CN103605858A - Steady-state characteristic analysis method for linear induction motor - Google Patents
Steady-state characteristic analysis method for linear induction motor Download PDFInfo
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Abstract
The invention discloses a steady-state characteristic analysis method for a linear induction motor. The steady-state characteristic analysis method includes the following steps: 1), creating an unidimensional magnetic-density distribution model of the linear induction motor; 2), calculating the magnetic density of a y-axis according to the unidimensional magnetic-density distribution model; 3), acquiring electric field intensity through the magnetic density of the y-axis according to characteristics of magnetic barrier surfaces; 4), calculating plural forms of amplitudes of a normal magnetic-density travelling wave, an inlet-end magnetic-density reflecting wave and an outlet-end magnetic-density reflecting wave; 5), calculating impedance of the normal magnetic-density travelling wave, the inlet-end magnetic-density reflecting wave and the outlet-end magnetic-density reflecting wave; 6), calculating total impedance of a single-phase circuit of the linear induction motor; 7), analyzing performance parameters of the linear induction motor in different stable states. By the steady-state characteristic analysis method, analysis difficulty and calculation time of the magnetic characteristics of the linear induction motor are reduced; the steady-state characteristic analysis method is high in accuracy and can be conveniently applied to initial electromagnetism optimization design and middle-late-period electromagnetism parameter and driving performance analysis of the linear induction motor.
Description
Technical Field
The invention belongs to the technical field of computer aided design of linear induction motors, and particularly relates to a modeling method for a steady-state characteristic analysis equivalent circuit of a linear induction motor.
Background
The linear induction motor can directly generate linear mechanical motion without an intermediate transmission conversion device, has the advantages of simple structure, firmness, durability, low cost and the like, and is widely applied to occasions such as transportation, mine lifting, parcel distribution, electric doors, roller coasters and the like. However, the linear induction motor has different degrees of transverse and longitudinal air gap flux density distortion due to inconsistent primary and secondary widths, the influence of a primary open-close magnetic circuit and half-filled slots at two ends of the primary, and the thrust of the linear induction motor can be obviously reduced and the safe operation of the linear induction motor can be influenced along with the nonlinear change of different slip, the excitation frequency of a primary coil and the operation speed of the motor in serious cases. How to adopt effective electromagnetic design and driving characteristic analysis model to accurately research the electromagnetic and driving characteristics of the linear induction motor is very important.
The current linear induction motor analysis method mainly comprises an electromagnetic field element limiting method and a parameter equivalent model method, which are called field and path analysis methods for short. The electromagnetic field analysis method can carry out qualitative or quantitative analysis on the steady-state and dynamic characteristics of the motor, however, because the secondary guide plate of the linear induction motor has induced eddy current, an analysis model must be solved by using a transient eddy current field, and the method has the defects of large subdivision area, large number of grids, long calculation time and the like. In addition, if the initial boundary conditions and mesh subdivision sizes are not appropriate, reasonable calculation results are difficult to obtain, and electromagnetic optimization design cannot be performed (S.A. Nasar and I.Boldea, Electric drives. Boca Raton, FL: CRC, 1999.). The lumped parameter equivalent model method is used for correspondingly simplifying the linear induction motor, and how to reasonably describe the special properties of the motor is particularly critical, and mainly comprises the influences of transverse edge effect, longitudinal edge effect, half-filled slot and the like. Duncan proposed a T-type Equivalent model of a Linear induction motor in 1983, considering only the longitudinal edge effect, and assuming that the air gap flux density decays exponentially from the entry end to the exit end of the primary running direction, a simple Equivalent model of the motor is derived therefrom (j. The model has clear concept and short calculation time, and can reasonably describe the change of the electromagnetic parameters and the driving characteristics of the motor to a certain extent. However, the assumption of the premise is too simple, the model cannot reasonably describe the motor characteristics under the working conditions of transverse edge effect, high speed, large current excitation and the like, and cannot be applied to the electromagnetic optimization design of the linear induction motor (G.Kang and K.Nam, Field-oriented control scheme for linear induction motor with the end effect, Proc.Inst.Electron.Eng. -electric.Power application, vol.152, No.6, pp.1565-1572, Nov.2005).
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides the method for analyzing the steady-state characteristics of the linear induction motor, which considers the accuracy of an electromagnetic field analysis method and the rapidity of a parameter-integrating method, adopts an analysis idea of combining a field and a circuit, obviously reduces the analysis difficulty and the calculation time of the electromagnetic characteristics of the linear induction motor, has high accuracy, can be conveniently applied to the initial electromagnetic optimization design and the middle and later electromagnetic parameter and driving performance analysis of the linear induction motor, and can provide beneficial reference for the dynamic characteristic analysis and the high-level control strategy design of the linear induction motor.
