset, the output voltage of the system could be stabilized at 100 V. Subsequently, the high-order compensation topology can be introduced into the WPT system with a miniaturized secondary side, leading to the freedom of system parameter design and the transmission efficiency of the system being further improved.