Method for calculating frequency conversion power supply loss of permanent magnet synchronous motor

Abstract

The invention belongs to the technical field of motors, and provides a method for calculating variable-frequency power supply loss of a permanent magnet synchronous motor, which comprises the following steps of: S1, establishing a finite element simulation model of the motor by utilizing simulation software, and taking sinusoidal current as excitation; s2, extracting a three-phase flux linkage in an electric period, and calculating quadrature-axis and direct-axis incremental inductances; s3, calculating the loss of the motor according to a simulation result, and calculating a loss coefficient in combination with a flux linkage; s4, calculating harmonic flux linkage under PWM harmonic voltage power supply according to a simulation result; and S5, calculating the variable-frequency power supply loss of the motor by combining the harmonic flux linkage, the loss coefficient and the frequency. The invention discloses a built-in permanent magnet synchronous motor variable-frequency power supply loss rapid calculation method based on quadrature-axis and direct-axis equivalent circuits, and aims to calculate the loss of a built-in permanent magnet synchronous motor in a variable-frequency power supply mode in a short time and ensure the accuracy of a calculation result.

Description

Technical Field

[0001] This invention belongs to the field of motor technology, and in particular relates to a rapid calculation method for the frequency conversion power supply loss of a built-in permanent magnet synchronous motor based on the equivalent circuits of quadrature axis and direct axis. Background Technology

[0002] Built-in permanent magnet synchronous motors have a wide operating range and are typically powered by pulse width modulation (PWM) voltage. PWM voltage contains numerous high-frequency harmonics, which generate significant losses during motor operation. Calculating the losses introduced by PWM harmonic voltage helps in optimizing motor efficiency during the initial design phase.

[0003] In the existing technology, accurately calculating PWM harmonic losses requires finite element simulation of the motor with extremely small step sizes, which takes a lot of time and reduces the efficiency of the motor design process.

[0004] Therefore, considering that harmonic magnetic fields have a relatively small impact on the saturation of the motor's magnetic circuit, the commonly used method for calculating frequency conversion losses is the small-signal method. First, the fundamental sinusoidal current is used as the excitation to solve for the incremental permeability of the motor's magnetic circuit in each region. Then, the PWM harmonic voltage is treated as a small signal, and the response of each frequency harmonic in the magnetic circuit is calculated, and the losses are further calculated. Finally, the losses calculated at each harmonic frequency are superimposed to obtain the total loss introduced by the PWM harmonics, which is then added to the loss under the fundamental power supply to obtain the motor's loss under frequency conversion power supply. However, this method requires multiple permeability freezes and still takes considerable time. Summary of the Invention

[0005] To address the aforementioned technical problems, this application proposes a method for calculating the power supply loss of a permanent magnet synchronous motor via frequency conversion. The specific technical solution is as follows:

[0006] This application provides a rapid calculation method for the frequency conversion power supply loss of a built-in permanent magnet synchronous motor based on quadrature-axis and direct-axis equivalent circuits. The calculation method includes the following steps:

[0007] S1. Establish a finite element simulation model of the motor using simulation software, and use sinusoidal current as excitation.

[0008] S2. Extract the three-phase flux linkage within one electrical cycle and calculate the quadrature-axis and direct-axis incremental inductances;

[0009] S3. Calculate the motor losses based on the simulation results, and calculate the loss coefficient in combination with the flux linkage;

[0010] S4. Calculate the harmonic flux under PWM harmonic voltage power supply based on the simulation results;

[0011] S5. Calculate the motor frequency converter power supply loss by combining harmonic flux linkage, loss coefficient and frequency.

[0012] In some implementations, the order of steps S3 and S4 can be interchanged.

