# A Six-Switch Mode Decoupled Wireless Power Transfer System with Dynamic Parameter Self-Adaption

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

_{1}. However, the system requires precise control for switch S

_{2}, and its switching times must be strictly aligned with the zero crossing point of the resonant current. Otherwise, the soft switching condition will not be satisfied. This shortcoming causes strong adhesion between the converter and the resonance network, fails to achieve complete decoupling, has high requirements for the accuracy of the control system, is sensitive to parameter changes, and needs better dynamic performance. Article [21] proposes a full-bridge IPIFR–WPT system with six switches. The switches are used to periodically connect or isolate the resonant capacitor and the DC power supply into or out of the system to achieve power injection and free resonant mode switching. The single-switch IPIFR–WPT system uses only one switch to control mode switching, greatly reducing system switching losses and improving system efficiency [22,23]. The energy of the injection system can be adjusted by controlling the turn-on time of the switch to achieve the regulation of power, but the injection time cannot be too large. Furthermore, it is necessary to ensure that the current flowing through the primary inductor can be less than zero during the resonance process. Therefore, there is a theoretical power peak for the single-switch IPIFR–WPT system, which means the system cannot achieve wide-range power regulation.

## 2. Circuit Structure and Mode Analysis

#### 2.1. Circuit Structure and Mode Analysis

_{0}and a DC power supply E

_{dc}. The purpose of a one-way power supply is to ensure that energy entering the system does not return to the power supply. Switches S

_{1}–S

_{4}form a full-bridge converter to connect power E

_{dc}to the system and inject energy into the system. Switches S

_{5}and S

_{6}let the primary compensation capacitor C

_{p}be isolated from or connected to the system. Diodes D

_{1}–D

_{6}are the bypass diodes of switches S1–S6, wherein bypass diodes D

_{1}–D

_{4}do not function during the entire working process due to their different directions from isolation diode D

_{0}; the bypass diodes D

_{5}and D

_{6}are used for continuous current conduction during the resonance process and can isolate C

_{p}from the system. The self-inductances of the primary and secondary coils are L

_{p}and L

_{s}, while M is the mutual inductance of the coils. R

_{p}and R

_{s}are the parasitic resistance of the primary and secondary coils, respectively. The load R

_{0}consumes the energy received by the secondary circuit after being rectified by the back-end rectifying circuit of the secondary circuit. Supposing the inductive characteristics and the voltage drop of the back-end rectifier circuit are ignored, in that case, the equivalent load R

_{L}can be used to convert the load resistance R

_{0}to the input terminal of the rectifier circuit, and the conversion relationship is as follows:

_{dc}to the system in a forward direction, a forward power injection mode. Modes 2–4 are resonant modes, also called free resonance processes, due to the isolation of the power supply E

_{dc}from the system. Note that Modes 2 and 4 are transitional modes, both of which are unidirectional resonance processes. According to the symmetry of the full-bridge converter operation, Mode 5 reversely connects the power supply E

_{dc}to the system as a reverse power injection mode. Furthermore, Modes 6–8 are resonant processes opposite to the working processes of Modes 2–4.

_{1}, the primary capacitor voltage u

_{p}, and the primary inductor current i

_{p}of the six-switch IPIFR–WPT system under steady-state operation. According to Figure 2 and Figure 3, the operation modes of the six-switch IPIFR–WPT system can be analyzed as follows:

**Mode 1**[t

_{0}, t

_{1}]: This is a forward power injection mode with a duration of ξ

_{1}= t

_{1}–t

_{0}. Before the time t

_{0}, the switches S

_{1}and S

_{4}have been turned on in advance, and the switches S

_{2}and S

_{3}remain turned off. At this time, the primary capacitor voltage u

_{p}is greater than E

_{dc}, forcing D

_{0}to be turned off, isolating the power supply E

_{dc}from the system, thereby preventing the energy from being injected into the system. Until the time t

_{0}, the voltage u

_{p}drops to equal to E

_{dc}, causing diode D

_{0}to turn on, and the current i

_{p}flows from the branch D

_{6}–C

_{p}–S

_{5}to the switches S

_{1}and S

_{4}that have been turned on in advance. During the period [t

_{0}, t

_{1}], while the primary capacitor C

_{p}is isolated from the system, the DC power supply E

_{dc}directly injects energy into the primary inductor L

_{p}.

