CN114928278A - Method for calculating contribution of permanent magnet motor air gap field to electromagnetic force - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
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Abstract
The invention discloses a method for calculating contribution of an air gap field of a permanent magnet motor to electromagnetic force, which relates to the technical field of calculation of electromagnetic performance of the permanent magnet motor, and comprises the following steps of firstly, equating the electromagnetic force acting on a stator of the permanent magnet motor as concentrated force, and deducing an analytic model based on an air gap flux density harmonic expression; then, an electromagnetic force modulation coefficient is provided, and the air gap magnetic field modulation and the electromagnetic force modulation are decoupled; then, a method for calculating the contribution of the complex air gap field harmonic of the permanent magnet motor to the electromagnetic force is established; the method for calculating the contribution of the air gap field of the permanent magnet motor to the electromagnetic force can effectively decouple the modulation action of the stator on the magnetic field and the electromagnetic force, discloses the contribution of each subharmonic of the air gap field to the electromagnetic force, and can clearly reflect the influence of the rotating speed, the permanent magnet field and the armature field on the electromagnetic force.
Description
Technical Field
The invention relates to the technical field of calculation of electromagnetic performance of a permanent magnet motor, in particular to a method for calculating contribution of an air gap field of the permanent magnet motor to electromagnetic force.
Background
Most of the existing electromagnetic Force models are derived from electromagnetic Force density, and cannot accurately represent the contribution of each air-gap magnetic field harmonic to the electromagnetic Force, although the Investigation of breed-Loaf magnetic on Vibration Performance in FSCW PMSM conditioning Force Modulation Effect discusses the influence of the air-gap magnetic field harmonic to the electromagnetic Force, the analysis is only limited to analyzing the frequency and the order of the electromagnetic Force density, and only kp order air-gap magnetic field harmonic is considered, wherein k is an integer, and p is a permanent magnetic field polar pair, however, except for the kp order air-gap magnetic field harmonic, because of the air-gap magnetic field Modulation Effect, the air-gap magnetic field of the permanent magnetic motor contains rich Modulation harmonics, the calculation method of the Modulation magnetic field harmonic to the electromagnetic Force contribution is not reported, and in addition, the existing electromagnetic Force models only carry out qualitative analysis on the Modulation Effect of stator teeth to the electromagnetic Force, and cannot carry out quantitative analysis on the influence of the Force Modulation, therefore, the contribution of the air gap field harmonic to the electromagnetic force cannot be accurately represented by the conventional electromagnetic force calculation method, and therefore, a calculation method for the contribution of the air gap field of the permanent magnet motor to the electromagnetic force is provided.
Disclosure of Invention
In order to solve the above mentioned drawbacks in the background art, the present invention provides a method for calculating the contribution of the air-gap field of the permanent magnet motor to the electromagnetic force, and solves the technical problem that the contribution of the air-gap field harmonic to the electromagnetic force cannot be accurately represented by the existing electromagnetic force calculation method.
The purpose of the invention can be realized by the following technical scheme: a method for calculating contribution of an air gap field of a permanent magnet motor to electromagnetic force comprises the following steps:
determining the order m and frequency if of the target electromagnetic force e ；
According to the formula i ═ i 1 ±i 2 Determining i 1 And i 2 Corresponding air gap field harmonic frequency i 1 f e And i 2 f e ；
According to the formula m-min | N s -k(v 1 ±v 2 ) I condition, determining order v of air gap field harmonics 1 And v 2 In the formula v 1 And v 2 Is a non-negative integer, k is an integer, N s The number of stator slots is;
calculating the air gap magnetic field harmonic frequency which greatly contributes to the electromagnetic force;
considering the modulation effect of the air gap magnetic field, calculating the contribution of the air gap magnetic field harmonic amplitude;
and considering the force modulation effect, calculating the contribution of the air gap magnetic field harmonic to the electromagnetic force based on the force modulation coefficient, and calculating the amplitude and the phase of the electromagnetic force according to the magnetic field harmonic order and the frequency.
