CN117828244B - Linear induction motor chain type equivalent circuit and characteristic analysis method - Google Patents
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Abstract
The invention provides a linear induction motor chain equivalent circuit and a characteristic analysis method, solving each pair of pole harmonic magnetomotive force, and performing partial conduction of a position function on the linear induction motor chain equivalent circuit to obtain each pair of pole harmonic current layer density expression; solving domain boundary conditions and Maxwell equation sets established based on a permit-gram transformation method to solve expressions of each pair of pole harmonic air-gap magnetic fields considering longitudinal end effects; analyzing steady-state thrust characteristics of the linear induction motor; solving harmonic excitation inductance of each pair of poles according to excitation inductance definition; setting a three-phase winding current expression, and solving the harmonic secondary current of each pair of poles by combining the harmonic excitation inductance and the induced electromotive force of each pair of poles; based on the harmonic induction electromotive force and the secondary current of each pair of poles, solving a secondary impedance expression, and combining the primary impedance to obtain the linear induction motor chain type equivalent circuit. The invention can more comprehensively and accurately analyze the composition and the operation characteristics of the air gap field of the linear induction motor under different working conditions.
Description
Technical Field
The invention belongs to the field of linear induction motors, and particularly relates to a linear induction motor chain type equivalent circuit and a characteristic analysis method.
Background
The linear induction motor can directly generate linear motion without a transmission mechanism such as a gear box, has the advantages of simple structure, small maintenance amount, low cost and the like, and is widely applied to occasions such as urban rail transit, industrial driving and the like. However, due to the special structures of the two sides of the primary iron core, the half-filled slot double-layer lap winding and the like, the linear induction motor faces serious longitudinal end effect and three-phase asymmetry, so that the air gap magnetic field component and the action mechanism are very complex, and the influence of the longitudinal end effect is gradually aggravated along with the increase of the running speed. The above factors enable the equivalent parameters of the linear induction motor to have high-order, nonlinear and strong-coupling change characteristics. Therefore, deriving an accurate linear induction motor analysis method is important for the research of electromagnetic and driving characteristics of the linear induction motor.
And a part of scholars take secondary vortex generated by primary motion of the linear induction motor as an entry point, and assume that the air gap flux density decays exponentially from the entry end to the exit end of the primary running direction, and the distortion of the air gap flux is considered to influence the excitation inductance of the motor. And correcting the excitation inductance and the iron loss resistance by a function related to the speed and the motor structural parameters, thereby obtaining a motor equivalent model. However, the model cannot reasonably describe the motor characteristics under the working conditions of high speed, high current and the like due to the premise that the model is too simple, and the three-phase asymmetry of the winding is not considered. And the scholars equivalent the primary current-carrying winding to a traveling wave current layer, solve the end outside magnetic field distribution based on a permit-gram transformation method and establish a solution domain boundary condition, further solve the air gap magnetic field distribution through a partial differential equation, and then calculate the power of the primary transmitted to the secondary through the air gap through a Potentilla vector integral, so as to finally obtain the motor equivalent model. But this does not take into account the rich spatial harmonic magnetic field of the windings themselves.
Therefore, it is necessary to provide a linear induction motor chain equivalent circuit and a characteristic analysis method for accurately analyzing the composition of the air gap field of the linear induction motor and the operation characteristics under different working conditions.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a linear induction motor chain type equivalent circuit and a characteristic analysis method, and aims to solve the problems of insufficient magnetic field components and inaccurate operation characteristics of the conventional linear induction motor.