[0013] Furthermore, the motor losses in step S3 include:

[0014] Stator core hysteresis loss P s,hy The calculation formula is:

[0015]

[0016] In the above formula, k hy Let b be the hysteresis loss coefficient of silicon steel sheet material. s,i f is the amplitude of the i-th order magnetic flux density in the stator. s,i Let be the alternating frequency of the i-th order magnetic flux density in the stator core;

[0017] Stator core eddy current loss P s,ed The calculation formula is:

[0018]

[0019] In the above formula, k sc,i To account for the correction factor of eddy current effect in the stator core, k ed The eddy current loss coefficient of silicon steel sheet material;

[0020] Rotor core eddy current loss P r,ed The calculation formula is:

[0021]

[0022] In the above formula, k rc,i To account for the correction factor of eddy current effect in the stator core, b r,i f is the amplitude of the i-th order magnetic flux density in the rotor. r,i Let be the alternating frequency of the i-th order magnetic flux density in the rotor core;

[0023] Permanent magnet eddy current loss P PM,ed The calculation formula is:

[0024]

[0025] In the above formula, B PM,i Let denoted as the amplitude of the i-th harmonic magnetic flux density in the permanent magnet, w as the width of the permanent magnet in the circumferential direction, ξ as the leakage flux coefficient of the permanent magnet, d as the thickness of the permanent magnet in the radial direction, l as the length of the permanent magnet in the axial direction, and σ as the conductivity of the permanent magnet.

[0026] Furthermore, the loss coefficient in step S3 includes:

[0027] Stator core hysteresis loss coefficient k s,hy The calculation formula is:

[0028]

[0029] In the above formula, The stator core hysteresis loss under sinusoidal current excitation. For the i-th order component of the three-phase flux linkage under sinusoidal power supply, f s,i Let be the alternating frequency of the i-th order magnetic flux density in the stator core;

[0030] stator core eddy current loss coefficient k s,ed The calculation formula is:

[0031]

[0032] In the above formula, f is the stator core eddy current loss under sinusoidal current excitation. s,i Let be the alternating frequency of the i-th order magnetic flux density in the stator core;

[0033] Rotor core eddy current loss coefficient k r,ed The calculation formula is:

[0034]

[0035] In the above formula, f is the rotor core eddy current loss under sinusoidal current excitation. r,i Let be the alternating frequency of the i-th order magnetic flux density in the rotor core;

[0036] permanent magnet eddy current loss coefficient k PM,ed The calculation formula is:

[0037]

[0038] In the above formula, This refers to the eddy current loss of a permanent magnet under sinusoidal current excitation.

[0039] Furthermore, the calculation method for harmonic flux linkage in step S4 is as follows:

[0040] S4-1. Calculate the three-phase flux linkage of the motor in one electrical cycle using finite element simulation, and perform fast Fourier transform on the flux linkage to obtain the components of the three-phase flux linkage at each frequency.

[0041] S4-2. Calculate the terminal voltage of the current source under sinusoidal current excitation, perform fast Fourier decomposition on the voltage, and use the amplitude and phase of the fundamental voltage obtained by decomposition to generate pulse width modulation voltage. First, perform Clark transformation and Park transformation on the PWM voltage, and then perform fast Fourier transformation to obtain the order components of the PWM voltage on the quadrature axis and the direct axis.

[0042] S4-3. Establish the quadrature-axis and direct-axis equivalent circuits, establish a set of voltage equations based on the quadrature-axis and direct-axis equivalent circuits, and solve for the harmonic flux under PWM harmonic voltage power supply.

[0043] Furthermore, the equations for solving the quadrature-axis and direct-axis harmonic flux linkages in step S4-3 are as follows:

[0044]

[0045] In the above formula, ψ d ,i is the direct-axis flux linkage under i-th order harmonic voltage excitation, r s L is the stator winding resistance. d For direct-axis incremental inductance, ω h,i Let u be the alternating frequency of the i-th harmonic voltage in the rotor coordinate system. d,i Let ψ be the direct-axis component of the i-th order PWM harmonic voltage. q, i For the quadrature-axis flux linkage under i-th order harmonic voltage excitation, u q,i denoted as the quadrature-axis component of the i-th order PWM harmonic voltage, and p is the number of pole pairs of the motor;

[0046] By superimposing the quadrature-axis and direct-axis harmonic flux linkages of each order, the total quadrature-axis and total direct-axis harmonic flux linkages ψd and ψq under PWM harmonic voltage excitation are obtained.

