Multistage magnetic resonance WPT system energy flow regulation and control method based on current phase configuration

Abstract

The invention relates to the technical field of multi-stage magnetic resonance wireless power transmission (WPT), particularly discloses a multi-stage magnetic resonance WPT system energy flow regulation and control method based on current phase configuration, and aims to solve the problems of active reverse transmission, system detuning and the like caused by complex coil coupling relation of an existing multi-stage magnetic resonance WPT system. Obtaining a phase conversion matrix according to the conversion variable of the coil current phasor; multiplying the original impedance matrix by the phase conversion matrix, and transferring a multi-stage coil current phase relation to an equivalent impedance matrix; taking a voltage imaginary part of each stage of coil loop as zero, and reversely deriving an expression of each stage of coil current; substituting the coil loop containing the compensation capacitance in the voltage real part into the coil current of each stage, and solving the compensation capacitance of the corresponding coil loop; and a mathematical analysis relation among the system power, the efficiency and the to-be-optimized variable is obtained, so that the loop power and the system efficiency of each stage of coil are regulated and controlled by configuring the to-be-optimized variable.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-stage magnetic resonance wireless power transfer (WPT), and particularly to an energy flow regulation method for a multi-stage magnetic resonance WPT system based on current phase configuration. Background Art

[0002] Wireless power transfer based on the principle of near-field magnetic coupling resonance is a new emerging power supply technology that is safe, flexible, and wire-free, and can adapt to various harsh weather environments. It has currently been widely applied in fields such as biomedicine, consumer electronics, electric vehicles, and intelligent industries. For the current grid security, a large number of modern monitoring devices need to be put into operation, and the working state of the power transmission network can be remotely observed through the monitoring devices. In recent years, some scholars have combined a wireless power supply system with an insulator to form a wireless power supply system based on the insulator to supply power to the monitoring devices. The structural shape of the insulator remains unchanged, but it has two electrical characteristics: insulation and energy transfer. To solve the problem of the transmission distance limitation of the WPT system, more and more scholars have adopted multi-relay coil structures and domino coil structures to increase the transmission distance of the system. The current method for long-distance wireless power transfer is to add a relay side structural unit between the energy transmitting end structural unit and the energy receiving end structural unit, and use the magnetic coupling resonance of the relay coil to achieve energy transfer at medium and long distances. With the increase in the number of components, the coupling relationship between multi-stage coils becomes very complex, resulting in active power feedback from the subsequent coils to the previous coils, bringing problems such as system detuning and decreased transmission efficiency. Therefore, how to control the power flow between the coils and ensure the efficient transmission of system power is crucial for the operation of the multi-stage magnetic resonance WPT system. Currently, there is no simple and effective solution for the energy flow regulation of the multi-stage magnetic resonance WPT system. Summary of the Invention

[0003] The present invention provides an energy flow regulation method for a multi-stage magnetic resonance WPT system based on current phase configuration, and the technical problem to be solved is that in the existing multi-stage magnetic resonance WPT system, there is power feedback under complex cross-coupling, resulting in system detuning and decreased transmission efficiency.

[0004] To solve the above technical problems, the present invention provides an energy flow regulation method for a multi-stage magnetic resonance WPT system based on current phase configuration. The multi-stage magnetic resonance WPT system includes a transmitting coil loop, n - 2 relay coil loops, and a receiving coil loop arranged in sequence. The key lies in that the energy flow regulation method includes the following steps:

[0005] S1. Establish a circuit impedance model of the multi-stage magnetic resonance WPT system U = ZI, where U and I respectively represent the voltage matrix and current matrix composed of the voltages and currents of each stage of coils, and Z is the impedance matrix describing the impedance relationship between the n-stage magnetic resonance coils;

[0006] S2. Determine that the phases of some relay coils are variables to be optimized, and preset the phases of the currents of the remaining coils as constants;

[0007] S3. Decompose the phases of the currents of each level of coils to obtain the corresponding phase conversion matrix T, and obtain the equivalent impedance matrix Z based on the phase conversion matrix T T =ZT and the converted current matrix I T =T -1 I;

[0008] S4. Based on the current phases in I T , extract the elements or the real parts or the imaginary parts of the elements at the corresponding positions in Z to construct the permutation matrix Z T , and obtain the current expressions I T0 of each level of coils based on Z T0 =Z T =Z T0 -1 U;

[0009] S5. Construct the loop voltage equations of the n-level coils, solve the loop voltage equations corresponding to the element terms in Z T whose real and imaginary parts simultaneously contain compensation capacitors, obtain the analytical solutions of the corresponding compensation capacitors and substitute them into I T =Z T0 -1 U to obtain new coil current expressions, and substitute the new coil current expressions into the remaining loop voltage equations of the coils to solve the analytical solutions of the remaining compensation capacitors;

[0010] S6. Based on the currently determined information, obtain the relationships between the loop powers of each level of coils, the system transmission efficiency and the variables to be optimized, and based on this relationship, regulate the loop powers of each level of coils and the system efficiency by configuring the variables to be optimized.

[0011] Further, the step S2 specifically includes the steps:

[0012] S21. Taking the AC input voltage of the transmitting coil loop as the reference 0 phase, set the phase of the transmitting coil current to 0°;

[0013] S22. When the system requires constant voltage output, set the current phase of the receiving coil to 0° or -180°; when the system requires constant current output, set the current phase of the receiving coil to 90° or -90°;

[0014] S23. Set the current phases of some relay coils to 0°, 90°, -90° or -180°, and the current phases of the remaining relay coils are variables θ k .