In order to achieve the above object, the present invention provides a linear induction motor chain type equivalent circuit and a characteristic analysis method, comprising the following steps:
S1: carrying out partial conductance of a position function on the primary harmonic magnetomotive force of each pair of poles according to the primary harmonic magnetomotive force obtained by a short primary linear motor winding magnetomotive force analysis method to obtain a density expression of a primary harmonic current layer of each pair of poles;
s2: solving domain boundary conditions and Maxwell equation sets established based on a permit-gram transformation method to solve expressions of each pair of pole harmonic air-gap magnetic fields considering longitudinal end effects;
s3: analyzing steady-state thrust characteristics of the linear induction motor based on density expressions of the harmonic air gap magnetic fields and the current layers of each pair of poles;
S4: solving each pair of pole harmonic induction electromotive force expressions of the three-phase winding according to each pair of pole harmonic air gap magnetic field expressions and winding arrangement modes;
S5: solving harmonic excitation inductance of each pair of poles according to excitation inductance definition; setting three-phase winding current expressions, and solving the secondary current expressions of the harmonic waves of each pair of poles by combining the excitation inductance and the induced electromotive force of the harmonic waves of each pair of poles;
S6: based on the harmonic induction electromotive force and the secondary current of each pair of poles, solving a secondary impedance expression, and combining the primary impedance to obtain a linear induction motor chain type equivalent circuit and a characteristic analysis method.
Further, in the step S2, the density expression of each pair of pole harmonic current layers is:
Wherein the method comprises the steps of ，/>，/>。
Wherein v is harmonic pole pair number, L is primary iron core longitudinal length, omega e is primary angular frequency, J 1v+、J1v- is positive and negative harmonic travelling wave current layer density amplitude of each pair of poles, and F v+、Fv-、φ+、φ- is positive rotation magnetomotive force and negative rotation magnetomotive force amplitude and phase obtained by a short primary linear motor winding magnetomotive force analysis method.
Further, the respective pairs of pole harmonic air gap field expressions accounting for longitudinal end effects at said step S2 are:
；
Wherein B 1v+、B2v+、B3v+、B1v-、B2v-、B3v- is the amplitude of the magnetic density of each pair of pole harmonic normal traveling wave, entrance traveling wave and exit traveling wave of forward traveling wave and reverse traveling wave respectively, alpha 1、α2 is the attenuation coefficient of the magnetic density of the entrance traveling wave and exit traveling wave, and tau e is the pole distance of the magnetic density of the entrance traveling wave and the exit traveling wave.
Further, in the step S3, the steady-state thrust characteristic of the linear induction motor is the characteristic of thrust variation with time under the steady-state operation condition of the motor, and the thrust is calculated by the density of harmonic current layers of each pair of poles and the air gap magnetic field, and the expression is as follows:
；
wherein W is the transverse length of the primary core.
Further, the harmonic induced electromotive forces of the respective pairs at the step S4 take into consideration the distortion effect of the longitudinal end effect on the air gap flux density.
Further, the method is applied to a linear induction motor which does not consider iron loss, skin effect and lateral edge effect.
The linear induction motor chain equivalent circuit in the step S6 can analyze the rule of influence of each pair of pole harmonics on motor performance.
In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:
Compared with the existing method, the method fully considers the harmonic wave of the method of the winding, takes the density of the harmonic current layer of each pole pair number as an excitation source, and solves the composition and the change rule of the air gap magnetic field by combining the solving domain boundary condition and the Maxwell equation set established based on the permit-gram transformation method; solving the steady-state thrust characteristic of the linear induction motor by using the density of the pole pair harmonic current layer and the air gap magnetic field, analyzing the steady-state thrust and time-varying characteristic of the linear induction motor under different working conditions, revealing the reason of the linear induction double frequency thrust fluctuation, and calculating the influence rule of the pole pair harmonic magnetic field on the thrust characteristic; according to the winding arrangement mode and the pole pair number harmonic magnetic field, solving the pole pair number harmonic induction electromotive force of each phase winding, then solving the pole pair number excitation inductance of each harmonic according to definition, further solving the pole pair number secondary current and the secondary impedance of each harmonic, and combining the primary impedance to obtain the linear induction motor chain type equivalent circuit.
The method provided by the invention can more comprehensively and accurately analyze the composition and the operation characteristics of the air gap field of the linear induction motor.
