CN113452209A - Method and system for calculating magnetic field of multi-phase cage type induction motor - Google Patents
Method and system for calculating magnetic field of multi-phase cage type induction motor Download PDFInfo
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Abstract
A method and a system for calculating a magnetic field of a multi-phase cage type induction motor are provided, wherein the method comprises the following steps: dividing a motor solving area according to the type of an excitation source so as to obtain a motor model, and solving a distribution function of the current density of a stator winding based on the motor model; aiming at the influence of the kth current density harmonic wave, vector magnetic potential in each sub-domain is taken as a solving object of a control equation, a Laplace equation, a Poisson equation and a Helmholtz equation are respectively established, and a general solution of the vector magnetic potential is obtained according to boundary conditions between interfaces; solving the harmonic coefficient of each sub-domain based on the general solution of the vector magnetic potential of each sub-domain; and based on the harmonic coefficients of the sub-domains, solving the radial and tangential components of the air gap flux density according to the vector magnetic potential expression of the air gap sub-domain, and solving the torque caused by the kth space harmonic of the magnetomotive force and the total electromagnetic torque according to the Maxwell tensor method and the radial and tangential components of the air gap flux density.
Description
Technical Field
The invention relates to the field of motor magnetic field calculation, in particular to a multiphase cage type induction motor magnetic field calculation method and system based on a sub-domain harmonic model.
Background
"analytical calculations of edge currencies in the slots of electrical models," IEEE transactions. Magn., vol.47, No.11, pp.4650-4659, Nov.2011. The method uses an equivalent current layer at the edge of a stator to replace a stator winding as an excitation source, calculates the eddy current distribution and the electromagnetic performance in a rotor conducting bar of the cage type rotor induction motor based on a subdomain method, but does not consider the stator slotting with tooth tips and cannot calculate the influence of the stator slotting on the electromagnetic performance of the motor;
xue Zhi is strong, round feather, Lihuai tree, surface-mounted permanent magnet motor no-load magnetic field analytic calculation [ J ] when considering stator and rotor bilateral slotting, Motor engineering reports, 2017,33 (8). The method is an analytic calculation method considering the distribution of the open-circuit magnetic field of the motor when the stator and the rotor are subjected to bilateral slotting. According to the permanent magnet equivalent surface current method, an open-circuit field generated by radial parallel permanent magnets is equivalent to an open-circuit field generated by surface current, and the influence of the motor cogging is solved.
Boughhrara, F.Dubas, and R.Ibtituen, "2-D Analytical Prediction of Eddy Currents, Circuit Model Parameters, and Steady-State Performance in Solid Rotor indication Motors," IEEE transactions. Mag., vol.50, No.12, pp.1-14,2014. The method calculates the magnetic field distribution, eddy current, circuit model parameters and steady-state performance of the induction motor, considers the influence of stator slots and stator tooth tips, but does not consider the influence of rotor slots and cast aluminum guide bars aiming at the magnetic potential Helmholtz equation established by the solid rotor.
Boughrara, n.takorabe, r.ibtion, o.touhami, and f.dubas, "Analytical Analysis of gage Rotor indication Motors in health, defect and brooken Bars Conditions," IEEE trans.magn., vol.02, no.c., pp.1-1,2014. The method assumes that the air gap of the rotating cage type induction motor only contains fundamental wave magnetic potential, and the established sub-domain model cannot further research the influence of the space harmonic of the magnetic potential on the electromagnetic performance of the motor, so that the optimization design of the motor is limited.
Disclosure of Invention
In view of the technical defects and technical drawbacks in the prior art, embodiments of the present invention provide a method for calculating a magnetic field of a multi-phase cage-type induction motor based on a sub-domain harmonic model, which overcomes or at least partially solves the above problems, and the method includes:
as a first aspect of the present invention, there is provided a method of calculating a magnetic field of a multi-phase cage-type induction motor, the method including:
step 1, dividing a motor solving area according to the type of an excitation source so as to obtain a motor model, and solving a distribution function of the current density of a stator winding based on the motor model;
step 2, aiming at the influence of the kth current density harmonic wave, taking the vector magnetic potential in each sub-domain as a solving object of a control equation, respectively establishing a Laplace equation, a Poisson equation and a Helmholtz equation, and solving a general solution of the vector magnetic potential according to boundary conditions between interfaces;
step 3, solving the harmonic coefficient of each sub-domain based on the general solution of the vector magnetic potential of each sub-domain;
and 4, solving radial and tangential components of the air gap flux density according to a vector magnetic potential expression of the air gap sub-domain based on the harmonic coefficient of each sub-domain, and solving the torque and the total electromagnetic torque caused by the kth space harmonic of the magnetomotive force according to the radial and tangential components of the air gap flux density and a Maxwell tensor method.
