A communication-free WPT system based on transmitter-side hybrid topology switching for battery charging applications

Typical CC and CV charging profile of the Li-ion battery.

In order to simplify the complexity of control technology, many researchers have concentrated on the study of compensation topology and have published a large number of specialized literature studies in recent years.^22–27 Reference 22 shows the designed hybrid topology switching based on inductor-capacitor-inductor/series (LCL/S) or LCL–LCL compensation topology, which meets the load-independent output characteristics of the battery. Authors in Ref. 23 adopted the combination of series-series (SS) and series/inductor-capacitor-capacitor (S/LCC) topology to obtain the same characteristics as those shown in Ref. 22. A three-coil WPT system with additional AC switches and a large number of passive components in the receiver to achieve the characteristics of load-independent output current and voltage is presented in Ref. 24. Although these typical receiver-side switching methods eliminate communication links, they take up more space and weight in the receiver due to the introduction of more passive components.^22–24 In Ref. 13, two hybrid topologies with the combination of SS and parallel-series (PS) or the combination of series-parallel (SP) and parallel-parallel (PP) are proposed to meet the CC and CV charging features. A novel variable coil structure based WPT system to obtain CC and CV output characteristics for charging applications for electric bicycles (EBs) is presented in Ref. 25. Authors in Ref. 26 proposed that the inductor-capacitor-capacitor-capacitor/series (LCCC/S) compensated WPT system can achieve CC and CV output characteristics with the ZPA condition at two different operating frequency points. In addition, in Ref. 27, a novel three-coil structure WPT system has been proved to have the same characteristics as those shown in Ref. 26. However, the wireless communication links between the transmitter and the receiver are inevitable, as shown in Refs. 13 and 25–27.

In order to eliminate wireless communication links and ensure that the receiver of the WPT system is compact and lightweight, some researchers have proposed transmitter-side identification schemes to predict the receiver-side information in real time by detecting the transmitter-side electrical parameters.^28–30 Reference 28 employs the energy injection mode and the free resonance mode to identify the load information for kitchen appliances. In Ref. 29, a transmitter-side identification approach is proposed for estimating the charging voltage of an implantable WPT system. However, both methods require sampling the inverter’s AC output voltage and current and the phase difference between them, which increases hardware cost and system design complexity. In addition, the calculation process of the method is cumbersome, and the control is complicated. Reference 30 uses the SS topology operating in a non-resonant mode to estimate receiver-side charging information. However, this approach inevitably introduces a large amount of reactive power, resulting in an increase in system losses. In addition, this method also faces a complicated calculation process.

In this paper, a communication-free transmitter-side switching hybrid topology approach for battery charging applications is proposed. It is worth emphasizing that the proposed method is applicable to various types of batteries with typical CC/CV two-stage charging characteristics, such as lithium batteries, lead-acid batteries, and so on. The advantages of the presented method are as follows: (1) the components switched by the AC switches are mounted on the transmitter, ensuring the principle that the receiver is compact and light and (2) the transmitter-side voltage identification method eliminates the wireless communication links between the transmitter and the receiver, thereby reducing the cost and increasing the reliability of the system. The basic principle of the identification method is to establish the exact function relationship between the battery charging voltage U_B and the rms value of the inverter output current I_I, thereby predicting U_B by measuring I_I. In other words, the transition point from the CC to CV mode can be accurately estimated in the absence of a real-time charging voltage value from the feedback from the receiver by wireless communication. In addition, the calculation process of the proposed transmitter-side identification method is very simple and easy to implement. It is worth mentioning that the research in this paper does not include the change in the coupling coefficient for the following reasons: (1) in low-power applications such as portable electronic devices, an approximately constant magnetic field can be established to overcome variations in the coupling coefficient due to misalignment between the transmitter and the receiver;^31,32 (2) in medium power applications such as electric bicycles (EBs), the EB is fixed to the charging post during charging without the coupling structure being misaligned;^23,33 and (3) in high-power applications such as electric vehicles, high-performance position sensors ensure the accuracy of parking and thus reduce coupling variations. The rest of this paper is organized as follows: Sec. II makes a systematically theoretical analysis of SS and LCC-S compensation topologies and proposes a hybrid topology with load-independent CC and CV outputs and the ZPA condition. Estimation of charging voltage and switching of charging modes are described in Sec. III. Section IV sets up an experimental setup and verifies the feasibility of the theoretical analysis. Finally, some conclusions are drawn in Sec. V.

II. THEORETICAL ANALYSIS

A. Analysis of the SS compensation topology

As one of the four basic compensation topologies in WPT systems, the SS topology has been extensively studied for the following reasons:³⁴

the SS topology has the characteristics of less components, simple structure, and low loss;
changes in the load and mutual coupling coefficient between transceiver coils do not impact the compensation capacitance and the resonant frequency; and
it has excellent CC output characteristics, ZPA conditions, perfect power transfer capability, and high efficiency when both the transmitter and the receiver are in resonance.

