A method for fast calculation of core loss of permanent magnet synchronous motor considering high frequency current harmonics

Abstract

The present invention discloses a method for rapidly calculating the core loss of a permanent magnet synchronous motor considering high-frequency current harmonics, determining the operating range of the permanent magnet motor to be analyzed, regularly sampling the current and rotor position within the operating range, and then performing finite element calculation to obtain the vector magnetic potential of the triangular unit node, thereby constructing a sample matrix; performing singular value decomposition on the sample matrix to obtain the standard orthogonal basis of the reduced-order model; calculating the motor core unit magnetic density at different rotor positions under fundamental current based on the standard orthogonal basis of the reduced-order model; obtaining the differential magnetic permeability according to the motor core unit magnetic density at different rotor positions under fundamental current, and then obtaining the motor core unit magnetic density at different rotor positions under high-frequency current by frequency domain finite element method; calculating the core loss using a modified core loss formula according to the motor core unit magnetic density at different rotor positions under fundamental current and high-frequency current. The present invention can effectively improve the solution speed and accuracy.

Description

Technical Field

[0001] The invention belongs to the application field of motor electromagnetic loss calculation, and in particular relates to a method for quickly calculating the core loss of a permanent magnet synchronous motor taking high-frequency current harmonics into consideration. Background Art

[0002] Permanent magnet motors are widely used in aerospace, electric vehicles, and CNC machine tools due to their high efficiency and high power density. In order to accurately predict the efficiency and temperature field of permanent magnet motors, it is necessary to calculate the core loss accurately and quickly.

[0003] Traditional finite element simulation analyzes the input sinusoidal current and predicts some electromagnetic characteristics of permanent magnet motors, such as torque and core saturation. However, the current output by the pulse width modulated voltage source inverter contains not only the fundamental sinusoidal current, but also rich high-frequency harmonics. Although the amplitude of the high-frequency harmonics is lower than the fundamental component, due to its extremely high frequency, the additional core loss caused by the current harmonics cannot be ignored. The field-circuit coupled time-stepping finite element method can calculate the core loss caused by high-frequency current harmonics. However, according to the Nyquist-Shannon sampling theorem, the current sampling frequency of the pulse width modulated voltage source inverter output should be greater than twice the highest frequency of the current harmonics with greater influence, which requires the solution step size in the field-circuit coupled time-stepping finite element to be set very small, thereby increasing the solution time and memory resource usage. Summary of the invention

[0004] In view of the shortcomings in the prior art, the present invention provides a method for quickly calculating the core loss of a permanent magnet synchronous motor taking into account high-frequency current harmonics. The method can not only effectively improve the solution speed, but also combines the improved core loss formula to achieve the accuracy of the permanent magnet synchronous motor core loss calculation.

[0005] The present invention achieves the above technical objectives through the following technical means.

[0006] A method for quickly calculating the core loss of a permanent magnet synchronous motor considering high-frequency current harmonics:

[0007] Determine the operating range of the permanent magnet motor to be analyzed, regularly sample the current and rotor position within the operating range, perform finite element calculations, obtain the vector magnetic potential of the triangular unit nodes, and construct a sample matrix;

[0008] Performing singular value decomposition on the sample matrix to obtain a standard orthogonal basis of the reduced-order model;

[0009] The magnetic flux density of the motor core unit at different rotor positions under fundamental current is calculated based on the standard orthogonal basis of the reduced-order model;

[0010] The differential magnetic permeability is obtained according to the magnetic flux density of the motor core unit at different rotor positions under fundamental current, and then the magnetic flux density of the motor core unit at different rotor positions under high-frequency current is obtained by using the frequency domain finite element method;

[0011] According to the motor core unit magnetic density at different rotor positions under fundamental current and the motor core unit magnetic density at different rotor positions under high-frequency current, the core loss is accurately calculated based on the modified core loss formula.

[0012] A further technical solution is to perform singular value decomposition on the sample matrix, specifically:

[0013] X m,n =U m,m Λ m,n W n,n T

[0014] Among them, X m,n represents a sample matrix with m rows and n columns, m represents the number of nodes of the finite element triangle unit, and n represents the number of sampling times; U m,m represents the left singular value vector matrix, Λ m,n is the singular value matrix, W n,n T represents the matrix of right singular value vectors.

[0015] A further technical solution is to select the left singular value vector matrix U m,m The first q column vectors of are used as the standard orthogonal basis of the reduced-order model.