Further, step 1 specifically comprises:
dividing a motor solving area into 4 types of sub-areas according to the type of an excitation source to obtain a motor model, wherein the 4 types of sub-areas comprise a rotor slot I sub-area, an air gap II sub-area, a slot opening III sub-area and a stator slot IV sub-area;
to facilitate the analysis of the effects of the magnetomotive force sub-spatial harmonics, the vector magnetic potentials of the 4 sub-regions are expressed in complex form as follows:
wherein j is an imaginary unit, betascIs the stator slot angle, betarIs the rotor slot angle, betaskIs the stator slot opening angle, R1Is the radius of the inner surface of the rotor slot, R2Is the rotor outer surface radius, R3Radius of the stator inner surface, R4Is the radius of the inner surface of the stator slot, R5The number of turns of the winding in each stator slot is N for the radius of the outer surface of the stator slotwAnd Re { } represents taking the real part of a complex number, and setting the current density in the stator slot to be 0,2 pi according to a motor model]And expanding the interval into Fourier series related to a mechanical angle, and leading the stator winding to be introduced with symmetrical five-phase positive sequence current so as to obtain a distribution function of the current density of the stator winding, wherein the distribution function is expressed as the following formula I:
the formula I is as follows:
wherein, JkmIs the amplitude of k harmonics of current density, k is the space harmonic order, is related to the motor winding mode, and the sign thereof represents the rotating direction of rotating current density wave, thetasIs the stator side position angle.
Further, step 1 further comprises:
converting the distribution function expression of the current density of the stator winding into a form under a rotor reference system, and expressing the distribution function expression as the following formula II:
the formula II is as follows:
wherein the content of the first and second substances,
theta is the position angle of the stator side in the reference frame of the rotor, omegark＝[1-k(1-s)]ω and s is slip.
Further, step 2 specifically comprises:
to simplify the expression of the integral constants and the general solution within each sub-domain, the following functions are defined:
the formula III is as follows:
the formula four is as follows:
the formula five is as follows:
formula six:
aiming at the influence of the kth current density harmonic wave, vector magnetic potential in each sub-domain is taken as a solving object of a control equation, and the obtained general solutions of a Helmholtz equation and the vector magnetic potential in the rotor slot sub-domain are respectively expressed as a formula seven and a formula eight as follows:
the formula seven:
the formula eight:
in the formula, gamma2＝-jωrkσμ0，
Is of order of
The first type of the bezier function of (1),
is of order of
A second type of Bessel function of (1);
the Laplace equation and the general solution of the vector magnetic potential in the air gap sub-domain are expressed as the following formula nine and formula ten:
the formula is nine:
formula ten:
the general solution of the Laplace equation and the vector magnetic potential in the slot opening subfield is expressed as the following formula eleven and formula twelve:
formula eleven:
equation twelve:
the poisson equation of pure forced vibration in the stator slot sub-domain and the general solution of vector magnetic potential are expressed as the following formula thirteen and formula fourteen:
formula thirteen
The formula fourteen:
wherein A isk1i,Ak2,Ak3i',Ak4i'The vector magnetic potential of the rotor slot sub-region, the air gap sub-region, the slot opening sub-region and the stator slot sub-region are respectively represented.
Further, step 3 specifically comprises:
and (3) according to a general solution expression of vector magnetic bits in each sub-domain, arranging the following linear equation set to obtain the harmonic coefficient of each sub-domain, wherein the linear equation set is expressed as the following formula fifteen:
equation fifteen: m · X ═ S;
wherein:
further, in step 4, based on the harmonic coefficients of each sub-domain, the radial and tangential components of the air gap flux density calculated according to the vector magnetic potential expression of the air gap sub-domain are specifically:
after the harmonic coefficients of each sub-domain are solved, according to a vector magnetic potential expression of the air gap sub-domain, air gap flux density radial and tangential components generated by kth space harmonic of stator magnetomotive force are obtained in a two-dimensional plane, and the components are expressed as the following formula sixteen:
the formula sixteen:
further, in step 4, according to the radial and tangential components of the air gap flux density, the torque caused by the kth spatial harmonic of the magnetomotive force and the total electromagnetic torque obtained by the maxwell tensor method are specifically:
obtaining radial and tangential components of air gap flux density, obtaining torque and total electromagnetic torque caused by k-th space harmonic of magnetomotive force according to Maxwell tensor method based on given stator current and slip ratioRadius in the air gap of RcAs an integral path, electromagnetic torque TeExpressed as the following formula seventeen:
the formula seventeen:
wherein, TkeIs the electromagnetic torque, L, produced by the kth harmonic of the magnetomotive forcecIs the axial length of the motor, Bk2θ *Is Bk2θThe complex conjugate of (a).
