Reconfigurable Hybrid Resonant Topology for Constant Current/Voltage Wireless Power Transfer of Electric Vehicles

Abstract

This paper proposes a reconfigurable hybrid topology (RHT) for the constant current (CC)/constant voltage (CV) charging of electric vehicles. The proposed system combines the series–series and the inductor and double capacitors-series topologies. Two AC switches (ACSs) are utilized to change the CC and CV charging modes, without requiring an additional resonant network. A detailed analysis for designing the hybrid topology parameters is also presented; a three-kilowatt prototype was configured based on this analysis in order to validate the proposed system. The constructed prototype confirmed the stable mode changes, load fluctuations, CC/CV output characteristics and efficiency of the proposed system. The maximum efficiency of the proposed RHT was found to be 92.58%.

1. Introduction

Owing to their various advantages, wireless power transfer (WPT) systems have attracted significant attention for their applicability in charging the batteries of electric vehicles (EVs) [1,2,3]. However, compared to conductive charging, WPT is less efficient due to the low coupling coefficient and the various operating conditions. Thus, it is essential to improve the efficiency of this approach.

A constant current/constant voltage (CC/CV) has been widely used to charge EV batteries, because it combines the advantages of both the CC and CV charging methods [4]. Figure 1 presents the CC/CV charging profile. Several conventional schemes can be utilized to achieve CC/CV charging via a WPT system. For instance, additional power converters can be added to the front or post stages of the system for output regulation [5,6,7,8,9]. By adjusting the duty cycle, impedance tracking and CC/CV charging can be realized. However, using such large additional devices lowers the efficiency and increases the volume of the WPT system. Moreover, owing to the limited switching frequency variation (80–90 kHz), as defined by SAE J2954 [10], a few studies [11,12,13,14,15] have combined frequency control and phase-shift (PS) control to realize zero voltage switching and CC/CV charging. However, these methods can increase the reactive current due to the greater current phase angle, which leads to increased conduction losses in several components. Additionally, high-speed communication is required for real-time control, which, in turn, increases the complexity and cost of the system.

Compensation topologies, which consist of passive resonant networks, are used in WPT systems to compensate for the low coupling coefficient. Based on the structure of the resonant network, the compensation circuit features CC or CV characteristics. Thus, by integrating resonant networks and a reconfigurable switching structure, a zero phase angle (ZPA) and CC/CV output can be achieved simultaneously [16,17,18]. This method has garnered considerable research attention because compensation topologies provide easy controllability and are also relatively cheap. In [19], a composite topology, which was a combination of series–series (S–S) and series–parallel (S–P) topologies, is proposed, whereby a CC/CV output could be realized via switching. However, this required three AC switches (ACSs) and a center-tapped transformer, thereby increasing the complexity of the topology. In [20], compensation topologies that enable switching between four resonant networks, i.e., S–S, S–P, parallel–series (P–S) and parallel–parallel (P–P), in order to achieve a CC/CV output are proposed. However, these four compensated networks have limited parameter design freedom and are more sensitive to load variations. Additionally, three ACSs are required to switch between each operating mode. Based on the LCC-S compensation topology for charging EV batteries, a switching hybrid topology is proposed in [21], whereby the CC/CV charging modes can be switched via two ACSs, without changing the structure of the topology. However, because these two ACSs are placed on different sides, high-speed synchronous communication is necessary for accurate mode switching. In [22], for CC and CV outputs, a hybrid and reconfigurable WPT system with a high-misalignment tolerance is proposed. However, the four-coil structure and the large resonant devices utilized increase the cost and volume of the system. Although previous studies have focused on hybrid switching topologies for low-power systems (< one kilowatt), further research on such topologies for high-power systems that are suitable for EVs is essential.

This paper proposes a reconfigurable hybrid topology (RHT) based on the S–S and LCC-S compensation topologies for achieving CC/CV output characteristics. A detailed analysis of each operation mode is presented based on the transformer T model. The compensation circuit parameters are designed to satisfy charging requirements and the ZPA condition. Two ACSs are utilized to switch between the CC and CV charging modes. As these ACSs are both located on the primary side, only a single controller is required to realize load-independent CC/CV charging. The proposed RHT system was verified using a three-kilowatt experimental prototype.