The typical SS compensation topology model used in WPT systems is illustrated in Fig. 2. L_P and L_S represent the self-inductances of the transmitter-side coil and the receiver-side coil, respectively. R_P and R_S indicate the parasitic resistances of the transmitter-side and receiver-side coils, respectively. M is the mutual inductance between transceiver coils. Moreover, C_P and C_S are the transmitter-side and receiver-side compensation capacitors, respectively, which are used to increase the transmission power and efficiency from the input power source U_D to the battery of the WPT system. Besides, ${\vec{U}}_{I}$ stands for the phasor of the fundamental harmonics of HFI output voltage, and ${\vec{I}}_{I}$ is the corresponding current phasor. ${\vec{U}}_{O}$ and ${\vec{I}}_{O}$ are the input voltage and current phasor of the rectifier, respectively. U_B and I_B are the charging voltage and current of the battery, respectively.

FIG. 2.

The circuit topology of the SS compensated WPT system.

It is pointed out in Ref. 35 that the mutual inductance model is more appropriate for the case where self-inductance needs to be compensated by compensation capacitors than the T model. The mutual inductance model is consequently selected to study SS compensation topology used in the WPT system, which is presented in Fig. 3.

FIG. 3.

Equivalent circuit of the SS compensated WPT system.

Generally, fundamental harmonic approximation (FHA) is employed to explicate the equivalent circuits of WPT systems under a static-state condition. Then, the corresponding circuit parameters can be simplified as follows:

\{\begin{matrix} X_{P} = j ω L_{P} + \frac{1}{j ω C_{P}} + R_{P}, \\ X_{S} = j ω L_{S} + \frac{1}{j ω C_{S}} + R_{S}, \end{matrix})

(1)

where j is the imaginary unit, and ω is the operating angular frequency. R_E is the equivalent ac load resistance.

According to the Kirchhoff voltage law (KVL), mathematical expressions between voltage and current phasors can be expressed as

\{\begin{matrix} {\vec{U}}_{I} = X_{P} {\vec{I}}_{I} - j ω M {\vec{I}}_{O}, \\ 0 = (X_{S} + R_{E}) {\vec{I}}_{O} - j ω M {\vec{I}}_{I} . \end{matrix})

(2)

Usually, in order to ensure that the system works in resonance, the following equation can be derived:

\{\begin{matrix} j ω L_{P} + \frac{1}{j ω C_{P}} = 0, \\ j ω L_{S} + \frac{1}{j ω C_{S}} = 0 . \end{matrix})

(3)

Substituting (1) and (3) into (2), the solutions of the transmitter-side input current phasor and the receiver-side output current phasor can be derived as

\{\begin{matrix} {\vec{I}}_{I} = \frac{(R_{E} + R_{S}) {\vec{U}}_{I}}{ω^{2} M^{2} + R_{E} R_{P} + R_{P} R_{S}}, \\ {\vec{I}}_{O} = \frac{j ω M {\vec{U}}_{I}}{ω^{2} M^{2} + R_{E} R_{P} + R_{P} R_{S}} . \end{matrix})

(4)

In addition, since the coil windings are constructed using high-quality Litz wire, the parasitic resistances of transmitter-side and receiver-side coils are extremely small and can be ignored in the calculation. Hence, the expression of input and output current phasors can be further simplified to

\{\begin{matrix} {\vec{I}}_{I} = \frac{R_{E} {\vec{U}}_{I}}{ω^{2} M^{2}}, \\ {\vec{I}}_{O} = \frac{j {\vec{U}}_{I}}{ω M} . \end{matrix})

(5)

Then, the voltage and current gains between the transmitter and the receiver are obtained by

\{\begin{matrix} G_{U I} = |\frac{{\vec{I}}_{O}}{{\vec{U}}_{I}}| = \frac{1}{ω M}, \\ G_{I U} = |\frac{{\vec{U}}_{O}}{{\vec{I}}_{I}}| = ω M, \end{matrix})

(6)

where the first subscript letter of the gains represents the transmitter-side parameters, including voltage and current, while the second one indicates that of the receiver. Taking the first formula in (6) as an example, G_UI stands for the ratio of the receiver-side output current to the transmitter-side input voltage.

According to the first formula in (6), when the input voltage ${\vec{U}}_{I}$ of the transmitter remains constant, the output current ${\vec{I}}_{O}$ is not affected by the time-varying load.

Moreover, the corresponding total input impedance is derived as

Z_{I} = \frac{Ū_{I}}{{\vec{I}}_{I}} = \frac{ω^{2} M^{2}}{R_{E}} .

(7)

As evident from (7), Z_I has only the real part, and therefore, the system with the SS compensation topology can realize resistive input load.

In conclusion, the CC output against variable load and the ZPA condition can be obtained with a constant input voltage source through the SS compensation topology, when the transmitter and receiver are both in resonance. Besides, it is worth emphasizing that the ratio of output voltage to input current is approximately constant, which means the relationship between output voltage and input current is irrelevant to the fluctuating load. Therefore, an interesting idea of exploiting the HFI output current to estimate the charging voltage is put forward, which will be analyzed in detail in Sec. III. Due to these unique features, the SS topology is chosen to construct the constant current source of this study.

