CN104167828A - Design method for multi-repeater magnetic-coupling resonant wireless power transmission system - Google Patents

Abstract

Disclosed is a design method for a multi-repeater magnetic-coupling resonant wireless power transmission system. Through comparison of an MCR-WPT system provided with any number of repeaters and a multisection coupling resonator bandpass filter and use of a mature filter design theory, an internal constraint relation between transmission performance indexes (transmission efficiency, transmission power and transmission distance) and circuit parameters (inductance value, mutual induction coefficient, bandwidth, resonance frequency and tuning capacity) in the multi-repeater MCR-WPT system is proposed explicitly respectively for two conditions: a source resistance is zero Ohm and not zero Ohm. A typical design procedure obtained by a user on the basis is capable of rapidly and accurately extracting design parameters of a multi-repeater MCR-WPT system capable of meeting the transmission performance indexes, and meeting design and development demands of a long-distance-transmission MCR-WPT system with any number of repeaters. The method has no concrete constraint on the inductance value of hollow coils of repeaters so that is the design is significantly flexible.

Description

A kind of method for designing of multi-repeater magnet coupled resonant type wireless power transmission system

Technical field

The invention belongs to wireless energy transfer system design field.

Background technology

As a kind of novel wireless energy transmission technology, magnet coupled resonant type wireless charging (MCR-WPT) technology can be transmitted electric energy with higher efficiency in the distance times over inductance necklace bore, and having overcome induction type wireless charging technology can only be in the very near applicable drawback of distance.Be applicable to the various application scenarios from milliwatt level to multikilowatt.

Traditional magnetic resonance manifold type wireless charging system has two kinds of four coil forms and two coil forms.In four coil forms, power supply is coupled by a coupling coil and transmitting coil, and load is coupled by another coupling coil and receiving coil; And in four coil forms, coupling coil is cancelled, power supply, load are directly connected with transmitting coil, receiving coil.The transmission range of magnet coupled resonant type wireless charging technique is shorter, and its best transmission distance depends primarily on load, coil bore and operating frequency, but conventionally can be over 2～3 times of coil bore.When transmission range be greater than best transmission apart from time, the efficiency of system is along with the increase fast-descending of distance.

Theory and practice shows, utilizes superconductor technology can under the prerequisite that does not reduce efficiency of transmission, obviously improve transmission range, but this technical price is high, it is complicated to realize.And the method for another kind of simple and practical cheapness is suitably to insert one or more relaying resonators (hereinafter to be referred as repeater between transmitting coil and receiving coil, air-core inductance and tuning capacitance by high Q value are in series), can enlarge markedly the coverage of wireless energy transfer.Because repeater itself also has certain loss, therefore can cause efficiency of transmission and through-put power to reduce to a certain extent, adopt the relaying resonator of high Q value can effectively alleviate this defect.The application of repeater also contributes to people that geometric size and the locus of source coil, loading coil are set easily, improves design flexibility.Yet, repeating coil number increase the complexity that also can greatly increase analysis and design.And abuse irrelevantly relaying LC resonator, and not only can not raise the efficiency and through-put power, may cause reverse effect on the contrary.

At present, for magnetic resonance manifold type wireless charging system, traditional analysis design method mainly comprises coupled mode theory, lumped parameter equivalent circuit theory.From the angle of mathematics, coupled mode theory can be equivalent to the partial differential equations that solves N rank in time domain; Lumped parameter equivalent circuit theory can be equivalent to the matrix equation that solves N rank on frequency domain, and the N-2 here represents the number of repeating coil.When N is very large, the non-singular matrix equation that solves the partial differential equations on N rank or solve N rank is all quite complicated, is difficult to obtain solution with practical value.Also someone utilizes filter theory in recent years, MCR-WPT system is equivalent to filter, then analyzes design, its advantage is easy, quick, can directly obtain bandwidth, the isoparametric computing formula of efficiency of transmission, for people design WPT system, provide full and accurate theoretical foundation.But at present this technology mainly for or non-relay tradition four coil forms or the MCR-WPT system of two coil forms.Therefore be necessary the system for many relayings MCR-WPT, utilize a set of simple, the system of filter theory exploitation, effective analysis and design method.