[0016] A further technical solution is to calculate the motor core unit magnetic flux density at different rotor positions under fundamental current based on the standard orthogonal basis of the reduced-order model. Specifically, the right singular value vector matrix W n,n T Interpolation is performed to obtain the solution of the vector magnetic potential in the reduced-dimensional space, and then the standard orthogonal basis U of the reduced-order model is obtained by left-multiplying m,q and the singular value matrix Λ q,q , obtain the column vector of the magnetic potential of all nodes of the triangular unit in the original space, calculate the curl of the column vector of the magnetic potential of all nodes of the triangular unit, and obtain the magnetic density of the motor core unit at different rotor positions under the fundamental current; the singular value matrix Λ q,q Take Λ m,n The first q rows and q columns of .

[0017] A further technical solution is to obtain the motor core unit magnetic flux density at different rotor positions under high-frequency current by using the frequency domain finite element method, specifically:

[0018] The vector magnetic potential of the permanent magnet motor core region is determined by the differential magnetic permeability and the column vector of the vector magnetic potential and expressed in a two-dimensional Cartesian coordinate system, and then the weak form of the vector magnetic potential in the two-dimensional Cartesian coordinate system is solved by the weighted residual method;

[0019] The high frequency current is expressed in complex form and based on the weak form, a complex finite element equation group is obtained, and then the complex finite element method equation group is solved to obtain a complex vector magnetic potential;

[0020] The rotation of the complex vector magnetic potential is calculated to obtain the motor core unit magnetic density at different rotor positions under high-frequency current.

[0021] In a further technical solution, the modified core loss formula is:

[0022]

[0023] Among them, P core represents the core loss, f represents the frequency of the magnetic flux density of the motor core unit of each order, B m Indicates the amplitude of the magnetic flux density of the motor core unit of each order, k h , a, b and c are coefficients related to the hysteresis loss term, d represents the thickness of the core lamination, Δ represents the skin depth, k c is the eddy current loss coefficient, k e is the eddy current loss coefficient.

[0024] The beneficial effects of the present invention are:

[0025] (1) The present invention calculates the motor core unit magnetic flux density at different rotor positions under fundamental current based on the standard orthogonal basis of the reduced-order model, and can quickly obtain the motor core unit magnetic flux density at different rotor positions under fundamental current;

[0026] (2) The present invention adopts a frequency domain method based on differential magnetic permeability when calculating the magnetic flux density of the motor core unit at different rotor positions under high-frequency current, avoiding the need for extremely small time steps in the time domain finite element method to identify high-frequency current harmonics, thereby improving the solution speed;

[0027] (3) The present invention uses an improved core loss formula for calculation, and the core loss of the permanent magnet synchronous motor can be predicted more accurately when facing high-frequency effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a schematic diagram of the structure of the high-speed permanent magnet synchronous motor of the present invention;

[0029] Figure 2 The present invention uses the improved core loss formula to calculate the core material loss of the permanent synchronous motor and compares it with the experimental measurement value;

[0030] Figure 3 A flow chart of a method for rapidly calculating the core loss of a permanent magnet synchronous motor taking high-frequency current harmonics into consideration according to the present invention;

[0031] In the figure: 1- stator core, 2- rotor core, 3- stator teeth, 4- armature winding, 5- permanent magnet, 6- rotor sleeve. DETAILED DESCRIPTION

[0032] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0033] like Figure 3 As shown, the present invention provides a method for quickly calculating the core loss of a permanent magnet synchronous motor taking into account high-frequency current harmonics, which specifically includes the following steps:

[0034] Step (1) determines the operating range of the permanent magnet motor to be analyzed, that is, the current range and the rotor position range, and then regularly samples the current and rotor position within the operating range, and then performs finite element calculation to obtain the vector magnetic potential of the triangular unit node, thereby constructing a sample matrix.

[0035] like Figure 1 As shown, the permanent magnet motor analyzed in this embodiment is a high-speed permanent magnet synchronous motor, including a stator core 1, an armature winding 4, an air gap, a rotor sleeve 6, a rotor core 2 and a permanent magnet 5; the stator core 1 includes 48 stator teeth 3; the armature winding 4 adopts a single-layer distributed winding; the air gap is located between the stator and the rotor, wherein the air gap length is 1 mm, and the rotor sleeve 6 thickness is 0.5 mm; 8 permanent magnets 5 are installed on the surface of the rotor core 2, and the rotor sleeve 6 is sleeved on the permanent magnet 5; the material of the stator core 1 is JFE_10JNEX900, the material of the rotor core 2 is DT4C, and the material of the permanent magnet 5 is samarium cobalt.

[0036] The parameters of regular sampling are: sampling current range is 0-90A, sampling current interval is 10A, sampling position range is 0-360° electrical angle, and sampling position interval is 15°.

[0037] Step (2), performing singular value decomposition on the sample matrix by using the eigenorthogonal decomposition method to obtain the standard orthogonal basis of the reduced-order model.

