CN115081281A - Method for estimating size of wireless charging planar coil with magnetic core - Google Patents
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Abstract
The invention provides a size pre-estimation scheme aiming at a wireless charging plane circular coil under the conditions of given working frequency, rated transmission power, maximum transmission distance and maximum transverse deviation, on the basis of a mutual inductance mirror image method, an analytic formula of mutual inductance of an air coil is utilized, a corresponding mutual inductance turn number relation graph is drawn on MATLAB or other calculation software, the radius and the turn number of the air coil corresponding to a half of target mutual inductance are taken as initial values, the radius and the turn number of an infinite area sheet-shaped magnetic core coil corresponding to the target mutual inductance are within the search range of the radius and the turn number of the air coil corresponding to the target mutual inductance, and then finite element simulation correction is carried out, so that a reasonable coil model is obtained. The design process theoretically estimates the size range of the magnetic coupling mechanism, so that the times of finite element simulation and model correction can be reduced, and the simulation time is saved.
Description
Technical Field
The invention relates to the technical field of wireless charging, in particular to a size estimation method for a wireless charging planar coil with a magnetic core.
Background
As a new technology, wireless charging is safer and more convenient compared with traditional wired power supply, the characteristics of non-contact and full-sealing performance fundamentally avoid the defects caused by wired charging and are safer, and the wireless charging system has a good application scene and development trend. The magnetic coupling coil is a key design of the whole wireless power transmission system, and the coil which has a high quality factor and can generate a uniform magnetic field is a guarantee for obtaining higher transmission efficiency and more stable output power. At present, the parameter estimation and design of the air-core coil have been widely studied, but in a high-power situation, in order to increase the coupling degree and reduce the interference to the outside, the air-core coil and the magnetic core are usually selected to be matched. After the magnetic core is added, the quality factor, coupling coefficient, etc. of the coupling system are affected. Due to the complex nonlinear calculation of the system after the magnetic core is added, finite element simulation software is usually adopted for analysis during design. However, few studies provide theoretical estimation of the size of the coupling mechanism before finite element simulation modeling, which causes certain blindness in simulation, so that it is necessary to research a size estimation scheme for the wireless charging planar coil with the magnetic core to guide simulation analysis.
Finite element simulation analysis software is generally adopted in the design of the magnetic coupling coil, wherein the simulation times depend on the luck and the engineering experience of designers. Especially, due to the addition of the magnetic core, an original linear coupling system is converted into nonlinearity, and for complex parameter optimization analysis, if a reasonable method is used for theoretically estimating the size range of the magnetic coupling mechanism before modeling of the finite element coil, the times of finite element simulation and model correction can be reduced, and the simulation time is saved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for estimating the size of the wireless charging planar coil with the magnetic core, which estimates the size range of the magnetic coupling mechanism theoretically, reduces the finite element simulation and the correction times of a model and saves the simulation time.
The technical scheme adopted by the invention is as follows: the invention comprises the following steps:
A. according to the transmission requirement, determining the requirements of various technical indexes, wherein the various technical indexes comprise transmission power efficiency, working frequency, input and output voltage ranges, transmission distance ranges and offset;
B. according to a given maximum transmission distance and a maximum allowed transverse offset, a minimum target mutual inductance value is obtained firstly according to a compensation topology mode;
C. determining the current effective values of the primary coil and the secondary coil based on a coil effective value calculation formula, determining the cross-sectional area and the wire diameter of a conductor part of the wire, and determining the turn ratio;
D. utilizing a mutual inductance mirror image method calculation formula, programming, calculating and drawing a mutual inductance turn number relation graph of the air coil;
E. respectively finding out respective turn values corresponding to the minimum target mutual inductance value, half of the minimum target mutual inductance value and quarter of the minimum target mutual inductance value according to the curve graph, and respectively determining the outer radius of the turn values;
F. modeling is carried out by using the outer radius corresponding to half of the minimum target mutual inductance value, and in the outer radius range corresponding to the minimum mutual inductance and the quarter minimum mutual inductance respectively, the number of turns and the radius are continuously increased or decreased according to the finite element simulation result, and the model is corrected until the simulation result of the mutual inductance is close to the minimum target mutual inductance.