Summary of the invention

In view of this, the technical issues that need to address of the present invention are for the MCR-WPT system with multi-repeater, adopt filter theory, and a kind of convenient, fast and accurate method for designing is provided.This method for designing is utilized the similitude between arbitrary number repeater MCR-WPT and more piece coupled resonators band pass filter, utilizes the theoretical quantitative analysis formula that comprises the parameters such as inductance value, coefficient of mutual inductance, efficiency of transmission, through-put power and transmission range that obtains of ripe design of filter.On this basis, user can grow the design apart from multi-repeater MCR-WPT system rapidly and accurately.

For the many relayings MCR-WPT system shown in Fig. 1, its circuit structure comprises transmitting terminal TX, a plurality of repeater, receiving terminal RX.Transmitting terminal TX is by AC power (operating frequency f ₀, voltage amplitude value V _s), transmitting terminal air-core inductance L ₁, transmitting terminal tuning capacitance C ₁form R _sand R ₁be respectively source internal resistance and transmitting terminal line loss resistance.Repeater is by air-core inductance L _iwith tuning capacitance C _ibe in series, 1<i<N, R _ifor loss resistance.Receiving terminal RX is by air-core inductance L _n, receiving terminal tuning capacitance C _n, receiving terminal load R _lbe in series, R _nfor loss resistance.K _{i, i+1}(i=1 ..., N-1) be the coefficient of mutual inductance between adjacent inductance coil i and i+1.Air-core inductance turns to circle or rectangle conventionally, also triangle, pentagon, hexagon or other geometry.

System works frequency f ₀aC power V _sfrequency, be also the resonance frequency of each LC resonator (TX, RX and repeater).Resonance frequency can be selected in 125KHz, 133KHz, 225KHz, 13.56MHz or other ISM (industry, science, medical treatment) frequency range.

The AC power of transmitting terminal can be full-bridge or semi-bridge inversion power supply, also may be from high-frequency signal source output after power amplifier amplifies, and the former can be equivalent to source internal resistance R _sthe voltage source of=0 Ω, latter is equivalent to source internal resistance R _snecessarily but be not the voltage source of 0 Ω.According to R _swhether is 0 Ω, it is not the both-end filter of 0 Ω that the filter prototype that MCR-WPT is corresponding can be divided into single-ended filter and the source internal resistance that source internal resistance is 0 Ω; And according to amplitude-frequency response feature, can be divided into again the types such as Butterworth, Chebyshev, ellipse, in application, conventionally select to have the Butterworth type of maximally-flat characteristic.

Method for designing of the present invention, as follows:

Step 101: determine R _s, R _lvalue;

Step 102: determine operating frequency f ₀;

Step 103: corresponding filter type is set;

Step 201: according to efficiency of transmission and transmission range-coil relative aperture, number of repeaters N-2 is set;

Step 202: relative bandwidth w is set;

Step 203: determine filter prototype parameter g _i;

Step 204: counting circuit parameter L _i, C _i, K _{i, i+1};

Step 205: design air-core inductance;

Step 206: computing system performance index: efficiency of transmission, bearing power, transmission range;

Step 207: supply voltage amplitude is set;

Step 301: judging whether to meet design objective, is to go to step 401; Otherwise go to step 201;

Step 401: draw system detailed design parameter.

The filter prototype parameter g of step 203 of the present invention _idetermine:

For LC resonator number, be N (number of repeaters is N-2), relative bandwidth is w, system works frequency f ₀multi-repeater MCR-WPT system, according to the filter prototype of system equivalence, be single-ended or both-end, and amplitude-frequency response feature (Butterworth type, Chebyshev's type, ellipse etc.), determine the former shape parameter g of N rank filter low pass _i(i=0 ..., N+1).

The circuit parameter L of step 204 of the present invention _i, C _i, K _{i, i+1}calculating, by following formula:

(1) if R _s=0 Ω:

Transmitting terminal TX: $L_1=\frac{g_1{R}_L}{2\mathrm{\&pi;w}{f}_0},C_1=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_1}$

Receiving terminal RX: $L_N=\frac{g_N{R}_L}{2\mathrm{\&pi;w}{f}_0},C_N=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_N}$

Repeater: L _iwithout constraint, $C_i=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_i},(i=2,...,N-1)$

The coefficient of mutual inductance of adjacent windings: $k_{i,i+1}=\frac{w}{\sqrt{g_i{g}_{i+1}}},(i=1,...,N-1)$

(2) if R _sfor being not equal to zero pure resistance (for non-pure resistance load, can utilize impedance transformer network to be transformed to pure resistance at load end):

Transmitting terminal TX: $L_1=\frac{g_1{R}_S}{2\mathrm{\&pi;w}{f}_0},C_1=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_1}$

