DOUBLE-SIDED LCC COMPENSATION METHOD

FOR WIRELESS POWER TRANSFER

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Application 14/328,077 filed on July 10, 2014 and the benefit of U.S. Provisional Application No. 61 /844,987 filed on July 1 1 , 2013. The entire disclosures of the above application is incorporated herein by reference. FIELD

[0002] The present disclosure relates to a double-sided LCC compensation network and its tuning method for wireless power transfer.

BACKGROUND

[0003] The wireless power transfer (WPT) using magnetic resonant concept was proposed by Nikola Tesla more than 100 years ago. Until recently, with the development of power electronics technology, it is realized that a wireless power transfer system can be implemented economically enough to have a commercial value. Several companies have already developed products which can transfer power with acceptable power level and efficiency through a certain air gap.

[0004] In a wireless power transfer system, the energy is transferred through the mutual inductance of the transmit coil and receive coil, while the leakage inductance does not have a direct contribution to the active power transfer. Because of the large gap between the transmit coil and receive coil, the coupling coefficient between the two coils is small, typically in the range of 5% to 30% depending on the distance, alignment, and size of the coils. This causes the wireless power transfer systems to have a large leakage inductance but a small mutual inductance. To increase the coupling, the coil design, without a doubt, is important. Meanwhile, the compensation circuit which is used to cancel the leakage inductance, is also of great importance. Usually, capacitors, which can be lumped or parasitic, are added to form a resonant circuit, which is known as the magnetic resonant method. [0005] Different compensation topologies have been proposed and implemented to tune the two coils working at a resonant frequency in a wide range of applications. There are four basic topologies depending on how the compensation capacitors are added to the transmit and receive coils, namely, series-series (SS), series-parallel (SP), parallel-series (PS), and parallel-parallel (PP) topologies. Some other novel topologies have also been proposed in the literature. For example, a dual-topology is realized by switching between a parallel compensated and a series compensated secondary side to realize both constant current mode and constant voltage mode. Moreover, the transmit and receive coils need to be connected to the power electronics converters. To achieve high efficiency for the complete wireless power transfer system, some additional topologies have been proposed. In another example, a LCL converter is formed by adding LC compensation network between the converter and the transmit coil. There are two advantages for the LCL converter when the system works at the resonant frequency. First, the inverter only supplies the active power required by the load; second, the current in the primary side coil is independent of the load condition. In yet another example, a LC compensation network at both primary and secondary sides is proposed for bidirectional power transfer. The design of a LCL converter usually requires the same value for the two inductors.

[0006] One of the uniqueness of wireless power transfer systems is the high spatial freedom of the coils. This means the air gap variation and misalignment of the transmit and receive coils are inevitable. Usually, the system parameters and resonant frequency of the primary and secondary resonant tanks change when the coupling condition changes. With traditional compensation topologies, in order to achieve high efficiency, a tuning method is needed to maintain the resonance when the air gap changes or misalignment happens. There are two main methods, namely frequency control and impedance matching. Phase-locked loop techniques are able to tune the operating frequency to track the resonant frequency which will change due to the variation of gap length, misalignment and tolerance variation of the tuning components. Alternatively, impedance matching can be applied. Either method is difficult to implement in practice due to the uncertainty of the variations of the system. The overall system efficiency has also been constrained.

[0007] In this disclosure, a double-sided LCC compensation topology and its parameter design method is proposed. The topology consists of one inductor and two capacitors at both the primary and secondary sides. With the proposed method, the resonant frequency of the compensated coils is independent of the coupling coefficient and the load condition. The wireless power transfer system can work at a constant frequency, which eases the control and narrows the occupation of frequency bandwidth. Nearly unit power factors can be achieved for both the primary side and the secondary side converters in the whole range of coupling and load conditions, thus high efficiency for the overall system is easily achieved. A parameter tuning method is also proposed and analyzed to achieve ZVS operation for the MOSFET-based inverter. The proposed method is more attractive in an environment where the coupling coefficient keeps changing, like the electric vehicle charging application. Also, due to its symmetrical structure, the proposed method can be used in a bidirectional WPT system. Simulation and experimental results verified analysis and validity of the proposed compensation network and the tuning method. A prototype with 7.7kW output power for electric vehicles was built, and 96% efficiency from DC power source to battery load is achieved.

[0008] This section provides background information related to the present disclosure which is not necessarily prior art.

SUMMARY

[0009] This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.

[0010] A double-sided LCC compensation network is provided for a wireless power transfer system. The wireless power transfer system is comprised generally of a send unit configured to transfer power using inductive power transfer and a receive unit configured to receive the power from the send unit. The send unit includes an inverter configured to receive a DC input signal and convert the DC input signal to an AC output signal at a desired resonant frequency; a send coil configured to receive the AC output signal from the inverter and generate an alternating electromagnetic field; and a send side compensation circuit interconnecting the inverter with the send coil. More specifically, the send side compensation circuit is comprised of a send side inductor and a send side series capacitor serially coupled together and coupled to a positive terminal of the send coil, as well as a send side parallel capacitor coupled in parallel with the send coil.

[001 1 ] The receive unit includes a receive coil configured to receive the alternating electromagnetic field from the send coil of the send unit and output an AC charging signal ; a receive side converter configured to receive the AC charging signal from the receive coil and convert the AC charging signal to a DC charging signal ; and a receive side compensation circuit interconnecting the receive coil with the receive side converter. Likewise, the receive side compensation circuit is comprised of a receive side inductor and a receive side series capacitor serially coupled together and coupled to a positive terminal of the receive coil, as well as a receive side parallel capacitor coupled in parallel with the receive coil.

[001 2] In one embodiment, the inverter is further defined as a full bridge converter circuit comprised of four MOSFET switches. A controller is electrically coupled to the four switches and operates to turn the switches on and off at a zero voltage switching condition.