Drawings
FIG. 1 is a flow chart of a linear induction motor chain type equivalent circuit and a characteristic analysis method provided by the invention;
FIG. 2 (a) is a schematic diagram of a linear induction motor according to the present invention;
FIG. 2 (b) is a linear induction motor analysis model for use in the present invention;
FIG. 3 is a graph of air gap flux density versus speed rating provided by an embodiment of the invention;
fig. 4 is a linear induction motor chain equivalent circuit provided by the invention;
fig. 5 is a graph of motor thrust characteristics analysis provided by the embodiment.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention provides a linear induction motor chain type equivalent circuit and a characteristic analysis method flow chart, as shown in fig. 1, specifically comprising the following steps:
S1: according to the magnetomotive force of each pair of poles solved by the short primary linear motor winding magnetomotive force analysis method, performing partial conductance of a position function on the magnetomotive force to obtain density expressions of each pair of poles harmonic current layers;
S2: solving the expressions of each pair of pole harmonic air-gap magnetic fields considering the longitudinal end effect by combining the solving domain boundary condition and the Maxwell equation set established based on the Kernel transformation method;
s3: analyzing steady-state thrust characteristics of the linear induction motor based on density expressions of the harmonic air gap magnetic fields and the current layers of each pair of poles;
S4: solving each pair of pole harmonic induction electromotive force expressions of the three-phase winding according to each pair of pole harmonic air gap magnetic field expressions and winding arrangement modes;
S5: solving harmonic excitation inductance of each pair of poles according to excitation inductance definition; setting three-phase winding current expressions, and solving the secondary current expressions of the harmonic waves of each pair of poles by combining the excitation inductance and the induced electromotive force of the harmonic waves of each pair of poles;
S6: based on the harmonic induction electromotive force and the secondary current of each pair of poles, solving a secondary impedance expression, and combining the primary impedance to obtain the linear induction motor chain type equivalent circuit.
The following specifically describes a linear induction motor chain equivalent circuit and a characteristic analysis method.
Under the precondition of neglecting the core loss, the skin effect and the transverse edge effect, the chain type equivalent circuit of the linear induction motor and the characteristic analysis method are deduced.
(1) Establishing a one-dimensional field analysis model of a linear induction motor
As shown in fig. 2 (a), the primary core movement direction is the x-axis (longitudinal direction), the primary winding current flow direction is the z-axis (transverse direction), and the effective direction of the air gap flux density is the y-axis. The arrangement mode of the windings is half-filled slot double-layer lap windings which are most commonly used in the current rail transit linear induction motor. The one-dimensional field analysis model satisfies the following conditions:
(a) The magnetic permeability of the primary iron core and the secondary iron yoke is infinite, and the iron core loss is not considered;
(b) The air gap magnetic field value comprises a y-axis component, is irrelevant to a y-axis coordinate y, and the traveling wave magnetic field and the running direction of the motor are along an x-axis, and all electromagnetic field parameters are sine functions of the x-axis coordinate x and time t;
(c) The secondary skin effect is not considered and the secondary-side electrical parameters are all reduced to the primary.
(2) According to the linear winding magnetomotive force analysis method, solving the harmonic magnetomotive force of each pole pair number:
；
Wherein the method comprises the steps of 。
Wherein v is harmonic pole pair number, L is longitudinal length of the primary iron core, omega e is primary angular frequency, and F v+、Fv-、φ+、φ- is amplitude and phase of primary forward rotation magnetomotive force and reverse rotation magnetomotive force respectively.
(3) Performing partial conductance of a position function x on each pole pair number harmonic magnetomotive force, and solving the density of a primary pole pair number harmonic current layer:
；
In the method, in the process of the invention, ，/>；
(4) Based on the linear induction motor magnetic field analysis model shown in fig. 2 (a) and the solving domain boundary conditions established based on the k-gram transformation method, solving the air gap magnetic field:
；
Wherein B 1v+、B2v+、B3v+、B1v-、B2v-、B3v- is the amplitude of the magnetic density of each pair of pole harmonic normal traveling wave, entrance traveling wave and exit traveling wave of forward traveling wave and reverse traveling wave respectively, alpha 1、α2 is the attenuation coefficient of the magnetic density of the entrance traveling wave and exit traveling wave, and tau e is the pole distance of the magnetic density of the entrance traveling wave and the exit traveling wave.