Further, the step a specifically comprises:
A1. with reference to the international telecommunications union and the relevant standards for electromagnetic environment limits, the standard referred to SAE-2954 was selected during the period;
a2, SAE-2954, on the basis of a wireless charging system with a two-coil mode, the working frequency is selected to be 90kHz, and the requirements of various technical indexes including transmission power efficiency, input and output voltage ranges, a transmission distance range and offset are determined;
further, the step B specifically includes:
B1. according to a given maximum transmission distance and a maximum allowed transverse offset, designating a compensation topological structure as a resonance topological structure;
B2. obtaining a power expression from the topological structure, and obtaining a minimum target mutual inductance value expression from the power expression;
B3. and substituting the minimum target mutual inductance expression into the minimum target mutual inductance expression to calculate to obtain a value corresponding to the minimum target mutual inductance value.
Further, the step C specifically includes:
C1. determining the primary and secondary coil current effective values based on the derivation formula of the coil current effective values;
C2. determining the wire diameter and the sectional area of the wire according to the current effective value of the primary coil and the secondary coil;
C3. and confirming the turn ratio of the primary coil and the secondary coil by the wire diameter.
Further, the step D specifically includes:
D1. the mutual inductance of the air coil has an analytic solution, and the programming calculation is carried out by utilizing a mutual inductance mirror image method calculation formula;
D2. and drawing a curve graph of the relation between the corresponding turns and the mutual inductance according to a programming calculation result.
Further, the step E specifically includes:
E1. respectively finding out corresponding turn values when the minimum target mutual inductance value, half of the minimum target mutual inductance value and quarter of the minimum target mutual inductance value are obtained according to the curve graph;
E2. the outer radii are determined separately from the respective turn values.
Further, the step F specifically includes:
F1. in finite element simulation software, modeling is carried out by using an outer radius corresponding to half of a minimum target mutual inductance value;
F2. in the outer radius range corresponding to the minimum mutual inductance and the quarter minimum mutual inductance respectively, according to the finite element simulation result, increasing or reducing the number of turns and the radius continuously, and carrying out simulation;
F3. and correcting the model until the simulation result of the mutual inductance is close to the minimum target mutual inductance, and taking the number of turns and the radius at the moment as final values.
Further, the power expression in the step B2 is:
wherein omega in the above formula 0 Is an angular frequency, P m For maximum transmission power, U 1 For input voltage, U 2 For output voltage, M is the target minimum mutual inductance between coils, L f1 And L f2 The primary and secondary resonant inductance values are provided.
The minimum target mutual inductance value expression in the step B2 is:
wherein the formula (1) omega 0 Is an angular frequency, P m For maximum transmission power, U 1 For the input voltage, U 2max Is the maximum value of the output voltage, λ 1 And λ 2 Respectively, the proportionality coefficients of the fundamental wave amplitudes of the primary and secondary side currents, M min Is the target minimum mutual inductance between coils, L f1 And L f2 The primary and secondary resonant inductance values are provided.
Further, the derivation of the effective value of the coil current in step C1 is as follows:
wherein I in formula (2) and formula (3) p Effective value of current flowing through the primary coil, I s Effective value of current, omega, flowing through the secondary winding 0 Is an angular frequency, P m For maximum transmission power, U 1 For input voltage, U 2max Is the maximum value of the output voltage, λ 1 And λ 2 Respectively the primary and secondary side current fundamental wave amplitudeProportional coefficient of (D), L f1 And L f2 The primary and secondary resonant inductance values are provided.
Further, in the step D1, the calculation formula of the mutual inductance and mutual inductance mirror image method of the hollow coil is as follows:
wherein in formula (4): mu.s 0 In order to achieve a magnetic permeability in a vacuum,
as an integral variable, r 0 R are respectively the inner radius and the outer radius of the two coils, a 1 ＝δ 1 /2π，a 2 ＝δ 2 /2π，δ 1 、δ 2 The thread pitches of the two coils are respectively, and d is the wire diameter of the hollow coil.
The invention has the beneficial effects that: the invention provides a size pre-estimation scheme aiming at a wireless charging plane circular coil under the conditions of given working frequency, rated transmission power, maximum transmission distance and maximum transverse offset, on the basis of a mutual inductance mirror image method, an analytic formula of mutual inductance of an air coil is utilized, a corresponding mutual inductance turn relation graph is drawn on MATLAB or other calculation software, the radius and the turn number of the air coil corresponding to a half of target mutual inductance are taken as initial values, the radius and the turn number of an infinite large-area sheet-shaped magnetic core coil corresponding to the target mutual inductance are within the search range of the radius and the turn number of the air coil corresponding to the target mutual inductance, and then finite element simulation correction is carried out, so that a reasonable coil model is obtained; the design process theoretically estimates the size range of the magnetic coupling mechanism, so that the times of finite element simulation and model correction can be reduced, and the simulation time is saved.