B. Analysis of the LCC-S compensation topology

The LCC compensation topology has attracted much attention because of its numerous advantages such as constant current in the transmitter-side coil, ZPA conditions, and CV output characteristics. The structure of the LCC-S topology for WPT systems with stable load-independent CV output is shown in Fig. 4. L_R is the compensation inductance on the transmitter, and R_R is the corresponding parasitic resistance. C_R and C_PP indicate the compensation capacitances. The meanings of the remaining parameter symbols are consistent with those involved in the SS compensation topology.

FIG. 4.

The circuit topology of the LCC-S compensated WPT system.

Similar to the analysis of the SS structure, the mutual inductance model, which is employed to interpret the LCC-S compensation topology, is shown in Fig. 5.

FIG. 5.

Equivalent circuit of the LCC-S compensated WPT system.

The related system parameters can be simplified by

\{\begin{matrix} Y_{R} = j ω L_{R} + R_{R}, \\ Y_{C} = \frac{1}{j ω C_{R}}, \\ Y_{P} = j ω L_{P} + \frac{1}{j ω C_{P P}} + R_{P}, \\ Y_{S} = j ω L_{S} + \frac{1}{j ω C_{S}} + R_{S} . \end{matrix})

(8)

According to Kirchhoff’s voltage law (KVL), the system can be described by

\{\begin{matrix} {\vec{U}}_{I} = (Y_{R} + Y_{C}) {\vec{I}}_{I} - Y_{C} {\vec{I}}_{P}, \\ 0 = - Y_{C} {\vec{I}}_{I} + (Y_{C} + Y_{P}) {\vec{I}}_{P} - j ω M {\vec{I}}_{O}, \\ 0 = - j ω M {\vec{I}}_{P} + (Y_{S} + R_{E}) {\vec{I}}_{O} . \end{matrix})

(9)

To maintain the system to operate in resonance, the following formula should be met:

\{\begin{matrix} j ω L_{R} + \frac{1}{j ω C_{R}} = 0, \\ \frac{1}{j ω C_{R}} + \frac{1}{j ω C_{P P}} + j ω L_{P} = 0, \\ j ω L_{S} + \frac{1}{j ω C_{S}} = 0 . \end{matrix})

(10)

Substituting (8) and (10) into (9), the input and output current phasors can be expressed by the following equations:

\{\begin{matrix} {\vec{I}}_{I} = \frac{(R_{E} R_{P} + R_{P} R_{S} + ω^{2} M^{2}) {\vec{U}}_{I}}{(R_{E} + R_{S}) (R_{P} R_{S} + ω^{2} L_{R}^{2}) + R_{R} ω^{2} M^{2}}, \\ {\vec{I}}_{O} = \frac{ω^{2} L_{R} M {\vec{U}}_{I}}{(R_{E} + R_{S}) (R_{P} R_{S} + ω^{2} L_{R}^{2}) + R_{R} ω^{2} M^{2}} . \end{matrix})

(11)

By neglecting the parasitic resistance of the transceiver coil and series inductance, Eq. (11) can be further simplified to

\{\begin{matrix} {\vec{I}}_{I} = \frac{M^{2} {\vec{U}}_{I}}{L_{R}^{2} R_{E}}, \\ {\vec{I}}_{O} = \frac{M {\vec{U}}_{I}}{L_{R} R_{E}} . \end{matrix})

(12)

Then, the voltage and current gains between the transmitter and the receiver are given by

\{\begin{matrix} G_{U U} = |\frac{{\vec{U}}_{O}}{{\vec{U}}_{I}}| = \frac{M}{L_{R}}, \\ G_{I I} = |\frac{{\vec{I}}_{O}}{{\vec{I}}_{I}}| = \frac{L_{R}}{M} . \end{matrix})

(13)

According to the first formula in (13), the receiver-side output voltage ${\vec{U}}_{O}$ remains constant, regardless of changes in the load.

Moreover, the total input impedance of the resonant tank is derived as

Z_{I} = \frac{Ū_{I}}{{\vec{I}}_{I}} = \frac{L_{R}^{2}}{M^{2}} R_{E} .

(14)

As evident from (14), Z_I does not contain an imaginary part, and therefore, the LCC-S topology can realize unity power factor input characteristics.

In conclusion, load-independent CV output performance and the ZPA condition can be achieved with a constant input voltage source through the LCC-S compensation topology operating in a resonant state. Besides, based on the second formula in (13), the ratio of the output current to the input current is almost constant. In other words, the relationship between the output current and the input current with the LCC-S topology is independent of the load. Therefore, another interesting idea of using input current to identify the output current with the LCC-S topology working in resonance is conceived. However, this idea is not the focus of this article and will be explained in depth in future research.