[0013] The turn off current delivered by the controller can be computed in accordance with

where U _A B is first order root mean square value of input voltage to the inverter, U _ab is first order root mean square value of output voltage of receive side converter, L _fl is inductance of send side inductor, L ₂ is inductance of receive side inductor, ω ₀ is resonant frequency and AL _e2 is an increase in value of L ₂ to ensure the turn off current is positive. [0014] In some embodiments, the circuit parameters are tuned

1 I ¹ ■ of L · L ² such that AL _e2 is computed in accordance with AL _e2 = -L _/2 + ^0FF - ^NM ₂ ⁰ — ^— ^ where ί/ _{α6 min} is the minimum first order root mean square value of output voltage of receive side converter and I OFF min is minimum turn off current to achieve U _{ab min} .

[0015] In other embodiments, the receive side converter is further defined as a full wave rectifier circuit. A battery may be configured to receive the DC charging signal from the receive side converter and the receive unit is integrated into a vehicle.

[0016] Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.

DRAWINGS

[0017] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.

[0018] Figure 1 is a schematic of a double-sided LCC compensation topology for wireless power transfer;

[0019] Figure 2 is a schematic of an equivalent circuit of the topology shown in Figure 1 ;

[0020] Figure 3A is a schematic depicting circuit characteristics of the equivalent circuit at resonant frequency when only an input voltage is applied;

[0021] Figure 3B is a schematic depicting circuit characteristics of the equivalent circuit at resonant frequency when only an input voltage divided by the turns-ratio is applied;

[0022] Figure 4 is a schematic of an equivalent circuit having system parameters tuned to ensure that MOSFETs turn off at a positive current; [0023] Figure 5 is a graph illustrating the effect of all high order currents;

[0024] Figure 6 is a diagram of a vehicle illustrating two types of misalignments;

[0025] Figures 7A-7C are graphs depicting simulation and theoretical calculation results of the power levels for the designed system;

[0026] Figure 8 is a graph depicting simulation waveforms of output voltage u _ab and current through diodes i _Lf2 when U _in = 1S0V, U _b = 4S0V;

[0027] Figures 9A-9C are graphs depicting simulation and theoretical results of the MOSFETs turn-off current I _0FF with fc = 0.32, k = 0.24, k = 0.18, respectively;

[0028] Figures 10A-10C are graphs depicting experimental and theoretical calculation results of the power levels for the wireless charger system with k = 0.32, k = 0.24, k = 0.18, respectively;

[0029] Figures 1 1 A-1 1 C are graphs depicting experimental and theoretical calculation results of the MOSFETS turn-off current I _0FF with k=0.32, k=0.24, k=0.18, respectively;

[0030] Figures 12A and 12B are graphs depicting waveforms of the input voltage u _AB and current i _Lfl and output voltage u _ab and current i _Lf2 when deliver 7.7kW power;

[0031] Figures 13A-13C are graphs depicting simulation and experimental efficiencies of the system when output voltages are 300V, 400V and 450V at different X-misalignments;

[0032] Figure 14 is a schematic of an alternative embodiment of an integrated double-sided LCC compensation topology for wireless power transfer;

[0033] Figure 15A is a schematic of an equivalent decoupled circuit model for the integrated LCC compensation topology;

[0034] Figure 15B is a schematic of a simplified equivalent circuit model for the integrated LCC compensation topology;

[0035] Figure 16 is a schematic depicting an open circuit condition for the integrated LCC compensation topology; [0036] Figures 17A-17F are schematics of equivalent circuit models of the integrated LCC compensation topology over a full cycle;

[0037] Figure 18 is a diagram illustrating different operating modes for the integrated LCC compensation topology;

[0038] Figures 19A-19D are graphs illustrating waveforms for the different operating modes of the integrated LCC compensation topology; and

[0039] Figure 20 is a graph depicting the relationship between efficiency and the different operating modes.

[0040] Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.

DETAILED DESCRIPTION

[0041] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0042] Figure 1 depicts an example embodiment of a double-sided

LCC compensation network and corresponding power electronics circuit components in the context of a wireless power transfer system 10. The wireless power transfer system 10 is comprised generally of a send unit 12 and a receive unit 14. The send unit 12 is configured to transfer power using inductive power transfer; whereas, the receive unit 14 is configured to receive power via inductive power transfer from the send unit. In one embodiment, the send unit 12 is implemented as a pad for placement in a garage and the receive unit 14 is attached to the underside on an electric or hybrid electric vehicle. Other applications for the power transmission system 10 also fall within the scope of this disclosure.

[0043] The send unit 12 includes a DC power source 21 , an inverter 22, a send side compensation circuit 23 and a send coil 24. The inverter 22 receives a DC input signal from the power source 21 and converts the DC input signal to an AC output signal at a desired resonant frequency. In one embodiment, the inverter 22 is a full bridge converter circuit comprised of four power MOSFETs S-rS ₄ although other circuit arrangements for the inverter are contemplated by this disclosure. A controller 25 interfaced with each of the MOSFETs controls the switching operation of the inverter 22. The controller 25 turns the switches on and off to generate the AC output signal at the desired resonant frequency. In some embodiments, a rectifier (not shown) may be connected between an AC power source and the inverter 22.

[0044] The send side compensation circuit 23 interconnects the inverter 22 with the send coil 24. In the example embodiment, the compensation circuit is comprised of a send side inductor L , a send side series capacitor Ci and a send side parallel capacitor C _n . The send side inductor and the send side series capacitor are serially coupled together and coupled to a positive terminal of the send coil; whereas, the send side parallel capacitor is coupled in parallel with the send coil.

[0045] The receive unit 14 includes a receive coil 32, a receive side converter 33 and a receive side compensation circuit 34. The receive side converter 33 receives an AC charging signal from the receive coil 32 and converts the AC charging signal to a DC charging signal. In one embodiment, the converter is a bridge rectifier circuit comprised of four diodes D-i~D ₄ although other circuit arrangements for the converter are contemplated by this disclosure. In some embodiments, a battery is configured to receive the DC charging signal from the converter 33. M is the mutual inductance between the send coil and the receive coil.