To achieve the above object, according to one aspect of the present invention, there is provided a method for analyzing steady-state characteristics of a linear induction motor, comprising the steps of:
(1) establishing a one-dimensional flux density distribution model of the linear induction motor, wherein the primary mechanical motion direction is taken as an x axis, the effective flux density direction of an air gap is taken as a y axis, and the one-dimensional flux density distribution model meets the following conditions:
(A) the primary windings are distributed in a limited area, and the magnetic permeability of the primary iron core lamination and the secondary iron yoke is infinite;
(B) the air gap magnetic field only contains y-axis components and is irrelevant to y-axis coordinates, the traveling wave magnetic field and the motor running direction are along the x-axis, all electromagnetic field parameters are sine functions of the x-axis coordinates x and time t, only the fundamental component of each field quantity is considered, and the influence of space harmonics and time harmonics is ignored;
(C) the secondary skin effect is not considered, and the secondary end electrical parameters are all reduced to the primary;
(2) calculating y-axis magnetic flux density according to one-dimensional magnetic flux density distribution model
Wherein,
and
the amplitudes of the normal flux density traveling wave, the input flux density reflected wave and the output flux density reflected wave are in complex forms, tau is the half wavelength of the normal flux density traveling wave, tau is the amplitude of the normal flux density traveling wave, and tau is the amplitude of the normal flux density traveling waveeIs a half wavelength, alpha, of the incident-end magnetic flux density reflected wave and the emergent-end magnetic flux density reflected wave1For inputting the attenuation coefficient of magnetic density reflected wave, alpha2The attenuation coefficient of the outgoing magnetic flux density reflected wave is shown, and omega is the primary angular frequency;
(3) two end faces in the primary x-axis direction are used as magnetic barrier faces, and the following characteristics of the magnetic barrier faces are utilized: (A) all field quantities of the linear induction motor are distributed between the magnetic barrier surfaces; (B) the magnetic flux density outside the area between the magnetic barrier surfaces is zero, and the component of each field quantity between the magnetic barrier surfaces, which is vertical to the two end surfaces, is zero; (C) the sum of the area integrals of the air gap flux density between the magnetic barrier surfaces is zero; (D) the electric field intensity outside the region between the magnetic barrier surfaces is zero, and the area of the electric field intensity between the magnetic barrier surfaces is zero; magnetic flux density b from y-axisyIs expressed to obtain the electric field intensity ezAnd the complex form of the amplitude of the normal flux density traveling wave back emf
Inputting complex form of amplitude of magnetic density reflected wave counter potentialAnd the complex form of the amplitude of the magnetic density reflected wave counter potential at the output end
(4) According to the principle of the rotating electrical machine, obtaining the complex form of the amplitude of the normal magnetic flux density traveling wave
According to the one-dimensional magnetic flux density distribution model and the magnetic barrier surface characteristics, the magnetic flux density b is measured from the y-axisyThe expression of (a) obtains the complex form of the amplitude of the incoming magnetic flux density reflected wave
And the complex form of the amplitude of the outgoing magnetic dense reflected wave
(5) Based on the equality of the primary and secondary complex powers and conservation of energy, the complex form of the amplitude of the normal flux density traveling waveAnd the complex form of the amplitude of the normal flux density traveling wave back emf
Obtaining normal magnetic density traveling wave impedance
The complex form of the amplitude of the magnetic flux density reflected wave from the input end
And the complex form of the amplitude of the counter potential of the magnetic density reflected wave at the input endObtaining the impedance of the input end magnetic density reflected wave
Wherein,
the impedance correction coefficient of the magnetic density reflection wave at the input end; complex form of amplitude of magnetic dense reflected wave from output end
And the complex form of the amplitude of the magnetic density reflected wave counter potential at the output end
Obtaining the magnetic density reflected wave impedance of the output end
Wherein,
the impedance correction coefficient of the outgoing end magnetic density reflected wave;
(6) impedance of normal magnetic flux density traveling wave
Impedance of input end magnetic density reflection wave
And output end magnetic density reflected wave impedance
Calculating to obtain the total impedance of the single-phase circuit of the linear induction motor
Wherein r is0And x0Respectively primary phase resistance and primary phase leakage reactance, corrected normal magnetic flux density traveling wave impedance
Corrected longitudinal edge effect impedance
And KpRespectively a transverse flux density distortion correction coefficient, a longitudinal flux density distortion correction coefficient and a primary half-filled slot correction coefficient;
(7) total impedance of single-phase circuit of linear induction motor
And analyzing the performance parameters of the linear induction motor under different stable states.