**Mode 2**[t

_{1}, t

_{2}]: This is a transitional mode of the first free resonance process. At the moment t

_{1}, the switches S

_{1}and S

_{4}turn off, and at the same time, the current i

_{p}will continuously conduct through the bypass diode D

_{6}. At this time, the turning off of switches S

_{1}and S

_{4}meets the ZVS condition. In Mode 2, the primary inductor L

_{p}and the primary compensation capacitor C

_{p}form a resonant cavity and begin passive free resonance. The duration of Mode 2 is very short and can generally be taken as 1–2 μs, even a few hundred nanoseconds.

**Mode 3**[t

_{2}, t

_{3}]: This is a bidirectional free resonant mode. Since the switch S

_{6}turns on at t

_{2}, the primary current i

_{p}can achieve bidirectional free resonance in the resonant network L

_{p}–C

_{p}. During Mode 3, after the value of the current i

_{p}resonates to less than zero, the flow direction of i

_{p}in the branch is S

_{5}–C

_{p}–S

_{6}. After that, at time t

_{3}, the switch S

_{5}turns off, and the current i

_{p}can still continuously conduct through the bypass diode D

_{5}. The switch S

_{5}turns off to meet the ZVS condition. At the same time, at t

_{3}, the switches S

_{2}and S

_{3}turn on. Due to the capacitance voltage u

_{p}being less than −E

_{dc}at this time, the isolation diode cannot be turned on, and the current cannot be exchanged from the branch D

_{5}–C

_{p}–S

_{6}to the switches S

_{2}and S

_{3}. That is, before and after the turn-on of S

_{2}and S

_{3}, the current flowing through them is zero, satisfying the zero current switching (ZCS) condition.

**Mode 4**[t

_{3}, t

_{4}]: In this mode, the system remains in a state of free resonance. In addition, the current i

_{p}continuously conducts through the branch D

_{5}–C

_{p}–S

_{6}during the time span until the time of t

_{4}, when the value of u

_{p}rises to equal to −E

_{dc}through resonance. At time t

_{4}, because the switches S

_{2}and S

_{3}have turned on in advance at t

_{3}, the current i

_{p}can be naturally switched from the branch D

_{5}–C

_{p}–S

_{6}to the switches S

_{2}and S

_{3}, thereby switching to Mode 5.

**Mode 5**[t

_{4}, t

_{5}]: This is a reverse power injection mode, which is reversed with Mode 1. Due to the natural commutation of the current i

_{p}from the branch D

_{5}–C

_{p}–S

_{6}to the switches S

_{2}and S

_{3}that have turned on before t

_{4}, the power supply E

_{dc}is reversely connected to the system and injects energy into the primary inductor L

_{p}.

**Mode 6**[t

_{5}, t

_{6}]: This is a transitional mode of the second free resonance process, which is symmetric to Mode 2 and has a short duration. At time t

_{5}, the switches S

_{2}and S

_{3}turn off. Since the current i

_{p}will be continuously conducted through the bypass diode D

_{5}, turning off switches S

_{2}and S

_{3}meets the ZVS condition. In Mode 6, the primary inductor L

_{p}and the primary compensation capacitor C

_{p}form a resonant network and begin free resonance.

**Mode 7**[t

_{6}, t

_{7}]: This is a bidirectional free resonant mode symmetric to Mode 3. At t

_{6}, the switch S

_{5}turns on. Due to the capacitance voltage u

_{p}greater than E

_{dc}, the current i

_{p}continuously conduct through the bypass diode D

_{5}without commutation to S

_{1}and S

_{4}. Therefore, the turn-on of switch S

_{5}satisfies the ZVS condition. Then the primary current i

_{p}can achieve bidirectional free resonance in the resonant network L

_{p}–C

_{p}during [t

_{6}, t

_{7}].

**Mode 8**[t

_{7}, t

_{8}]: This is a transitional mode symmetric to Mode 4. At t

_{7}, switch S

_{6}turns off while turning on switches S

_{1}and S

_{4}. Because of the voltage u

_{p}being greater than E

_{dc}, D

_{0}is turned off, and the current i

_{p}continuously conducts through D

_{6}without commutation to S

_{1}and S

_{4}. Therefore, S

_{6}meets the ZVS condition, while the opening of S

_{1}and S

_{4}satisfies the ZCS condition. The resonant network maintains resonance during [t

_{7}, t

_{8}]. Until t

_{8}, the voltage up is equal to E

_{dc}, and the current i

_{p}naturally commutates from the resonant network to S

_{1}and S

_{4}. Meanwhile, the system operates into Mode 1.