Further, the order v of the airgap magnetic field harmonics is determined 1 And v 2 The process comprises the following steps: according to the formula m-min | N s -k(v 1 ±v 2 ) L, obtaining the frequency i corresponding to the m-order electromagnetic force 1 、i 2 Are combined to obtain corresponding air gap magnetic field order K v1,j1 ＝v 1 +j 1 N s And K v2,j2 ＝v 2 +j 2 N s Wherein j is 1 、j 2 Are integers.
Further, m ═ min | N s -k(v 1 ±v 2 ) I in idle load, m is min | N s -p(i 1 ±i 2 )|。
Further, the expression for calculating the air gap field harmonic frequency that contributes a large amount to the electromagnetic force is:
in the formula
Is of order K v1,j1 Frequency i 1 f e The amplitude of the air gap flux density harmonic of (c),
is order K v2,j2 Frequency i 2 f e Air gap flux density harmonic amplitude of l e Is the motor stack thickness, R s Is the stator inner diameter, mu 0 Is the vacuum permeability, k ecf Is the force modulation factor.
Further, the force modulation factor is defined as:
further, the air-gap magnetic field modulation effect is considered, and the air-gap magnetic field harmonic wave is calculatedThe contribution process of the amplitude is as follows:
further, the process of calculating the amplitude and phase of the electromagnetic force by the magnetic field harmonic order and frequency is as follows: the amplitude of the electromagnetic force is calculated as
The phase of the electromagnetic force is calculated as
In the formula
Is an amplitude of
The phase corresponding to the harmonic of (a) is,
is an amplitude of
Corresponding to the phase of the harmonic of (a).
The invention has the beneficial effects that:
in the using process of the invention, firstly, the order and the frequency of the target electromagnetic force are determined; then determining the corresponding air gap magnetic field harmonic frequency; determining the order of the air gap magnetic field harmonic wave; then calculating the air gap magnetic field harmonic frequency which has larger contribution to the electromagnetic force; considering the air gap magnetic field modulation effect, and calculating the contribution of the air gap magnetic field harmonic amplitude; finally, based on the force modulation coefficient, calculating the contribution of the air gap magnetic field harmonic waves to the electromagnetic force, and calculating to obtain the amplitude and the phase of the electromagnetic force; the invention provides force modulation coefficient decoupling magnetic field modulation and force modulation for a permanent magnet motor, and through the model, the contribution of the magnetic field harmonic amplitude and the force modulation action to the electromagnetic force can be more accurately quantified and calculated, so that the defect that the conventional permanent magnet motor electromagnetic force model cannot accurately represent the contribution of a complex air gap magnetic field to the electromagnetic force is overcome; the invention provides a method for calculating contribution of an air gap field of a permanent magnet motor to electromagnetic force based on decoupling magnetic field modulation and force modulation. Compared with the existing electromagnetic force model of the permanent magnet motor, the method takes the contribution of the magnetic field harmonic waves to the amplitude and the phase of the electromagnetic force harmonic waves into consideration, and is beneficial to analyzing the electromagnetic force of different rotor magnetic pole designs and armature reactions.
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In order to more clearly illustrate the embodiments or technical solutions in the prior art of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious for those skilled in the art to obtain other drawings without creative efforts;
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic representation of a permanent magnet motor model of the present invention;
fig. 3 is a schematic diagram of the electromagnetic force of the permanent magnet motor of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1-3, a method for calculating contribution of an air gap field of a permanent magnet motor to electromagnetic force includes the following steps:
determining the order and frequency of the target electromagnetic force;
determining a corresponding air gap magnetic field harmonic frequency;
determining the order of the air gap magnetic field harmonics;
calculating the air gap magnetic field harmonic frequency which greatly contributes to the electromagnetic force;
considering the modulation effect of the air gap magnetic field, calculating the contribution of the air gap magnetic field harmonic amplitude;
and calculating the contribution of the air gap magnetic field harmonic waves to the electromagnetic force based on the force modulation coefficient, and calculating to obtain the amplitude and the phase of the electromagnetic force.
It should be further noted that, in the implementation process, a method for calculating the contribution of the air gap field harmonic to the electromagnetic force is taken as an example of a 12-slot 10-pole interior permanent magnet synchronous motor.