Receiving terminal RX: $C_N=\frac{1}{4{\mathrm{\&pi;}}^2{f_0}^2{L}_N}$

Repeater: L _iwithout constraint, $C_i=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_i},(i=2,...,N-1)$

The coefficient of mutual inductance of adjacent windings: $k_{i,i+1}=\frac{w}{\sqrt{g_i{g}_{i+1}}},(i=1,...,N-1)$

The air-core inductance design of step 205 of the present invention: determine the shape of air-core inductance and allow bore scope according to the requirement of design, then according to air-core inductance L _ithe calculated value of inductance value is determined the concrete bore of the geometric parameter of air-core inductance, the number of turn and wire diameter, estimation coil loss resistance and Q value.Inductance value can adopt Neumann formula to calculate, and other call parameter can be estimated with following formula:

Loss resistance: $R=\sqrt{\frac{{\mathrm{\&mu;}}_0{\mathrm{\&omega;}}_0}{2\mathrm{\&sigma;}}}\frac{l}{2\mathrm{\&pi;a}}$

Quality factor: $Q=\frac{{\mathrm{\&omega;}}_{0}L}{R}$

μ ₀be the magnetic permeability in vacuum, σ is wire conductivity.L is that conductor bus is long, and a is wire radius.

The system performance index of step 206 of the present invention can be estimated by following formula:

Efficiency of transmission η: $\mathrm{\&eta;}=100\exp (-\frac{0.0691}{{\mathrm{wf}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{g_i{R}_i}{L_i}).$

Bearing power P _l: to R _sthe voltage source of ≠ 0 Ω, bearing power

To R _sthe voltage source of=0 Ω, bearing power

Because the relative position that the transmission range of multi-repeater MCR-WPT system is put with coil is relevant, after determining the geometric parameter of coil, according to coefficient of mutual inductance k _{i, i+1}theoretical value, can utilize the Neumann formula of calculating self-inductance/mutual inductance to determine relative position between coil and the reasonable value of transmission range.The circle of take is close is example around air-core inductance, if all coaxial parallel placements of the transmitting coil in system, repeating coil and receiving coil can obtain the distance d of its adjacent two coils according to Neumann formula _{i, i+1}with coefficient of mutual inductance k _{i, i+1}pass be:

$k_{i,i+1}=\frac{{\mathrm{\&mu;}}_0{n}_i{n}_{i+1}\sqrt{r_i{r}_{i+1}}[(2-G^2)K\left(G\right)-2E\left(G\right)]}{{\mathrm{GL}}_i{L}_{i+1}}$

Wherein n _i, n _i+1for coil turn, r _i, r _i+1for coil bore (radius), K (G) and E (G) are the first kind and complete elliptic integral of the second kind.

Transmit total distance: $D=\underset{i=1}{\overset{N-1}{\mathrm{\&Sigma;}}}{d}_{i,i+1}$

The present invention there is no concrete constraint to the inductance value of repeater air core coil, but in order to reduce the loss on circuit, should adopt the inductance coil of low-loss, high Q value as repeater coil as far as possible.

The effect of invention: the present invention is directed to complicated multi-repeater MCR-WPT system, provided the counting circuit component parameters (L of a cover system _i, C _i, k _{i, i+1}) and the quantitative analysis formula of system index (efficiency of transmission, through-put power and transmission range).According to these detailed and perfect computing formula, user can carry out the design and development of MCR-WPT system of the multi-repeater longer transmission distance of arbitrary number rapidly and accurately.The present invention there is no constraint to the concrete value of the inductance value of repeater air core coil, and this realizes also to the design of many relayings MCR-WPT system and brings the great degree of freedom.

Accompanying drawing explanation

Fig. 1 be the present invention for circuit system schematic diagram.Wherein, transmitting terminal TX is by AC power V _s, transmitting terminal air-core inductance L ₁, transmitting terminal tuning capacitance C ₁form R _sand R ₁be respectively source internal resistance and transmitting terminal line loss resistance.Repeater is by air-core inductance L _iwith tuning capacitance C _ibe in series, 1<i<N, R _ifor loss resistance.Receiving terminal RX is by air-core inductance L _n, receiving terminal tuning capacitance C _n, receiving terminal load R _lbe in series, R _nfor loss resistance.K _{i, i+1}(i=1 ..., N-1) be the coefficient of mutual inductance between adjacent inductance coil i and i+1.

Fig. 2 is the system detail flowchart of embodiment.