[0015] Further, in step S3, the phase conversion matrix T is composed of the phase conversion coefficients of each level of coils, and the phase conversion coefficients of each level of coils are valued according to the following rules:

[0016] The conversion coefficients corresponding to the coil currents with phases of 0°, 90°, -90°, and -180° are 1, that is, the phase of the coil current remains unchanged before and after conversion;

[0017] For the coil current with a phase of θ k and 0° < |θ k | < 90°, the corresponding conversion coefficient is cosθ k +jsinθ k , and the phase of the coil current after conversion is 0°;

[0018] For the coil current with a phase of θ k and 90° < |θ k | < 180°, the corresponding conversion coefficient is -cos(180° - θ k ) + jsin(180° - θ k ), and the phase of the coil current after conversion is 0°.

[0019] Further, in step S4, the rule for constructing the permutation matrix Z T0 is as follows:

[0020] Extract the real part of the diagonal elements of the equivalent impedance matrix Z T as the diagonal elements of the permutation matrix Z T0 ;

[0021] For the coil loops with current phases of 0° and -180°, when the phases of the coupled coil currents are also 0° and -180°, extract the real part of the corresponding elements of the equivalent impedance matrix Z T as the elements at the corresponding positions of the permutation matrix Z T0 ; when the phases of the coupled coil currents are 90° and -90°, extract the imaginary part of the corresponding elements of the equivalent impedance matrix Z T as the elements at the corresponding positions of the permutation matrix Z T0 ;

[0022] For the coil loops with current phases of 90° and -90°, when the phases of the coupled coil currents are 0° and -180°, extract the imaginary part of the corresponding elements of the equivalent impedance matrix Z T as the elements at the corresponding positions of the permutation matrix Z T0 ; when the phases of the coupled coil currents are also 90° and -90°, extract the real part of the corresponding elements of the equivalent impedance matrix Z T as the elements at the corresponding positions of the permutation matrix Z T0 ;

[0023] Further, in the step S6, based on the currently determined information, the relationship between the power of each level of coil circuit and the variable to be optimized is obtained, specifically:

[0024] According to the phase conversion matrix T and the new coil current expression I T Restore to obtain the coil current matrix I before conversion: I = TI T ;

[0025] Multiply the column elements in the impedance matrix Z by the row elements in the current matrix I, and then multiply them by the conjugates of the respective coil circuit currents to obtain the power expression for the coupling between each level of coil circuits.

[0026] Further, the compensation capacitor of each level of coil circuit is connected in series with the coil of that level.

[0027] Further, in step S1, the voltage matrix U is a column vector composed of the voltages of each level of coil, and the current matrix I is a column vector composed of the currents of each level of coil.

[0028] Further, in step S1, the impedance matrix Z is an n×n square matrix, and the element Z at the i-th row and j-th column ij The value rule is:

[0029] When i = j ≠ n, Z ij Is equal to R i + j(ωL i - 1 / ωC i );

[0030] When i = j = n, Z ij Is equal to R n + j(ωL n - 1 / ωC n ) + R Leq ;

[0031] When i ≠ j, Z ij Is equal to jωM ij ;

[0032] Among them, ω represents the working angular frequency of the system, I i , R i , L i , C i Successively represent the currents, internal resistances, inductances, and compensation capacitors of each level of coil, M ij Represents the mutual inductance between the i-th level coil and the j-th level coil, R Leq Represents the AC equivalent load at the receiving end, and i, j = 1, 2,..., n.

[0033] A method for regulating the energy flow of a multi - stage magnetic resonance WPT system based on current phase configuration provided by the present invention presets the current phases of each stage of coils according to the zero - phase - angle input at the transmitting end of the system and the output performance requirements at the load end, obtains the phase conversion matrix based on the conversion variables of the coil current phasors, and transfers the multi - stage coil current phase relationship to the equivalent impedance matrix by multiplying the original impedance matrix by the phase conversion matrix. With the imaginary part of the voltage in each stage of the coil loop being zero, the expressions for the current of each stage of the coil are derived inversely, and then the coil loops with compensation capacitors in the real part of the voltage are substituted into the current of each stage of the coil to solve for the compensation capacitors of the corresponding coil loops, and thereby obtain the mathematical analytical relationship between the system power, efficiency, and variables to be optimized. Through the precise calculation of the compensation capacitors of each stage of the coil loop, the present invention not only realizes the zero - phase - angle input and constant - voltage output of the system, but also finds a method for regulating the energy flow through the quantitative relationship between the phase variables and the transmitted power and efficiency, improving the transmitted power and transmission efficiency of the system. Description of the Drawings

[0034] Figure 1 is the circuit topology diagram of the 5 - stage magnetic resonance WPT system provided by the embodiment of the present invention;

[0035] Figure 2 is the flowchart of a method for regulating the energy flow of a multi - stage magnetic resonance WPT system based on current phase configuration provided by the embodiment of the present invention;

[0036] Figure 3 is the current phase diagram before phase configuration provided by the embodiment of the present invention;

[0037] Figure 4 is the active power flow diagram before phase configuration provided by the embodiment of the present invention;

[0038] Figure 5 is the output voltage diagram before phase configuration provided by the embodiment of the present invention;

[0039] Figure 6 is the current phase diagram under the first phase configuration provided by the embodiment of the present invention;

[0040] Figure 7 is the active power flow diagram under the first phase configuration provided by the embodiment of the present invention;

[0041] Figure 8 is the output voltage diagram under the first phase configuration provided by the embodiment of the present invention;