2. Theoretical Analysis of Reconfigurable Topologies

Figure 2 presents the structure of the proposed WPT system based on the RHT. It consists of a full-bridge inverter (FBI), primary-loop compensation inductor L_IN, primary-loop series-compensation capacitor C_p, primary-loop shunt-compensation capacitor C_F, primary-loop additional-shunt compensation capacitor C_AF, secondary-loop series-compensation capacitor C_S, rectifier and two additional switches S₁ and S₂ for the reconfigurable compensation network.

Here, U_DC, U_AB and I_IN are the input DC-link voltage, FBI output voltage and the FBI output current, respectively. U_AB can be expanded by using the Fourier series as follows:

$$U_{\mathrm{AB}}=\frac{4U_{\mathrm{DC}}}{\pi }{\displaystyle \sum _{n=1,3,5\cdots }\frac{\sin (n\phi )}{n}}$$

(1)

where φ is the phase difference and n is the harmonics order number. It should be noted that S₁ and S₂ are the switches to change between the CC and CV modes, respectively. A full bridge rectifier is applied to generate the charging voltage U_Bat and current I_Bat, U_Bat, I_Bat and R_Bat can be derived by applying the fundamental harmonic analysis according to [23]:

$$U_{\mathrm{Bat}}=\frac{\pi \sqrt{2}}{4}{U}_{\mathrm{ab}}$$

(2)

$$I_{\mathrm{Bat}}=\frac{2\sqrt{2}}{\pi }{I}_{\mathrm{S}}$$

(3)

$$R_{\mathrm{Bat}}=\frac{{\pi }^2}{8}{R}_{\mathrm{ac}}$$

(4)

where U_ab and I_S are the RMS values. The output AC and DC equivalent resistance are defined as R_ac = U_AB/I_S and R_Bat = U_Bat/I_Bat, respectively.

In the WPT system, the primary and secondary coils are considered as a loosely coupled transformer (LCT) because of the small coupling coefficient k. Two LCT circuits models are presented in Figure 3. Here, U_P and I_p are the primary coil voltage and current, respectively; U_S and I_S are the secondary coil voltage and current, respectively; and L_P and L_S are the self-inductances of the primary and secondary coils, respectively. Moreover, M is the LCT mutual inductance. The voltage equations for Figure 3a can be derived by Kirchhoff’s voltage law, as follows:

$$\{\begin{array}{l}{U}_{\mathrm{P}}=j\omega L_{\mathrm{P}}{I}_{\mathrm{P}}-j\omega M{I}_{\mathrm{S}}\\ U_{\mathrm{S}}=j\omega L_{\mathrm{S}}{I}_{\mathrm{S}}+j\omega M{I}_{\mathrm{P}}\end{array}$$

(5)

In addition, the T model parameters can be derived as:

$$\{\begin{array}{l}{L}_{\mathrm{T}}=L_{\mathrm{P}}-M\\ L_{\mathrm{R}}=L_{\mathrm{S}}-M\end{array}$$

(6)

where L_T and L_R are the primary and secondary leakage inductances of the coils, respectively.

2.1. Constant Current Output Characteristics of Proposed RHT System

As shown in Figure 2, the ACSs S₁ and S₂ are both turned-off, and the parasitic resistance of each component is neglected. The equivalent T model for the CC mode is shown in Figure 4, where L_P and L_S are the primary and secondary self-inductances of coils, respectively; M is the mutual inductance; and L_T′ is the series equivalent inductance of L_T and L_IN.

$${L_{\mathrm{T}}}^{\prime }=L_{\mathrm{T}}+L_{\mathrm{IN}}$$

(7)

In order to operate system in ZPA condition, each resonance frequency of the proposed system is defined as one resonance frequency ω₀ (hereinafter referred to as the operating angular frequency of the compensation network). If C_F is sufficiently high, the series connected L_T′ and C_F can be considered as an equivalent capacitance C′, that is,

$$C^{\prime }=\frac{C_{\mathrm{F}}}{1-{\omega }_0^2{L}_{\mathrm{T}}^{\prime }{C}_{\mathrm{F}}}$$

