A communication-free wireless power transfer system based on transmitter-side hybrid topology switching for various battery charging applications is proposed in this paper. The method realizes the stable and reliable constant current (CC) and constant voltage (CV) outputs by the inherent characteristics of the designed hybrid topology. Besides, the zero phase angle condition can be obtained, which enhances the power transmission capability and improves system efficiency. The transition point from the CC to CV charging mode is determined by the battery charging voltage, which is estimated in real-time by measuring the root-mean-square value of high-frequency inverter output current. Then, the whole charging process can be operated by the transmitter-side controller; hence, the receiver-side controller is unnecessary. The advantages are that wireless communication links for real-time feedback of charging parameters between the transmitter and receiver are avoided, sophisticated control strategies are no longer required, and a lightweight, miniaturized, and compact receiver is guaranteed. Finally, to verify the effectiveness and practicability of the proposed approach, a confirmatory experimental setup with 80 V charging voltage and 5 A charging current is constructed. The experimental results match the theoretical analysis.

## I. INTRODUCTION

The wireless power transfer (WPT) technology, which is in a position to deliver electrical energy to the load safely, efficiently, and conveniently through magnetic coupling without a wire connection, has been attracting much attention in the scientific community and academia in recent decades. This emerging and promising technology is rapidly evolving and has been widely implemented in many commercial areas such as train power supplies,^{1} electric vehicles (EVs),^{2–4} underwater systems,^{5} consumer electronics,^{6} implacable biomedical devices,^{7–9} and other industrial areas.^{10–12} However, the most commonly used charging method for these applications is traditional plug-in charging, which is inconvenient to users and has safety problems such as electrical shock, especially in a wet environment. In order to solve these problems, the WPT technology has been extensively researched and is expected to replace the existing plug-in charging system in most future applications.

Rechargeable lithium-ion (*Li*_*ion*) batteries are used extensively as power sources in various practical applications for their superior performance, including inherent high energy, high power tolerance, light weight, and environment friendliness. There are two main modes in the charging process of *Li*_*ion* batteries: the constant current (CC) mode and the constant voltage (CV) mode The typical charging profile is depicted in Fig. 1.^{13} Initially, the charging voltage rises gradually during the CC charging mode with the preset constant charging current, *I*_{B_P}. When the battery charging voltage rises to the preset voltage level *U*_{B_P}, the charger immediately executes the CV charging mode. Then the charging process continues until the charging current decreases to one tenth of the preset current value. Obviously, the equivalent resistance of the battery varies in a wide range throughout the charging process. The realization of this special charging profile poses an enormous challenge to the designers of the WPT system. To realize the expected constant current and constant voltage charging outputs against a variable load, a lot of schemes for WPT systems have been reported in several recent publications.^{13–15,18–20,22–27} Among them, control schemes and compensation topologies are the main research hotspots for realizing the desired battery charging profile. Various control schemes have been investigated to solve these proposed charging problems.^{13–15,18–20} These control schemes consist of two parts: the transmitter-side control and the receiver-side control. First of all, the transmitter-side control technology is mainly implemented by three methods, which are dc–dc conversion, frequency conversion control (FCC), and phase shift modulation (PSM). An additional dc–dc converter is installed at the front end of a high-frequency inverter (HFI) at the transmitter of WPT systems to regulate the charging current or the charging voltage of the load.^{14} This approach adds extra volume and weight due to the system requiring more components, affecting system efficiency. The FCC technology utilized in an HFI at the transmitter can control the output characteristics.^{15} However, due to the occurrence of the frequency bifurcation phenomenon,^{16} this method may cause a stability problem with the time-varying load. Besides, it can hardly realize zero phase angle (ZPA) operation of the inverter and dramatically decreases the power transmission capability when the operating frequency deviates from the optimal frequency point.^{17} The WPT system based on the PSM technology is another method to charge the variable load with CC and CV modes during the entire charging process,^{18} which may make it difficult for an HFI to realize zero voltage switching (ZVS) in the full load range, especially under a light load. None of the three transmitter-side control schemes mentioned can realize the expected charging characteristics without communication links between the transmitter and the receiver. Hence, the receiver-side control technology can be employed to eliminate the communication links. In Ref. 19, a back-end dc–dc converter is used to achieve the desired CC and CV outputs, which adds extra components and lowers the overall efficiency of WPT systems. Another approach for the receiver-side control technology is to employ an active rectifier to control the charging characteristics of the battery, which increases control complexity.^{20} Currently, communication links applied to WPT systems are typically constructed by matured technologies such as Bluetooth, WiFi, and Zigbee.^{21} However, due to the introduction of communication modules, the cost of systems is increased. In addition, when wireless communication is disturbed, CC or CV charging in WPT systems will be unstable and even causes charging failure. Although the receiver-side control can implement the desired control requirement without wireless communication, it has a higher control complexity and violates the compact and lightweight principle of a receiver for some special charging applications due to additional components.