The method comprises the following specific steps:
Since expressions of the forward rotation component and the reverse rotation component are almost the same, the description will be made with respect to the forward rotation component as an analysis example.
(4-1) One-dimensional field analysis model of linear induction motor applied according to the present invention fig. 2 (b), by ampere's loop law, it is possible to obtain:
；
Wherein g e is an equivalent electromagnetic air gap, mu 0 is air permeability, j 1v+ is positive rotation primary v antipodal harmonic surface current density, and j 2v+ is v antipodal harmonic equivalent traveling wave current layer density of a positive rotation secondary conductor.
(4-2) Introducing vector magnetic potential, and obtaining a relational expression of the density of each pole-pair harmonic equivalent current layer of the forward secondary conductor and the vector magnetic potential according to the relation of current density, conductivity and air gap electric field:
；
the relation between the vector magnetic potential and the air gap magnetic flux density and the electric field intensity is as follows:
，
；
wherein σ s is the surface conductivity of the secondary conductor, σ s =σd, and σ is the secondary conductor bulk conductivity; d is the thickness of the secondary conductor plate; v 2 is the secondary movement speed.
(4-3) The full solution of the vector magnetic bits available according to the relation in (4-1), (4-2) is:
；
Wherein c 1、c2 is a coefficient to be determined, and other coefficient expressions For the special solution of equation,/>，，/>。
Wherein,，/>，/>，/>，/>，/>，，/>。
Where τ v is the V antipodal harmonic pole pitch, s v+ is the forward V antipodal harmonic slip, and V sv+ is the forward V antipodal harmonic synchronous speed.
(4-4) Solving the air-gap field according to the full solution of the vector magnetic potential and the relation between the full solution and the air-gap magnetic flux density:
；
Further, it can be modified as follows:
；
wherein B 1v+、B2v+、B3v+ is the amplitude of each pair of pole harmonic normal traveling wave, entrance traveling wave and exit traveling wave magnetic density of the forward traveling wave respectively.
And (4-5) the same as the inverse component solving process of the pole pair harmonic air gap flux density, and finally obtaining the expression:
；
(4-6) analyzing the air gap flux density distribution condition of the Japanese 12000 type motor under each working condition according to the expression, comparing the air gap flux density distribution condition with a finite element calculation result, and giving an air gap flux density comparison chart under the rated working condition, wherein as shown in figure 3, the analysis result is highly matched with the simulation result, and the effectiveness of the method is verified.
(5) Based on the density expressions of the harmonic air gap magnetic fields and the current layers of each pair of poles, the steady-state thrust characteristics of the linear induction motor are analyzed:
；
wherein W is the transverse length of the primary core.
The linear induction motor steady-state thrust characteristics can be analyzed, and steady-state thrust frequency doubling fluctuation characteristics can be accurately reflected.
(6) According to the harmonic air gap magnetic field expressions of each pair of poles and the winding arrangement mode, solving the harmonic induction electromotive force expressions of each pair of poles of the three-phase winding:
Since expressions of the forward rotation component and the reverse rotation component are almost the same, the description will be made with respect to the forward rotation component as an analysis example.
Integrating the position function x on the air gap flux density, and further deriving the time t to obtain:
；
(7) Solving harmonic excitation inductance of each pair of poles according to excitation inductance definition; setting three-phase winding current expressions, and solving the secondary current expressions of the harmonic waves of each pair of poles by combining the excitation inductance and the induced electromotive force of the harmonic waves of each pair of poles;
，/>，/>；
Wherein i mv+ is positive rotation of each pair of pole harmonic excitation current, i 2v+ is each pair of pole harmonic secondary current, i s is stator current, N ϕ is each phase of series turns, and k Np is each pair of pole harmonic winding coefficient
(8) Based on the harmonic induced electromotive force and the secondary current of each pair of poles, solving a secondary impedance expression:
；
(9) And the primary impedance is combined to obtain a linear induction motor chain type equivalent circuit, as shown in fig. 4.