[0038] Perform singular value decomposition on the sample matrix:

[0039] X m,n =U m,m Λ m,n W n,n T (1)

[0040] Among them, X m,nrepresents a sample matrix with m rows and n columns, m represents the number of nodes of the finite element triangle unit, and n represents the number of sampling times; U m,m represents the left singular value vector matrix, Λ m,n is the singular value matrix, W n,n T represents the right singular value vector matrix, the right singular value vector matrix W n,n T Each column of is regarded as the solution vector of the node vector magnetic potential of the triangular element under a certain working condition in the reduced-order space.

[0041] Then select the left singular value vector matrix U m,m The first q column vectors of are used as the standard orthogonal basis of the reduced-order model. The selection principle is that for the singular value matrix Λ m,n For example, the first q singular values ​​account for more than 99% of the total singular values. This can retain most of the characteristics of the motor model system and help improve the accuracy of the model.

[0042] Step (3), performing fast Fourier decomposition on the current output by the pulse width modulation voltage source inverter to obtain fundamental current and high-frequency current, and respectively solving the magnetic flux density of the motor core unit at different rotor positions under fundamental current and high-frequency current.

[0043] The working condition of the permanent magnet motor is determined according to the magnitude of the fundamental current. For this working condition, the right singular value vector matrix W n,n T Interpolation is performed to obtain the solution of the vector magnetic potential in the reduced-dimensional space, and then the standard orthogonal basis U of the reduced-order model is obtained by left-multiplying m,q and the singular value matrix Λ q,q (Take Λ m,n The first q rows and q columns of the vector are used to obtain the solution of the vector magnetic potential of all nodes of the triangular element in the original space.

[0044] For this condition, W n,n T Interpolation, get the solution of the vector magnetic potential in the reduced dimensional space f q , and then use the following formula to quickly get the solution of the vector magnetic potential of all nodes of the triangular element in the original space:

[0045] A=U m,q Λ q，q f q (2)

[0046] Where A represents the column vector of the magnetic potential of all nodes of the triangular element.

[0047] By calculating the curl of the column vector A of the vector magnetic potential of all nodes of the triangular unit, the motor core unit magnetic density at different rotor positions under the fundamental current can be obtained. The differential magnetic permeability is obtained based on the motor core unit magnetic density at different rotor positions under the fundamental current, and then the motor core unit magnetic density at different rotor positions under high-frequency current is obtained by the frequency domain finite element method.

[0048] The differential magnetic permeability is obtained by the following formula:

[0049]

[0050] Among them, γ represents the differential permeability, v represents the magnetic resistivity of each core unit, and B x It represents the component of the magnetic flux density of the motor core unit along the x-axis direction, B y It represents the component of the magnetic flux density of the motor core unit along the y-axis direction, and B represents the total magnetic flux density of the motor core unit.

[0051] Then, based on the differential magnetic permeability, the frequency domain finite element method is used to quickly calculate the motor core magnetic flux density at different rotor positions under high-frequency current excitation; the specific method is as follows:

[0052] The vector magnetic potential of the permanent magnet motor core area is determined by the differential magnetic permeability γ and the column vector A of the vector magnetic potential:

[0053]

[0054] In a two-dimensional Cartesian coordinate system, equation (4) can be expressed as:

[0055]

[0056] Using the weighted residual method, the weak form of equation (4) is obtained as:

[0057]

[0058] Where W is a weight function, for which the shape function of the unit is usually selected, and G represents the integration area;

[0059] The high-frequency current is expressed in complex form and based on the above weak form, a complex finite element equation system is obtained. Then, the complex finite element method equation system is solved to obtain the complex vector magnetic potential The complex vector magnetic potential is expressed in the time domain as:

[0060]

[0061] Where, ω is the angular frequency of the high-frequency current, A R and A I are the real and imaginary components of the complex vector magnetic potential, and t represents time.

[0062] Complex vector magnetic potential By calculating the curl, we can get the magnetic flux density of the motor core unit at different rotor positions under high-frequency current.

[0063] Step (4), according to the motor core unit magnetic density at different rotor positions under fundamental current and the motor core unit magnetic density at different rotor positions under high-frequency current, a revised core loss calculation formula is introduced to accurately calculate the core loss;

[0064] The corrected core loss calculation formula is:

[0065]

[0066] Among them, P core represents the core loss, f represents the frequency of the magnetic flux density of the motor core unit of each order, B m Indicates the amplitude of the magnetic flux density of the motor core unit of each order, k h , a, b and c are coefficients related to the hysteresis loss term, d represents the thickness of the core lamination, Δ represents the skin depth, k c is the eddy current loss coefficient, k e is the eddy current loss coefficient.