(8)

if C′ is designed to resonate with M, the following equations can be derived:

$$0=j({\omega }_{0}M+\frac{1}{{\omega }_0{C}^{\prime }})$$

(9)

$${\omega }_0{}^2=\frac{1}{M{C}^{\prime }}=\frac{1}{L_{\mathrm{P}}{C}_{\mathrm{F}}}$$

(10)

$$I_{\mathrm{S}}=-j{U}_{\mathrm{AB}}\sqrt{\frac{C_{\mathrm{F}}}{M}}=\frac{U_{\mathrm{AB}}}{j{\omega }_{0}M}$$

(11)

on substituting Equation (11) in Equation (3), under the CC mode, I_Bat can be derived as:

$$I_{\mathrm{Bat}}=\frac{2\sqrt{2}}{\pi }{I}_{\mathrm{S}}=\frac{2\sqrt{2}{U}_{\mathrm{AB}}}{{\omega }_0\pi M}$$

(12)

Provided U_AB and mutual inductance M are constant, and the resonant condition in Equation (10) is satisfied, according to Equation (12), I_Bat is constant and independent of the load, and ZPA can be achieved using a zero reactive power. The total input impedance Z_IN can be expressed as:

$$Z_{\mathrm{IN}}=j\left(w_0{L}_{\mathrm{T}}-\frac{1}{w_0{C}_{\mathrm{F}}}\right)+\left(j{w}_{0}M\Vert Z_{\mathrm{S}}\right)$$

(13)

where the secondary-side equivalent impedance is $Z_{\mathrm{S}}=j\left({\omega }_0{L}_{\mathrm{R}}-\frac{1}{{\omega }_0{C}_{\mathrm{S}}}\right){+R}_{\mathrm{ac}}$. Under the condition of ω₀² = 1/(L_PC_F) = 1/(L_SC_S) and by substituting Equation (2) and Equation (3) into Equation (6), the total input impedance in CV mode Z_IN.CV can be simplified as:

$$Z_{\mathrm{IN}.\mathrm{CV}}=\frac{{\left(\pi {\omega }_{0}M\right)}^2}{8R_{\mathrm{Bat}}}$$

(14)

Based on Equation (7), Z_IN.CV presents a resistive characteristic, i.e., ZPA can be achieved. From Equation (4) and Equation (14), the input current in CC mode I_IN.CC can be calculated as:

$$I_{\mathrm{IN}.\mathrm{CC}}=\frac{U_{\mathrm{AB}}}{Z_{\mathrm{IN}.\mathrm{CC}}}=\frac{U_{\mathrm{AB}}{R}_{\mathrm{ac}}}{{({\omega }_{0}M)}^2}$$

(15)

According to Equation (15), I_IN.CC is proportional to R_ac. The input phase angle θ_IN can be calculated using the imaginary (Im) and real (Re) parts of the input impedance as follows:

$$G_V=\frac{U_{\mathrm{ab}}}{U_{\mathrm{AB}}}=\frac{U_{\mathrm{Bat}}}{U_{\mathrm{DC}}}$$

(16)

To calculate the output current and voltage, the voltage gain G_V and the transconductance gain G_T of the proposed system are defined as follows:

$$G_T=\frac{I_{\mathrm{Bat}}}{U_{\mathrm{AB}}}=\frac{I_S}{U_{\mathrm{DC}}}$$

(17)

Based on the abovementioned equations, the primary curves of the frequency characteristics under the CC mode, based on the parameters listed in

Table 1. Key parameters of the proposed system.

Note	Symbol	Value
DC-link voltage	UDC	300 V
Resonance frequency	f0	85 kHz
Maximum charging power	Po	3000 W
Constant charging voltage	VCV	130 V
Constant charging current	ICC	23 A
Coupling coefficient	k	0.09
Primary coil self-inductance	LP	203.37 µH
Secondary coil self-inductance	LS	226.22 µH
Primary-loop compensation inductance	LIN	44.68 µH
Primary-loop series compensation capacitance	CP	78.54 nF
Primary-loop additional-series compensation capacitance	CAF	8.03 nF
Primary-loop shunt-compensation capacitance	CF	22.22 nF
Secondary-loop series-compensation capacitance	Cs	15.33 nF

, are presented in Figure 5. ZPA can be achieved at the resonance frequency and the current gain is identical to that at the resonance frequency, as shown in Figure 5c. However, the voltage gain is altered because of the CC characteristic.