(10) The 12000 linear induction motor constant current constant frequency (210A, 22 Hz) characteristic curve can be analyzed based on the linear induction motor chain type equivalent circuit, as shown in figure 5.
By applying the analysis method and combining with computer-aided calculation, the composition and the operation characteristics of the linear induction motor for analyzing the air gap field of the linear induction motor can be calculated comprehensively and accurately.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (2)
1. The linear induction motor chain type equivalent circuit and the characteristic analysis method are characterized by comprising the following steps:
S1: according to the harmonic magnetomotive force of each pair of poles of the primary winding solved by the short primary linear motor winding magnetomotive force analysis method, performing partial conductance of a position function on the primary winding to obtain a density expression of a harmonic current layer of each pair of poles of the primary winding;
In the step S1, the density expression of the primary harmonic current layers of each pair of poles is:
；
Wherein the method comprises the steps of ，/>，/>；
Wherein v is harmonic pole pair number, L is primary iron core longitudinal length, omega e is primary angular frequency, J v+、Jv- is primary travelling wave current layer density amplitude of each pair of positive and negative harmonic, and F v+、Fv-、φv+、φv- is amplitude and phase of positive rotation magnetomotive force and negative rotation magnetomotive force solved by a short primary linear motor winding magnetomotive force analysis method respectively;
s2: solving domain boundary conditions and Maxwell equation sets established based on a permit-gram transformation method to solve expressions of each pair of pole harmonic air-gap magnetic fields considering longitudinal end effects;
The pole harmonic air gap field pairs accounting for the longitudinal end effect at step S2 are expressed as:
；
Wherein B 1v+、B2v+、B3v+、B1v-、B2v-、B3v- is the amplitude of the magnetic density of each pair of pole harmonic normal traveling wave, the input traveling wave and the output traveling wave of the forward traveling wave and the reverse traveling wave respectively, alpha 1、α2 is the attenuation coefficient of the magnetic density of the input traveling wave and the output traveling wave, and tau e is the pole distance of the magnetic density of the input traveling wave and the output traveling wave;
s3: analyzing steady-state thrust characteristics of the linear induction motor based on density expressions of the harmonic air gap magnetic fields and the current layers of each pair of poles;
in the step S3, the steady-state thrust characteristic of the linear induction motor is the characteristic that the thrust changes with time under the steady-state operation condition of the motor, and the expression is as follows:
；
wherein W is the transverse length of the primary iron core;
S4: solving each pair of pole harmonic induction electromotive force expressions of the three-phase winding according to each pair of pole harmonic air gap magnetic field expressions and winding arrangement modes;
S5: solving harmonic excitation inductance of each pair of poles according to excitation inductance definition; setting three-phase winding current expressions, and solving the secondary current expressions of the harmonic waves of each pair of poles by combining the excitation inductance and the induced electromotive force of the harmonic waves of each pair of poles;
S6: based on the harmonic induction electromotive force and the secondary current of each pair of poles, solving a secondary impedance expression, and combining the primary impedance to obtain the linear induction motor chain type equivalent circuit.
2. The linear induction motor chain equivalent circuit and characteristic analysis method according to claim 1, wherein the distortion of the air gap flux density by the longitudinal end effect is taken into account by each pair of pole harmonic induced electromotive forces in the step S4.
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| CN115758485A (en) * | 2022-11-11 | 2023-03-07 | 中国人民解放军海军工程大学 | Method for modeling equivalent circuit of linear phase-shifting transformer and obtaining performance parameters of equivalent circuit |
| CN116191807A (en) * | 2023-01-16 | 2023-05-30 | 合肥工业大学 | Alternating pole magnetic flux reversing motor and analytic modeling method thereof |
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