First, order m and frequency if of the target electromagnetic force are determined e (ii) a Next, the corresponding airgap field harmonic frequency i is determined 1 f e And i 2 f e (ii) a Then, the order v of the airgap field harmonics is determined 1 And v 2 (ii) a Calculating the air gap magnetic field harmonic frequency which greatly contributes to the electromagnetic force; considering the modulation effect of the air gap magnetic field, calculating the contribution of the air gap magnetic field harmonic amplitude; and considering the force modulation effect, calculating the contribution of the air gap magnetic field harmonic to the electromagnetic force based on the force modulation coefficient, and calculating the amplitude and the phase of the electromagnetic force according to the magnetic field harmonic order and the frequency.
In the air gap magnetic field harmonic waves provided by this embodiment, the air gap magnetic field harmonic waves of the permanent magnet motor can be written as follows:
wherein v and j are integers, i is a positive integer, N s Number of stator teeth, ω e Is the electrical frequency, phi v,j,i Is the phase.
It should be further noted that in the present embodiment, in determining the target electromagnetic force order and frequency, a main electromagnetic force order needs to be determined according to the critical modal order of the motor, and in the permanent magnet motor shown in fig. 2, the main electromagnetic force order is 2 orders. According to m-min | N s -k(v 1 ±v 2 ) The condition of obtaining the frequency (i) corresponding to the electromagnetic force of m order 1 ±i 2 )f e . In idle time, for example, m is min | N s -p(i 1 ±i 2 ) The following table can be calculated:
in the motor, the frequency of the 2-order electromagnetic force is 2f e 、10f e And 14f e 。
It should be further noted that in determining the corresponding air gap field harmonic frequency as proposed in the present embodiment, i is required to be the same as i 1 ±i 2 Determining the corresponding air gap magnetic field harmonic frequency i under the condition of i 1 f e And i 2 f e ；
It should be further noted that, in the order of determining the airgap magnetic field harmonics proposed in the present embodiment, the order of the airgap magnetic field harmonics is calculated as K v1,j1 ＝v 1 +j 1 N s And K v2,j2 ＝v 2 +j 2 N s Wherein v is 1 、v 2 Is an integer, j 1 、j 2 Is a positive integer.
It should be further noted that, in the air gap field harmonic frequency, which is proposed in the present embodiment and has a large contribution to the electromagnetic force, the electromagnetic force model has an order of m and a frequency of if as shown in fig. 3 e The electromagnetic force amplitude of (a) can be calculated as:
wherein,
is the air gap flux density harmonic amplitude, l e Is the motor stack thickness, R s Is the stator inner diameter, mu 0 Is the vacuum permeability, k ecf Is the force modulation factor. The air gap magnetic field harmonic frequency with large contribution to the electromagnetic force in the calculation proposed in the invention can be screened out according to the formula (2).
It should be further noted that the present embodiment proposes to calculate the amplitude of the airgap field harmonic in consideration of the airgap field modulation effectIn the contribution, the contribution of each order of airgap field harmonic amplitude needs to be calculated according to equation (1):
it should be further noted that, based on the force modulation coefficient, the proposed embodiment is defined according to the following formula:
it should be further noted that, in calculating the contribution of the air-gap magnetic field harmonic to the electromagnetic force and calculating the amplitude and the phase of the electromagnetic force, the amplitude and the phase of the electromagnetic force need to be calculated according to the order and the frequency of the determined main magnetic field harmonic, and the amplitude of the electromagnetic force is calculated as
The phase of the electromagnetic force is calculated as
As shown in the following table, it can be seen that the invention can accurately calculate the amplitude and phase contributions of the air gap magnetic field harmonics with different orders and frequencies to the electromagnetic force.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are given by way of illustration of the principles of the present invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, and such changes and modifications are within the scope of the invention as claimed.