[0047] Furthermore, the total quadrature axis and total direct axis harmonic flux linkages are transformed into three-phase flux linkages to participate in the calculation of motor frequency converter power supply losses. The transformation of the total quadrature axis and total direct axis harmonic flux linkages into three-phase flux linkages is achieved using the following formula:

[0048]

[0049] In the above formula, ω f ω is the fundamental angular frequency.

[0050] The beneficial effects of this invention are as follows:

[0051] This invention presents a rapid calculation method for the power supply losses of an embedded permanent magnet synchronous motor (PMSM) under variable frequency power supply mode, based on equivalent circuits of quadrature and direct axes. The aim is to calculate the losses of an embedded PMSM in a shorter time. First, the invention calculates the incremental inductances and losses of the motor under fundamental sinusoidal current power supply. Then, it uses equivalent circuits of quadrature and direct axes to calculate the harmonic flux linkage under PWM harmonic voltage power supply, significantly reducing calculation time. Finally, the loss under variable frequency power supply is calculated using the loss coefficient and harmonic flux linkage, ensuring the accuracy of the calculation results. Attached Figure Description

[0052] Figure 1 This is a flowchart of the calculation method of the present invention;

[0053] Figure 2 These are the order components of the PWM voltage on the direct axis;

[0054] Figure 3 These are the order components of the PWM voltage on the quadrature axis;

[0055] Figure 4 Schematic diagrams of equivalent circuits for the perpendicular and direct axes;

[0056] Figure 5 A comparison diagram showing the harmonic flux linkage simulated using finite element method and the harmonic flux linkage calculated in this application;

[0057] Figure 6 A comparison chart showing the actual loss at different operating points and the loss calculated by this method. Detailed Implementation

[0058] In the following description, certain specific details are set forth in order to provide a thorough understanding of various embodiments. However, those skilled in the art will understand that the invention can be practiced without these details. In other instances, well-known structures have not been shown or described in detail to avoid unnecessarily obscuring the description of the embodiments. Unless the context otherwise requires, throughout the specification and appended claims, the word "comprising" should be interpreted in an open-ended, inclusive sense, i.e., as "including but not limited to".

[0059] See Table 1 below for examples, which shows the parameters of an example of a built-in permanent magnet synchronous motor.

[0060]

[0061] Table 1: Parameters of Built-in Permanent Magnet Synchronous Motor

[0062] And, in conjunction with the built-in permanent magnet synchronous motor shown in Table 1, this application details a rapid calculation method for the frequency conversion power supply loss of the built-in permanent magnet synchronous motor, combined with... Figure 1The flowchart shown illustrates that the method includes the following steps:

[0063] S1. Establish a finite element simulation model of the built-in permanent magnet synchronous motor using simulation software. Using sinusoidal current as excitation, calculate the quadrature-direct axis incremental inductance of the motor using the following formula:

[0064]

[0065] Commonly used simulation software includes ANSYS Maxwell, JMAG, AltairFlux, etc.

[0066] The quadrature-axis incremental inductance of the motor calculated using the motor provided in this embodiment is 0.0014H, and the direct-axis incremental inductance is 0.000522H.

[0067] S2. Calculate the stator core hysteresis loss, stator core eddy current loss, rotor core eddy current loss, and permanent magnet eddy current loss.

[0068] Stator core hysteresis loss P s,hy The calculation formula is:

[0069]

[0070] In the above formula, k hy Let b be the hysteresis loss coefficient of silicon steel sheet material. s,i f is the amplitude of the i-th order magnetic flux density in the stator. s,i Let be the alternating frequency of the i-th order magnetic flux density in the stator core;

[0071] Stator core eddy current loss P s,ed The calculation formula is:

[0072]

[0073] In the above formula, k sc,i To account for the correction factor of eddy current effect in the stator core, k ed is the eddy current loss coefficient of silicon steel sheet material.