[0042] Figure 9 is the current phase diagram under the second phase configuration provided by the embodiment of the present invention;

[0043] Figure 10 is the active power flow diagram under the second phase configuration provided by the embodiment of the present invention;

[0044] Figure 11 It is the output voltage diagram under the second phase configuration provided by the embodiments of the present invention;

[0045] Figure 12 It is the current phase diagram under the third phase configuration provided by the embodiments of the present invention;

[0046] Figure 13 It is the active power flow diagram under the third phase configuration provided by the embodiments of the present invention;

[0047] Figure 14 It is the output voltage diagram under the third phase configuration provided by the embodiments of the present invention;

[0048] Figure 15 It is the output power comparison diagram when the phase configuration changes provided by the embodiments of the present invention;

[0049] Figure 16 It is the transmission efficiency comparison diagram when the phase configuration changes provided by the embodiments of the present invention. Detailed implementation manners

[0050] The following specifically illustrates the implementation manners of the present invention in conjunction with the attached drawings. The given embodiments are only for illustrative purposes and should not be construed as a limitation of the present invention. The attached drawings are only for reference and illustration, and do not constitute a limitation on the protection scope of the present invention. Because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0051] Before describing the energy flow control method of the multi-stage magnetic resonance WPT system of the present invention, it is necessary to briefly introduce the structure of the multi-stage magnetic resonance WPT system. The multi-stage magnetic resonance WPT system includes a transmitting coil circuit, n - 2 relay coil circuits, and a receiving coil circuit arranged in sequence. Among them, the transmitting coil circuit includes an equivalent AC source, a transmitting coil compensation network, and a transmitting coil. The relay coil circuit includes a relay coil and a relay coil resonance network. The receiving coil circuit includes a receiving coil, a receiving coil compensation network, and an equivalent AC load. The equivalent AC source is generally equivalent to a DC source and a high-frequency inverter. The equivalent AC load is generally equivalent to a rectifying and filtering circuit and a load resistor. The transmitting coil compensation network, the relay coil resonance network, and the receiving coil compensation network adopt compensation networks with the same structure. For the convenience of energy flow control, the compensation network in this embodiment adopts a series compensation capacitor. The circuit structure of the multi-stage magnetic resonance WPT system when n = 5 is as Figure 1 shown, where I i , R i , L i , C i successively represent the coil current, internal resistance, inductance, and compensation capacitor of each stage, and M ij(i≠j) represents the mutual inductance between the i-th and j-th coils, R Leq represents the AC equivalent load at the receiving end, i, j = 1, 2, …, n, U in represents the DC source, MOS transistor S 1 to S 4 are connected to form a high-frequency inverter, U inv represents the AC voltage output by the inversion. Diode D 1 to D 4 are connected to form a full-bridge rectifier, and the filter capacitor C f together constitute a rectifier filter circuit. R L represents the load resistance, I out and U out respectively represent the system output current and voltage.

[0052] Based on the above multi-stage magnetic resonance WPT system, an embodiment of the present invention provides a method for regulating the energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration, as Figure 2 shown in the flowchart of, including the steps:

[0053] S1. Establish a circuit impedance model of the multi-stage magnetic resonance WPT system U = ZI, where U and I respectively represent the voltage matrix and current matrix composed of the voltages and currents of each coil, and Z is the impedance matrix describing the impedance relationship between the n-stage magnetic resonance coils;

[0054] S2. Determine that the phases of some relay coils are variables to be optimized, and preset the current phases of the remaining coils as constants;

[0055] S3. Decompose the current phases of each coil to obtain the corresponding phase conversion matrix T, and obtain the equivalent impedance matrix Z T = ZT and the converted current matrix I T = T -1 I;

[0056] S4. Based on the current phases in I T , extract the elements or the real parts or the imaginary parts of the elements at the corresponding positions of Z T to construct a permutation matrix Z T0 , and based on Z T0 obtain the current expressions of each coil I T = Z T0 -1 U;

[0057] S5. Construct the loop voltage equations of the n-stage coils, solve the loop voltage equations corresponding to the element terms in Z T whose real and imaginary parts simultaneously contain the compensation capacitors, obtain the corresponding analytical solutions of the compensation capacitors and substitute them into I T = Z T0-1 The new coil current expression is obtained for U, and the new coil current expression is substituted into the remaining coil loop voltage equations to solve the analytical solutions of the remaining compensation capacitors;

[0058] S6. Based on the currently determined information, obtain the relationships between the powers of each stage of coil loops, the system transmission efficiency, and the variables to be optimized. Based on these relationships, configure the variables to be optimized to regulate the powers of each stage of coil loops and the system efficiency.

[0059] An energy flow regulation method for a multi-stage magnetic resonance WPT system based on current phase configuration provided by the present invention presets the current phases of each stage of coils according to the zero-phase angle input at the transmitting end of the system and the output performance requirements at the load end, and obtains a phase conversion matrix according to the conversion variables of the coil current phasors. By multiplying the original impedance matrix by the phase conversion matrix, the multi-stage coil current phase relationship is transferred to the equivalent impedance matrix. With the imaginary parts of the voltages of each stage of coil loops being zero, the expressions of the coil currents of each stage are deduced inversely, and then the coil loops in the real parts of the voltages that contain compensation capacitors are substituted into the coil currents of each stage, so as to solve the compensation capacitors of the corresponding coil loops, and thereby obtain the mathematical analytical relationships between the coil currents and compensation capacitors of each stage and the variables to be optimized. Through the precise calculation of the compensation capacitors of each stage of coil loops, the present invention not only realizes the zero-phase angle input and constant voltage output of the system, but also finds an energy flow regulation method through the quantitative relationships between the phase variables, the transmission power, and the efficiency, improving the system transmission power and transmission efficiency.