Preferably, the step (2) comprises the sub-steps of:
(2-1) obtaining the following parameters according to a one-dimensional flux density distribution model by using an ampere loop law:
wherein j is1Is primary area current density, j2Is the secondary surface current density;
(2-2) obtaining an air gap magnetic field magnetic flux density equation according to the relationship among the current density, the resistivity and the air gap electric field:
wherein v is the running speed of the motor;
(2-3) simultaneously considering the influence of the normal flux density traveling wave, the incoming flux density reflected wave and the outgoing flux density reflected wave on the air gap flux linkage to obtain the y-axis flux density byIs described in (1).
Preferably, in the step (3),
wherein,
and
are respectively as
Wherein v issThe synchronous speed of the motor.
Preferably, in the step (4),
wherein, mu0In order to have a magnetic permeability of air,
is the primary current density amplitude, g is the equivalent length of the electromagnetic air gap, s is the slip ratio of the motor, and the quality factor <math>
<mrow>
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</math> 
Andrespectively as follows:
wherein L ispIs the primary length.
Preferably, is prepared from
Solving a figure of merit expression wherein LmIs mutual inductance of r2Is the secondary equivalent resistance.
Preferably, in the step (5),
wherein the air gap reactance
Secondary resistanceWherein m is the primary winding phase number, f is the primary excitation frequency, w1For each phase of the primary winding, Kw1Is the winding distribution coefficient, /)wThe width of the primary lamination, P is the actual pole pair number of the motor, and sigma is the conductivity of the secondary guide plate; <math>
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preferably, in the step (6), the transverse magnetic flux density distortion correction coefficient
Wherein G is the equivalent length of the electromagnetic air gap, s is the slip ratio of the motor, G is the quality factor,
as a function of the motor configuration and operating conditions, a is half the primary width, <math>
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</math> longitudinal magnetic flux density distortion correction coefficient <math>
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</math> Primary half-filled cell correction factor
Wherein, P is the actual pole pair number of the motor, y1The number of short-distance slots of the winding is shown, m is the number of phases of the primary winding, and q is the number of slots of each phase of the motor.
Preferably, the function of the motor structure and the operating state
Comprises the following steps:
where c is half the difference between the primary and secondary widths.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
1. by adopting the field and path combined analysis idea, the analysis difficulty and the calculation time of the electromagnetic characteristics of the linear induction motor are obviously reduced. The electromagnetic characteristics of the linear induction motor are described by using 4 correction coefficients, so that the electromagnetic parameters and the driving characteristics of the linear induction motor under different working conditions can be reasonably researched. The special properties of linear induction motors are embodied in the variation of the associated correction coefficients.
2. The accuracy is high. In the process of establishing the air gap flux density equation, the influence of normal flux density traveling waves, incoming-end flux density reflected waves and outgoing-end flux density reflected waves on an air gap flux linkage is considered at the same time, and the changes of the attenuation coefficient of the incoming-end reflected waves, the attenuation coefficient of the outgoing-end reflected waves and the half wavelength of the side-end effect waves along with the primary length and the running speed of the motor are fully analyzed.
3. A one-dimensional analysis model is combined, a geometric integral method is adopted, a novel quality factor expression is deduced by utilizing the relation between current density and magnetic flux density, and the energy conversion capability of the linear induction motor can be more reasonably described.
4. The method can be conveniently applied to initial electromagnetic optimization design and middle and later electromagnetic parameter and driving performance analysis of the linear induction motor, and can provide beneficial reference for dynamic characteristic analysis and design of high-level control strategies of the linear induction motor.
Drawings
Fig. 1 is a schematic flow chart of a steady-state characteristic analysis method of a linear induction motor according to an embodiment of the present invention;
fig. 2 is a one-dimensional diagram of a linear induction motor according to an embodiment of the present invention, wherein (a) is a schematic structural diagram; (b) is an analytical model;
FIG. 3 is a schematic view of a magnetic barrier surface of an embodiment of the present invention;
FIG. 4 is a figure of merit derivation for a linear induction motor according to an embodiment of the present invention;
fig. 5 is a normal traveling wave impedance equivalent circuit diagram of a linear induction motor according to an embodiment of the present invention;
fig. 6 is a schematic view of a lateral structure of a linear induction motor according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of the total impedance composition of a single phase circuit of a linear induction motor in accordance with an embodiment of the present invention;
fig. 8 is a comparison graph of the steady-state torque variation of the simulated linear induction motor at different speeds by the analysis method of the embodiment of the invention and the actual test result.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the method for analyzing the steady-state characteristics of the linear induction motor according to the embodiment of the present invention includes the following steps:
(1) and establishing a one-dimensional flux density distribution model of the linear induction motor.