#### 2.2. Calculation of System Soft Switching Operating Point

_{p}to form a voltage clamp with the power supply voltage E

_{dc}through the diode D

_{0}. In Mode 8, the switch groups S

_{1}and S

_{4}have turned on, but at this time, the voltage u

_{p}is greater than E

_{dc}, and the system remains in the free resonance process. Meanwhile, i

_{p}> 0, that is, u

_{p}will continue to decrease until u

_{p}drops to equal to E

_{dc}, and the diode D

_{0}reaches the critical conduction condition. At the same time, the current is commutated from branch S

_{6}–C

_{p}–S

_{5}to branch S

_{4}–E

_{dc}–D

_{0}–S

_{1}. The system switches from a free resonance process to a forward power injection process, and the voltage u

_{p}on the primary capacitor C

_{p}will maintain the voltage clamp at E

_{dc}. Similarly, when switching from Mode 4 to Mode 5, it is necessary to clamp the voltage u

_{p}on the primary capacitor C

_{p}to −E

_{dc}, and the free resonance process completes the switching to the reverse power injection process.

_{1}, β

_{2}, β

_{3}, and β

_{4}between the four operation processes are shown in Figure 4 and written in parallel:

- β
_{1}: S_{1}= 0 and S_{4}= 0; - β
_{2}: u_{p}= −E_{dc}and i_{p}< 0; - β
_{3}: S_{2}= 0 and S_{3}= 0; - β
_{4}: u_{p}= E_{dc}and i_{p}> 0.

_{dc}and −E

_{dc}, respectively. At the same time, the system models for the first and second free resonance processes are also entirely consistent, with their equivalent circuit models shown in Figure 5b, and there is no power input in the free resonance process.

_{p}is isolated from the system by the switches S

_{5}and S

_{6}being turned off. The DC power supply directly charges the primary inductance L

_{p}through full-bridge forward conduction (switches S

_{1}and S

_{4}) or reverse conduction (switches S

_{2}and S

_{3}), with input voltages of E

_{dc}or −E

_{dc}, respectively. At the same time, due to the isolation diode D

_{0}, the current i

_{1}only flows in one direction, i

_{1}> 0, and energy can only be injected into the system from the power source and cannot be returned to the power source. In the free resonance process shown in Figure 5b, the DC power source is isolated from the system, while the inductance L

_{p}and capacitance C

_{p}in the primary circuit are directly connected to form a resonance circuit. Hence, through mutual inductance coupling, electrical power is transferred from the primary circuit to the secondary circuit.

_{p}on the primary capacitor C

_{p}, the current i

_{p}on the primary coil inductance L

_{p}, the current i

_{s}on the secondary coil inductance L

_{s}, and the voltage u

_{o}on the secondary capacitor C

_{s}, that is, x = [u

_{p}, i

_{p}, i

_{s}, u

_{o}]

^{T}. Because the secondary capacitance C

_{s}and the equivalent load resistance R

_{L}are in parallel, the voltage u

_{o}can also be considered as the equivalent output voltage. Assuming the system input is u = [E

_{dc}], differential equations can be listed as follows for each state variable according to Kirchhoff’s voltage law and current law:

_{0}, the corresponding time domain solution can be expressed as follows [24]:

_{zi}(t) is the zero input response, x

_{zt}(t) is the zero state response, and x

_{0}is the initial state of the system at the initial time t

_{0}.

_{1}and A

_{3}of the power injection process are irreversible, it is impossible to bring them into Equation (11) directly. Furthermore, the voltage u

_{p}on the primary capacitor C

_{p}is clamped at E

_{dc}during the power injection process. Hence, the differential equation of u

_{p}can be rewritten as follows:

_{1}, A

_{3}and input matrices B

_{1}, B

_{3}of the power injection process will be rewritten to be reversible as follows:

_{0}is x

_{0}, the time domain solutions of the subsystems can be expressed as follows:

_{1}. Set the time interval between two power injection processes as ξ

_{2}. Let the initial value of the system in the nth cycle be x

_{n}, and the terminal values of the four subsystems be x

_{n}

_{1}, x

_{n}

_{2}, x

_{n}

_{3}, and x

_{n}

_{+1}, respectively, where x

_{n}

_{+1}is the terminal value of the system in the nth cycle and also the initial value of the system in the (n + 1) cycle. The expressions for the terminal values x

_{n}

_{1}, x

_{n}

_{2}, x

_{n}

_{3}, and x

_{n}

_{+1}of each subsystem are as follows:

_{n}= −x

_{n}

_{2}= x

_{n}

_{+1}. Generally, x

_{n}= x

_{n}

_{+1}is called a fixed point, and the mapping relationship between x

_{n}and x

_{n+}

_{1}becomes a fixed point mapping. To simplify the iterative process, take x

_{n}= −x

_{n}

_{2}for fixed point mapping calculations, and the following equation can be obtained:

_{2}= 1/2T − ξ

_{1}for Equation (23), we can obtain the following equation:

_{4:}u

_{p}= E

_{dc}and i

_{p}> 0. Namely, the element up in the fixed point x

_{n}is constant, and the following equation can be expressed:

_{1}) to solve Equation (25):

_{1}) with T = 110 μs is shown in Figure 6. There are two results of g(ξ

_{1}) = 0, that is, ξ

_{1a}= 11.11 μs and ξ

_{1b}= 36.02 μs. Then, we bring ξ

_{1a}and ξ

_{1b}into (20) to solve the corresponding fixed point x

_{n}, listed in Table 3.

_{n}is both the initial and final values of the steady-state period. Moreover, the fixed point x

_{n}must satisfy the boundary condition β

_{4}(u

_{p}= E

_{dc}and i

_{p}> 0). In Table 3, when taking ξ

_{1a}= 11.11 μs, the value of fixed point x

_{n}satisfies the boundary condition β

_{4}., and when taking ξ

_{1b}= 36.02 μs, i

_{p}= −3.272 A < 0 does not meet the boundary condition β

_{4}. Therefore, the root ξ

_{1b}= 36.02 μs could be abandoned (x

_{n}= −x

_{n}

_{2}= x

_{n}

_{+1}).

_{n}and the transition state quantity x

_{n}

_{1}of the six-switch IPIFR–WPT system, according to the proposed symmetry of the full-bridge converter, there are x

_{n}= −x

_{n}

_{2}= x

_{n}

_{+1}, x

_{n}

_{1}= −x

_{n}

_{3}. Then, in order to more intuitively represent the trade-off between the two results mentioned above, by substituting x

_{n}and x

_{n}

_{1}obtained in Table 3 into Equations (19)–(22), the curves of state variables in the complete steady-state cycle can be obtained, and the curves of current i

_{p}and voltage u

_{p}in them can be plotted in Figure 7.

_{1a}= 11.11 μs, the simulation waveform is consistent with the mode analysis, and all boundary conditions can be satisfied within a steady-state cycle. However, taking ξ

_{1b}= 36.02 μs, the calculated operating waveform is inconsistent with the expected, and the boundary conditions β

_{2}(u

_{p}= −E

_{dc}and i

_{p}< 0) and β

_{4}(u

_{p}= E

_{dc}and i

_{p}> 0) cannot be satisfied, so that ξ

_{1b}can be abandoned.

## 3. System Characteristics and Experimental Results

#### 3.1. Experimental Devices

_{s}and C

_{p}are MKPH–R 0.4 μF. In Figure 8b, the isolation diode D

_{0}used in the system is FR607 (1000 V, 6 A) and the switches S

_{1}–S

_{6}are IXFN56N90P (900 V, 56 A).

_{p}and L

_{s}of the primary and secondary coils are 660 μH and 585 μH, respectively. The internal resistances R

_{p}and R

_{s}are both 0.2 Ω. The relationship between the coupling coefficient k and the coil distance d is shown in Figure 9.

#### 3.2. Soft Switching Margin Characteristic

_{p}is greater than E

_{dc}so that the diode D

_{0}is turned off and the power supply is isolated from the system. Since the free resonance process will maintain until the voltage u

_{p}is equal to E

_{dc}, the switches of the full-bridge converter could turn on before in a very time margin when the voltage u

_{p}is greater than E

_{dc}. Hence, in this time margin, the system itself will achieve the soft switching condition and determine the operation point without any switching action. The time margin is called the soft switching margin.