[0060] The following details each step.

[0061] (1) Step S1

[0062] In step S1, the circuit impedance model of the multi-stage magnetic resonance WPT system is determined as U = ZI:

[0063]

[0064] Among them, the voltage matrix is a column vector composed of the voltages of each stage of coils. The current matrix is a column vector composed of the currents of each stage of coils.

[0065] The impedance matrix Z is an n×n square matrix, and the element Z ij in its i-th row and j-th column has the following value rule:

[0066] Z ij = jωM ij , i ≠ j,

[0067]

[0068] That is:

[0069] When \(i = j\neq n\), \(Z\) ij That is, \(Z\) ii equals \(R\) i +\(j(\omega L\) i - 1 / \(\omega C\) i );

[0070] When \(i = j = n\), \(Z\) ij That is, \(Z\) ii equals \(R\) n +\(j(\omega L\) n - 1 / \(\omega C\) n )+\(R\) Leq ;

[0071] When \(i\neq j\), \(Z\) ij equals \(j\omega M\) ij ;

[0072] where \(\omega\) represents the working angular frequency of the system.

[0073] Taking \(n = 5\) as an example, the corresponding circuit impedance model is described as:

[0074]

[0075] Among them,

[0076] (2) Step S2

[0077] Step S2 is to determine that the phases of some relay coils are variables to be optimized, and preset the phases of the currents of the remaining coils as constants. Here, at least two variables to be optimized are set.

[0078] The specific steps of step S2 include:

[0079] S21. Taking the AC input voltage of the transmitting coil circuit as the reference 0 phase, set the phase of the transmitting coil current to 0°, so that the voltage and current phases of the transmitting end coil circuit are in phase, realizing zero-phase angle input at the transmitting end;

[0080] S22. When the system requires constant voltage output, set the current phase of the receiving coil to 0° or -180°; when the system requires constant current output, set the current phase of the receiving coil to 90° or -90°;

[0081] S23. Set the current phases of some relay coils to 0°, 90°, -90° or -180°, and the current phases of the remaining relay coils are variables to be optimized \(\theta\) k .

[0082] Taking \(n = 5\), realizing constant voltage output, \(k = 2,4\) as an example, the specific steps of step S2 include:

[0083] S21. Set the AC input voltage of the transmitting coil circuit as the reference 0 phase, and set the phase of the transmitting coil current as 0°.

[0084] S22. Set the phase of the receiving coil current as -180° to make the system output a constant voltage.

[0085] S23. Set the phase of the second relay coil (the 3rd - stage coil) as -90°, and the phases of the first relay coil (the 2nd - stage coil) and the third relay coil (the 4th - stage coil) are variables θ 2 and θ 4 , and the corresponding coil currents are expressed as I 2 ∠θ 2 、I 4 ∠θ 4 .

[0086] (3) Step S3

[0087] In this step S3, the phase - conversion matrix T is composed of the phase - conversion coefficients of each stage of the coil. The phase - conversion coefficients of each stage of the coil are taken according to the following rules:

[0088] The conversion coefficients corresponding to the coil currents with phases of 0°, 90°, -90°, and -180° are 1, that is, the coil current phases remain unchanged before and after conversion;

[0089] The conversion coefficient corresponding to the coil current with a phase of θ k and 0° < |θ k | < 90° is cosθ k +jsinθ k , and the coil current phase after conversion is 0°;

[0090] The conversion coefficient corresponding to the coil current with a phase of θ k and 90° < |θ k | < 180° is -cos(180° - θ k )+jsin(180° - θ k ), and the coil current phase after conversion is 0°.

[0091] After extracting the phase - conversion matrix T, the equivalent impedance matrix and the converted current matrix form of the multi - stage magnetic resonance WPT system are further obtained:

[0092]

[0093]

[0094] Among them,

[0095] After the coil current phase relationship is transferred to the equivalent impedance matrix, there are only four cases for the coil current phase of the multi-stage magnetic resonance WPT system: 0°, 90°, -90°, and -180°.

[0096] Continuing with the above example, the phase decomposition of the 5-stage coil current is as follows:

[0097] (1) Given that the phases of the first, third, and fifth stages are 0°, -90°, and -180° respectively, the conversion coefficients corresponding to their coil currents are 1.

[0098] (2) The phase θ of the second-stage coil current 2 is unknown. It is distributed between the first-stage coil and the third-stage coil. Therefore, the value range is -90° < θ 2 < 0°. The conversion coefficient corresponding to the second-stage coil current is cosθ k +jsinθ k , and the phase of the coil current after conversion is 0°.

[0099] (3) The phase of the fourth-stage coil current is θ 4 is unknown. It is distributed between the third-stage coil and the fifth-stage coil. Therefore, the value range is -180° < θ 2 < -90°. The conversion coefficient corresponding to the fourth-stage coil current is -cos(180° - θ k ) + jsin(180° - θ k ), and the phase of the coil current after conversion is 0°.