Further, step 4 further comprises: based on the harmonic coefficient of each subdomain, calculating the induced current density J induced on the ith rotor bar by the kth space harmonic of the magnetomotive forcekri(r, theta) and the total induced current density Jri(r, θ), expressed as the following equation eighteen:
eighteen formulas:
and obtaining the distribution of the induced current on the ith rotor bar according to the formula eighteenth, wherein the distribution is expressed as the following formula nineteen:
the formula is nineteen:
as a second aspect of the present invention, there is provided a magnetic field calculation system for a multi-phase cage-type induction motor, the system comprising a region division module, a vector magnetic potential calculation module, a harmonic coefficient calculation module, and an electromagnetic torque calculation module;
the region division module is used for dividing a motor solving region according to the excitation source type so as to obtain a motor model, and solving a distribution function of the current density of the stator winding based on the motor model;
the vector magnetic potential calculation module is used for aiming at the influence of the kth current density harmonic wave, taking the vector magnetic potential in each sub-domain as a solving object of a control equation, respectively establishing a Laplace equation, a Poisson equation and a Helmholtz equation, and solving a general solution of the vector magnetic potential according to boundary conditions among interfaces;
the harmonic coefficient calculation module is used for solving the harmonic coefficient of each sub-domain based on the general solution of the vector magnetic potential of each sub-domain;
the electromagnetic torque calculation module is used for solving the radial and tangential components of the air gap flux density according to the vector magnetic potential expression of the air gap sub-domain based on the harmonic coefficient of each sub-domain, and solving the torque and the total electromagnetic torque caused by the kth space harmonic of the magnetomotive force according to the Maxwell tensor method and the radial and tangential components of the air gap flux density.
The invention has the following beneficial effects:
1. the physical significance is clear: in contrast, the subdomain harmonic model of the invention takes each space harmonic of stator magnetomotive force as independent excitation and analyzes the influence of each space harmonic on the performance of the motor from a physical angle.
2. The applicability is wide: the subdomain harmonic model is suitable for various types of multi-phase cage type induction motors, such as stator windings with structures of integer slots, fractional slots, single layers, double layers and the like. Compared with the traditional subdomain model calculation, the method has wider applicability.
3. Rapidity: compared with a finite element analysis method, the method has the advantages that the optimization design efficiency of the motor is higher, the time is saved, and the method can be used for the design of the initial stage of the motor.
Drawings
Fig. 1 is a flowchart of a method for calculating a magnetic field of a multi-phase cage-type induction motor according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a motor model according to an embodiment 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 present invention, and not all 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, as a first embodiment of the present invention, there is provided a magnetic field calculation method for a polyphase cage-type induction motor, the method including:
step 1, dividing a motor solving area according to the type of an excitation source so as to obtain a motor model, and solving a distribution function of the current density of a stator winding based on the motor model;
step 2, aiming at the influence of the kth current density harmonic wave, taking the vector magnetic potential in each sub-domain as a solving object of a control equation, respectively establishing a Laplace equation, a Poisson equation and a Helmholtz equation, and solving a general solution of the vector magnetic potential according to boundary conditions between interfaces;
step 3, solving the harmonic coefficient of each sub-domain based on the general solution of the vector magnetic potential of each sub-domain;
and 4, solving radial and tangential components of the air gap flux density according to a vector magnetic potential expression of the air gap sub-domain based on the harmonic coefficient of each sub-domain, and solving the torque and the total electromagnetic torque caused by the kth space harmonic of the magnetomotive force according to the radial and tangential components of the air gap flux density and a Maxwell tensor method.