[0067] Figure 2 The display shows the comparison between the core loss calculated by the improved core loss formula for the permanent synchronous motor and the experimental measured value. It can be seen that the core loss value calculated by the improved core loss formula of the present invention is closer to the experimental measured value.

[0068] Step (5), by using traditional finite element software, the calculated core loss results are compared to verify the effectiveness of the present invention. Table 1 shows the comparison between the method proposed in the present invention and the traditional finite element results. It can be found that the core loss results of the permanent magnet motor calculated by the method proposed in the present invention and the traditional finite element method are close, and the calculation speed is very fast.

[0069] Table 1 Comparison of the proposed method and traditional finite element results

[0070]

[0071] Table 2 compares the core loss calculated by the method of the present invention with the experimental measurement value. It can be found that the proposed method is very close to the experimental result, indicating that the core loss calculated by the method of the present invention has good accuracy.

[0072] Table 2 Comparison of core loss calculated by the method of the present invention and experimental measurement value

[0073]

[0074]

[0075] The embodiments are preferred implementations of the present invention, but the present invention is not limited to the above-mentioned implementations. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essential content of the present invention belong to the protection scope of the present invention.

Claims

1. A method for quickly calculating the core loss of a permanent magnet synchronous motor taking into account high-frequency current harmonics, characterized in that: Determine the operating range of the permanent magnet motor to be analyzed, regularly sample the current and rotor position within the operating range, perform finite element calculations, obtain the vector magnetic potential of the triangular unit nodes, and construct a sample matrix; Performing singular value decomposition on the sample matrix to obtain a standard orthogonal basis of the reduced-order model; The motor core unit magnetic flux density at different rotor positions under fundamental current is calculated based on the standard orthogonal basis of the reduced-order model; specifically: for the right singular value vector matrix W n,n T Interpolation is performed to obtain the solution of the vector magnetic potential in the reduced-dimensional space, and then the standard orthogonal basis U of the reduced-order model is obtained by left-multiplying m,q and the singular value matrix Λ q,q , obtain the column vector of the magnetic potential of all nodes of the triangular unit in the original space, calculate the curl of the column vector of the magnetic potential of all nodes of the triangular unit, and obtain the magnetic density of the motor core unit at different rotor positions under the fundamental current; the singular value matrix Λ q,q Take Λ m,n The first q rows and q columns of ; The differential magnetic permeability is obtained according to the magnetic flux density of the motor core unit at different rotor positions under fundamental current, and then the magnetic flux density of the motor core unit at different rotor positions under high-frequency current is obtained by using the frequency domain finite element method; According to the motor core unit magnetic density at different rotor positions under fundamental current and the motor core unit magnetic density at different rotor positions under high-frequency current, the core loss is accurately calculated based on the modified core loss formula; The performing singular value decomposition on the sample matrix is ​​specifically as follows: X m,n =U m,m Λ m,n W n,n T Among them, X m,n represents a sample matrix with m rows and n columns, m represents the number of nodes of the finite element triangle element, and n represents the number of sampling times; U m,m represents the left singular value vector matrix, Λ m,n is the singular value matrix, W n,n T represents the matrix of right singular value vectors.

2. The method for rapidly calculating the core loss of a permanent magnet synchronous motor taking into account high-frequency current harmonics according to claim 1 is characterized in that: Select the left singular value vector matrix U m,m The first q column vectors of are used as the standard orthogonal basis of the reduced-order model.

3. The method for rapidly calculating the core loss of a permanent magnet synchronous motor taking into account high-frequency current harmonics according to claim 2 is characterized in that: The motor core unit magnetic flux density at different rotor positions under high-frequency current is obtained by the frequency domain finite element method, specifically: The vector magnetic potential of the permanent magnet motor core region is determined by the differential magnetic permeability and the column vector of the vector magnetic potential and expressed in a two-dimensional Cartesian coordinate system, and then the weak form of the vector magnetic potential in the two-dimensional Cartesian coordinate system is solved by the weighted residual method; The high frequency current is expressed in complex form and based on the weak form, a complex finite element equation group is obtained, and then the complex finite element method equation group is solved to obtain a complex vector magnetic potential; The rotation of the complex vector magnetic potential is calculated to obtain the motor core unit magnetic density at different rotor positions under high-frequency current.

4. The method for rapidly calculating the core loss of a permanent magnet synchronous motor taking into account high-frequency current harmonics according to claim 3 is characterized in that: The modified core loss formula is: Among them, P core represents the core loss, f represents the frequency of the magnetic flux density of the motor core unit of each order, B m Indicates the amplitude of the magnetic flux density of the motor core unit of each order, k h , a, b and c are coefficients related to the hysteresis loss term, d represents the thickness of the core lamination, Δ represents the skin depth, k c is the eddy current loss coefficient, k e is the eddy current loss coefficient.

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