2.2. Constant Voltage Output Characteristics of Proposed RHT System

Figure 6 presents the equivalent circuit for the CV mode when both the ACSs S₁ and S₂ are ON; this circuit is identical to the LCC-S topology. Here, C_F′ is the equivalent parallel capacitance of C_F and C_AF. To ensure that L_IN resonates with C_P, that is, ω₀² = 1/(L_IN C_P), the primary coil current I_P is determined as follows:

$$I_P=-j{U}_{\mathrm{AB}}\sqrt{\frac{C_{\mathrm{P}}}{L_{\mathrm{IN}}}}=-j\frac{U_{\mathrm{AB}}}{{\omega }_0{L}_{\mathrm{IN}}}$$

(18)

The primary current I_P has a constant value and is independent of the other parameters under constant U_AB and L_IN. Provided M resonates with C_F’ and combining with Equation (18), the following equation can be derived:

$${\omega }_0{}^2=\frac{1}{M{C_{\mathrm{F}}}^{\prime }}=\frac{1}{L_{\mathrm{S}}{C}_{\mathrm{S}}}$$

(19)

$$U_{\mathrm{ab}}=j\omega M{I}_{\mathrm{P}}=\frac{M{U}_{\mathrm{AB}}}{L_{\mathrm{IN}}}$$

(20)

Substituting Equation (20) into Equation (2), the output battery charging voltage U_Bat of the CV mode can be expressed as follows:

$$U_{\mathrm{Bat}}=\frac{\pi \sqrt{2}}{4}{U}_{\mathrm{ab}}=\frac{\pi \sqrt{2}}{4}\frac{M{U}_{\mathrm{AB}}}{L_{\mathrm{IN}}}$$

(21)

According to Equation (21), the battery-charging voltage U_Bat is constant and independent of the output load. As shown in Figure 6, the total input impedance Z_IN of Figure 6 is calculated as:

$$Z_{\mathrm{IN}}=\left[\left(j{\omega }_0{L}_{\mathrm{T}}+\frac{1}{j{\omega }_0{C}_{\mathrm{F}}}+\left(j{\omega }_{0}M\Vert Z_S\right)\right)\Vert \frac{1}{j{\omega }_0{C}_{\mathrm{P}}}\right]+j{\omega }_0{L}_{\mathrm{IN}}$$

(22)

If ω₀² = 1/(L_INC_P) = 1/(L_SC_S) and by substituting Equation (22) into Equation (4), the condition to achieve ZPA can be derived as:

$$L_{\mathrm{IN}}=\left(\frac{{C_{\mathrm{F}}}^{\prime }}{{C_{\mathrm{F}}}^{\prime }+C_{\mathrm{P}}}\right)L_{\mathrm{P}}$$

(23)

Under the condition expressed in Equation (13) and by combining it with Equation (2), the input impedance in CV mode Z_IN.CV at ZPA the condition can be calculated as:

$$Z_{\mathrm{IN}.\mathrm{CV}}=\frac{8}{{\pi }^2}\frac{L_{\mathrm{IN}}{}^2{R}_{\mathrm{Bat}}}{M^2}$$

(24)

According to Equation (23), it is evident that the ZPA condition can also be achieved in the CV charging mode. From Equation (4) and Equation (24), the input current in CV mode I_IN.CV can be calculated as:

$$I_{\mathrm{IN}.\mathrm{CV}}={\left(\frac{M}{L_{\mathrm{IN}}}\right)}^2\frac{U_{\mathrm{AB}}}{R_{\mathrm{ac}}}$$

(25)

According to Equation (25), I_IN.CV is inverse proportional to R_ac.

Based on the abovementioned equations, Figure 6 presents the primary curves of the frequency characteristics under the CV mode, considering the parameters listed in Table 1. ZPA can be achieved at the resonance frequency. Compared with Figure 5, the voltage gain remains the same at the resonance frequency, as shown in Figure 7b, whereas the transconductance gain is altered because of the CV characteristic.