Preferably, step 1 is specifically:
as shown in fig. 2, dividing a motor solution area into 4 types of sub-areas according to the type of an excitation source to obtain a motor model, wherein the 4 types of sub-areas comprise a rotor slot I sub-area, an air gap II sub-area, a slot opening III sub-area and a stator slot IV sub-area;
to facilitate the analysis of the effects of the magnetomotive force sub-spatial harmonics, the vector magnetic potentials of the 4 sub-regions are expressed in complex form as follows:
the main parameter symbols of the cage type induction motor prototype are shown in the following table:
according to a motor model, the current density in the stator slot is expanded into Fourier series related to a mechanical angle in a [0,2 pi ] interval, and if symmetrical five-phase positive sequence current is led into the stator winding, a distribution function of the current density of the stator winding can be obtained and expressed as the following formula I:
the formula I is as follows:
wherein, JkmIs the amplitude of current density k subharmonic, k is space harmonic order, and is related to motor winding mode, and its sign represents the rotating direction of rotating current density wave, thetasIs the stator side position angle. The rotating magnetic field distribution and the torque of the induction motor have a close relation with the slip ratio, in order to analyze the electromagnetic characteristics of the induction motor under different working conditions, the solving calculation of multi-sub-field vector magnetic potential needs to be carried out under a rotor reference system, and a stator winding current density expression can be converted into a form under the rotor reference system, and is expressed as a formula II:
the formula II is as follows:
wherein the content of the first and second substances,
theta is the position angle of the stator side in the reference frame of the rotor, omegark＝[1-k(1-s)]ω and s is slip.
Preferably, in step 2, the solving of the control program in each sub-domain specifically includes:
for the influence of the kth harmonic current density, the vector magnetic bit (A) in each sub-domain is usedk1i,Ak2,Ak3i',Ak4i') As the solution object of the control equation, in each sub-fieldEstablishing a Laplace equation, a Poisson equation and a Helmholtz equation, solving a general solution of vector magnetic potential according to boundary conditions among interfaces, and defining the following functions for simplifying integral constants and expressions of the general solution in each sub-domain, such as formulas III-VI:
the formula III is as follows:
the formula four is as follows:
the formula five is as follows:
formula six:
aiming at the influence of the kth current density harmonic wave, vector magnetic potential in each sub-domain is taken as a solving object of a control equation, and the obtained general solutions of a Helmholtz equation and the vector magnetic potential in a rotor slot domain are respectively expressed as a formula seven and a formula eight as follows:
the formula seven:
the formula eight:
in the formula, gamma2＝-jωrkσμ0，
Is of order of
The first type of the bezier function of (1),
is of order of
A second type of Bessel function of (1);
the Laplace equation and the general solution of the vector magnetic potential in the air gap sub-domain are expressed as the following formula nine and formula ten:
the formula is nine:
formula ten:
the general solution of the Laplace equation and the vector magnetic potential in the slot opening subfield is expressed as the following formula eleven and formula twelve:
formula eleven:
equation twelve:
the poisson equation of pure forced vibration in the stator slot sub-domain and the general solution of vector magnetic potential are expressed as the following formula thirteen and formula fourteen:
formula thirteen
The formula fourteen:
wherein A isk1i,Ak2,Ak3i',Ak4i'The vector magnetic potential of the rotor slot sub-region, the air gap sub-region, the slot opening sub-region and the stator slot sub-region are respectively represented.
Preferably, step 3 is specifically:
according to a general solution expression of vector magnetic potential in each sub-domain, the following linear equation set is listed, namely 13 unknown harmonic coefficients are obtained, and the linear equation set is expressed as the following formula fifteen:
equation fifteen: m · X ═ S;
wherein:
preferably, in step 4, based on the harmonic coefficients of each sub-domain, the radial and tangential components of the air gap flux density calculated according to the vector magnetic potential expression of the air gap sub-domain are specifically:
after the harmonic coefficients of each sub-domain are solved, according to a vector magnetic potential expression of the air gap sub-domain, air gap flux density radial and tangential components generated by kth space harmonic of stator magnetomotive force are obtained in a two-dimensional plane, and the components are expressed as the following formula sixteen:
the formula sixteen:
and the air gap total flux density distribution can be obtained after each time of superposition.