As shown in fig. 2 (a), the primary mechanical motion direction is x-axis (also called longitudinal), the primary winding effective current direction is z-axis (also called transverse), and the air gap effective flux density direction is y-axis. The one-dimensional magnetic flux density distribution model meets the following conditions:
(A) the primary windings are distributed in a limited area, and the permeability of the primary core lamination and the secondary iron yoke is infinite.
(B) The air gap magnetic field only contains a y-axis component and is irrelevant to a y-axis coordinate y, the traveling wave magnetic field and the motor running direction are along an x-axis, all electromagnetic field parameters are sine functions of the x-axis coordinate x and time t, only the fundamental component of each field quantity is considered, and the influence of space harmonics and time harmonics is ignored.
(C) The secondary skin effect is not taken into account and the secondary end electrical parameters are all relegated to the primary.
(2) Calculating y-axis magnetic flux density according to one-dimensional magnetic flux density distribution model
Wherein,
andthe amplitudes of the normal flux density traveling wave, the input flux density reflected wave and the output flux density reflected wave are in complex forms, tau is the half wavelength of the normal flux density traveling wave, tau is the amplitude of the normal flux density traveling wave, and tau is the amplitude of the normal flux density traveling waveeIs a half wavelength, alpha, of the incident-end magnetic flux density reflected wave and the emergent-end magnetic flux density reflected wave1For inputting the attenuation coefficient of magnetic density reflected wave, alpha2The attenuation coefficient of the outgoing magnetic flux density reflected wave is shown.
The method specifically comprises the following steps:
(2-1) fig. 2 (b) is a one-dimensional analysis model of the linear induction motor according to the embodiment of the present invention. From ampere-loop law, one can derive:
wherein j is1Is primary area current density, j2Is the secondary surface current density.
(2-2) obtaining an air gap magnetic field magnetic flux density equation according to the relationship among the current density, the resistivity and the air gap electric field, wherein the air gap magnetic field magnetic flux density equation is as follows:
wherein v is the motor running speed.
(2-3) considering the influence of normal flux density traveling wave, incoming flux density reflected wave and outgoing flux density reflected wave on air gap flux linkage, and obtaining y-axis flux density b according to the formula (2) and the formula (3)yIs described in (1).
(3) Taking two end faces EF and GH in the primary x-axis direction as magnetic barrier faces, as shown in fig. 3, the following characteristics of the magnetic barrier faces are utilized: (A) all field quantities of the linear induction motor are distributed between the magnetic barrier surfaces; (B) the magnetic flux density outside the area between the magnetic barrier surfaces is zero, and the component of each field quantity between the magnetic barrier surfaces, which is vertical to the two end surfaces, is zero; (C)the sum of the area integrals of the air gap flux densities between the surfaces of the magnetic barriers is zero (first class boundary condition); (D) the field strength outside the region between the barrier surfaces is zero, and the area of the field strength between the barrier surfaces is zero (second type boundary condition) determined by the y-axis magnetic flux density byObtaining the electric field intensity
Wherein the complex form of the amplitude of the counter-electromotive force of the normal magnetic density traveling waveInputting complex form of amplitude of magnetic density reflected wave counter potential
And the complex form of the amplitude of the magnetic density reflected wave counter potential at the output end
Are respectively as
Wherein v issThe synchronous speed of the motor.
The specific calculation procedure is as follows.
According to the second type of boundary condition of the magnetic barrier surface, the electric field intensity eZHas a distribution of zero over the surface of the magnetic barrier. Assuming that one plane is parallel to the xy-plane and cuts the secondary guide plate, the secondary current is divided into zero in the area of this cut plane, i.e.:
according to the electromagnetic field theory and the first boundary condition of the magnetic barrier surface, the following conditions can be obtained:
further derivation and simplification from equations (7) - (10) yields the electric field strength eZThe expression of (a) is:
depending on the nature of the magnetic barrier surface, the distribution of the tangential component of the electric field strength over the magnetic barrier surface is zero, which can be obtained:
the distribution of the electric field strength between the two barrier surfaces is:
combining the formulas (1) and (14), deriving the electric field intensity eZIs described in (1).