[0100] The phase conversion matrix T of the 5-stage magnetic resonance WPT system is obtained:

[0101]

[0102] According to the phase conversion matrix, the system impedance matrix can be equivalently expressed as:

[0103]

[0104] After the current phase decomposition, the matrix form composed of the coil currents at each stage is:

[0105]

[0106] (4) Step S4

[0107] In this step S4, the reverse derivation of the coil current expressions at each stage depends on a permutation matrix Z T0 , which is a full-rank matrix of order n. The relationship between it and the converted coil current I T is as follows:

[0108] I T = ZT0 -1 U

[0109] Construct the permutation matrix Z T0 The rule is as follows:

[0110] Extract the equivalent impedance matrix Z T Take the real part of the diagonal elements of the equivalent impedance matrix Z as the diagonal elements of the permutation matrix Z T0 ;

[0111] For the coil loops with current phases of 0° and -180°, when the current phases of the coupled coils are also 0° and -180°, extract the equivalent impedance matrix Z T Take the real part of the corresponding elements of the equivalent impedance matrix Z as the elements of the permutation matrix Z T0 at the corresponding positions; when the current phases of the coupled coils are 90° and -90°, extract the equivalent impedance matrix Z T Take the imaginary part of the corresponding elements of the equivalent impedance matrix Z as the elements of the permutation matrix Z T0 at the corresponding positions;

[0112] For the coil loops with current phases of 90° and -90°, when the current phases of the coupled coils are 0° and -180°, extract the equivalent impedance matrix Z T Take the imaginary part of the corresponding elements of the equivalent impedance matrix Z as the elements of the permutation matrix Z T0 at the corresponding positions; when the current phases of the coupled coils are also 90° and -90°, extract the equivalent impedance matrix Z T Take the real part of the corresponding elements of the equivalent impedance matrix Z as the elements of the permutation matrix Z T0 at the corresponding positions.

[0113] Following the above example, the steps to construct the permutation matrix Z T0 include:

[0114] Extract the equivalent impedance matrix Z T Take the real part of the diagonal elements of the equivalent impedance matrix Z as the diagonal elements of the permutation matrix Z T0 , that is, Z T0ii = real(Z Tii ), i = 1, 2,..., 5, real() represents the real part;

[0115] For the 1st, 2nd, 4th, and 5th level coil loops with current phases of 0° and -180°, when they are mutually coupled, extract the equivalent impedance matrix Z T Take the real part of the corresponding elements of the equivalent impedance matrix Z as the elements of the permutation matrix Z T0 ; conversely, when the coupled coil is the 3rd level coil with a current phase of -90°, extract the equivalent impedance matrix Z T Take the imaginary part of the corresponding elements of the equivalent impedance matrix Z as the elements of the permutation matrix Z T0 , imag() represents the imaginary part;

[0116] For the third - level coil circuit with a current phase of - 90°, the first - level, second - level, fourth - level, and fifth - level coils coupled to it all have current phases of 0° and - 180°. Then, the imaginary part of the corresponding elements of the equivalent impedance matrix Z T is taken as the elements of the permutation matrix Z T0 .

[0117] Therefore, the permutation matrix expression of the 5 - level magnetic resonance WPT system is as follows:

[0118]

[0119] Its specific form is:

[0120]

[0121] Based on the permutation matrix Z T0 the coil currents at each level can be derived. They are determined by the internal resistances and mutual inductances of all coils, the load, the current phases θ 2 and θ 4 , the self - inductance and compensation capacitance of the second - level coil, and the self - inductance and compensation capacitance of the fourth - level coil.

[0122] (5) Step S5

[0123] For the element terms in the equivalent impedance matrix where both the real and imaginary parts contain the compensation capacitance, they are always located on the diagonal of the matrix and are caused by the decomposition of the coil current phase in the corresponding loop. Its specific form can be expressed as:

[0124] Z kk (cosθ k +jsinθ k ), or Z kk (-cos(180° - θ k )+jsin(180° - θ k ))

[0125] Also, according to the reverse - deduction method of the coil current described above, from the characteristics of the diagonal elements of the permutation matrix Z T0 , it can be known that the capacitance parameters included in the coil current expression are exactly the compensation capacitances of the corresponding coil loops. Thus, the compensation capacitances to be found can be obtained from the coil loop voltage equations with current phase decomposition.

[0126] In the parameter design of the multi - level magnetic resonance WPT system, generally, parameters such as the self - inductance, mutual inductance, and internal resistance of the coils are known, while the compensation capacitances resonating with them are the quantities to be found. To obtain the coil currents independent of the compensation capacitances to be found, the following steps are required:

[0127] To eliminate the coil current expression I TTo determine the compensation capacitor in the equivalent impedance matrix, it is necessary to first determine the element item in the real and imaginary parts of the equivalent impedance matrix that contains the compensation capacitor and the matrix row (coil loop) where it is located.

[0128] By constructing the coil loop voltage equations of this type of matrix rows, the coil current expression I can be solved. T The compensation capacitor in

[0129] Substituting the compensation capacitor into the existing coil current expression can achieve the purpose of eliminating the compensation capacitor parameters, and then substituting the new coil current expression I T Substitute the voltage equation of each coil loop into the equation to solve for the compensation capacitance of the remaining coil loops.

[0130] Continuing with the above example, in order to obtain the coil current that is independent of the compensation capacitance to be determined, the following steps are required:

[0131] First, determine the elements of the equivalent impedance matrix that contain both the real and imaginary parts of the compensation capacitor and the matrix rows (coil loops) where they are located, i.e., the 2nd and 4th rows;

[0132] Construct the coil loop voltage equations for the 2nd and 4th rows:

[0133]

[0134] The system of equations contains 2 equations and 2 compensation capacitors C to be determined. 2 With C 4 , solve this set of equations and get the compensation capacitor C 2 With C 4 Analytical solution, and C 2 With C 4 The analytical solution is about θ 2 and θ 4 expression.