2.3. Design Procedure of Proposed RHT System

The proposed system is based on the S–S and LCC-S compensation networks. Thus, the design procedure is similar with the conventional compensation network design except C_AF and C_F. In the first, essential system-level parameters for the WPT system should be determined. In this paper, system is designed based on Table 1. U_DC, f₀, P_o, U_CV and I_CC are 300 V, 85 kHz, 3000 W, 130 V and 23-A, respectively. Where U_CV is the constant charging voltage, and I_CC is the constant charging current. Moreover, then the primary-loop compensation inductance L_IN can be calculated. The primary-loop series compensation capacitance C_P is deduced by ω₀ and L_IN. The primary-loop shunt-compensation capacitance C_F is determined by the ω₀ and L_P, and the equation is deduced by Equation (10). The primary-loop additional-series compensation capacitance C_AF can be calculated by using ω₀, L_IN, L_P and C_F. Finally, the Secondary-loop series-compensation capacitance is determined by ω₀ and L_S. In order to operate system under ZPA condition, all parameters should be calculated under same resonance frequency. This design procedure is presented in Figure 8.

The reconfigurable structure of the proposed system with AC switches has a different point compared with conventional system. In the CC mode, two ACSs are turned off, thus, each switch and the additional capacitor current are zero. Voltages of each switch can be calculated by KVL as follows:

$$V_{S2}=\left|U_{\mathrm{AB}}-j{\omega }_0{L}_{\mathrm{IN}}{I}_{\mathrm{IN}}\right|=\sqrt{U_{\mathrm{AB}}{}^2+{\left(\frac{L_{\mathrm{IN}}{U}_{\mathrm{AB}}{R}_{\mathrm{ac}}}{{\omega }_0{M}^2}\right)}^2}$$

(26)

$$V_{S2}=\left|\frac{I_{\mathrm{IN}}}{j{\omega }_0{C}_{\mathrm{F}}}\right|=\frac{U_{\mathrm{AB}}{R}_{\mathrm{ac}}}{{\omega }_0{}^3{M}^2{C}_{\mathrm{F}}}$$

(27)

In the CV mode, two ACSs are turned on and voltages of ACSs are zero. Currents of ACSs can be deduced by KCL as follows:

$$I_{CAF}=I_{S2}=\left|\frac{C_{\mathrm{AF}}}{C_{\mathrm{F}}+C_{\mathrm{AF}}}\cdot I_{\mathrm{P}}\right|=\frac{U_{\mathrm{AB}}{C}_{\mathrm{AF}}}{{\omega }_0{L}_{\mathrm{IN}}\left(C_{\mathrm{F}}+C_{\mathrm{AF}}\right)}$$

(28)

$$I_{\mathrm{CP}}=I_{\mathrm{S}1}=\left|I_{\mathrm{IN}}-I_{\mathrm{P}}\right|=\sqrt{{\left(\frac{M}{L_{\mathrm{IN}}}\right)}^4{\left(\frac{U_{\mathrm{AB}}}{R_{\mathrm{ac}}}\right)}^2+{\left(\frac{U_{\mathrm{AB}}}{{\omega }_0{L}_{\mathrm{IN}}}\right)}^2}$$

(29)

Voltage stresses of C_F and C_AF are same because of parallel connection. The voltage stress of the additional capacitor V_CAF can be calculated by using ohm’s law as:

$$V_{CAF}=V_{CF}=\left|\frac{I_{\mathrm{IN}}}{j{\omega }_0{C}_{\mathrm{F}}^{\prime }}\right|=\frac{U_{\mathrm{AB}}}{{\omega }_0{}^2{L}_{\mathrm{IN}}{C}_{\mathrm{F}}^{\prime }}$$

(30)

Because of high voltage and current stress in IPT system, it is important to analyze maximum voltage and current of each capacitor. From the above equations,

Table 2. Current and voltage stress of capacitors.