[0074] Rotor core eddy current loss P r,ed The calculation formula is:

[0075]

[0076] In the above formula, k rc,i To account for the correction factor of eddy current effect in the stator core, b r,i f is the amplitude of the i-th order magnetic flux density in the rotor. r,i Let be the alternating frequency of the i-th order magnetic flux density in the rotor core;

[0077] Permanent magnet eddy current loss P PM,edThe calculation formula is:

[0078]

[0079] In the above formula, B PM,i Let denoted as the amplitude of the i-th harmonic magnetic flux density in the permanent magnet, w as the width of the permanent magnet in the circumferential direction, ξ as the leakage flux coefficient of the permanent magnet, d as the thickness of the permanent magnet in the radial direction, l as the length of the permanent magnet in the axial direction, and σ as the conductivity of the permanent magnet.

[0080] The stator hysteresis loss calculated using the motor provided in this embodiment is 72.45W, the stator eddy current loss is 289.95W, the rotor eddy current loss is 12.64W, and the permanent magnet eddy current loss is 38.65W.

[0081] S3. Calculate the three-phase flux linkage of the motor in one electrical cycle using finite element simulation, and perform a fast Fourier transform on the flux linkage to obtain the components of the three-phase flux linkage at each frequency.

[0082] S4. Using the obtained stator core hysteresis loss, stator core eddy current loss, rotor core eddy current loss, permanent magnet eddy current loss, and flux linkage, calculate the stator core hysteresis loss coefficient, stator core eddy current loss coefficient, rotor core eddy current loss coefficient, and permanent magnet eddy current loss coefficient.

[0083] Stator core hysteresis loss coefficient k s,hy The calculation formula is:

[0084]

[0085] In the above formula, The stator core hysteresis loss under sinusoidal current excitation. f is the i-th order component of the magnetic flux linkage of phase A under sinusoidal power supply. s,i Let be the alternating frequency of the i-th order magnetic flux density in the stator core.

[0086] stator core eddy current loss coefficient k s,ed The calculation formula is:

[0087]

[0088] In the above formula, This refers to the eddy current loss in the stator core under sinusoidal current excitation.

[0089] Rotor core eddy current loss coefficient k r,ed The calculation formula is:

[0090]

[0091] In the above formula, f is the rotor core eddy current loss under sinusoidal current excitation.r,i Let be the alternating frequency of the i-th order magnetic flux density in the rotor core.

[0092] permanent magnet eddy current loss coefficient k PM,ed The calculation formula is:

[0093]

[0094] In the above formula, This refers to the eddy current loss of a permanent magnet under sinusoidal current excitation.

[0095] The stator core hysteresis loss coefficient, the stator core eddy current loss coefficient, the rotor core eddy current loss coefficient, and the permanent magnet eddy current loss coefficient obtained by calculation using the motor provided in this embodiment are 262.48, 262.48, 516.02, and 273.05, respectively.

[0096] S5. Calculate the terminal voltage of the current source under sinusoidal current excitation, perform fast Fourier decomposition on the voltage, and use the fundamental voltage amplitude and phase obtained from the decomposition to generate pulse width modulation (PWM) voltage. Perform Clark transform and Park transform on the PWM voltage first, and then perform fast Fourier transform to obtain the order components of the PWM voltage on the quadrature axis and the direct axis.

[0097] The PWM voltage obtained from the motor provided in this embodiment has the following order components on the quadrature and direct axes: Figure 2 and Figure 3 As shown.

[0098] S6. Establish the quadrature-axis and direct-axis equivalent circuits. Based on the quadrature-axis and direct-axis equivalent circuits, establish a system of voltage equations and solve for the harmonic flux linkage under PWM harmonic voltage supply. See [link to quadrature-axis and direct-axis equivalent circuits]. Figure 4 As shown, Figure 4 In the figure, 1 represents direct-axis voltage, 2 represents direct-axis current, 3 represents direct-axis resistance, 4 represents direct-axis back electromotive force, 5 represents direct-axis leakage inductance, 6 represents the equivalent current source of the permanent magnet, 7 represents direct-axis magnetizing inductance, 8 represents quadrature-axis voltage, 9 represents quadrature-axis current, 10 represents quadrature-axis resistance, 11 represents quadrature-axis back electromotive force, 12 represents quadrature-axis leakage inductance, and 13 represents quadrature-axis magnetizing inductance.