[0135] The compensation capacitance C of the 2nd and 4th coils will be solved 2 With C 4 Substituting into the existing coil current expression, the purpose of eliminating the compensation capacitor parameters can be achieved. Then the new coil current expression I T Substitute the voltage equations of the 1st, 3rd and 5th coil loops to solve for the compensation capacitor C 1 , C 3 With C 5 The analytical solution of C 1 , C 3 With C 5 The analytical solution is about θ 2 and θ 4 expression.

[0136] (6) Step S6

[0137] The coil current and the compensation capacitor are both related to the current phase θ 2 and θ 4 have a clear mathematical analytical relationship, where the coil current before conversion is restored according to the phase conversion matrix T:

[0138] I(θ 2 ,θ 4 ) = T(θ 2 ,θ 4 )I T

[0139] Based on the system impedance matrix, the induced coupling voltages in the coil circuits at all levels are:

[0140] G ij (θ 2 ,θ 4 ) = Z ij (θ 2 ,θ 4 )I j (θ 2 ,θ 4 )

[0141] In the above formula, I j represents the coil current at the j-th level, and G ij represents the induced voltage of the j-th coil in the i-th coil.

[0142] Furthermore, the power calculation formula for the coil circuits at all levels is obtained:

[0143] P ij (θ 2 ,θ 4 ) = real(G ij (θ 2 ,θ 4 )I i * (θ 2 ,θ 4 ))

[0144] Among them, I i * is the conjugate of the coil current at the i-th level, and P ij represents the active power flow exchanged between the j-th coil and the i-th coil. The power flow is an expression regarding the variables θ 2 and θ 4 . According to the quantitative relationship between the power distribution of the coil circuits at all levels and the current phase, the energy flow regulation of the multi-stage magnetic resonance WPT system can be achieved by configuring the current phase. The system efficiency is calculated based on the input and output powers:

[0145]

[0146] Among them, R Leq is the AC equivalent load at the receiving end, and U inv is the AC voltage of the inverter output. It can be seen that the input, output power and transmission efficiency of the system are also expressions related to the variables θ 2 and θ 4 . By changing the values of θ 2 and θ 4 , the transmission power and efficiency of the system can be regulated.

[0147] (7) Experimental simulation

[0148] In order to verify the effectiveness of the energy flow regulation method provided by the present invention, numerical simulation verification is carried out below for a 5-level magnetic resonance WPT system.

[0149] The parameters of the 5-level magnetic resonance WPT system, such as the self-inductance, mutual inductance, system operating frequency, DC input voltage, etc. of the coils are shown in Table 1.

[0150] Table 1

[0151]

[0152] From the foregoing derivation, it is known that there is a quantitative relationship between the current phases of the second and fourth-level coils and the system power and efficiency, and the configuration of the current phases is realized by adjusting the compensation capacitors of each coil circuit. Based on the reverse solution process of energy flow → current phase → compensation capacitor, taking the current phase as the intermediate quantity, the compensation capacitors that meet the system power and efficiency requirements are finally found to achieve the energy flow regulation of the system. Therefore, under different current phase configurations, according to the method of the present invention, the compensation capacitors of each coil, the currents of each coil, the input and output powers, and the power flow conditions between each coil can be calculated in sequence.

[0153] As a comparison, first, according to the traditional tuning method, i.e., C i = 1 / ω 2 L i , the compensation capacitors of each coil are calculated as C 1 = 3.73e-09, C 2 = 3.67e-09, C 3 = 3.68e-9, C 4 = 3.75e-09, C 5 = 3.71e-09, and the corresponding currents of each coil are I 1 = 0.7888 + 0.1588i, I 2 = 0.2135 - 0.9956i, I 3 = -0.6907 - 0.4150i, I 4 = -0.5671 + 0.7941i, I 5= 0.5392 + 0.6269i, and its phase relationship is as Figure 3 shown. At this time, the input power of the system is 21.3 W, the output power is 20.5 W, the AC / AC (alternating current to alternating current) transmission efficiency is 96.2%, and the power flow between each coil is as Figure 4 shown. As can be seen from Figure 4 , according to the traditional tuning method, both the 4th and 5th coils send active power back to the 1st coil, and the 5th coil also sends active power back to the 2nd coil at the same time, resulting in a decrease in the system output power. In addition, by changing the load value, the system output voltage curve under the load change of 20 - 100 Ω is obtained, as Figure 5 shown, and it can be seen that the system cannot achieve zero phase angle input and constant voltage output.

[0154] In order to configure the current phases of the 1st to 5th coils to be θ 1 = 0°, θ 2 = -30°, θ 3 = -90°, θ 4 = -150°, θ 5 = -180°, according to the system parameter values in Table 1, the compensation capacitors of each coil are calculated as C 1 = 3.19e-09, C 2 = 3.52e-09, C 3 = 7.91e-10, C 4 = 3.62e-09, C 5 = 3.11e-09, and the current of each coil is I 1 = 1.0172 + 0.0000i, I 2 = 1.5473 - 0.8934i, I 3 = 0.0000 - 0.0615i, I 4 = -1.5913 - 0.9188i, I 5 = -0.9270 - 0.0000i, and its phase relationship is as Figure 6 shown, and the system realizes zero phase angle input. At this time, the input power of the system is 27.5 W, the output power is 25.8 W, the AC / AC transmission efficiency is 93.8%, and the power flow between each coil is as Figure 7 shown. As can be seen from Figure 7 , in this current phase configuration, the active power of each coil always transmits from the previous stage to the next stage, and there is no active power feedback. In addition, by changing the load value, the system output voltage curve under the load change of 20 - 100 Ω is obtained, as Figure 8 shown, and it can be seen that the change range of the system output voltage is only 1.7 V, indicating that the system also has the characteristic of constant voltage output.