Claims (8)
1. A method for calculating contribution of an air gap field of a permanent magnet motor to electromagnetic force is characterized by comprising the following steps:
determining the order m and frequency if of the target electromagnetic force e ；
According to the formula i ═ i 1 ±i 2 Determining i 1 And i 2 Corresponding air gap field harmonic frequency i 1 f e And i 2 f e ；
According to the formula m-min | N s -k(v 1 ±v 2 ) I condition, determining order v of airgap magnetic field harmonics 1 And v 2 In the formula v 1 And v 2 Is a non-negative integer, k is an integer, N s The number of stator slots is;
calculating the air gap magnetic field harmonic frequency which greatly contributes to the electromagnetic force;
considering the modulation effect of the air gap magnetic field, calculating the contribution of the air gap magnetic field harmonic amplitude;
and considering the force modulation effect, calculating the contribution of the air gap magnetic field harmonic waves to the electromagnetic force based on the force modulation coefficient, and calculating the amplitude and the phase of the electromagnetic force according to the magnetic field harmonic order and the frequency.
2. Method for calculating the contribution of the air-gap field of a permanent-magnet machine to the electromagnetic force of claim 1, wherein the order v of the harmonics of the air-gap field is determined 1 And v 2 The process comprises the following steps: according to the formula m-min | N s -k(v 1 ±v 2 ) To obtain the frequency i corresponding to the electromagnetic force of m order 1 、i 2 Are combined to obtain corresponding air gap magnetic field order K v1,j1 ＝v 1 +j 1 N s And K v2,j2 ＝v 2 +j 2 N s 。
3. The method for calculating the contribution of the permanent magnet motor air gap field to the electromagnetic force according to claim 2, wherein K is v1,j1 ＝v 1 +j 1 N s And K v2,j2 ＝v 2 +j 2 N s In the formula j 1 、j 2 Is an integer.
4. The method of claim 2, wherein the formula m-min | N is a formula s -k(v 1 ±v 2 ) I in idle load, m is min | N s -p(i 1 ±i 2 )|。
5. The method for calculating the contribution of the air-gap field of the permanent magnet motor to the electromagnetic force according to claim 1, wherein the expression for calculating the air-gap field harmonic frequency with a large contribution to the electromagnetic force is as follows:
in the formula
Is order v 1 The air gap flux density harmonic amplitude of (a),
is of order v 2 Air gap flux density harmonic amplitude of l e Is the motor stack thickness, R s Is the stator inner diameter, mu 0 Is a vacuum permeability, k ecf Is the force modulation factor.
6. The method of claim 5, wherein the force modulation factor is defined as:
7. the method for calculating the contribution of the air-gap field of the permanent magnet motor to the electromagnetic force according to claim 1, wherein the contribution process for calculating the amplitude of the air-gap field harmonic in consideration of the air-gap field modulation effect is as follows:
8. the method for calculating the contribution of the air-gap field of the permanent magnet motor to the electromagnetic force according to claim 1, wherein the process of calculating the amplitude and the phase of the electromagnetic force according to the harmonic order and the frequency of the magnetic field comprises the following steps: the magnitude of the electromagnetic force is calculated as
The phase of the electromagnetic force is calculated as
In the formula
Is an amplitude of
The phase corresponding to the harmonic of (a),
is an amplitude of
Corresponding to the phase of the harmonic of (a).
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112436706A (en) * | 2020-11-24 | 2021-03-02 | 江苏大学 | Loss analysis and suppression method for magnetic field modulation permanent magnet motor |
| WO2022083014A1 (en) * | 2020-10-19 | 2022-04-28 | 江苏大学 | Fractional slot concentrated winding permanent magnet motor-based duplex-winding low-harmonic design method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2022083014A1 (en) * | 2020-10-19 | 2022-04-28 | 江苏大学 | Fractional slot concentrated winding permanent magnet motor-based duplex-winding low-harmonic design method |
| CN112436706A (en) * | 2020-11-24 | 2021-03-02 | 江苏大学 | Loss analysis and suppression method for magnetic field modulation permanent magnet motor |
Non-Patent Citations (1)
| Title |
|---|
| HANG YIN等: "Quantitative Analysis of Electromagnetic Forces by Decoupling Air-Gap Field Modulation and Force Modulation in Rotor-Permanent-Magnet Machines", IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 29 March 2022 (2022-03-29), pages 1 - 11 * |
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