_{p}and the primary inductor current i

_{p}, respectively.

_{4}(u

_{p}= E

_{dc}and i

_{p}> 0), and switches S

_{1}and S

_{4}have been turned on in advance. It can be known from the waveforms of voltage u

_{p}and current i

_{p}in Figure 10 that the timing of turn-on of S

_{1}and S

_{4}must meet the following conditions: u

_{p}> E

_{dc}and i

_{p}> 0. Therefore, the margin that satisfies the soft switching condition is [t

_{0}, t

_{1}]. Namely, the maximum pulse width for S

_{1}and S

_{4}is D

_{max}= t

_{2}− t

_{0}, and the minimum opening pulse width is D

_{min}= t

_{2}− t

_{1}. Based on the symmetry of the full-bridge converter, there are D

_{max}= t

_{5}− t

_{3}= t

_{2}− t

_{0}and D

_{min}= t

_{5}− t

_{4}= t

_{2}− t

_{1}. The pulse widths of switch groups (S

_{1}, S

_{4}) and (S

_{2}, S

_{3}) can meet the conditions by taking any value of [D

_{min}, D

_{max}]. Therefore, the time range [D

_{min}, D

_{max}] can be called the wide soft switching margin of a six-switch IPIRF–WPT system, and M

_{ZVS}is defined as the wide soft switching margin of the system, and its calculation formula is as follows:

_{L}= 10 Ω, and the period be T = 110 μs. Then, taking the positive pulse widths of the switching strategy as (a) D = 15 μs, (b) D = 20 μs, and (c) D = 26 μs, the system can self-determine the same operating point, ξ

_{1}= 10.52 μs, very close to the theoretical value, ξ

_{1}= 11.11 μs. Meanwhile, the waveform shape and amplitude of the capacitor voltage u

_{p}and the inductor current i

_{p}are consistent. According to the measurement results in Figure 11, the soft switching margin under the above static parameters is D

_{min}= 10.52 μs to D

_{max}= 29.95 μs. In Figure 11, the three positive pulse widths of (a), (b), and (c) are all within the range of [D

_{min}, D

_{max}] and can enable the system to operate at the same operating point and meet soft switching conditions. Therefore, it can be proven that the unique topology of the six-switch IPIFR–WPT system enables it to have a wide soft switching margin, which provides a wide tolerance for the control system, improves system stability, and reduces control difficulty.

#### 3.3. Dynamic Parameter Adaptation Characteristic

_{L}will change as the charging process progresses. Therefore, the coil coupling coefficient k and the equivalent resistance R

_{L}are the main dynamic parameters for research. When the power injection process switches to the free resonance process, the boundary condition depends on the values of the system state variables instead of the switches. The wide soft switching margin characteristic analyzed above, that is, any switching duty D

_{1}∈ [D

_{min}, D

_{max}] allows the system to operate at ξ

_{1}= D

_{min}, the soft switching operating point. When parameters change dynamically, its soft switching margin has a certain degree of overlap, which can ensure that the system has the characteristics of resisting changes in dynamic parameters, called dynamic parameter adaptive characteristics.

_{ZVS}, D

_{min}, and D

_{max}concerning the coupling coefficient k. The system parameters are taken according to Table 2, and D

_{min}and D

_{max}are measured under different k. As seen from Figure 12, in the process of gradually increasing the coupling coefficient k from 0.30 to 0.60, although the soft switching margin has decreased, it has maintained more than 15%.

_{1}, during the process of changing the coupling coefficient k, the system can determine its own soft switching operating point, and its power injection times ξ

_{1}are self-determined as (a) 12.26 μs, (b) 10.52 μs, (c) 9.26 μs, and (d) 7.86 μs. The waveform trends of the capacitor voltage u

_{p}and the inductor current i

_{p}are always consistent, and the soft switching boundary conditions are satisfied at the boundaries of the free resonance process and the power injection process. In particular, the capacitor voltage u

_{p}can clamp at E

_{dc}and −E

_{dc}during the power injection process at different coupling coefficients k, which indicates the soft switching conditions have been met. Therefore, this experiment proves that the six-switch IPIFR–WPT system can adapt to the dynamic change of the coupling coefficient k in a great range.