C. Analysis and design of the hybrid topology

Based on the abovementioned analysis, it can be seen that the SS compensation topology applied to WPT systems has reliable CC output characteristics, whereas the LCC-S topology has a stable CV output independent of load variation, and both of them can realize the ZPA condition.

Therefore, by properly switching these two topologies, the CC and CV outputs can be implemented to meet the battery charging curve. Then, a hybrid topology with stable and reliable CC and CV output characteristics, which is involved in the S or LCC switching compensation topology in the transmitter and the S topology in the receiver, is proposed, as shown in Fig. 6.

FIG. 6.

(a) Compensation topology for the CC charging mode, (b) the compensation topology for the CV charging mode, and (c) the designed hybrid topology of the WPT system.

Figure 7 shows the two additional high-frequency AC switches K₁ and K₂ in the reconstructed WPT system as well as their corresponding control logics for the switching from the CC to the CV charging mode. The AC switches comprised two antiseries MOSFETs for processing the resonant bidirectional currents.¹³

FIG. 7.

(a) AC switch with two anti-series MOSFETs and (b) corresponding control logics.

When the two switches K₁ and K₂ are disconnected, the WPT system executes the CC charging mode, with the equivalent SS compensation topology shown in Fig. 6(a). Then, the total impedance of L_R and C_PA should be equal to that of C_P introduced in the SS topology,

j ω L_{R} + \frac{1}{j ω C_{P A}} = \frac{1}{j ω C_{P}} .

(15)

Similarly, when both switches are simultaneously turned on, the system operates in the CV charging mode, with the equivalent LCC-S topology shown in Fig. 6(b). Then, the total impedance of C_PA and C_PB should be equal to that of C_PP in the LCC-S topology,

C_{P P} = C_{P A} + C_{P B} .

(16)

In the transmitter of the hybrid topology, the input square voltage is modulated by the full-bridge HFI with 50% duty cycle. U_I, which is the rms value of the HFI output voltage, can be expressed as

U_{I} = \frac{2 \sqrt{2}}{π} U_{D} .

(17)

In the receiver, U_O, which is the rms value of the full-bridge diode rectifier input voltage, can be derived as

U_{O} = \frac{2 \sqrt{2}}{π} U_{B} .

(18)

Moreover, the relationship between the charging current I_B and the rms value of the rectifier input current I_O can be expressed by

I_{B} = \frac{2 \sqrt{2}}{π} I_{O} .

(19)

Substituting (17) and (19) into (6), the mutual inductance between the transmitter-side and receiver-side coils can be determined as

M = \frac{8 U_{D}}{π^{2} ω I_{B}} .

(20)

Similarly, substituting (17), (18) and (20) into (13), the series inductance L_R can be calculated by

L_{R} = \frac{8 U_{B}}{π^{2} ω I_{B}} .

(21)

Then, based on (10) and (21), the corresponding shunt capacitor C_R applied in the transmitter and series capacitor C_S employed in the receiver can be derived as

\{\begin{matrix} C_{R} = \frac{π^{2} I_{B}}{8 ω U_{B}}, \\ C_{S} = \frac{1}{ω^{2} L_{S}} . \end{matrix})

(22)

According to (3), (10), (15), (16), (21) and (22), the capacitors C_PA and C_PB can be obtained by

\{\begin{matrix} C_{P A} = \frac{π^{2} I_{B}}{ω (π^{2} ω L_{P} I_{B} + 8 U_{B})}, \\ C_{P B} = \frac{16 π^{2} U_{B} I_{B}}{ω (π^{4} ω^{2} {L_{P}}^{2} {I_{B}}^{2} - 64 {U_{B}}^{2})} . \end{matrix})

(23)

For a given battery, both the charging voltage and the charging current can be determined, and the self-inductances of the coils can be measured once the WPT system is set up. Thus, as long as the dc input voltage U_D is constant, the remaining parameters of the WPT system can be accurately calculated.

III. ESTIMATION OF CHARGING VOLTAGE AND SWITCHING OF CHARGING MODES

Based on the abovementioned analysis, the designed WPT charging system has expected CC and CV outputs by reasonably switching the transmitter-side compensation topologies, and both CC and CV charging modes can realize the ZPA condition. However, according to previous studies, it is essential for wireless apparatus feeding back the charging parameters of the battery in the receiver to the controller in the transmitter when the switching compensation topology on the transmitter is employed to realize CC and CV charging modes.

In this section, a new method is proposed to estimate the charging voltage in the CC charging mode by measuring the rms value of the HFI output current without the need of wireless communication.

A. Estimation of charging voltage

It is well known that when the battery is connected to a charging system, the CC charging mode is first performed. In the CC charging mode, when the charging voltage rises to the preset voltage level, it switches to the CV charging mode. In the absence of communication routes built by wireless apparatus, there is a key issue that must be addressed, namely, estimating the battery charging voltage in real-time. Discovering the functional relationship between the battery charging voltage and the transmitter-side variables is key to solving the problem.