[0046] The receive side compensation circuit 34 interconnects the receive coil 32 with the converter 33. In the example embodiment, the compensation circuit is comprised of a receive side inductor L _f2 , a receive side series capacitor C2 and a receive side parallel capacitor C _f2 . The receive side inductor and the receive side series capacitor are serially coupled together and coupled to a positive terminal of the send coil; whereas, the receive side parallel capacitor is coupled in parallel with the send coil. It is to be understood that the relevant components of the send unit and the receive unit are discussed in relation to Figure 1 , but that other components may be needed to implement the wireless power transfer system.

[0047] For a first step, a concise characteristic of the proposed compensation network will be given by analyzing the first order harmonics of the square voltage waveform at the switching frequency. The resistance on all the inductors and capacitors are neglected for simplicity of analysis. The accuracy of the approximations will be verified by circuit simulation and experiments in the latter sections. The equivalent circuit of the circuit in Figure 1 referred to the primary side is derived as shown in Figure 2. The apostrophe symbols indicate the variables of the secondary side referred to the primary side. The turns-ratio of the secondary to primary side is defined as n = ^L ₂ I L _y , (1 ) where L is self-inductance of the send coil and L ₂ is self-inductance of the receive coil. The variables in Figure 2 can be expressed by the following equations:

L _m = k - L _l ,

U _s2 = {\- k) - L ₂ l n ² ,

C ₂ ' = n ² C ₂ ,

where U _A B is the first order root mean square of the input voltage and U _AB is the first order root mean square of the output voltage from the converter 33. For a high order system in Fig. 1 , there are multiple resonant frequencies. This disclosure does not focus on the overall frequency domain characteristics.

Rather, only one frequency point, which could be tuned to a constant resonant frequency, is studied. Here, the resonant means the input voltage U _AB and current I _Lfl of the compensated coil system are in phase. The circuit parameters are designed by the following equations to achieve a constant resonant frequency for the topology.

1

T ■ c

tVg

L ^L 'f 2 c -- (OL

(3)

L ^{f2 ~} ciC, where ω ₀ is the angular constant resonant frequency, which is only relevant to inductors and capacitors in the system, independent of coupling coefficient k and load conditions.

[0048] Under the above rules, the circuit characteristics will be analyzed at resonant frequency ω ₀ . According to superposition theory, the effect of U _AB and U _a ' _b can be analyzed separately, as shown in Figures 3A and 3B. The dashed line means there is no current on that path. Figure 3A is used to analyze the effect of U _AB The additional subscript indicates that current is contributed by U _AB . To make the analysis clear, the series connected capacitor and inductor branches, C ₁ , L _sl and C ₂ , L' _s2 are expressed using an equivalent inductance L _el and L' _e2 , where J°>o (5)

L _f ' ₂ and C _f ' ₂ form a parallel resonant circuit, which can be regarded as an open circuit at the resonant frequency ω ₀ . Thus, l ₂ ' _AB = 0. In the left part of the circuit, L _e i , L _m are connected in series, and

Ai ⁺ A _» ⁼ L _fl — k ^■ L[ + k · Lj = L _fl

[0049] It forms another parallel resonant circuit with C _n at the same resonant frequency ω ₀ . Thus, I _LflAB = 0. Because there is no current through L _fl and L' _e2 , the voltage on C _fl equals U _AB , and the voltage on C _f2 equals the voltage on L _m . I _1AB and I _L ' _f2A can be easily solved:

When U _a ' _b is applied, the analysis is similar to that when U _AB is applied. An additional subscript _ab is added to indicate that the current is contributed by U _ab . The solutions are i' _Lf2ab = 0, i _lab = 0 and

[0050] U _a ' _b is a passive voltage generated according to the conduction mode of diodes D-i ~D ₄ . It should be in phase with i _L ' _f2 . Since _L ' _i2ab = °^ά _¾ ^{is in} phase with l _L ' _f2AB . If ϋ _ΑΒ as the reference, ϋ _ΑΒ and U _a ' _b can be expressed as

U _AB = U _AB (1 1 ) b = - ^u f = -i - K _b (12)

On the other hand,

b = Ua„ ^■ (coscp + j ^■ sincp) (13) where φ = -π/2 is the phase by which d _ab leads ϋ _ΑΒ .

[0051] Substitute (2), (1 1 ), (12) into (7)-(10), and sum up the current generated by U _AB and U _a ' _b to get

J _ kh _x u _a ' _h _

Lflab (i> ₀ Lf _X l!f

I _ ^l Lf2 _ ^l Lf2AB _ ^' UAB (M)

^Lf2 n n j-a) ₀ L _fl L _f2

From (1 1 ), (12) and (14), it can be seen that the input voltage and current are in phase. Unit power factor for the converter is achieved. Consequently, the transferred power can be calculated by

Ρ = ϋ _ΑΒ - i _lF1 = - ^- ^■ kU _AB U _ab (18)

It can be seen that the output power is proportional to the coupling coefficient k, the input voltage U _AB , and the output voltage U _AB . Thus, power can be easily controlled by changing the input voltage or output voltage. It is also noted that a buck or boost converter can be inserted either before the sending side inverter or after the receiving side rectifier to control the output power. [0052] If the coils and compensation network parameters are designed exactly according to the above rules, all the MOSFETs will be turned on and off at a zero current switching (ZCS) condition. However, ZCS is not a perfect soft switching condition in converters containing MOSFETs and diodes. To minimize the switching loss, it is better that all switches are turned on and off at a zero voltage switching (ZVS) condition. The parasitic output capacitance of the MOSFET holds the voltage close to zero during the turn-off transition. So the turn-off switching loss is very small. However, in the turn-on transition, ZVS operation is required to prevent both body diode reverse recovery and parasitic output capacitance from inducing switching loss. To realize ZVS for a MOSFET, the body diode should conduct before the MOSFET does. It is essential that the MOSFET needs to be turned on at a negative current. For a full-bridge converter, this means the input impedance of the resonant network should be inductive. In this case, the resonant current lags the resonant voltage which forms the ZVS operation condition for all MOSFETs.