Preferably, in step 4, the step of obtaining the torque caused by the kth spatial harmonic of the magnetomotive force and the total electromagnetic torque according to the maxwell tensor method based on the radial and tangential components of the air gap flux density is specifically as follows:
obtaining radial and tangential components of air gap flux density, obtaining torque and total electromagnetic torque caused by kth space harmonic of magnetomotive force according to Maxwell tensor method based on given stator current and slip ratio, and setting radius in air gap as RcAs an integral path, magnetic torque TeExpressed as the following formula seventeen:
the formula seventeen:
wherein, TkeIs the electromagnetic torque, L, produced by the kth harmonic of the magnetomotive forcecIs the axial length of the motor, Bk2θ *Is Bk2θThe complex conjugate of (a).
Preferably, step 4 further comprises: based on the harmonic coefficient of each subdomain, calculating the induced current density J induced on the ith rotor bar by the kth space harmonic of the magnetomotive forcekri(r, theta) and the total induced current density Jri(r, θ), expressed as the following equation eighteen:
eighteen formulas:
and obtaining the distribution of the induced current on the ith rotor bar according to the formula eighteenth, wherein the distribution is expressed as the following formula nineteen:
the formula is nineteen:
as a second embodiment of the present invention, there is also provided a magnetic field calculation system for a multi-phase cage-type induction motor, the system including a region division module, a vector magnetic potential calculation module, a harmonic coefficient calculation module, and an electromagnetic torque calculation module;
the region division module is used for dividing a motor solving region according to the excitation source type so as to obtain a motor model, and solving a distribution function of the current density of the stator winding based on the motor model;
the vector magnetic potential calculation module is used for aiming at the influence of the kth current density harmonic wave, taking the vector magnetic potential in each sub-domain as a solving object of a control equation, respectively establishing a Laplace equation, a Poisson equation and a Helmholtz equation, and solving a general solution of the vector magnetic potential according to boundary conditions among interfaces;
the harmonic coefficient calculation module is used for solving the harmonic coefficient of each sub-domain based on the general solution of the vector magnetic potential of each sub-domain;
the electromagnetic torque calculation module is used for solving the radial and tangential components of the air gap flux density according to the vector magnetic potential expression of the air gap sub-domain based on the harmonic coefficient of each sub-domain, and solving the torque and the total electromagnetic torque caused by the kth space harmonic of the magnetomotive force according to the Maxwell tensor method and the radial and tangential components of the air gap flux density.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (9)
1. A method for calculating a magnetic field of a multi-phase cage-type induction motor, the method comprising:
step 1, dividing a motor solving area according to the type of an excitation source so as to obtain a motor model, and solving a distribution function of the current density of a stator winding based on the motor model;
step 2, aiming at the influence of the kth current density harmonic wave, taking the vector magnetic potential in each sub-domain as a solving object of a control equation, respectively establishing a Laplace equation, a Poisson equation and a Helmholtz equation, and solving a general solution of the vector magnetic potential according to boundary conditions between interfaces;
step 3, solving the harmonic coefficient of each sub-domain based on the general solution of the vector magnetic potential of each sub-domain;
and 4, solving radial and tangential components of the air gap flux density according to a vector magnetic potential expression of the air gap sub-domain based on the harmonic coefficient of each sub-domain, and solving the torque and the total electromagnetic torque caused by the kth space harmonic of the magnetomotive force according to the radial and tangential components of the air gap flux density and a Maxwell tensor method.
2. The method for calculating the magnetic field of the multi-phase cage-type induction motor according to claim 1, wherein the step 1 specifically comprises:
dividing a motor solving area into 4 types of sub-areas according to the type of an excitation source to obtain a motor model, wherein the 4 types of sub-areas comprise a rotor slot I sub-area, an air gap II sub-area, a slot opening III sub-area and a stator slot IV sub-area;
to facilitate the analysis of the effects of the magnetomotive force sub-spatial harmonics, the vector magnetic potentials of the 4 sub-regions are expressed in complex form as follows:
wherein j is an imaginary unit, betascIs the stator slot angle, betarIs the rotor slot angle, betaskIs the stator slot opening angle, R1Is the radius of the inner surface of the rotor slot, R2Is the rotor outer surface radius, R3Radius of the stator inner surface, R4Is the radius of the inner surface of the stator slot, R5The number of turns of the winding in each stator slot is N for the radius of the outer surface of the stator slotwAnd Re { } represents taking the real part of a complex number, and setting the current density in the stator slot to be 0,2 pi according to a motor model]And expanding the interval into Fourier series related to a mechanical angle, and leading the stator winding to be introduced with symmetrical five-phase positive sequence current so as to obtain a distribution function of the current density of the stator winding, wherein the distribution function is expressed as the following formula I:
the formula I is as follows:
wherein, JkmIs the amplitude of the current density k harmonic, k is the space harmonic order, ω is the stator current angular frequency, t is time, τsIs the slot pitch, thetasIs the stator side position angle.