In the CC charging mode of the WPT system, the SS compensation topology, in which both transmitter-side and receiver-side circuits are in resonance, is applied to charge the battery. The receiver-side output voltage ${\vec{U}}_{O} ({\vec{U}}_{O} = {\vec{I}}_{O} R_{E})$ indicates the product of the output current ${\vec{I}}_{O}$ and the equivalent ac resistance R_E. Then, combined with (1) and (3), (2) can be represented as

\{\begin{matrix} {\vec{U}}_{I} = R_{P} {\vec{I}}_{I} - j ω M {\vec{I}}_{O}, \\ j ω M {\vec{I}}_{I} = R_{S} {\vec{I}}_{O} + {\vec{U}}_{O} . \end{matrix})

(24)

Eliminating ${\vec{I}}_{O}$ in (24), the mathematical relationship between ${\vec{I}}_{I}$ and ${\vec{U}}_{O}$ is obtained as

j ω M {\vec{U}}_{O} = R_{S} {\vec{U}}_{I} - (ω^{2} M^{2} + R_{P} R_{S}) {\vec{I}}_{I} .

(25)

According to the analysis in Sec. II, the designed SS topology for achieving CC output characteristics can realize the ZPA condition. In other words, ${\vec{U}}_{I}$ and ${\vec{I}}_{I}$ are in phase. Therefore, the variables in (25) can be transformed into the form of rms values, and (25) can be converted to

U_{O} = \frac{ω^{2} M^{2} + R_{P} R_{S}}{ω M} I_{I} - \frac{R_{S} U_{I}}{ω M} .

(26)

Then, substituting (17) and (18) into (26), the relationship between the charging voltage U_B and the rms value of the HFI output current I_I can be deduced as

U_{B} = \frac{\sqrt{2} π (ω^{2} M^{2} + R_{P} R_{S})}{4 ω M} I_{I} - \frac{R_{S} U_{D}}{ω M} .

(27)

It can be observed in (27) that U_B is related to I_I and U_D. However, which of these two variables (I_I and U_D) has a deeper impact on U_B is highly worth considering. Then, the numerical analysis for (27) is conducted. According to the experimental parameters listed in Table II, the variable U_B in the CC charging mode against the various group values of I_I and U_D is depicted in Fig. 8.

FIG. 8.

Charging voltage U_B against the rms value of the HFI output current I_I and the DC input voltage U_D.

As evident from Fig. 8, I_I is the main factor affecting U_B, and U_D has little effect on U_B. The reasonable explanation is as follows: in practical applications, in order to minimize power loss and improve system transmission efficiency, high-quality Litz wire is commonly used in the design of coils in the WPT system. Therefore, the coil parasitic resistance R_S is much smaller than ωM (R_S ≪ ωM), resulting in the relatively weak influence of U_D.

According to the analysis mentioned above, a practical conclusion can be drawn that the charging voltage of the battery can be adjusted by controlling the rms value of the HFI output current. Based on this point of view, an interesting idea is proposed that the preset charging voltage U_{B_P}, which is the transition point from the CC to CV charging mode, can be replaced by collecting the rms value of the HFI output current.

In this study, assume that the DC voltage source provides a constant DC voltage U_D to the system. Although the parasitic resistances of the coils cause a very minimal error to the calculation result, it is still considered in order to obtain a more accurate estimation result.

As evident from (27), when U_D is constant, both I_I and U_B increase simultaneously in the CC charging mode and maintain a certain linear relationship.

In this experiment, combined with the practical parameters provided in Table II, the specific correspondence between U_B and I_I can be expressed as

U_{B} = 13.96 I_{I} - 0.64 .

(28)

Obviously, there is a simple consistent one-to-one match between U_B and I_I. Moreover, the mathematical expression belongs to a linear function.

In order to verify the rationality and correctness of the abovementioned theoretical analysis, values of U_B and I_I are measured by the simulation of MATLAB Simulink based on the parameters provided in Table II. The map function from I_I to U_B is drawn in Fig. 9.

FIG. 9.

Comparison between simulation results and theoretical calculations.

It can be seen that U_B and I_I maintain the ideal linear relationship in the simulation. The slope of the linear function is nearly equal to that of the theoretical arithmetic, and the vertical axis intercept has a slight deviation, which is caused by neglecting the loss of the rectifier. However, this error is small enough to not affect the overall effect, which is considered acceptable.

B. Switching of charging modes

Based on the analysis mentioned above, an idea of evaluating the charging voltage U_B by measuring the rms value of HFI output current I_I is proposed. The key is the transition point from CC charging mode to CV mode. This transition point is determined by the preset charging voltage U_{B_P}. Based on (27), the reference HFI output current I_{I_R} for the preset charging voltage U_{B_P} can be obtained as

I_{I_R} = \frac{2 \sqrt{2} ω M}{π (ω^{2} M^{2} + R_{P} R_{S})} U_{B_P} + \frac{2 \sqrt{2} R_{S} U_{D}}{π (ω^{2} M^{2} + R_{P} R_{S})} .