[0053] In this disclosure, the ZVS operation condition refers to ensuring the turn-off current to be positive to realize ZVS turn-on of another MOSFET in the same arm. There can be several ways to tune the system parameters to ensure the MOSFETs turn off at a positive current. Here, one example way is introduced and analyzed.

[0054] To achieve ZVS, the value of L _e2 is increased slightly. As shown in Figure 4, the change of L _e2 is L' _e2 . Also, superposition method is used to analyze the tuned circuit. When U _AB is applied to the circuit, the equivalent circuit is the same as in Figure 3A. I _LflAB is zero. While, when U _a ' _b is applied, _L ' _f2ab ^{is not zero anv} more. The circuit is again solved with the variation of L' _e2 , and the following equations can be derived.

V —— ί ^ ^ab M Q^

Ό _Λ ' -(cos^+v ^' -sin^) AZ/.

(20) jd) ₀ L _fl L _f2 <¾ · L _f2 L _f2

υ _Λ ' - ϊηφ-Α , U _ab ^■ cos (p-AL ₂ W^L,

(¾(L ₂ ) <¾(L ₂ )

I

I

_/ (21)

_U _ab -sm -AL _e2 kUg U _ab cos AL ₂

J _J '

CO ₀ L _f2 CO ₀ L _fl L _f2

where the subscript 1 ^st means the first harmonic component.

[0055] The phase of i/ _afc is different from the phase of i _{Lf2 lst} - From

(12), (13) and (20), <p is - whenAL _e2 is zero. When L _e2 is increased to realize

ZVS, the change ofL _e2 is relative small so φ is still close to -π/2 and sin<p=-1, οοεφ=0,Δ ₂ «L _/2 < L ₂ . Usually, the additional inductors, L _n and .^, used as a reactive power compensator, are designed such that they are much smaller than the main coils. The following approximation can be obtained from (21): cos φ _ι ~— cot <p _l ~ .

L ₂ -ki _t jL _l L ₂

(22) where φ^-90 ⁰ < φ ₁ « -180°) is the phase by which i _{Lf2 lst} leads ϋ _ΑΒ .

[0056] To reduce the switching loss, it is preferred to achieve ZVS condition at a minimum turn-off current. This means at the switching point, the current is close to zero. The current slew rate at the switching point is high. A small phase error in the analysis will bring relatively large current error. If the phase error falls into the inductive region, it means a higher turn-off current and higher switching loss. If the phase error falls into the capacitive region, the turn- off current may be negative. It means ZVS is lost and severe reverse recovery in the MOSFET diode will occur. This will bring high switching loss and electromagnetic interference (EMI) problem. Therefore, the analysis accuracy of the turn-off current is very important. The high order harmonics of the square voltage should be considered. The inductor-capacitor network from the sending side to the receiving side is a high order filter. For the high order harmonics, the interaction between the sending and receiving side can be neglected. Thus, the high order current on L& can be roughly calculated by:

u 31J

2

8<¾L _/2

j ^■ 3<¾L _/2 +

j-3a) ₀ C 2

-j _ U

2 ~ ϊ ^— J~ ~,

j-5^L + ¹

f ^{l '} j-5co ₀ C 2

(23)

-j _ U

2_(2t ~ J

j-(2k + l)a^L _f2 +

j-(2fe + l)<y ₀ C _/2

(2fc + l)U _{a 2(£+1)th}

7

((2fc + l) ² -l)<y ₀ L _/2

[0057] According to (23), the phase difference between (J _{ab mth} and i _Lf2 mth isn/2. So when J _ab jumps at the time that i _Lf2 = 0, i _{Lf2 mth} reaches the peak. And the peak value can be calculated b 4 i¾L _/2

The phase by which (j _ab leads / _{L 2} i _st φ, is close to 0 (0 < φ ₂ « π/2) and can be easily obtained by

[0058] Figure 5 shows the effect of the high order harmonic currents.

The sign of u _ab is determined by i _Lf2 , which is a composition of both the first and high order harmonic currents. From (22) and (25), the following equation can be derived: cos φ = cos ( φ _ι + φ ₂ ) = cos φ _ι cos φ ₂ — sin φ _ι sin

~ cos ¾ + sin φ ₂ (26)

£t/^ (cos >+./ ^■ sin )^

I

ja> ₀ L _fl L _f2 ja> ₀ L _fl L _f2

kU^' sin ^ W^coscL,

7 ^' · (O ₀ L _fl L _f2

(27)

L _/2

From (27), an additional reactive current item is introduced. This current will increase the MOSFET turn-off current to achieve ZVS. For the sending side, similar to the analysis of the receiving side for the high order harmonics effect, the following equations can be obtained:

51L

I

j-5o) ₀ L _fl

^■ 5d) ₀ C _fl

U

I

. (2fe + l)U _AB

((2/t + l) ² -l)i¾L,

(28)

4 fl¾L _/1

[0059] The MOSFET turn-off current is a composition of both the first order and the high order harmonic currents. From (27) and (29), the MOSFET turn-off current can be calculated as:

Λ

L _{f 2}

(30) i¾L _/2 4<¾L

According to the MOSFET parameters, a minimum turn-off current to achieve ZVS can be determined. Then a suitable AL _E2 can be designed to ensure there is enough turn-off current to achieve ZVS for the whole operation range. To ensure IOFF is greater than a certain positive value, the following equation should be satisfied:

AL .