[0099] The system of equations used to solve for quadrature-axis and direct-axis harmonic flux linkages is as follows:

[0100]

[0101] In the above formula, ψ d ,i is the direct-axis flux linkage under i-th order harmonic voltage excitation, r s L is the stator winding resistance. d For direct-axis incremental inductance, ω h,iLet u be the alternating frequency of the i-th harmonic voltage in the rotor coordinate system. d,i Let ψ be the direct-axis component of the i-th order PWM harmonic voltage. q, i For the quadrature-axis flux linkage under i-th order harmonic voltage excitation, u q,i denoted as the quadrature-axis component of the i-th order PWM harmonic voltage, and p is the number of pole pairs of the motor.

[0102] By superimposing the quadrature-axis and direct-axis harmonic flux linkages of each order, the total quadrature-axis and total direct-axis harmonic flux linkages ψd and ψq under PWM harmonic voltage excitation are obtained.

[0103] To transform the total quadrature-axis and total direct-axis harmonic flux linkages into three-phase flux linkages, the following formula is required:

[0104]

[0105] In the above formula, ω f ω is the fundamental angular frequency.

[0106] Comparison of the A-phase harmonic flux linkage calculated by the finite element method with that calculated by this method, for example... Figure 5 As shown.

[0107] S7. Calculate the losses of PWM harmonic voltage in the stator core, rotor core, and permanent magnet using the loss coefficient, harmonic flux linkages of each order, and their frequencies. The calculation formula is as follows:

[0108]

[0109] Based on the above calculation method, this application compares the calculations and actual measurements under seven different working conditions (A to G). See [link / reference]. Figure 6 Taking condition A as an example, in the figure, label 14 represents the measured total loss, label 15 represents the mechanical loss, label 16 represents the permanent magnet loss calculated by the method of this application, label 17 represents the iron loss calculated by the method of this application, and label 18 represents the copper loss.

[0110] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it.

Claims

1. A method for calculating the power supply loss of a permanent magnet synchronous motor via frequency conversion, characterized in that, Includes the following steps: S1. Establish a finite element simulation model of the motor using simulation software, and use sinusoidal current as excitation. S2. Extract the three-phase flux linkage within one electrical cycle and calculate the quadrature-axis and direct-axis incremental inductances; S3. Calculate the motor losses based on the simulation results, and calculate the loss coefficient in combination with the flux linkage; S4. Calculate the harmonic flux under PWM harmonic voltage power supply based on the simulation results; S5. Calculate the motor frequency converter power supply loss by combining harmonic flux linkage, loss coefficient and frequency.

2. The method for calculating the power supply loss of a permanent magnet synchronous motor according to claim 1, characterized in that, The order of steps S3 and S4 can be interchanged.

3. The method for calculating the power supply loss of a permanent magnet synchronous motor according to claim 1, characterized in that, The motor losses in step S3 include: Stator core hysteresis loss P s,hy The calculation formula is: In the above formula, k hy Let b be the hysteresis loss coefficient of silicon steel sheet material. s,i f is the amplitude of the i-th order magnetic flux density in the stator. s,i Let be the alternating frequency of the i-th order magnetic flux density in the stator core; Stator core eddy current loss P s,ed The calculation formula is: In the above formula, k sc,i To account for the correction factor of eddy current effect in the stator core, k ed The eddy current loss coefficient of silicon steel sheet material; Rotor core eddy current loss P r,ed The calculation formula is: In the above formula, k rc,i To account for the correction factor of eddy current effect in the stator core, b r,i f is the amplitude of the i-th order magnetic flux density in the rotor. r,i Let be the alternating frequency of the i-th order magnetic flux density in the rotor core; Permanent magnet eddy current loss P PM,ed The calculation formula is: In the above formula, B PM,i Let denoted as the amplitude of the i-th harmonic magnetic flux density in the permanent magnet, w as the width of the permanent magnet in the circumferential direction, ξ as the leakage flux coefficient of the permanent magnet, d as the thickness of the permanent magnet in the radial direction, l as the length of the permanent magnet in the axial direction, and σ as the conductivity of the permanent magnet.