Fig. 3 is in embodiment, the frequency of the multi-repeater MCR-WPT system (curve chart of kHz) – efficiency of transmission (%).When frequency is 133kHz (operating frequency), efficiency of transmission η=90.3%.

Fig. 4 is in embodiment, the frequency of the multi-repeater MCR-WPT system (curve chart of kHz) – bearing power (W).When frequency is 133kHz (operating frequency), bearing power P _l=10.45W.

Embodiment

Below with reference to accompanying drawing, the preferred embodiments of the present invention are described in detail: should be appreciated that preferred embodiment is only for the present invention is described, rather than in order to limit the scope of the invention.

Embodiment.Designing a operating frequency is 133kHz, and efficiency of transmission is greater than 90%, load 20 Ω, and bearing power 10W, coil bore (radius) 25cm, transmission range is greater than many relay wireless power transmission system of 75cm, and voltage source adopts full bridge inverse conversion power.Its detailed design flow process as shown in Figure 2.

Step 101: determine R _s=0 Ω, R _l=20 Ω.

Step 102: determine f ₀=133kHz.

Step 103: it is R that corresponding filter type is set _sthe single-ended Butterworth type of=0 Ω.

Step 201: according to efficiency of transmission and transmission range-coil relative aperture, the initial value that N is set is 4.

Step 202: w=0.05 is set.

The step 203:4 rank former shape parameter of single-ended Butterworth filter is g ₀=0, g ₁=1.5307, g ₂=1.5772, g ₃=1.0824, g ₄=0.3827, g ₅=1.

Step 204: determine $L_1=\frac{g_i{R}_L}{2\mathrm{\&pi;w}{f}_0}=732\mathrm{\&mu;H},L_4=\frac{g_4{R}_L}{2\mathrm{\&pi;w}{f}_0}=183\mathrm{\&mu;H}.$ C ₁＝1.9nF，C ₄＝7.8nF。k ₁₂＝0.032，k ₂₃＝0.038，k ₃₄＝0.077。

Step 205: utilize Nuo Yiman formula to carry out comprehensively, L ₄for close around 10 circles with the copper cash of copper wire diameter 1.26mm, the circular hollow inductance coil that bore (radius) is 24.2cm, its inductance is about 183 μ H.L ₁the number of turn is 20, other same L ₄.Estimation L ₁q value be about 850, L ₄q value be about 425.And in order to improve the efficiency of transmission of system, L ₂and L ₃q value should be larger.Therefore by L ₂and L ₃the number of turn is set to 25.Its inductance is about 1146 μ H, and Q value is about 1055.

Step 206,207: calculate η=0.900, meet index request.When these 4 during with the parallel placement of bore air core coil coaxial line, according to k ₁₂=0.032, k ₂₃=0.038, k ₃₄=0.077 can determine that transmission range is about 92cm, is greater than the 75cm of requirement.For making bearing power P _l=η | V _s| ²/ (2R _l)=0.0225|V _s| ²=10W, arranges | V _s|=21V.

Step 301,401: efficiency of transmission 90%, transmission range 92cm, bearing power 10W, therefore meets index request.To sum up, list system detailed design parameter:

Power work frequency 133kHz, supply voltage amplitude 21V;

Load resistance value 20 Ω;

Number of repeaters 2;

Air-core inductance:

L ₁copper wire diameter 1.26mm, 20 circles, bore (radius) 24.2cm, circle;

L ₂with L ₃copper wire diameter 1.26mm, 25 circles, bore (radius) 24.2cm, circle;

L ₄copper wire diameter 1.26mm, 10 circles, bore (radius) 24.2cm, circle;

Tuning capacitance C ₁=1.9nF, C ₂=C ₃=1.21nF, C ₄=7.8nF;

Coefficient of mutual inductance k ₁₂=0.032, k ₂₃=0.038, k ₃₄=0.077;

Bearing power 10W, efficiency of transmission 90%, transmission range >90cm.

Fig. 3-Fig. 4 has provided frequency (kHz) – efficiency of transmission (%) and the frequency (simulation curve of kHz) – bearing power (W) of embodiment.Compare with theoretical value, when frequency is 133kHz (operating frequency), bearing power P _l=10.45W, efficiency of transmission η=90.3%, error is less than 5%.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, obviously, those skilled in the art can carry out various changes and modification and not depart from the spirit and scope of the present invention the present invention.Like this, if within of the present invention these are revised and modification belongs to the scope of the claims in the present invention and equivalent technologies thereof, the present invention is also intended to comprise these changes and modification interior.