3. The method of calculating the magnetic field of a polyphase cage-type induction motor according to claim 2, wherein the step 1 further comprises:
converting the distribution function expression of the current density of the stator winding into a form under a rotor reference system, and expressing the distribution function expression as the following formula II:
the formula II is as follows:
wherein the content of the first and second substances,
theta is the position angle of the stator side in the reference frame of the rotor, omegark＝[1-k(1-s)]ω and s is slip.
4. The method for calculating the magnetic field of the multi-phase cage-type induction motor according to claim 1, wherein the step 2 specifically comprises:
to simplify the expression of the integral constant and the general solution in each sub-domain, such as the formula three to the formula five, the following functions are defined:
the formula III is as follows:
the formula four is as follows:
the formula five is as follows:
formula six:
in the formula, gamma2＝-jωrkσμ0σ is the conductivity, μ0Aiming at the influence of the kth current density harmonic, the air track rate is obtained by taking the vector magnetic potential in each sub-domain as a solving object of a control equation, and the obtained solutions of the Helmholtz equation and the vector magnetic potential in the rotor slot domain are respectively expressed as a formula seven and a formula eight as follows:
the formula seven:
the formula eight:
in the formula (I), the compound is shown in the specification,
is of order of
The first type of the bezier function of (1),
is of order of
A second type of Bessel function of (1);
the Laplace equation and the general solution of the vector magnetic potential in the air gap sub-domain are expressed as the following formula nine and formula ten:
the formula is nine:
formula ten:
the general solution of the Laplace equation and the vector magnetic potential in the slot opening subfield is expressed as the following formula eleven and formula twelve:
formula eleven:
equation twelve:
the poisson equation of pure forced vibration in the stator slot sub-domain and the general solution of vector magnetic potential are expressed as the following formula thirteen and formula fourteen:
formula thirteen
The formula fourteen:
wherein A isk1i,Ak2,Ak3i',Ak4i'The vector magnetic potential of the rotor slot sub-region, the air gap sub-region, the slot opening sub-region and the stator slot sub-region are respectively represented.
5. The method for calculating the magnetic field of the multi-phase cage-type induction motor according to claim 1, wherein the step 3 specifically comprises:
according to a general solution expression of vector magnetic potential in each sub-domain, the following linear equation sets are listed to obtain harmonic coefficients of each sub-domain, wherein M is a linear relation matrix, X is a harmonic coefficient matrix to be solved, S is an excitation source matrix, and the linear equation set is expressed as the following formula fifteen:
equation fifteen: m · X ═ S;
wherein:
6. the method for calculating the magnetic field of the multi-phase cage-type induction motor according to claim 1, wherein in the step 4, the radial and tangential components of the air gap flux density are calculated according to the vector magnetic potential expression of the air gap sub-field based on the harmonic coefficient of each sub-field, specifically:
after the harmonic coefficients of each sub-domain are solved, according to a vector magnetic potential expression of the air gap sub-domain, air gap flux density radial and tangential components generated by kth space harmonic of stator magnetomotive force are obtained in a two-dimensional plane, and the components are expressed as the following formula sixteen:
the formula sixteen:
7. the method for calculating the magnetic field of the multiphase cage type induction motor according to claim 6, wherein in the step 4, the torque caused by the kth spatial harmonic of the magnetomotive force and the total electromagnetic torque are obtained according to the Maxwell tensor method and the radial and tangential components of the air gap flux density, specifically:
obtaining radial and tangential components of air gap flux density, obtaining torque and total electromagnetic torque caused by kth space harmonic of magnetomotive force according to Maxwell tensor method based on given stator current and slip ratio, and setting radius in air gap as RcAs an integral path, electromagnetic torque TeExpressed as the following formula seventeen:
the formula seventeen:
wherein, TkeIs the electromagnetic torque, L, produced by the kth harmonic of the magnetomotive forcecIs the axial length of the motor, Bk2θ *Is Bk2θThe complex conjugate of (a).