(29)

As shown in Fig. 6(c), once the HFI output current I_I reaches the reference value I_{I_R}, that is, once the charging voltage rises to the preset value U_{B_P}, the transmitter-side controller immediately operates AC switches K₁ and K₂ to switch the hybrid topology from the CC charging mode to the CV mode. Then, the WPT charging system operates in the CV charging mode with the LCC-S compensation topology.

Table I shows the measured current I_I, the actual charging voltage U_B, the estimated voltage U_{B_EST}, and the error Δ between U_B and U_{B_EST}, which are consistent with the corresponding parameters shown in Fig. 9. A more intuitive conclusion can be drawn from Table I that the errors of the estimated results are less than 3.64%. Furthermore, once the charging voltage U_B hits the preset charging voltage U_{B_P} = 80 V, the rms value of the HFI output current I_I is 5.78 A, which is the transition point from the CC to the CV charging mode. In other words, the controller of the transmitter operates the AC switches K₁ and K₂ from the disconnect state to the conducting state to complete the switching from the CC to the CV mode at I_I = 5.78 A. Besides, the error of the estimated charging voltage U_{B_EST} is only 1.22% at the transition point, which does not cause large voltage fluctuation during the transition from the CC to the CV charging mode.

TABLE I.

Simulation results for charging voltage estimation.

I_I (A)	U_B (V)	U_{B_EST} (V)	Δ%
1.59	20.80	21.56	3.64
2.30	30.76	31.47	2.30
3.02	40.50	41.52	2.52
3.71	50.20	51.15	1.90
4.39	59.77	60.64	1.46
5.07	69.20	70.14	1.35
5.78	78.95	80.00	1.22
6.40	87.75	88.70	1.09
7.05	97.00	97.78	0.80

I_I (A)	U_B (V)	U_{B_EST} (V)	Δ%
1.59	20.80	21.56	3.64
2.30	30.76	31.47	2.30
3.02	40.50	41.52	2.52
3.71	50.20	51.15	1.90
4.39	59.77	60.64	1.46
5.07	69.20	70.14	1.35
5.78	78.95	80.00	1.22
6.40	87.75	88.70	1.09
7.05	97.00	97.78	0.80

It is also noteworthy that in the CV charging mode with the LCC-S topology, when the battery is fully charged or when the receiver is moved away, the HFI output current I_I will drop to a certain value, and the transmitter-side controller will cut off the electricity from the power source to avoid waste of electric energy. This situation is not the focus of this paper, so no detailed analysis is performed.

IV. EXPERIMENTAL VERIFICATION

A. Experimental setup

To verify the correctness and feasibility of the theoretical analysis, an experimental prototype with a rated power of 400 W, whose charging parameters are set as 5 A charging current in the CC mode and 80 V charging voltage in the CV mode, is constructed based on the schematic in Fig. 6(c). The photograph of the experimental setup is shown in Fig. 10, and the system parameters are provided in Table II. Four semiconductor switching devices [MOSFETs (C2M0080120D)] are adopted for the construction of the HFI, and the types of the MOSFETs for the two AC switches K₁ and K₂ are the same as those of the HFI. Four receiver-side fast recovery diodes (DSE160-12A) are used to build the rectifier. A high-precision single-chip rms converter, AD637, which can calculate the rms of various complex waveforms, is used to calculate the rms value of the output current of the HFI. The detailed specifications of each component are provided in Table III for better visibility.

FIG. 10.

Prototype of the designed WPT system.

TABLE II.

The experimental parameters of the hybrid topology structure.

Symbol	Value	Symbol	Value
f	100 kHZ	L_P	101.8 μH
k	0.195	R_P	0.12 Ω
C_PA	20.82 nF	L_S	100.9 μH
C_PB	10 nF	R_S	0.11 Ω
C_R	129 nF	L_R	19.68 μH
C_S	25.08 nF	R_R	0.08 Ω

Symbol	Value	Symbol	Value
f	100 kHZ	L_P	101.8 μH
k	0.195	R_P	0.12 Ω
C_PA	20.82 nF	L_S	100.9 μH
C_PB	10 nF	R_S	0.11 Ω
C_R	129 nF	L_R	19.68 μH
C_S	25.08 nF	R_R	0.08 Ω

TABLE III.

The detailed specifications of each component.

Component	Type
MOSFETs for the HFI	C2M0080120D
MOSFETs for switches	C2M0080120D
Diodes for the rectifier	DSE160-12A
RMS detection module for I_I	AD637

The finite-element analysis (FEA) by Maxwell is used to accurately design the sizes and turns of the transmitter-side and the receiver-side coils. The square coil structure with circular corners, which has the advantages of both the circular coil structure and the square coil structure,²² is employed to construct the loosely coupled transformer in this paper. The coils and the resonant inductor are constructed by Litz wire (a diameter of 2.8 mm and with 400 strands) with a lower equivalent resistance and a smaller skin effect. Ferrite (PC 40) is applied for magnetic shielding. Specifications of the designed coil are 360 mm diameter and 9 turns. The transmitter-side and receiver-side coils are the same and construct the loosely coupled transformer with a fixed gap of 120 mm, as shown in Fig. 11. The detailed specifications of the designed loosely coupled transformer are listed in Table IV.