(31 )

[0060] According to (30) and (31 ), the lower the output voltage is, the smaller the turn-off current is. The minimal turn-off current can be derived as:

where U _{AB MIN} is the minimum RMS value of the output voltage. The turn-off current is reached when

[0061 ] Once the minimum MOSFET turn-off current is obtained, AL, can be calculated by

[0062] Next, an 8kW wireless power transfer system is designed according to the above principle. Then, a comparison between the simulation results and the analytical results will be given in the next section to verify the effectiveness of the above analysis. The specifications of wireless battery charger are listed in Table I.

Spec ^■' ?sf»ss»«r

DC

0»¾>»S wstwjy Se&dl_tg iS>¾«T32C* ^;

.¾ai¾a§ cii AC sesjstexs ϋθθ ssiil

i cetvtag s>& iSj.-iy£ts««- ^!

SwrJteliiag fi

Mssimuia power* -S feVv

ΜΛ.<ΟΪ»»Π> efiSssftac?' The coupling coefficient varies because of misalignment. Its value is related to the coil design, which is not the focus of this disclosure. The main coil inductance changes a little bit when the position of the two coils changes. A middle value 360 μΗ was selected in the design stage. The rated output power is designed as 8kW with the maximum efficiency of 97.1 %. Due to the parameter variations, the maximum efficiency of 96% was reached at 7.7kW.

[0063] Since the ratio between the input voltage and the output voltage is around 1 , the transmit and receive coils are designed to have to same size. Thus, from (3),L _vl = L ₂ . From Table I and (1 8),

^■ 6Ίμΐί

The value of C _fl and C _f2 can be calculated from (3),

C _fl = C _f2 =—^— = 60.6nF (36)

(O ₀ L _fl

C _x and C ₂ can also be calculated from (3)

Then, a variation of Ah _e2 should be designed to increase the turn-off current for MOSFETs to achieve ZVS. Once the minimum turn-off current for ZVS is obtained, Ah _e2 can be designed using (34). For different MOSFET and dead- time setting, the minimum turn-off current is different. For a 8kW system, usually a MOSFET with 80A continuous conduction capability can be adopted. In the example implementation, Fairchild FCH041 N60E N-Channel MOSFETs were chosen as the main switches. The switches are rated at 600V, 48A (75 °C) to 77 (25 °C). According to the parameters of the MOSFET, the calculated dead- time is 600 ns. In order to guarantee ZVS in this mode, the turn-off current must be large enough to discharge the junction capacitors within the dead-time, which can be represented by:

j AC u

(38) where U _{AB MAX} is the maximum input voltage, C _oss is the junction capacitance and t _d is the dead-time. By using the MOSFET parameters, the turn-off current can be calculated, which should be larger than 2A to realize ZVS. Thus, the minimum turn-off current/ _{0FF min} is designed to be 3A.

[0064] By subs ~ (37) and I _{0FF min} into (34), we can get

« 21μΗ (39)

The equivalent inductance L _e2 is determined by C ₂ and leakage inductance L _s2 . Because L _s2 is related to the self-inductance and coupling, it is more complicated if L _s2 is tuned to change the value of L _el . It is easier to tune C ₂ to change the value of L _e2 . From (3),

l l

AL ,

of ₀ C ₂ of ₀ (C ₂ + AC ₂ )

(40)

Then, the variation of C ₂ can be calculated: <4 l. lnF

\- e& -AL _? - C _? ΙΑΛ \

Thus, to achieve ZVS, the value of C ₂ should be tuned such that it is 1 .1 nF larger than the value calculated by (37). All the designed values for the example compensation network are listed in Table II.

X- ¾, . COMPENSATION NETWORK ?AKA ^¾ ETSSS Parameter Des ga value

Lf _: 6 ί uH

Qi. 60.€aF

€β δϋ,δ Β

C\ 14J<F " ' ^;

[0065] Both simulation and experiments are undertaken to verify the proposed double sided LLC compensation network and its tuning method. The circuit parameters have been shown in Table I and Table II. Two kinds of misalignments are defined, i.e. X-misalignment (door-to-door, or right-to-left), and Y-misalignment (front-to-rear), as shown in Figure 6. When parking a car, the X-misalignment is much harder for the driver to adjust. So X-misalignments is chosen for the simulation and experiments. Various misalignments are reflected by the different coupling coefficients. In this section, three coupling coefficients, namely, / =0.18, 0.24, 0.32, corresponding to X=310mm, 230mm, and 0mm respectively, as well as three output voltages, 400V, 450V, are chosen as case studies. The switching frequency is fixed at 79 kHz for all the cases.

[0066] A model was built in LTspice to simulate the performance of proposed topology. The simulation results for different coupling coefficients, input voltages and output voltages were obtained. Figures 7A-7C show the comparison between simulated and calculated output power for various conditions. The output power varies linearly with the input voltages for different coupling coefficients and output voltages. [0067] For high input voltage and high coupling coefficients, the simulation and theoretical analysis agree well with each other. But for low input voltage and low coupling coefficients, the simulation does not agree well with the analytical results. This is because at low input voltage and low coupling coefficient, the diodes at the secondary side do not conduct all the time between t _x + n - T/2 and t _x + (n + 1) ^■ T/2, which is shown in Figure 8. A similar situation can also be found in the comparison results of turn-off current, as shown in Figures 9A-9C.

[0068] In the experimental set up, the coil dimension is 800mm in length and 600mm in width. The gap between the two coils is 200mm. A ~\ 0μΡ capacitor (C ₀ ) and 10μΗ inductor (L ₀ ) are selected as the output filter. Figures 10A-10C show the comparison of experimental and simulation output power as a function of input voltage for three coupling coefficients and three output voltages. Different coupling coefficients are obtained by adjusting the gap and misalignment between sending and receiving coils. The output power matches well between simulation and experimental results, and they vary linearly with the input voltage. The same inconsistency phenomenon happens at the low input voltage and low coupling conditions as mentioned earlier. The calculated and simulated maximum efficiency is 97.1 %. Because of the resistance and parameter variations in the real system, the maximum efficiency of 96% was reached at 7.7kW output power, which is a little lower than the simulated result.