Drawings
FIG. 1 is a flow chart of a scheme for estimating the size of a wireless charging planar coil with a magnetic core;
FIG. 2 is a topology diagram of a bilateral LCC topology model of a wireless charging system;
FIG. 3 is a graph of the relationship between the number of turns in a planar circular coil and the mutual inductance of an air coil;
FIG. 4 is a diagram of a simulation model of a planar circular coil.
Detailed Description
In this embodiment, as shown in fig. 1, the present invention includes the following steps:
step A: with reference to the international telecommunications union and the relevant standards for electromagnetic environment limits, the standard referred to SAE-2954 was selected during the period; in the embodiment, the wireless charging system SAE-2954 mainly based on the two-plane circular coil mode has the working frequency f0 set to 90kHz and requires the maximum transmission power P m Is 4kw, input voltage U 1 650V, output voltage U 2 Maximum value U 2max 400V, the maximum transmission distance hmax is set to 65mm, and the maximum lateral offset dmax is set to 50 mm;
and B: according to the maximum transmission distance hmax and the maximum lateral offset dmax, the topology is designated as a resonant bilateral LCC topology, and the topology is shown in FIG. 2, wherein U in FIG. 2 in Inputting a voltage for the converter; u shape 2 Is the output voltage; i is 0 Is an output current; RL is the load resistance of the converter; Q1-Q4 form a full bridge inverter circuit; resonant inductor Ln and resonant capacitor C f1 、C f2 、C 1 、C 2 And the coil forms a resonant network; l is 1 、L 2 And M is the primary self-inductance, the secondary self-inductance and the mutual inductance of the coil respectively; D1-D4 form a rectifying circuit; c 0 Is an output filter capacitor; i is f1 、I f2 Respectively outputting current for the inverter circuit and inputting current for the rectifier circuit; inverter circuit output voltage U AB And a rectifier circuit input voltage U ab Are respectively amplitude U 1 And U 2 Thus the power expression is derived from the topology:
wherein omega in the above formula 0 Is an angular frequency, P m For maximum transmissionPower, U 1 For input voltage, U 2 For output voltage, M is the target minimum mutual inductance between coils, L f1 And L f2 Respectively the primary and secondary resonant inductance values; obtaining a minimum target mutual inductance calculation formula according to a power expression of the topological structure:
wherein the formula (1) omega 0 Is an angular frequency, P m For maximum transmission power, U 1 For input voltage, U 2max Is the maximum value of the output voltage, λ 1 And λ 2 Respectively, the proportionality coefficients of the fundamental wave amplitudes of the primary and secondary side currents, M min Is the target minimum mutual inductance between coils, L f1 And L f2 Respectively the primary and secondary resonant inductance values;
take lambda 1 And λ 2 Respectively 0.27 and 0.17, and substituting into the calculation index to obtain M min ＝98.5uH。
And C: the calculation formula based on the coil effective value is respectively as follows:
wherein I in the formulae (2) and (3) p Effective value of current flowing through the primary coil, I s Effective value of current, omega, flowing through the secondary winding 0 Is an angular frequency, P m For maximum transmission power, U 1 For input voltage, U 2max Is the maximum value of the output voltage, λ 1 And λ 2 Respectively is the proportionality coefficient of the primary and secondary side current fundamental wave amplitude, L f1 And L f2 Respectively the primary and secondary resonant inductance values; substituting numerical value, calculating to obtain the effective value of current flowing through the primary coil to be 8A, selecting litz wire with single wire diameter of 0.1 and strand number of 250 strands and total wire diameter2.1mm, correspondingly, the effective value of the current flowing through the secondary coil is 9A, so that litz wires with the diameter of a single wire of 0.1 and the number of strands of 300 are selected, the diameter of a total wire is 2.3mm, a reference standard is provided in the wire industry, and the diameter and the number of strands of the wire are determined according to the amount of the current flowing through the coil by the copper wire; the turn ratio is thus N1: n2 ═ 1.1.