FIG. 11.

Manufactured loosely coupled transformer.

TABLE IV.

Detailed specifications of the designed loosely coupled transformer.

Parameter	Specification
Transmitter-side coil	Size of 320 mm × 320 mm, 9 turns
Receiver-side coil	Size of 320 mm × 320 mm, 9 turns
Litz wire	400 stands with diameter of 2.8 mm
Ferrite	PC 40
Air-gap	120 mm

Parameter	Specification
Transmitter-side coil	Size of 320 mm × 320 mm, 9 turns
Receiver-side coil	Size of 320 mm × 320 mm, 9 turns
Litz wire	400 stands with diameter of 2.8 mm
Ferrite	PC 40
Air-gap	120 mm

B. Experimental result

In this section, the output characteristics of the hybrid topology are validated. Based on the theoretical analysis in Sec. II, when the AC switches K₁ and K₂ are turned off, the WPT system operates in the CC charging mode with the SS topology.

The waveforms of the charging voltage U_B, charging current I_B, output voltage ${\vec{U}}_{I}$ ⁠, and output current ${\vec{I}}_{I}$ of the HFI are presented in Fig. 12. It is obvious that the charging current remains nearly unchanged against the equivalent resistance of the load increasing from 5 Ω to 10 Ω, which proves the load-independent CC output characteristics. Besides, the phase difference between ${\vec{U}}_{I}$ and ${\vec{I}}_{I}$ is nearly zero, which meets the ZPA condition and eliminates a large amount of reactive power in the resonant tank.

FIG. 12.

Experimental waveforms of U_B, I_B, ${\vec{U}}_{I}$ ⁠, and ${\vec{I}}_{I}$ in the CC mode, respectively: (a) R_B = 5 Ω and (b) R_B = 10 Ω.

Besides, the corresponding transient waveforms against the variable load (from 10 Ω to 5 Ω) are shown in Fig. 13. It can be clearly observed that the charging current I_B is almost constant at 5 A in the course of instantly changing the load. Moreover, the undershoot and overshoot of the HFI output voltage and current waveforms have hardly been found, which fully verifies the stability and reliability of the designed WPT system in the CC charging mode.

FIG. 13.

Transient waveforms in the CC mode with a sudden change in load from 10 Ω to 5 Ω.

During the CC charging mode, the charging voltage U_B rises with the increase in the load equivalent resistance. When I_I reaches the HFI reference output current I_{I_R} = 5.78 A, the WPT system immediately operates in the CV charging mode with the LCC-S compensation topology by turning on the AC switches K₁ and K₂.

The measured transient waveforms of the switching point from CC to CV are shown in Fig. 14. The charging voltage U_B and current I_B remain almost unchanged during the switching process, which fully proves that it is feasible to judge the switching point by detecting the rms value of the HFI output current.

FIG. 14.

Transient waveforms of the switching point from the CC to the CV mode.

Figure 15 shows the measured waveforms of U_B, I_B, ${\vec{U}}_{I}$ ⁠, and ${\vec{I}}_{I}$ ⁠. Apparently, when the load equivalent resistance varies from 20 Ω to 40 Ω, the charging voltage maintains a constant value. Besides, the HFI output voltage ${\vec{U}}_{I}$ and current ${\vec{I}}_{I}$ are in phase. Consequently, the WPT system can realize constant and reliable output voltage with time-varying load and the ZPA condition in the CV mode with the LCC-S topology, which is consistent with the aforementioned theoretical analysis.

FIG. 15.

Experimental waveforms of U_B, I_B, ${\vec{U}}_{I}$ ⁠, and ${\vec{I}}_{I}$ in the CV mode, respectively: (a) R_B = 20 Ω and (b) R_B = 40 Ω.

Furthermore, the transient waveforms of U_B, I_B, ${\vec{U}}_{I}$ ⁠, and ${\vec{I}}_{I}$ with time-varying load resistance, which suddenly increases from 20 Ω to 40 Ω, are shown in Fig. 16. Similarly, a constant charging voltage of approximately 80 V can be maintained against the variable load resistance, and the smoothness of the HFI output voltage and current waveforms can be guaranteed, which effectively validates the correctness of the aforesaid theoretical analysis.

FIG. 16.

Transient waveforms in the CV mode with a sudden change in load from 20 Ω to 40 Ω.