[0069] Figure 1 1 A-1 1 C show the comparison of experimental and theoretical calculated turn-off currents of the MOSFETs. The experimental results agree well with the analytical results. The sending side waveforms and receiving side waveforms are shown in Figure 12A and 12B when the system operates at steady state delivering 7.7W to the load. At this operating point, input voltage U _in = 42SV, output voltage U _b = 4S0V, coupling coefficient / =0.32. The results indicate a good ZVS condition with I _0FF = 6A. The turn-off current maintains higher than required, while it is quite small relative to the peak current.

[0070] Figure 13A-13C show the simulation and experimental efficiencies from DC power source to the battery load for the proposed double- sided LCC compensation network for wireless power transfer system. From Figure 1 3C, it can be seen that the efficiency is very high even at a large X- misalignment condition. The maximum simulated efficiency is 97.1 %, while the maximum measured efficiency is about 96% when U _in = 42SV, U _b = 4S0V and k = 0.32 as shown in Figure 13A.

[0071] In an alternative embodiment, not only the two main coils, Li and l_2 are coupled to each other, but the main coil and the secondary coil on the same side are coupled with each other as shown in Figure 14. That is L is coupled with L and L ₂ is coupled with U?. Consequently, L _fl and share the ferrite core and space with the main coil and thereby reduce the overall size of the system. Copper wire usage is also reduced in this alternative embodiment. The mutual inductances are M, M-i , M ₂ , respectively.

M = k^LJ^ ,

where k, / i , and k ₂ are the coupling coefficients. [0072] M and M ₂ are considered as constant while M varies with the changing of the vehicle ground clearance and misalignment. In this disclosure, the range of coupling coefficient is limited between 0.14 and 0.30 according to the coil design. Generally, the wireless power transfer system for hybrid electric or electric vehicles has a large leakage inductance but a small mutual inductance. Only the mutual inductance has contribution to the power transfer. So it is essential to compensate the self-inductance. Usually, the self-inductance is compensated by adding a series capacitor. For simplicity, in this disclosure the main coils on both the transmitter and receiver sides are designed as the same.

[0073] In the alternating current analysis, the square-wave input voltage and output voltage are replaced by their first fundamental sinusoidal equivalents. The power transferred is assumed to be only through the fundamental component and the contribution of all the high order harmonics is ignored. The internal resistances on all inductors and capacitors are neglected. The two main coils L1 and L2 can be regarded as a transformer which can be equivalent to two decoupled circuits containing controlled sources. So the decoupled model of the compact wireless charger system can be obtained, as shown in Figure 15B.

[0074] Assuming the circuit in Figures 15A and 15B are driven by sinusoidal voltage source, of which the angular frequency is ω ₀ . The circuit can be simplified by the followed equations.

L _f2e = L _{f 2} + M ₂ ,

Then the equivalent circuit can be simplified as shown in Figure 15B.

[0075] Both sides are a simple LCL resonant converter. One of the characteristics of LCL resonant converters is that the output current is constant, only related to the input voltage, if it works at the resonant frequency. As for this work, on the sending side, assume:

From (43) and (45), the following relationship can be obtained

From (43), (44) and (46), the following equation can be derived

From (46) and (47) Li , L , Cn, Ci are determined, the resonant frequency will be fixed. So the resonant frequency is independent of coupling coefficient and load condition.

[0076] By Kirchhoff's Laws, it is easy to get j iW ₀ L

(48)

Mi,

[0077] Similarly, on the receiver side, when

ox

f ^2e , the following equations can be obtained

Mi,

(50) j iW ₀ L _f

(51 )

Substitute (42), (51 ) and (42), (48) into (49) and (50) respectively, we can get J<¾ (53)

Take i/ _AB as reference, and define

^ (54) where is the RMS value of the input voltage. It is obviously that ^s has features of unit vector.

[0078] As U _ab is a passive voltage, its direction is determined by the conduction mode of the diodes D-i~D ₄ of the rectifier. It should be in phase with ^{/i 2} . So the following equation can be obtained

δ

u _ai = u _ab -.

J (55) Then (48), (51 ), (52), and (53) can be expressed as

/ _{1 =} ^Uab δ= ^ δ,

JL^s=

L _fl — i¾ (L _/ ^ ₂ +— δ,

O) ₀ M ₂ )

(57) «0 ^L /le ^L /2e «0 ( ^L f l + ^M l )( ^L f 2 + ^M 2 ) ' ( ₅₈ ) j«0 ^L /le ^L /2e j «0 ( ^L f l + X ^L /2 + ^M 2 ) ^' (59)

[0079] It is obvious that current on the transmitter coil /_i is constant, only related to input voltage UAB- This is very important if the transmitter coil transfers power to several receiver coils at the same time. Furthermore, when a PHEV/EV with a wireless charger is parked, the coupling coefficient of the main coils will be determined. As a result, the output current \u≥ is also constant, which only depends on the input voltage. This is suitable for battery charging.

[0080] From(54) and (58) it is obvious that the phase difference between input current ^{7i 1} and input voltage ^Uab is zero. The power factor is 1 . So the delivered power can be expressed as (60) where UAB and Uab are RMS values of the input voltage and output voltage. The receiver side main coil size is limited by the space of the bottom of the car. Therefore, the sizes of the main coils and their inductances, Li and L ₂ are limited. This will result in a limitation for the output power of the WPT system. It can be seen from (60) that the desired power can be got by designing proper inductances of the additional coils and proper couplings between additional coils and the main coils. Moreover, if delivering the same power from the transmitter side to the receiver side, the inductances of the additional coils will be smaller, compared with the one that has no couplings between the additional coils and the main coils.