_{L}changes dynamically, the six-switch IPIFR–WPT system can maintain its adaptive characteristics. As shown in Figure 14, there are curves of the soft switching margin D

_{min}and D

_{max}concerning the equivalent resistance R

_{L}. In Figure 14, when the equivalent load resistance R

_{L}increases from 5 Ω to 20 Ω, although the soft switching margin can maintain more than 14%, and when the equivalent load resistance R

_{L}changes in the range of 5 Ω to 20 Ω, there is a significant overlap range, which allows the system to resist changes in load resistance over a large range.

_{L}changes, (a) 10 Ω, (b) 15 Ω, and (c) 20 Ω, the waveforms of the current i

_{1}indicate that the system can determine its own soft switching operating point and power injection times ξ

_{1}are self-determined as (a) 10.52 μs, (b) 11.29 μs, and (c) 11.94 μs. The waveform trends of the capacitive voltage u

_{p}and the inductive current i

_{p}are consistent. The larger the equivalent load resistance R

_{L}, the smaller the amplitude of u

_{p}and i

_{p}, indicating that the larger the load resistance, the less energy the system inputs. At the same time, the boundary conditions for switching between the free resonance process and the power injection process can be satisfied. Significantly, the capacitor voltage u

_{p}can be clamped at E

_{dc}and −E

_{dc}during the power injection process under different equivalent load resistances R

_{L}, which means the soft switching conditions have been satisfied. Therefore, this experiment proves that the six-switch IPIFR–WPT system can adapt to the dynamic changes in the equivalent load resistance R

_{L}over a large range.

_{L}.

#### 3.4. Decoupling Characteristic of Power Injection and Free Resonance

_{1}, ξ

_{2}) are shown in Figure 16. In Figure 16, as the period T increases, the injection time ξ

_{1}rises significantly, and ξ

_{2}remains unchanged, increasing the power injected into the system. Furthermore, due to ξ

_{2}remaining unchanged, the power injection and free resonance processes exhibit significant decoupling characteristics, which makes the power regulation strategy of the six-switch IPIRF–WPT system extremely simple, that is, directly adjusting the length of the period T.

_{1}. As shown in Figure 17, when the periods T of the system are (a) 100 μs, (b) 110 μs, (c) 120 μs, and (d) 130 μs, respectively, the determined power injection times ξ

_{1}are (a) 5.94 μs, (b) 10.52 μs, (c) 13.10 μs, and (d) 20.07 μs. Therefore, as the period T grows, the duration of the power injection time ξ

_{1}also increases. Meanwhile, the amplitudes of u

_{p}and i

_{p}both increase significantly with the rise of T, meaning the input power increases synchronously.

_{in}, the output power P

_{out}, and the efficiency η are expressed as follows:

_{1}is the average value of i

_{1}, and U

_{o,rms}is the root mean square (RMS) value of u

_{o}.

_{out}and the operation efficiency of the six-switch IPIFR–WPT system varying with the period T are shown in Figure 18. It can be seen from Figure 18 that the output power monotonically increases as the period T increases.

_{1}, and increasing T can make ξ

_{1}grow, which results in a monotonic relationship between the output power and the period T. Therefore, compared to the fully resonant WPT system, the six-switch IPIFR–WPT system eliminates the peak power point, significantly simplifying power regulation strategies, eliminating system detuning caused by frequency splitting, and improving system stability.

## 4. Conclusions

_{L}, respectively. Furthermore, the power injection and the free resonance processes are decoupled. Namely, the converter and the resonant network are decoupled. Hence, the power injected into the system is completely controlled, and the curve of output power is monotonic with the injection time ξ

_{1}or the period T. Moreover, according to the experiments, the power loss is greatest on the coils instead of the diode D

_{0}. However, in this paper, without precise parameter design, the system efficiency could still achieve 88%.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**The operation mode diagram of the six-switch IPIFR–WPT system: (

**a**) Mode 1, (

**b**) Mode 2, (

**c**) Mode 3, (

**d**) Mode 4, (

**e**) Mode 5, (

**f**) Mode 6, (

**g**) Mode 7, and (

**h**) Mode 8.

**Figure 5.**The equivalent circuits of the operation processes of the six-switch IPIFR–WPT system: (

**a**) power injection process and (

**b**) self–resonance process.

**Figure 7.**The waves of system state variables under the calculated steady-state operation points: (

**a**) ξ

_{1}= 11.11 μs and (

**b**) ξ

_{1}= 36.02 μs.