4. The method for calculating the power supply loss of a permanent magnet synchronous motor according to claim 1, characterized in that, The loss factor in step S3 includes: Stator core hysteresis loss coefficient k s,hy The calculation formula is: In the above formula, The stator core hysteresis loss under sinusoidal current excitation. For the i-th order component of the three-phase flux linkage under sinusoidal power supply, f s,i Let be the alternating frequency of the i-th order magnetic flux density in the stator core; stator core eddy current loss coefficient k s,ed The calculation formula is: In the above formula, f is the stator core eddy current loss under sinusoidal current excitation. s,i Let be the alternating frequency of the i-th order magnetic flux density in the stator core; Rotor core eddy current loss coefficient k r,ed The calculation formula is: In the above formula, f is the rotor core eddy current loss under sinusoidal current excitation. r,i Let be the alternating frequency of the i-th order magnetic flux density in the rotor core; permanent magnet eddy current loss coefficient k PM,ed The calculation formula is: In the above formula, This refers to the eddy current loss of a permanent magnet under sinusoidal current excitation.

5. The method for calculating the power supply loss of a permanent magnet synchronous motor according to claim 1, characterized in that, The method for calculating harmonic flux linkage in step S4 is as follows: S4-1. Calculate the three-phase flux linkage of the motor in one electrical cycle using finite element simulation, and perform fast Fourier transform on the flux linkage to obtain the components of the three-phase flux linkage at each frequency. S4-2. Calculate the terminal voltage of the current source under sinusoidal current excitation, perform fast Fourier decomposition on the voltage, and use the amplitude and phase of the fundamental voltage obtained by decomposition to generate pulse width modulation voltage. First, perform Clark transformation and Park transformation on the PWM voltage, and then perform fast Fourier transformation to obtain the order components of the PWM voltage on the quadrature axis and the direct axis. S4-3. Establish the quadrature-axis and direct-axis equivalent circuits, establish a set of voltage equations based on the quadrature-axis and direct-axis equivalent circuits, and solve for the harmonic flux under PWM harmonic voltage power supply.

6. The method for calculating the power supply loss of a permanent magnet synchronous motor according to claim 5, characterized in that, The equations for solving the quadrature-axis and direct-axis harmonic flux linkages in step S4-3 are as follows: In the above formula, ψ d ,i is the direct-axis flux linkage under i-th order harmonic voltage excitation, r s L is the stator winding resistance. d For direct-axis incremental inductance, ω h,i Let u be the alternating frequency of the i-th harmonic voltage in the rotor coordinate system. d,i Let ψ be the direct-axis component of the i-th order PWM harmonic voltage. q, i For the quadrature-axis flux linkage under i-th order harmonic voltage excitation, u q,i denoted as the quadrature-axis component of the i-th order PWM harmonic voltage, and p is the number of pole pairs of the motor; By superimposing the quadrature-axis and direct-axis harmonic flux linkages of each order, the total quadrature-axis and total direct-axis harmonic flux linkages ψd and ψq under PWM harmonic voltage excitation are obtained.

7. The method for calculating the frequency conversion power supply loss of a permanent magnet synchronous motor according to claim 6, characterized in that, The total quadrature-axis and total direct-axis harmonic flux linkages are transformed into three-phase flux linkages for use in calculating the motor frequency converter power supply losses. The transformation of the total quadrature-axis and total direct-axis harmonic flux linkages into three-phase flux linkages is achieved using the following formula: In the above formula, ω f ω is the fundamental angular frequency.

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