Claims (8)

1. A design method of a multi-repeater magnetically coupled resonant wireless power transmission system, characterized in that the steps are as follows: Step 101: Determine the values of R _S and _RL ; Step 102: Determine the working frequency f ₀ ; Step 103: setting the corresponding filter type; Step 201: Set the number of repeaters N-2 according to the transmission efficiency and transmission distance-coil aperture ratio; Step 202: setting the relative bandwidth w; Step 203: Determine filter prototype parameters g _i ; Step 204: Calculate circuit parameters L _i , C _i , K _i,i+1 ; Step 205: designing the air-core inductance coil; Step 206: Calculate system performance indicators: transmission efficiency, load power, transmission distance; Step 207: Set the amplitude of the power supply voltage; Step 301: Judging whether the design index is met, if yes, go to step 401; otherwise, go to step 201; Step 401: Obtain the detailed design parameters of the system. 2. design method according to claim 1, it is characterized in that the determination of the filter prototype parameter _gi of described step 203 is: be N for LC resonator number, relative bandwidth is w, system operating frequency f ₀ In the multi-repeater MCR-WPT system, according to the equivalent filter prototype of the system is single-ended or double-ended, and its amplitude-frequency response characteristics, determine the N-order filter low-pass prototype parameters g _i (i=0,...,N +1). 3. The design method according to claim 1, characterized in that the circuit parameters L _i in the step 204, C _i , K _{i, the calculation of i+1} is as follows: (1) If R _S =0Ω: Transmitter TX: $L_1=\frac{g_1{R}_L}{2\mathrm{\&pi;w}{f}_0},C_1=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_1}$ Receiver RX: $L_N=\frac{g_N{R}_L}{2\mathrm{\&pi;w}{f}_0},C_N=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_N}$ Repeater: L _i unconstrained, $C_i=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_i},(i=2,...,N-1)$ Mutual inductance of adjacent coils: $k_{i,i+1}=\frac{w}{\sqrt{g_i{g}_{i+1}}},(i=1,...,N-1)$ (2) If R _S ≠ 0: Transmitter TX: $L_1=\frac{g_1{R}_S}{2\mathrm{\&pi;w}{f}_0},C_1=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_1}$ Receiver RX: $C_N=\frac{1}{4{\mathrm{\&pi;}}^2{f_0}^2{L}_N}$ Repeater: L _i unconstrained, $C_i=\frac{1}{{4\mathrm{\&pi;}}^2{f_0}^2{L}_i},(i=2,...,N-1)$ Mutual inductance of adjacent coils: $k_{i,i+1}=\frac{w}{\sqrt{g_i{g}_{i+1}}},(i=1,...,N-1)$ 4. design method according to claim 1, is characterized in that the air-core inductance coil design of described step 205: determine the shape and the allowable diameter range of air-core inductance coil according to the requirement of design, then according to air-core inductance coil L _i inductance The calculated value determines the geometric parameters of the air-core inductance coil, the specific diameter, number of turns and wire diameter, and estimates the coil loss resistance and Q value; the inductance can be calculated using the Neumann formula, and other necessary parameters can be estimated by the following formula: Loss resistance: $R=\sqrt{\frac{{\mathrm{\&mu;}}_0{\mathrm{\&omega;}}_0}{2\mathrm{\&sigma;}}}\frac{l}{2\mathrm{\&pi;a}}$ Quality factor: $Q=\frac{{\mathrm{\&omega;}}_{0}L}{R}$ μ ₀ is the magnetic permeability in vacuum, σ is the electrical conductivity of the wire, l is the total length of the wire, and a is the radius of the wire. 5. The design method according to claim 1, characterized in that the system performance index in the step 206 is estimated by the following formula: Transmission efficiency η: $\mathrm{\&eta;}=100\exp (-\frac{0.0691}{{\mathrm{w\; f}}_0}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{g_i{R}_i}{L_i}).$ Load power P _L : For a voltage source with RS≠0Ω, the load power For a voltage source with R _S =0Ω, the load power 6. The design method according to claim 1, characterized in that said operating frequency f ₀ is 125KHz, 133KHz, 225KHz or 13.56MHz. 7. The design method according to claim 1, characterized in that said air-core inductance coil is wound into a circular, rectangular, triangular, pentagonal or hexagonal shape. 8. The design method according to claim 1 or 3, characterized in that the repeater coil is an inductance coil with low loss and high Q value.