As mentioned in Sec. III, the mathematical treatment between the rms value of the HFI output current I_I and the charging voltage U_B for the battery can be expressed as a linear function, and these experimental waveforms are measured and displayed in Fig. 17. Waveform trends of ${\vec{I}}_{I}$ and U_B can be clearly observed as the load resistance has different values of 5 Ω, 10 Ω, and 20 Ω. Apparently, ${\vec{I}}_{I}$ and U_B increase simultaneously with the increase in the load resistance. The corresponding measured values of I_I and U_B almost satisfied (28) with a slight error, which is to an acceptable extent. Consequently, the idea that U_B can be accurately estimated by I_I without measuring the receiver-side charging parameters is reasonably verified.

FIG. 17.

Experimental waveforms of charging voltage estimation.

The entire charging profile with the charging current I_B and the charging voltage U_B against the variable load R_B is presented in Fig. 18, which matches well with the profile shown in Fig. 1.

FIG. 18.

Measured charging profile vs log₁₆(R_B).

It is clearly seen that the charging current I_B varies from 5.08 A to 4.94 A against the time-varying resistance R_B from 5 Ω to 16 Ω in the CC mode, and the fluctuation range of I_B is less than 2.84%. Furthermore, the charging voltage U_B changes from 77.75 V to 79.95 V with R_B increasing from 16 Ω to 160 Ω in the CV mode, and the fluctuation amplitude of U_B does not exceed 2.83%. The CC and CV output characteristics of the proposed hybrid topology are verified again.

The whole curve of the system’s overall efficiency (from the DC input of the HFI to the load) is shown in Fig. 19. Obviously, the efficiency increases from 86.4% to 92.2% as the equivalent resistance increases and then gradually declines to 80.6% throughout the charging process.

FIG. 19.

https://doi.org/10.1109/tie.2015.2417122

Measured efficiency profile of the whole charging process.

In order to clearly show the advantages of the proposed method, the characteristics of the proposed converter were compared in detail with related studies previously reported. The detailed comparison results are shown in Table V. The superiorities of the proposed approach are shown below:

The proposed method can minimize the passive components in the receiver, thereby ensuring that the receiver is lighter and more compact, which is an advantage compared to those mentioned in Refs. 22–24.
Wireless communication links for real-time feedback of charging parameters between the transmitter and the receiver can be eliminated, which is superior to the method proposed in Refs. 13 and 25.

TABLE V.

Comparison results between this work and previous related works.

Proposed in	Reference 13	Reference 22	Reference 23	Reference 24	Reference 25	This work
Number of coils	2	2	2	3	4	2
Number of switches	3	2	2	2	2	2
Number of transmitter-side compensation components	2	3	1	2	3	4
Number of receiver-side compensation components	1	4	4	4	1	1
Max.power	15 W	1.3 kW	192 W	384 W	345.6 W	400 W
Peak efficiency (%)	93.0	90.94	92.81	90.8	91.014	92.2
Compact and lightweight on the receiver	Yes	No	No	No	Yes	Yes
Eliminating communication links	No	Yes	Yes	Yes	No	Yes

Proposed in	Reference 13	Reference 22	Reference 23	Reference 24	Reference 25	This work
Number of coils	2	2	2	3	4	2
Number of switches	3	2	2	2	2	2
Number of transmitter-side compensation components	2	3	1	2	3	4
Number of receiver-side compensation components	1	4	4	4	1	1
Max.power	15 W	1.3 kW	192 W	384 W	345.6 W	400 W
Peak efficiency (%)	93.0	90.94	92.81	90.8	91.014	92.2
Compact and lightweight on the receiver	Yes	No	No	No	Yes	Yes
Eliminating communication links	No	Yes	Yes	Yes	No	Yes

The designed communication-free WPT system based on transmitter-side hybrid topology switching not only reduces the cost and avoids potential interference due to elimination of the wireless communication devices applied in both the transmitter and the receiver but also ensures the portability, miniaturization, and compactness of the receiver, which is also suitable for some typical charging applications, such as biomedical implants, portable electronic devices, etc.

V. CONCLUSION

In this paper, the SS compensation topology with CC output and the LCC-S compensation topology with CV output of the WPT system have been analyzed in detail with the mutual inductance model. Besides, the ZPA condition can be achieved with the designed hybrid topology, which helps minimize the volt-ampere (VA) rating of the power supply and improve system efficiency. The novel charging voltage estimation method realized by measuring the rms value of HFI output current is introduced into the designed hybrid topology for eliminating wireless communication links. The advantages of the system are that it avoids the measurement of charging parameters in the receiver and maintains a lightweight, miniaturized, and compact receiver.

An experimental prototype was constructed to verify the feasibility of the proposed WPT system. During the whole charging process, the fluctuation margins of the charging voltage and current do not exceed 2.84% and 2.83%, respectively. Besides, the charging voltage estimation method by measuring the rms value of the HFI output current is proved to be accurate and feasible, especially at the key transition point from the CC to the CV charging mode, where the estimation error is negligible. Furthermore, the maximum efficiency goes up to 92.2% with a charging power level of 400 W. The experimental results are in excellent agreement with the theoretical analysis. Overall, the proposed method is a promising candidate for various charging applications, such as the charging of high-power EVs and low-power biomedical implants and charging applications of portable electronic devices.

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