[0155] For configuring the current phases of the first - fifth - level coils to be θ 1 = 0°, θ 2 = - 45°, θ 3 = - 90°, θ 4 = - 135°, θ 5 = - 180°, according to the system parameter values in Table 1, the compensation capacitors of each - level coil calculated are C 1 = 3.42e - 09, C 2 = 3.32e - 09, C 3 = 2.57e - 9, C 4 = 3.41e - 09, C 5 = 3.38e - 09, and the currents of each - level coil are I 1 = 0.9800+0.0000i, I 2 = 0.7964-0.7964i, I 3 = 0.0000-0.4659i, I 4 = - 0.8186-0.8186i, I 5 = - 0.9227+0.0000i, and their phase relationships are as Figure 9 shown. The system realizes zero - phase - angle input. At this time, the input power of the system is 26.5W, the output power is 25.5W, and the AC / AC transmission efficiency is 96.5%. The power flow conditions between each - level coil are as Figure 10 shown. It can be seen from Figure 10 that under this current - phase configuration, the active power of each - level coil always transmits from the previous level to the next level, and there is no situation of reverse active - power transmission. In addition, by changing the load value, the system output - voltage curve under the load variation from 20 - 100Ω is obtained, as Figure 11 shown. It can be seen that the variation range of the system output voltage is 0.8V, indicating that the system has the characteristic of constant - voltage output at the same time.

[0156] For configuring the current phases of the first - fifth - level coils to be θ 1 = 0°, θ 2 = - 60°, θ 3 = - 90°, θ 4 = - 120°, θ 5 = - 180°, according to the system parameter values in Table 1, the compensation capacitors of each - level coil calculated are C 1 = 3.59e - 09, C 2 = 2.91e - 09, C 3 = 3.24e - 9, C 4 = 2.99e - 09, C 5 = 3.56e - 09, and the currents of each - level coil are I 1= 0.9540 + 0.0000i, I 2 = 0.3643 - 0.6310i, I 3 = 0.0000 - 1.1558i, I 4 = -0.3717 - 0.6438i, I 5 = -0.9117 + 0.0000i, and its phase relationship is as Figure 12 shown. It can be seen that the system achieves zero-phase-angle input. At this time, the input power of the system is 25.8 W, the output power is 24.9 W, and the AC / AC transmission efficiency is 96.8%. The power flow situation between each stage of coils is as Figure 13 shown. From Figure 13 it can be seen that under this current phase configuration, the active power of each stage of coils is always transmitted from the previous stage to the next stage, and there is no situation of reverse active power transmission. In addition, by changing the load value, the system output voltage curve under the load change from 20 - 100 Ω is obtained, as Figure 14 shown. It can be seen that the variation range of the system output voltage is 0.5 V, indicating that the system has the characteristic of constant-voltage output at the same time.

[0157] Comparing the coil currents and energy flow distribution results of the above three phase configurations, it can be seen that as the phase difference between I 1 and I 2 , I 4 and I 5 increases, the current amplitude of I 2 and I 4 gradually decreases, and the amplitude of I 3 gradually increases; the active power transmitted from the first-stage coil to the second-stage coil gradually decreases, the active power transmitted from the first-stage coil to the third-stage coil gradually increases, and the active power transmitted from the first-stage coil to the fourth and fifth-stage coils gradually decreases; the active power transmitted from the second-stage coil to the third-stage coil gradually increases, and the active power transmitted from the second-stage coil to the fourth and fifth-stage coils gradually decreases; the active power transmitted from the third-stage coil to the fourth and fifth-stage coils gradually increases; the active power transmitted from the fourth-stage coil to the fifth-stage coil gradually decreases. Therefore, by configuring the phase of the current of each stage of coils, not only zero-phase-angle input and constant-voltage output are achieved, but also the magnitude of the energy flow transmitted by each stage of coils can be effectively regulated, and the transmission efficiency and transmission power of the system can be adjusted. As Figure 15 and Figure 16 shown, the maximum AC / AC transmission efficiency of the system can reach 97.3% and the maximum transmission power can reach 25.8 W.

[0158] In summary, the energy flow regulation method for a multi-stage magnetic resonance WPT system based on current phase configuration provided by the embodiments of the present invention preset the current phases of each stage of coils, transfer the current phase relationship to the equivalent impedance matrix, and based on constructing an equivalent impedance replacement matrix that satisfies the voltage-current relationship of the multi-stage system, inversely deduce the expressions of the currents of each stage of coils. At the same time, the mathematical relationship between the compensation capacitors of each stage of coils and the variables to be optimized is analyzed, which not only makes the system in a resonant state but also avoids the reverse transmission of active power, realizes the zero-phase angle input at the transmitting end and the constant-voltage output characteristic at the receiving end, and effectively improves the transmission power and transmission efficiency of the system.