8. The method of calculating the magnetic field of a polyphase cage-type induction motor according to claim 6, wherein step 4 further comprises: based on the harmonic coefficient of each subdomain, calculating the induced current density J induced on the ith rotor bar by the kth space harmonic of the magnetomotive forcekri(r, theta) and the total induced current density Jri(r, θ), expressed as the following equation eighteen:
eighteen formulas:
and obtaining the distribution of the induced current on the ith rotor bar according to the formula eighteenth, wherein the distribution is expressed as the following formula nineteen:
the formula is nineteen:
9. a magnetic field calculation system of a multi-phase cage type induction motor is characterized by comprising a region division module, a vector magnetic potential calculation module, a harmonic coefficient calculation module and an electromagnetic torque calculation module;
the region division module is used for dividing a motor solving region according to the excitation source type so as to obtain a motor model, and solving a distribution function of the current density of the stator winding based on the motor model;
the vector magnetic potential calculation module is used for aiming at the influence of the kth current density harmonic wave, taking the vector magnetic potential in each sub-domain as a solving object of a control equation, respectively establishing a Laplace equation, a Poisson equation and a Helmholtz equation, and solving a general solution of the vector magnetic potential according to boundary conditions among interfaces;
the harmonic coefficient calculation module is used for solving the harmonic coefficient of each sub-domain based on the general solution of the vector magnetic potential of each sub-domain;
the electromagnetic torque calculation module is used for solving the radial and tangential components of the air gap flux density according to the vector magnetic potential expression of the air gap sub-domain based on the harmonic coefficient of each sub-domain, and solving the torque and the total electromagnetic torque caused by the kth space harmonic of the magnetomotive force according to the Maxwell tensor method and the radial and tangential components of the air gap flux density.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113886987A (en) * | 2021-09-29 | 2022-01-04 | 哈尔滨理工大学 | Cage type rotor induction motor modeling method based on improved winding function method |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101420157A (en) * | 2008-12-01 | 2009-04-29 | 中国人民解放军海军工程大学 | Magnetic circuit designing method for non-sine power supply multi-phase induction motor |
| CN112016172A (en) * | 2020-09-15 | 2020-12-01 | 国网湖南省电力有限公司 | Air gap magnetic field prediction method and system of solid rotor induction motor |
| CN112163362A (en) * | 2020-10-15 | 2021-01-01 | 国网湖南省电力有限公司 | Improved permanent magnet motor magnetic field analysis method considering segmented skewed poles and storage medium |
-
2021
- 2021-03-08 CN CN202110252124.9A patent/CN113452209B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101420157A (en) * | 2008-12-01 | 2009-04-29 | 中国人民解放军海军工程大学 | Magnetic circuit designing method for non-sine power supply multi-phase induction motor |
| CN112016172A (en) * | 2020-09-15 | 2020-12-01 | 国网湖南省电力有限公司 | Air gap magnetic field prediction method and system of solid rotor induction motor |
| CN112163362A (en) * | 2020-10-15 | 2021-01-01 | 国网湖南省电力有限公司 | Improved permanent magnet motor magnetic field analysis method considering segmented skewed poles and storage medium |
Non-Patent Citations (4)
| Title |
|---|
| EMAD ROSHANDEL等: "《Analytical Model and Performance ediction of Induction Motors using Subdomain Technique》", 《2020 IEEE ENERGY CONVERSION CONGRESS AND EXPOSITION (ECCE)》 * |
| EMILE DEVILLERS等: "《An Improved 2-D Subdomain Model of Squirrel-Cage Induction Machine Including Winding and Slotting Harmonics at Steady State》", 《IEEE TRANSACTIONS ON MAGNETICS》 * |
| EMILE DEVILLERS等: "《Tangential Effects on Magnetic Vibrations and Acoustic Noise of Induction Machines using Subdomain Method and Electromagnetic Vibration Synthesis 》", 《 2017 IEEE INTERNATIONAL ELECTRIC MACHINES AND DRIVES CONFERENCE (IEMDC)》 * |
| KAMEL BOUGHRARA等: "《2-D Analytical Prediction of Eddy Currents, Circuit Model Parameters, and Steady-State Performances in Solid Rotor Induction Motors》", 《IEEE TRANSACTIONS ON MAGNETICS》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113886987A (en) * | 2021-09-29 | 2022-01-04 | 哈尔滨理工大学 | Cage type rotor induction motor modeling method based on improved winding function method |
| CN113886987B (en) * | 2021-09-29 | 2023-06-30 | 哈尔滨理工大学 | Cage rotor induction motor modeling method based on improved winding function method |
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