[0081] As indicated by (59), the output current is related to input voltage U _A B, coupling coefficient k of the two main coils, and components parameters if the system operates at resonant frequency ω ₀ . The system is a current source, independent of the load. Figure 16 shows the open circuit of the system. The equivalent circuit of the sending side is the same as that shown in Figure 15. However, as an open circuit, the current on L _s is zero and the receiving side equivalent circuit is different. The inductance does not join the resonant circuit, but this does not change the resonant frequency of the resonant circuit according to the previous analysis. It just affects the voltage before the rectifier because of the coupling between L ₂ and

[0082] If the input voltage is a cosine waveform as shown below υ _Λ

— -cos(fi¾i),

V2 (61 ) then for the receiver side, the following equation can be derived

where u _c is the total voltage on the receiver side capacitors C ₂ and A and φ in (63) are determined by the initial condition.

[0083] According to (63), the voltage on the capacitors will increase with time. This is not allowed. In practice, there will be always internal resistances in the circuit. For simplicity, the internal resistances of the circuit are equivalent to the resistances of the main coils (Li and L ₂ ), the differential equation will be

where /¾ is the equivalent resistance of the receiver side in series with the main coil and is usually very small, R ₂ <4L ₂ /C. If 2 =R ₂ /L ₂ . Considering the initial condition the voltage on the capacitors is

[0084] The voltage on the capacitors will be steady over time as the second component of (67) shown. But the voltage will be high enough to cause the capacitors to break down if the battery is disconnected with the wireless charger suddenly when it is in operation. Therefore, open circuit protection is necessary for the integrated LCC compensation topology. [0085] On the other hand, due to the resistance of the system, the power will only transfer to the battery when the input voltage is high enough. For the open circuit, when the system is in steady state, the voltage before the rectifier is

[0086] The battery voltage is U _B . |f r ^< *l ^ , there will be no power output. So UAB should be bigger than a certain value as described in (67) to ensure power transfer.

C ₂ 1^ + Μ ₂ Μω _{0 (67)}

[0087] The operation of the integrated LCC compensation network for WPT is complex due to the high-order system and the resonant mechanism that the system has the same resonant frequency with and without inductor L/2. The resonant circuit without L/2 is formed when the diodes of the rectifier on the receiver side are all off. The system can operate in several stages within one switching cycle depending on the circuit component parameters, coupling coefficient between the two main coils, the input voltage, and load conditions (output voltage), when the operation frequency is fixed at the resonant frequency. Owing to the symmetry, only half switching cycle should be analyzed. In Figure 14, the diodes of the rectifier on the receiver side only conduct when the voltage between nodes a and b is higher than the battery voltage. Characterized by the voltage between nodes a and b, there are three possible resonant stages, namely, positive clamped stage (stage P), negative clamped stage (stage N) and open stage (stage O) in the half cycle when S1 , S4 are on and S2, S3 are off. As the proposed compensation topology is controlled by the input voltage, the WPT system will pass through four operation modes successively when the input voltage increase from zero to the maximum value. The operation modes are categorized by the conduction statuses of the rectifier as cutoff mode (CUTOFF), discontinuous conduction mode (DCM), and continuous conduction mode (CCM). Depending on the different sequential combinations of the three stages, DCM can be divided into DCM1 and DCM2. [0088] The six equivalent circuit models of the integrated LCC compensation topology over a full cycle are given in Figures 17A-17F. According to the analysis above, it is necessary to consider the resistances of the circuit. In the following sections, the resistances of the circuit are equivalent to the resistances connected to the main coils as R1 and R2 shown in Figures 17A-17F. And only the first half cycle is analyzed.

[0089] Open Stage (Stage O): Stage O, as shown in Fig. 17B, occurs when all of the diodes of the rectifier are off, the current on Ι_ _β is zero. Inductor Ι does not join the resonance with other circuit components, neither the battery. But as mentioned before, the system still has the same resonant frequency as other stages. During Stage O, the voltage between node a and b is lower than the battery voltage Ub. The differential equations can be expressed in a matrix form as

where

^■ -u _L ]

■[u^ u _ab ]

[0090] The elements in the matrices and other parameters are shown in the appendix.

[0091] Negative Clamped Stage (Stage N): When the voltage between note a and b is negative and higher than the battery voltage, diodes D1 and D4 are off, while D2 and D3 are on as shown in Fig. 14, the battery will be connected to the circuit in reverse, as shown in Fig. 1 7A. Similarly, referring to the appendix, the following equation can be obtained

x = A ₂ x + B ₂ u. (73)

[0092] Positive Clamped Stage (Stage P): When the voltage between nodes a and b is positive and higher than the battery voltage, diodes Di and D ₄ will be turned on while D ₂ and D ₃ turned off. As shown in Figure 1 7C, the battery is directly connected to the resonant circuit. According to the appendix, the equation is

x = A ₁ x + B^u. (74)

[0093] When operating near the resonant frequency and with the same load condition, the integrated LCC compensation wireless charger system passes through four operating modes as shown in Figure 1 8 with the input voltage increasing. The first one is the cutoff mode (CUTOFF), followed by discontinuous conduction mode I (DCM1 ), discontinuous conduction mode I I (DCM2), and continuous conduction mode (CCM). They are divided into the following three categories: CUTOFF, DCM, and CCM. The equations describing the modes are boundary value problems of ordinary differential equations. It is not possible to give analytical solutions for such high order differential equations. So in this work, the results are based on numerical solutions.

[0094] 1) Cutoff Mode (CUTOFF): There is no power transfer to the battery during the cutoff mode, only stage O is involved in this mode. The input voltage is small enough comparing to the output voltage and therefore, the voltage between nodes a and b never reaches U _b . This is caused by the resistances in the circuit and imperfect compensation. The equivalent circuit can be represented by Figure 1 7B and the waveforms are shown in Figure 1 9A. The equation describing the steady-state of the cutoff mode is (68) with boundary condition ^{(0) = ~x(T 1 2)} . This constraint boundary condition fits all of the operation modes.