	CP	CF	CAF	CS
Capacitance (nF)	78.54	22.22	8.03	15.33
Current (A)	16.85	11.28	3.00	25.76
Current Equation	(29)	(17)	(28)	(11)
Voltage (V)	631.26	953.71	953.71	3158.68

presents current and voltage stress of capacitors based on Table 1 parameters. Table 2 presents current equations for each capacitor, and the voltage stress can be calculated by using current equations and impedance of each capacitor. In this paper, each capacitor is designed by using multilayer ceramic capacitor (MLCC) with 20% voltage and current margin for safety operation.

3. System Verification and Performance Comparison

3.1. Experimental Results

To verify the validity and feasibility of the proposed RHT-based WPT system, a 3-kW experimental WPT prototype was fabricated, as shown in Figure 9, according to the parameters listed in Table 1. The practical parameters used are almost identical to the ideal design values.

The experimental waveforms are presented in Figure 10, Figure 11 and Figure 12. Figure 10a,b present the main waveforms of the CC and CV modes. The resonant current I_in and inverter output voltage U_AB have almost identical phases because the system is operated near the resonant frequency. Characteristics of the S–S and LCC-S topologies are shown in Figure 10a and Figure 10b, respectively.

The CC and CV mode waveforms under load fluctuations are shown in Figure 11a,b, respectively. When the equivalent DC output resistance changed from 3.2 Ω to 5.0 Ω, the charge current I_Bat is in the CC mode and the charge voltage U_Bat in the CV mode remains nearly constant when the load varies from 5.5 Ω to 19.7 Ω. In the CC mode, I_IN is varied proportional to R_Bat. However, in the CV mode, I_IN is varied inverse proportional to R_Bat. These results also can see in Equations (15) and (25). Figure 11 presents the waveforms for the transition from the CC mode to the CV mode. All the results indicate stable operation, which is maintained at nearly CC and CV during the transient state. These experimental results verify the validity of the proposed RHT.

In this study, the values of I_Bat and U_Bat are designed to be 23 A and 130 V, respectively. Figure 12 shows the CC/CV charging characteristics of the proposed system. As shown in Figure 13a, as R_Bat increases, the charge current in the CC mode and the charge voltage in the CV mode are almost constant. Figure 13b depicts the experimental efficiency and charging power. As R_Bat increases, the charging efficiency and power increase under the CC mode; however, they decrease under the CV mode. The maximum charging efficiency (92.28%) and charge power (3003 W) are observed at the transition point between the two modes (R_Bat = 5.55 Ω).

3.2. Performance Comparison

In order to evaluate a performance of the proposed RHT system, a comparative analysis is conducted.

Table 3. Comparison between the proposed RHT and conventional works.

	Proposed	[19]	[20]	[21]	[22]	[24]
Inductors	1	0	1	1	4	1
Capacitors	4	3	2	5	8	3
ACSs	2	3	3	2	2	1
Location of ACSs	Transmitter	Receiver	Transmitter	Both sides	Receiver	Transmitter
Coils	2	3	2	2	4	2
Control Frequency	Fixed	Fixed	Fixed	Fixed	Fixed	Changed
Power	3000 W	151 W	15 W	2500 W	1000 W	200 W
Efficiency	92.58%	88%	92.8%	89.28%	93.9%	87%

shows detail comparison results of conventional systems and the proposed system. The number of components of [19] and [24] is less than others. However, it cannot apply to the EV application because of low power rate. References [21,22] have over 1000 W power rate and efficiency is relatively high. However, they require many component numbers compared with the proposed system. It can be seen that the proposed system has a small number of components, high power and high efficiency.

4. Conclusions

This study proposes an RHT of a wireless charging system for EVs, whereby CC/CV charging and ZPA can be achieved simply by switching between two ACSs. As these ACSs are both located on the primary side, the proposed system can be easily controlled using a single primary controller, without requiring synchronous wireless communication between the primary and secondary sides. Therefore, the cost and control complexity of the entire WPT system is reduced significantly, than conventional WPT systems. To verify the performance of the proposed system, a three-kilowatt experimental prototype is configured. The experimental results indicate that a maximum charging efficiency of 92.28% and power of 3003 W is achieved. The results also validate the stable operation of the system, even during load fluctuations and mode changes. In conclusion, the proposed system is expected to serve as an effective alternative for various WPT applications.