Step D: the air core coil mutual inductance has an analytic solution, and is numerically calculated by using the following formula (4):
wherein in formula (4): mu.s 0 In order to achieve a magnetic permeability in a vacuum,
as an integral variable, r 0 R are respectively the inner radius and the outer radius of the two coils, a 1 ＝δ 1 /2π，a 2 ＝δ 2 /2π，δ 1 、δ 2 The pitches of the two coils are respectively, and d is the wire diameter of the hollow coil; get r 0 0.03m, 65mm for h, 50mm for d, delta 1 ＝0.0021m，δ 2 Substituting the value of 0.0023M into a formula, and drawing the number of turns N1 and the mutual inductance M of the air coil by using MATLAB air The graph of the relationship of (A) is shown in FIG. 3.
Step E: according to the relation curve of the turns and the mutual inductance drawn in the step D, respectively finding out respective turn values corresponding to the minimum target mutual inductance value, half of the minimum target mutual inductance value and quarter of the minimum target mutual inductance value in the curve chart, and respectively determining the outer radiuses as follows:
M air ＝M min n1 ═ N1a ═ 43 turns corresponding to 50uH, so ra ═ 30+43 × 2.1 is about 120 mm.
M air ＝M min N1 ═ N1b ═ 35 turns corresponding to 25uH, so rb ═ 30+35 × 2.1 was about 104 mm.
M air ＝M min N1-N1 a-53 turns for 100uH, so rc 30+53 × 2.1 is about 141 mm.
Step F: at half the minimum target mutual inductance valueModeling the corresponding outer radius, continuously increasing or decreasing the number of turns and the radius according to the finite element simulation result in the outer radius range respectively corresponding to the minimum mutual inductance and the quarter minimum mutual inductance, and correcting the model until the simulation result of the mutual inductance is close to the minimum target mutual inductance. Taking r as ra as an initial outer radius, N1 as N1a as 43 turns, N2 as N43/1.1 as 39 turns, wherein a small square magnetic core with the thickness of 6mm and the side length of 50mm is selected, 25 small magnetic cores are spliced into a whole flat magnetic core, the relative permeability is 3200, and a simulation model graph is shown in fig. 4, and the simulation result is 98.6 uH. Further optimization finally confirmed that N1-45, N2-41, r-124 mm, and M respectively min ＝107.52uH。
Finally, it should be emphasized that the above-described preferred embodiments of the present invention are merely examples of implementations, rather than limitations, of the invention, and that various changes and modifications may be effected therein by one of ordinary skill in the pertinent art, without departing from the spirit and scope of the present invention,
the invention is applied to the technical field of wireless charging.
While the embodiments of the present invention have been described in terms of practical embodiments, they are not to be construed as limiting the meaning of the present invention, and modifications of the embodiments and combinations with other embodiments will be apparent to those skilled in the art in light of the present description.
Claims (10)
1. A size estimation method for a wireless charging planar coil with a magnetic core is characterized by comprising the following steps:
A. according to the transmission requirement, determining the requirements of various technical indexes, wherein the various technical indexes comprise transmission power efficiency, working frequency, input and output voltage ranges, transmission distance ranges and offset;
B. according to a given maximum transmission distance and a maximum allowed transverse offset, a minimum target mutual inductance value is obtained firstly according to a compensation topology mode;
C. determining the current effective values of the primary coil and the secondary coil based on a coil effective value calculation formula, determining the cross-sectional area and the wire diameter of a conductor part of the wire, and determining the turn ratio;
D. utilizing a mutual inductance mirror image method calculation formula, programming, calculating and drawing a mutual inductance turn number relation graph of the hollow coil;
E. respectively finding out corresponding turn values when the minimum target mutual inductance value, the half of the minimum target mutual inductance value and the quarter of the minimum target mutual inductance value are obtained according to the curve chart, and respectively determining the outer radius of the turn values;
F. modeling is carried out by using the outer radius corresponding to half of the minimum target mutual inductance value, and in the outer radius range corresponding to the minimum mutual inductance and the quarter minimum mutual inductance respectively, the number of turns and the radius are continuously increased or decreased according to the finite element simulation result, and the model is corrected until the simulation result of the mutual inductance is close to the minimum target mutual inductance.
2. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 1, wherein the step A specifically comprises the following steps:
A1. with reference to the international telecommunications union and the relevant standards for electromagnetic environment limits, the standard referred to SAE-2954 was selected during the period;
sae-2954 specifies the core frequency of wireless charging, based on a two-coil mode wireless charging system, the operating frequency is selected to 90kHz, and various technical index requirements including transmission power efficiency, input and output voltage ranges, transmission distance ranges, and offset are specified.
3. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 2, wherein the step B specifically comprises the following steps:
B1. according to a given maximum transmission distance and a maximum allowed transverse offset, designating a compensation topological structure as a resonance topological structure;
B2. obtaining a power expression from the topological structure, and obtaining a minimum target mutual inductance value expression from the power expression;
B3. and substituting the minimum target mutual inductance expression into the minimum target mutual inductance expression to calculate to obtain a value corresponding to the minimum target mutual inductance value.
4. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 3, wherein the step C specifically comprises the following steps:
C1. determining the primary and secondary coil current effective values based on a derivation formula of the coil current effective values;
C2. determining the wire diameter and the sectional area of the wire according to the current effective value of the primary coil and the secondary coil;
C3. and confirming the turn ratio of the primary coil and the secondary coil by the wire diameter.
5. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 4, wherein the step D specifically comprises the following steps:
D1. the mutual inductance of the air coil has an analytic solution, and programming calculation is carried out by utilizing a mutual inductance mirror image method calculation formula;
D2. and drawing a curve graph of the relation between the corresponding turns and the mutual inductance according to a programming calculation result.
6. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 5, wherein the step E specifically comprises the following steps:
E1. respectively finding out corresponding turn values when the minimum target mutual inductance value, half of the minimum target mutual inductance value and quarter of the minimum target mutual inductance value are obtained according to the curve graph;
E2. the outer radii are determined separately from the respective turn values.
7. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 6, wherein the step F specifically comprises the following steps:
F1. in finite element simulation software, modeling is carried out by using an outer radius corresponding to half of a minimum target mutual inductance value;
F2. in the outer radius range corresponding to the minimum mutual inductance and the quarter minimum mutual inductance respectively, according to the finite element simulation result, increasing or reducing the number of turns and the radius continuously, and carrying out simulation;
F3. and correcting the model until the simulation result of the mutual inductance is close to the minimum target mutual inductance, and taking the number of turns and the radius at the moment as final values.
8. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 3, wherein the method comprises the following steps: the power expression in the step B2 is:
wherein omega in the above formula 0 Is an angular frequency, P m For maximum transmission power, U 1 For input voltage, U 2 For output voltage, M is the target minimum mutual inductance between coils, L f1 And L f2 The primary and secondary resonant inductance values are provided.
The minimum target mutual inductance value expression in the step B2 is:
wherein the formula (1) omega 0 Is an angular frequency, P m For maximum transmission power, U 1 For input voltage, U 2max Is the maximum value of the output voltage, λ 1 And λ 2 Respectively, the proportionality coefficients of the fundamental wave amplitudes of the primary and secondary side currents, M min Is the target minimum mutual inductance between coils, L f1 And L f2 The primary and secondary resonant inductance values are provided.
9. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 4, wherein the method comprises the following steps: the derivation formula of the effective value of the coil current in the step C1 is as follows:
wherein I in the formulae (2) and (3) p Effective value of current flowing through the primary coil, I s Effective value of current, omega, flowing through the secondary winding 0 Is an angular frequency, P m For maximum transmission power, U 1 For input voltage, U 2max Is the maximum value of the output voltage, λ 1 And λ 2 Respectively is the proportionality coefficient of the primary and secondary side current fundamental wave amplitude, L f1 And L f2 The primary and secondary resonant inductance values are provided.
10. The method for estimating the size of the wireless charging planar coil with the magnetic core according to claim 5, wherein the method comprises the following steps: the calculation formula of the hollow coil mutual inductance mirror image method in the step D1 is as follows:
wherein in formula (4): mu.s 0 In order to achieve a magnetic permeability in a vacuum,
as an integral variable, r 0 R are respectively the inner radius and the outer radius of the two coils, a 1 ＝δ 1 /2π，a 2 ＝δ 2 /2π，δ 1 、δ 2 The thread pitches of the two coils are respectively, and d is the wire diameter of the hollow coil.
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| CN115828647A (en) * | 2023-02-22 | 2023-03-21 | 广东电网有限责任公司湛江供电局 | Method, system, equipment and medium for determining coil model of wireless power supply system |
| CN117973299A (en) * | 2024-03-28 | 2024-05-03 | 中山大学 | Underwater wireless charging coil parameter design method, device, equipment and storage medium |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115828647A (en) * | 2023-02-22 | 2023-03-21 | 广东电网有限责任公司湛江供电局 | Method, system, equipment and medium for determining coil model of wireless power supply system |
| CN117973299A (en) * | 2024-03-28 | 2024-05-03 | 中山大学 | Underwater wireless charging coil parameter design method, device, equipment and storage medium |
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