[0095] 2) Discontinuous Conduction Mode (DCM): There are two cases of the discontinuous conduction mode as shown in Figures 1 9B and 1 9C. For case one (DCM1 ), which is after the cutoff mode, the system passes through stage O, stage N and stage O successively (0-N-O) in the first half cycle as shown in Fig.19B. The equations describing it are

k = A _l x+B _l u 0<t<t _l

x = A ₂ x+B ₂ u t _l <t<t ₂ .

x = A _l x+B _l u t ₂ <t<TI2 (75)

[0096] With the increase of input voltage, the WPT system operation mode changes from DCM1 (0-N-O) to DCM2 (N-O-P). In this process, the system will pass through a unique mode, namely, N-O. This mode is the boundary of DCM1 and DCM2 and it can be categorized into either of the two DCMs.

[0097] DCM2 mode, as shown in Figure 19C, occurs when the input voltage rises to a level beyond DCM1 mode, the equations are

x = A ₂ x+B ₂ u 0<t<t ₁

x=A ₂ x+B ₃ u t ₂ <t<TI2 (76)

[0098] 3) Continuous Conduction Mode (CCM): When the input voltage is high enough, the diodes of the rectifier will conduct all the time. The statuses of the circuit will shift between negative clamped stage (N) and positive clamped stage (P). The system will pass through N and P (N-P) in sequence during the first half resonant cycle as shown in Figure 19D. The equations are shown as following

[0099] The equations above can be solved using numerical method and the values of any states at any time can be obtained. Based on the analysis above, it is easy to get the output power and efficiency as

2 - p =— _j ^, J[ ₀ ² (U I \ γ)dt,'

[00100] It can be seen that both the output power and efficiency of the WPT system are related to the operation mode. Figure 20 illustrates the relationship between efficiency and operation mode. With the increasing input voltage, the efficiency will increase sharply during DCM1 mode and the rate of increase slows down when the system enters into DCM2 mode. At the end of the DCM2 mode and the entire CCM mode the efficiency will be stabilized at the maximal efficiency.

[00101] The fundamental element approximation is accurate enough when the system is operating at continuous conduction mode. However, if the system is operating at DCM modes, the error cannot be ignored. So it is essential to determine the range of different operation modes with various output voltage (battery voltage). The misalignments are inevitable in the wireless charger for EV/HEV, thus, it is of significant importance to analyze the impact of various coupling coefficients on the range of each operation mode.

[00102] The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

APPENDIX

Z ¹ =M ² L _fl -L _l L ₂ L _fl + L ₂ M _X (A.1)

= -Z^M _j , a _X3 = -Ι^Μ^ _χ ,α _Χ4 = -MM _X R ₂ ,

a _l5 =a _xl = - MM _X , a _x6 = -M ² + L _l L ₂ + L ₂ M _l ;

= L^L^, a ₃₃ = L^L^R^, a ₃₄ = ML _fx R ₂ ,

= ML _fx ,a ₄₃ = ML _fx R _x ,a ₄₄ = (L^ -M _X ² )R ₂

a _4S = a ₄₁ = L _y L _fl -M ² , a ₄₆ = -ML _fx -MM _x

½ ■ 1 / Cy ίϊγ^ ^■ l/C

L _x L ₂ ,b _X ^I ₃ =L ₂ M _x ,b _X ^I ₄ =MM _x (A3)

Π Π Π

0 a _X2 «13 a 4

0 0 0

Π n

0 a ₃₂ α ^π α 54

n n π

0 «42 «43 «44

Π

0 0 0 «54

0 0

Π

χ ^π =M ² L _t ,L

(Α.5)

1^ _ίΧ Μ ₂ +1^ Μ _χ -Μ _Χ Μ a ₂ =-L ₁ L _fz M _i + M _X M ² , a ₃ = (-L ₂ L _f2 M ₁ + M _X M ² )R _X , a = -ML _f2 M _x R ₂ , a _s = -ML _f M _x ,

a? ₆ = -M ² L _f2 + L _x L ₂ L _f2 - L, ² + L ₂ L _f2 M _x -M _x M ,

-^"^1 '

= ML _fx L _f2 R ₂ , a _s = ML _fx L _f2 ,

a ₆ =-L ₁ L _fx L _f2 -L ₂ L _f M _l + L _fl M ² +M _X M ₂ , αξ _Ί = ML _fx L _f2 +ML _fx M ₂ ;

a ₂ = ML _fx L _f2 , = ML _fx L _f2 R _x ,

= (^L _fx L _f2 - L _f2 M ² )R ₂ ,

¾ = ^nL^-L^M ² , α ₄ ^π ₆ = -ML _fx L _f2 -ML _f2 M _l , <¾ ₇ = L _x L _fx L _f2 +L _x L _fx M ₂ -L _f2 M ² -M ² M ₂ ;

α ₂ = -ML _fx M ₂ , αξ ₃ = -ML _fx M R _x ,

a = (-L _x L _fx M ₂ +M ² M ₂ )R ₂ ,

¾ ₅ = -L _l L _fl M ₂ +Μ ² Μ ₂ ,αξ ₆ = ML _fl M ₂ + MM _X M ₂ , =M L _fl - L _l L ₂ L _fl -L _l L _fl M ₂ + L.M ² + M ² M ₂ ; a ₂₃ = l/ C _j , = 1 / C ₂ , a^ _x = 1 / C _n ,

b =M ^~ L _t -L _x L ₂ L _f2 + L _x M ₂ ,b _x L ₂ L _f2 M _x -M _x M ₂

b =ML _f M _x ,b _x -MM ,Μ _Ί

(A.9)

= MM _X M ₂ , b ₃ = -ML _fl M ₂ , ¾ = -L _x L _fx M ₂ + M _X ² M ₂

b^=-M ² L _fl + L _l L ₂ L _j ^■ L ₂ M