CN-121980845-A - Method for calculating inductance of air gap winding of superconducting motor

CN121980845ACN 121980845 ACN121980845 ACN 121980845ACN-121980845-A

Abstract

The application discloses a superconducting motor air gap winding inductance calculation method which comprises the steps of establishing a planar polar coordinate system, determining a first radial coordinate and a first angular coordinate of an actual position of a first coil on the planar polar coordinate system, determining a first equivalent radial coordinate and a first equivalent angular coordinate of a first equivalent coil of a stator core corresponding to the first coil on the planar polar coordinate system, calculating a first self-excitation inductance of the first coil, calculating a second self-excitation inductance of the first equivalent coil based on a polar distance of a winding, an inner ring radius, the first radial coordinate, the first angular coordinate and a second preset radial coordinate of a second preset point on the planar polar coordinate system, and determining a separate excitation inductance of the stator core corresponding to the first coil based on the second self-excitation inductance, and determining a total self-excitation inductance of the first coil based on the first self-excitation inductance and the separate excitation inductance. By the method, the calculation difficulty and the test cost of the self inductance of the winding are reduced, and the calculation efficiency and the test efficiency are improved.

Inventors

FANG YOUTONG
LUO CHAO
ZHANG JIANCHENG
SHEN HAOCONG
HUA WEN
MA JIEN
Shou Jiabo

Assignees

浙江大学
国网浙江省电力有限公司电力科学研究院

Dates

Publication Date: 20260505
Application Date: 20251222

Claims (11)