**Figure 8.**Experimental devices of the six-switch IPIFR–WPT system: (

**a**) the whole system and (

**b**) the converter.

**Figure 9.**The relationship between the coupling coefficient k and coil distance d of the flat coils.

**Figure 11.**The verification waveforms of the wide soft switching margin: (

**a**) D = 15 μs, (

**b**) D = 20 μs, and (

**c**) D = 26 μs.

**Figure 13.**The waveforms of i

_{1}, i

_{p}, and u

_{p}when coil distance d changes in the open-loop state: (

**a**) d = 6 cm, (

**b**) d = 7 cm, (

**c**) d = 8 cm, and (

**d**) d = 9 cm.

**Figure 14.**The curves of the wide soft switching margin concerning the equivalent load resistance R

_{L}.

**Figure 15.**The waveforms of i

_{1}, i

_{p}, and u

_{p}when load resistance R

_{L}changes in the open–loop state: (

**a**) R

_{L}= 10 Ω, (

**b**) R

_{L}= 15 Ω, and (

**c**) R

_{L}= 20 Ω.

**Figure 16.**The curves of the self-determining soft switching operation points concerning the period T.

**Figure 17.**The waveforms of i

_{1}, i

_{p}, and u

_{p}when T changes in the open-loop state: (

**a**) T = 100 μs, (

**b**) T = 110 μs, (

**c**) T = 120 μs, and (

**d**) T = 130 μs.

**Figure 18.**The experimental curves of the output power and efficiency concerning the period T: (

**a**) output power and (

**b**) efficiency.

Ref. | Dynamic Performance Improving Strategy | Inductors/Capacitors/Switches on the Converter | Have Any Voltage/Current Sensors? | Control Strategy | Achieve Decoupling? | Sensibility to the Parameters |
---|---|---|---|---|---|---|

[14] | Impedance matching with a capacitor matrix | 1/(M × N)/(M × N + 1) | Yes | Close loop | No | Low |

[15] | Frequency tuning loops | 1/1/4 | Yes | Close loop | No | High |

[16] | Maximum power point tracking | 1/1/4 | Yes | Close loop | No | High |

[20] | Switch-mode adjusting | 2/3/2 | No | Open loop | Partially | High |

Proposed | Power injecting structure | 1/1/6 | No | Open loop | Yes | Low |

Parameter | Value | Parameter | Value |
---|---|---|---|

L_{p} | 660 μH | E_{dc} | 100 V |

L_{s} | 585 μH | k | 0.5 |

R_{p}, R_{s} | 0.2 Ω | R_{L} | 10 Ω |

C_{p}, C_{s} | 0.4 μF | T | 110 μs |

Operation Point | x_{n} | x_{n}_{1} | ||||||
---|---|---|---|---|---|---|---|---|

u_{p} (V) | i_{p} (A) | i_{s} (A) | u_{o} (A) | u_{p} (V) | i_{p} (A) | i_{s} (A) | u_{o} (A) | |

11.11 μs | 100.0 | 9.812 | 5.986 | 56.594 | 100.0 | 11.305 | 5.657 | 57.483 |

36.02 μs | 100.0 | −3.273 | −1.260 | −17.146 | 100.0 | 3.850 | 2.287 | 20.212 |

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## Share and Cite

**MDPI and ACS Style**

Wu, W.; Luo, D.; Hong, J.; Tang, Z.; Chen, W.
A Six-Switch Mode Decoupled Wireless Power Transfer System with Dynamic Parameter Self-Adaption. *Electronics* **2023**, *12*, 2314.
https://doi.org/10.3390/electronics12102314

**AMA Style**

Wu W, Luo D, Hong J, Tang Z, Chen W.
A Six-Switch Mode Decoupled Wireless Power Transfer System with Dynamic Parameter Self-Adaption. *Electronics*. 2023; 12(10):2314.
https://doi.org/10.3390/electronics12102314

**Chicago/Turabian Style**

Wu, Wei, Daqing Luo, Jianfeng Hong, Zhe Tang, and Wenxiang Chen.
2023. "A Six-Switch Mode Decoupled Wireless Power Transfer System with Dynamic Parameter Self-Adaption" *Electronics* 12, no. 10: 2314.
https://doi.org/10.3390/electronics12102314