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, $U\u2192I$ stands for the phasor of the fundamental harmonics of HFI output voltage, and $I\u2192I$ is the corresponding current phasor. $U\u2192O$ and $I\u2192O$ 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.

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.

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:

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

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

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

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

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

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 $U\u2192I$ of the transmitter remains constant, the output current $I\u2192O$ is not affected by the time-varying load.

Moreover, the corresponding total input impedance is derived as

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.

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.

The related system parameters can be simplified by

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

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

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

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

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

According to the first formula in (13), the receiver-side output voltage $U\u2192O$ remains constant, regardless of changes in the load.

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

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.

Figure 7 shows the two additional high-frequency AC switches *K*_{1} and *K*_{2} 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}

When the two switches *K*_{1} and *K*_{2} 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,

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,

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

In the receiver, *U*_{O}, which is the rms value of the full-bridge diode rectifier input voltage, can be derived as

Moreover, the relationship between the charging current *I*_{B} and the rms value of the rectifier input current *I*_{O} can be expressed by

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

Similarly, substituting (17), (18) and (20) into (13), the series inductance *L*_{R} can be calculated by

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

According to (3), (10), (15), (16), (21) and (22), the capacitors *C*_{PA} and *C*_{PB} can be obtained by

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 $U\u2192O(U\u2192O=I\u2192ORE)$ indicates the product of the output current $I\u2192O$ and the equivalent ac resistance *R*_{E}. Then, combined with (1) and (3), (2) can be represented as

Eliminating $I\u2192O$ in (24), the mathematical relationship between $I\u2192I$ and $U\u2192O$ is obtained as

According to the analysis in Sec. II, the designed SS topology for achieving CC output characteristics can realize the ZPA condition. In other words, $U\u2192I$ and $I\u2192I$ are in phase. Therefore, the variables in (25) can be transformed into the form of rms values, and (25) can be converted to

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

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.

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

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.

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

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 *K*_{1} and *K*_{2} 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 *K*_{1} and *K*_{2} 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.

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 *K*_{1} and *K*_{2} 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.

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 |

Component . | Type . |
---|---|

MOSFETs for the HFI | C2M0080120D |

MOSFETs for switches | C2M0080120D |

Diodes for the rectifier | DSE160-12A |

RMS detection module for I_{I} | AD637 |

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.

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 *K*_{1} and *K*_{2} 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 $U\u2192I$, and output current $I\u2192I$ 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 $U\u2192I$ and $I\u2192I$ is nearly zero, which meets the ZPA condition and eliminates a large amount of reactive power in the resonant tank.

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.

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 *K*_{1} and *K*_{2}.

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.

Figure 15 shows the measured waveforms of *U*_{B}, *I*_{B}, $U\u2192I$, and $I\u2192I$. 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 $U\u2192I$ and current $I\u2192I$ 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.

Furthermore, the transient waveforms of *U*_{B}, *I*_{B}, $U\u2192I$, and $I\u2192I$ 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.

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 $I\u2192I$ and *U*_{B} can be clearly observed as the load resistance has different values of 5 Ω, 10 Ω, and 20 Ω. Apparently, $I\u2192I$ 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.

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.

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.

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.

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.