1. The method for calculating the inductance of the air gap winding of the superconducting motor is characterized by comprising the following steps of: Establishing a planar polar coordinate system; determining a first radial coordinate and a first angular coordinate of an actual position of a first coil of a superconducting motor on the planar polar coordinate system based on the actual position of the first coil; Determining a first equivalent radial coordinate and a first equivalent angular coordinate of a first equivalent coil of the stator core on the planar polar coordinate system corresponding to the first coil based on an inner ring radius of a stator core of a superconducting motor, the first radial coordinate and the first angular coordinate; calculating a first self-excitation inductance of the first coil based on a polar distance of a winding, the first radial coordinate, the first angular coordinate, a first preset radial coordinate of a first preset point on the planar polar coordinate system, and a first preset angular coordinate; calculating a second self-excitation inductance of the first equivalent coil based on a polar distance of the winding, the inner ring radius, the first radial coordinate, the first angular coordinate, a second preset radial coordinate of a second preset point on the planar polar coordinate system and a second preset angular coordinate, and determining a separate excitation inductance of the stator core corresponding to the first coil based on the second self-excitation inductance; A total self inductance of the first coil is determined based on the first self inductance and the separately excited inductance.
2. The method of claim 1, wherein the superconducting motor air gap winding inductance calculation method comprises the steps of, The determining, based on the inner ring radius, the first radial coordinate and the first angular coordinate of the stator core of the superconducting motor, a first equivalent radial coordinate and a first equivalent angular coordinate of a first equivalent coil of the stator core corresponding to the first coil on the planar polar coordinate system includes: Determining the first equivalent radial coordinate based on a ratio of the square of the inner ring radius to the first radial coordinate; And determining the first equivalent angular coordinate based on the first angular coordinate, wherein the first angular coordinate comprises a first coordinate value and a second coordinate value which is opposite to the first coordinate value, and the first equivalent angular coordinate comprises a first equivalent value identical to the first coordinate value and a second equivalent value identical to the second coordinate value.
3. The method of claim 1, wherein the superconducting motor air gap winding inductance calculation method comprises the steps of, The calculating, based on the polar distance of the winding, the first radial coordinate, the first angular coordinate, a first preset radial coordinate of a first preset point on the planar polar coordinate system, and the first preset angular coordinate, a first self-excitation inductance of the first coil includes: Calculating a first constant value based on the first radial coordinate, the first angular coordinate, the first preset radial coordinate, and the first preset angular coordinate; The first self-excitation inductance is calculated based on the first constant value, the excitation current of the first coil, the air permeability, the axial effective length of the first coil, the pole pitch of the winding, and the angular difference due to the actual radius thickness of the first coil.
4. The method for calculating the inductance of the air gap winding of the superconducting motor according to claim 3, The calculating a first constant value based on the first radial coordinate, the first angular coordinate, the first preset radial coordinate, and the first preset angular coordinate includes: determining a first sine value of a difference between the first angular coordinate and the first preset angular coordinate, a second sine value of a sum of the first angular coordinate and the first preset angular coordinate, and determining a first sine product of the first radial coordinate and the first sine value and a second sine product of the first radial coordinate and the second sine value; determining a first sum of squares of the first radial coordinate and the first preset radial coordinate; determining a first cosine value of a difference between the first angular coordinate and the first preset angular coordinate and a second cosine value of a sum of the first angular coordinate and the first preset angular coordinate; Determining a first cosine product of the first radial coordinate, the first preset radial coordinate and the first cosine value, and determining a second cosine product of the first radial coordinate, the first preset radial coordinate and the second cosine value; calculating a first value based on a first difference between the first sum and the first cosine product, and a quotient of the first sine product and the first difference; calculating a second value based on a second difference of the first sum and the second cosine product, a quotient of the second sine product and the second difference; The first constant value is calculated based on a sum of the first value and the second value.
5. The method for calculating the inductance of the air gap winding of the superconducting motor according to claim 3, The calculating the first self-excitation inductance based on the first constant value, the excitation current of the first coil, the air permeability, the axial effective length of the first coil, the pole pitch of the winding, and the angular difference due to the actual radius thickness of the first coil, includes: Calculating a first magnetic field flux density of the first coil based on a product of the first constant value, the air permeability, and an excitation current of the first coil; Performing area integration on the magnetic density of the first magnetic field to determine first magnetic flux of the first coil; The first self-excitation inductance is calculated based on the first magnetic flux, an excitation current of the first coil, an axial effective length of the first coil, the air permeability, a pole pitch of the winding, and an angular difference due to an actual radius thickness of the first coil.
6. The method of claim 1, wherein the superconducting motor air gap winding inductance calculation method comprises the steps of, The calculating the second self-excitation inductance of the first equivalent coil based on the polar distance of the winding, the inner ring radius, the first radial coordinate, the first angular coordinate, a second preset radial coordinate of a second preset point on the planar polar coordinate system, and a second preset angular coordinate includes: calculating a second constant value based on the inner ring radius, the first radial coordinate, the first angular coordinate, the second preset radial coordinate, and the second preset angular coordinate; The second self-excitation inductance is calculated based on the second constant value, the inner ring radius, the first radial coordinate, a pole pitch of the winding, an air permeability, an axial effective length of the first coil.
7. The method of calculating the air gap winding inductance of a superconducting motor according to claim 6, The calculating a second constant value based on the inner ring radius, the first radial coordinate, the first angular coordinate, the second preset radial coordinate, and the second preset angular coordinate includes: Determining a third sine value of the difference between the first angular coordinate and the second preset angular coordinate, a fourth sine value of the sum of the first angular coordinate and the second preset angular coordinate, determining a third sine product of the first radial coordinate, the square of the inner ring radius and the third sine value, and determining a fourth sine product of the first radial coordinate, the square of the inner ring radius and the fourth sine value; Determining a first square product of the square of the second preset radial coordinate and the square of the first radial coordinate, and determining a second sum of the fourth power of the inner ring radius and the first square product; determining a third cosine value of the difference between the first angular coordinate and the second preset angular coordinate and a fourth cosine value of the sum of the first angular coordinate and the second preset angular coordinate; Determining a third cosine product of the square of the inner ring radius, the first radial coordinate, the second preset radial coordinate and the third cosine value, and determining a fourth cosine product of the square of the inner ring radius, the first radial coordinate, the second preset radial coordinate and the fourth cosine value; calculating a third value based on a third difference of the second sum and the third cosine product, a quotient of the third sine product and the third difference; Calculating a fourth value based on a fourth difference of the second sum and the fourth cosine product, a quotient of the fourth sine product and the fourth difference; The second constant value is calculated based on a sum of the third value and the fourth value.
8. The method of calculating the air gap winding inductance of a superconducting motor according to claim 6, The calculating the second self-excitation inductance based on the second constant value, the inner ring radius, the first radial coordinate, a pole pitch of the winding, an air permeability, an axial effective length of the first coil, comprising: calculating a second magnetic field flux density of the first equivalent coil based on a product of the second constant value, the air permeability, and an excitation current of the first coil; performing area integration on the second magnetic field density to determine second magnetic flux of the first equivalent coil; the second self-excitation inductance is calculated based on the second magnetic flux, the excitation current of the first coil, the axial effective length of the first coil, the air permeability, the inner ring radius, the first radial coordinate, and the pole pitch of the winding.
9. The method of claim 1, wherein the superconducting motor air gap winding inductance calculation method comprises the steps of, Further comprises: Determining a second radial coordinate and a second angular coordinate of an actual position of a second coil of the superconducting motor on the planar polar coordinate system based on the actual position of the second coil; determining a third radial coordinate and a third angular coordinate of the actual position of the first coil on the planar polar coordinate system based on the actual position of the first coil, the third radial coordinate being consistent with the first radial coordinate; calculating a first mutual inductance between the first coil and the second coil based on a polar distance of the winding, the third radial coordinate, the third angular coordinate, the second radial coordinate, the second angular coordinate, a third preset radial coordinate of a third preset point on the planar polar coordinate system, and a third preset angular coordinate; Determining a second equivalent radial coordinate and a second equivalent angular coordinate of a second equivalent coil of the stator core on the planar polar coordinate system corresponding to the first coil based on the inner ring radius, the third radial coordinate, the third angular coordinate, and a polar distance of the winding; calculating a second mutual inductance between the second equivalent coil and the first coil based on the second equivalent radial coordinate and a second equivalent angular coordinate; Determining a total mutual inductance between the first coil and the second coil based on the first mutual inductance and the second mutual inductance; and determining the self inductance of the winding based on the total mutual inductance and the total self inductance.
10. The method of claim 9, wherein the superconducting motor air gap winding inductance calculation method comprises the steps of, The calculating the first mutual inductance between the first coil and the second coil based on the polar distance of the winding, the third radial coordinate, the third angular coordinate, the second radial coordinate, the second angular coordinate, a third preset radial coordinate of a third preset point on the planar polar coordinate system, and a third preset angular coordinate includes: Calculating a third constant value based on the third radial coordinate, the third angular coordinate, the third preset radial coordinate, the third preset angular coordinate, and a polar distance of the winding; the first mutual inductance is calculated based on the third constant value, the excitation current of the first coil, the air permeability, the axial effective length of the first coil, the pole pitch of the winding, the third radial coordinate, the third angular coordinate, the second radial coordinate, and the second angular coordinate.
11. The method of claim 10, wherein the superconducting motor air gap winding inductance calculation method comprises the steps of, The calculating the first mutual inductance based on the third constant value, the exciting current of the first coil, the air permeability, the axial effective length of the first coil, the pole pitch of the winding, the third radial coordinate, the third angular coordinate, the second radial coordinate, and the second angular coordinate, includes: Calculating a third magnetic field flux density of the first coil based on a product of the third constant value, the air permeability, and an excitation current of the first coil; Performing area integration on the third magnetic field density to determine third magnetic flux of the first coil; The first mutual inductance is calculated based on the third magnetic flux, the excitation current of the first coil, the air permeability, an axial effective length of the first coil, a pole pitch of the winding, the third radial coordinate, the third angular coordinate, the second radial coordinate, and the second angular coordinate.