[0159] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A method for controlling energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration, wherein the multi-stage magnetic resonance WPT system comprises a transmitting coil loop, n-2 relay coil loops and a receiving coil loop arranged in sequence, characterized in that: The energy flow control method comprises the steps of: S1. Establish the circuit impedance model U=ZI of the multi-stage magnetic resonance WPT system, where U and I represent the voltage matrix and current matrix composed of the voltage and current of each stage coil respectively, and Z is the impedance matrix describing the impedance relationship between the n-stage magnetic resonance coils; S2, determining the phases of some relay coils as variables to be optimized, and presetting the current phases of the remaining coils as constants; S3. Perform phase decomposition on the coil currents at each level to obtain the corresponding phase conversion matrix T, and obtain the equivalent impedance matrix Z based on the phase conversion matrix T. T = ZT and converted current matrix I T =T -1 I; S4, based on I T Each current phase in the T The elements or the real part of the elements or the imaginary part of the elements at the corresponding positions construct the permutation matrix Z T0 , based on Z T0 The current expression of each coil is obtained as I T =Z T0 -1 U; S5. Construct the voltage equation of the n-level coil loop and solve for Z T The coil loop voltage equation corresponding to the element term of compensation capacitance in the real and imaginary parts is obtained, and the corresponding compensation capacitance analytical solution is substituted into I T =Z T0 -1 U obtains a new coil current expression, substitutes the new coil current expression into the remaining coil loop voltage equations, and solves the analytical solutions for the remaining compensation capacitors; S6. Based on the currently determined information, a relationship between the coil loop power at each level, the system transmission efficiency and the variables to be optimized is obtained, and based on the relationship, the coil loop power at each level and the system efficiency are regulated by configuring the variables to be optimized.

2. According to the method for controlling energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration according to claim 1, it is characterized in that: The step S2 specifically includes the following steps: S21, taking the AC input voltage of the transmitting coil loop as the reference 0 phase, the transmitting coil current phase is set to 0 ° ; S22. When the system requires constant voltage output, the current phase of the receiving coil is set to 0 ° or -180 ° ; When the system requires constant current output, the current phase of the receiving coil is set to 90 ° or -90 ° ; S23, set the current phase of some relay coils to 0 ° , 90 ° 、-90 ° or -180 ° , the current phase of the remaining relay coils is the variable to be optimized θ k .

3. According to claim 2, a method for controlling energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration is characterized in that: In step S3, the phase conversion matrix T is composed of the phase conversion coefficients of the coils at each level, and the phase conversion coefficients of the coils at each level are taken according to the following rules: Phase is 0 ° , 90 ° 、-90 ° , -180 ° The conversion coefficient corresponding to the coil current is 1, that is, the phase of the coil current remains unchanged before and after the conversion; Phase is θ k and 0 ° <|θ k |<90 ° The conversion coefficient corresponding to the coil current is c°sθ k +jsinθ k , after conversion, the coil current phase is 0 ° ; Phase is θ k And 90 ° <|θ k |<180 ° The conversion coefficient of the coil current is -cos(180 ° -θ k )+jsin(180 ° -θ k ), the coil current phase is 0 after conversion ° .

4. According to claim 3, a method for controlling energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration is characterized in that: In step S4, construct the permutation matrix Z T0 The rules are: Extract the equivalent impedance matrix Z T The real part of the diagonal elements is used as the permutation matrix Z T0 The diagonal elements of For the current phase to be 0 ° and -180 ° The coil loop, when the phase of the coil current coupled to it is also 0 ° and -180 ° When the equivalent impedance matrix Z is extracted T The real part of the corresponding element is used as the permutation matrix Z T0 The elements at the corresponding positions; when the phase of the coil current coupled to it is 90 ° and -90 ° When the equivalent impedance matrix Z is extracted T The imaginary part of the corresponding element is used as the permutation matrix Z T0 The elements at the corresponding positions; For current phase 90 ° and -90 ° The coil loop, when the phase of the coil current coupled to it is 0 ° and -180 ° When the equivalent impedance matrix Z is extracted T The imaginary part of the corresponding element is used as the permutation matrix Z T0 The elements at the corresponding positions; when the phase of the coil current coupled to it is also 90 ° and -90 ° When the equivalent impedance matrix Z is extracted T The real part of the corresponding element is used as the permutation matrix Z T0 The element at the corresponding position.

5. According to claim 4, a method for controlling energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration is characterized in that: In step S6, based on the currently determined information, a relationship between the power of each coil loop and the variable to be optimized is obtained, which is specifically: According to the phase conversion matrix T and the new coil current expression I T The coil current matrix before conversion is restored to I = TI T ; The column elements in the impedance matrix Z are multiplied by the row elements in the current matrix I, and then multiplied by the conjugate of each coil loop current to obtain the power expression of the coupling between each coil loop.

6. A method for controlling energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration according to any one of claims 1 to 5, characterized in that: The compensation capacitor of each coil loop is connected in series with the coil of that level.

7. The method for controlling energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration according to claim 6 is characterized in that: In step S1 , the voltage matrix U is a column vector composed of coil voltages at each level, and the current matrix I is a column vector composed of coil currents at each level.

8. The method for controlling energy flow of a multi-stage magnetic resonance WPT system based on current phase configuration according to claim 7 is characterized in that: In step S1, the impedance matrix Z is an n×n square matrix, and the element Z in the i-th row and j-th column is ij The value selection rules are: When i=j≠n, Z ij Equal to R i +j(ωL i -1 / ωC i ); When i=j=n, Z ij Equal to R n +j(ωL n -1 / ωC n )+R Leq ; When i≠j, Z ij Equal to jωM ij ; Where ω represents the operating angular frequency of the system, I i , R i , L i , C i It represents coil current, internal resistance, inductance and compensation capacitance of each level in turn. ij represents the mutual inductance between the i-th coil and the j-th coil, R Leq Represents the AC equivalent load at the receiving end, i,j=1,2,…,n.

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