Description

Method for calculating inductance of air gap winding of superconducting motor Technical Field The application relates to the field of performance analysis of superconducting motors, in particular to a method for calculating the inductance of an air gap winding of a superconducting motor. Background The superconducting motor is equipment which is matched with a stator core to realize work, the winding is used as a core component of the superconducting motor, the parameters of the winding directly influence the performance of the superconducting motor, the self inductance of the winding is used as an indispensable part of the parameters of the winding, the self inductance of the winding can be used for defining the coupling and storage of energy and can be used as a tool for measuring related physical quantities, and the self inductance of the winding is important for the efficient operation of the superconducting motor and the safety and stability of a power system. Because the influence of the stator core needs to be considered when the self inductance of the winding is calculated, if the influence caused by the corresponding stator core is directly calculated when the self inductance of the winding is calculated, on one hand, the calculation is more complex, the calculation difficulty of the self inductance of the winding is higher, the calculation efficiency is reduced, and on the other hand, the corresponding stator core needs to be manufactured in the test, so that the related test cost is higher and the test efficiency is lower. Disclosure of Invention The application aims to provide a superconducting motor air gap winding inductance calculation method which can reduce the calculation difficulty of winding self-inductance and improve the calculation efficiency and the efficiency of related experiments. In order to achieve the above purpose, the application adopts the following technical scheme: the application provides a superconducting motor air gap winding inductance calculation method, which comprises the following steps: Establishing a planar polar coordinate system; Determining a first radial coordinate and a first angular coordinate of the actual position of the first coil on a planar polar coordinate system based on the actual position of the first coil of the superconducting motor; Determining a first equivalent radial coordinate and a first equivalent angular coordinate of a first equivalent coil of the stator core corresponding to the first coil on a planar polar coordinate system based on an inner ring radius, the first radial coordinate and the first angular coordinate of the stator core of the superconducting motor; Calculating a first self-excitation inductance of the first coil based on the polar distance of the winding, the first radial coordinate, the first angular coordinate, the first preset radial coordinate of a first preset point on the planar polar coordinate system and the first preset angular coordinate; calculating a second self-excitation inductance of the first equivalent coil based on the pole distance of the winding, the radius of the inner ring, the first radial coordinate, the first angular coordinate, the second preset radial coordinate of a second preset point on the planar polar coordinate system and the second preset angular coordinate, and determining a separate excitation inductance of the stator core corresponding to the first coil based on the second self-excitation inductance; based on the first self-inductance and the separately-excited inductance, a total self-inductance of the first coil is determined. In some implementations, determining a first equivalent radial coordinate and a first equivalent angular coordinate of a first equivalent coil of a stator core on a planar polar coordinate system corresponding to a first coil based on an inner ring radius, the first radial coordinate, and the first angular coordinate of a stator core of a superconducting motor includes: determining a first equivalent radial coordinate based on a ratio of the square of the inner ring radius to the first radial coordinate; based on the first angular coordinate, determining a first equivalent angular coordinate, wherein the first angular coordinate comprises a first coordinate value and a second coordinate value which is opposite to the first coordinate value, and the first equivalent angular coordinate comprises a first equivalent value identical to the first coordinate value and a second equivalent value identical to the second coordinate value. In some implementations, calculating the first self-inductance of the first coil based on the pole distance of the winding, the first radial coordinate, the first angular coordinate, the first preset radial coordinate of the first preset point on the planar polar coordinate system, and the first preset angular coordinate includes: calculating a first constant value based on the first radial coordinate, the first angular coordinate, the f