(4) According to the principle of the rotating electrical machine, obtaining the complex form of the amplitude of the normal magnetic flux density traveling wave
Wherein, mu0Is airThe magnetic permeability of the magnetic material is improved,
is the primary current density amplitude, g is the equivalent length of the electromagnetic air gap, s is the slip ratio of the motor, and the quality factor
Wherein σ is the secondary guide plate conductivity and ω is the primary angular frequency. According to the one-dimensional magnetic flux density distribution model and the characteristics of the magnetic barrier surface, the magnetic flux density b is measured by the y-axisyThe complex form of the amplitude of the input end magnetic flux density reflected wave is obtained
And the complex form of the amplitude of the outgoing magnetic dense reflected wave
Wherein L ispIs the primary length.
Inputting complex form of amplitude of magnetic flux density reflected wave
And the complex form of the amplitude of the outgoing magnetic dense reflected wave
Specifically, the following method was used.
From the first class of boundary conditions:
in the one-dimensional model, the primary excitation current density has only z-axis component, and the vector magnetic potential is based on the electromagnetic field theory
Only containHas a z-axis component, namely:
from coulomb's law we can derive:
since the magnetic flux density outside the region between the two end faces is zero, the vector magnetic potential in the outer space is only time-dependent and does not vary with position, and can therefore be simplified to aZ=aZ(t) of (d). Since the energy of the magnetic field is limited,and each field quantity of the linear induction motor is distributed between two end faces in the primary x axial direction, and a is deducedZ=0。
According to the second class of boundary conditions, it can be deduced that the air gap flux density expression satisfies:
by bringing formulae (1) and (17) into formula (21), further simplification can be achieved:
wherein, <math>
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Andis described in (1).
Specifically, a figure of merit is calculated from a one-dimensional flux density distribution model
Wherein L ismIs mutual inductance of r2Is the equivalent resistance of the secondary side of the transformer,
the specific calculation procedure is as follows.
The energy (related to G) of the mechanical port on the secondary side of the linear induction motor is generated by the force and velocity, while the force is related to the current and flux linkage at the electrical port. From a microscopic point of view, the current is generated by an induced potential and the flux linkage is generated by the current, and thus it can be considered that
From microscopic ohm's law and magnetic circuit lawMeanwhile, the influence of the speed omega is considered, and the quality factor G and the mutual inductance L in the one-dimensional model can be determinedmPrimary angular frequency omega and secondary equivalent resistance r2Correlation gives the formula (23).
Real part B of normal magnetic flux density traveling wave through air gap magnetomotive force0And secondary surface current density amplitude J2Can derive B from the related mathematical equation0And J2The relationship of (1) is:
fig. 4 is a figure of merit derivation for a linear induction motor according to an embodiment of the present invention. As shown in fig. 4, the flux linkage expression of the closed loop ABCD area is:
wherein WsecThe secondary conductor plate width. Let the resistance of the closed loop ABCD be Deltar at the current density j2The voltage drop under action Δ u is:
let the inductance of ABCD be Δ L, T in equation (23)rExpressed as:
t can be obtained by bringing formulae (24) to (26) into formula (27)rIs described in (1).
(5) Based on the equality of the primary and secondary complex powers and conservation of energy, the complex form of the amplitude of the normal flux density traveling wave
And the complex form of the amplitude of the normal flux density traveling wave back emf
Obtaining normal magnetic density traveling wave impedance
Wherein the air gap reactanceSecondary resistance
Wherein m is the primary winding phase number, f is the primary excitation frequency, w1For each phase of the primary winding, Kw1Is the winding distribution coefficient, /)wThe width of the primary lamination is defined, and P is the actual pole pair number of the motor; the complex form of the amplitude of the magnetic flux density reflected wave from the input end
And the complex form of the amplitude of the counter potential of the magnetic density reflected wave at the input end
Obtaining the impedance of the input end magnetic density reflected wave
Wherein the correction coefficient
Complex form of amplitude of magnetic dense reflected wave from output end
And the complex form of the amplitude of the magnetic density reflected wave counter potential at the output end
Obtaining the magnetic density reflected wave impedance of the output end
Wherein the correction coefficient <math>
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The specific derivation process is as follows:
(5-1) calculating the normal magnetic flux density traveling wave impedance
The electromagnetic thrust F (x, t) of the linear induction motor is expressed as:
primary surface current amplitude J1The phase current amplitude I and the phase current amplitude I generate the same air gap magnetomotive force, and the air gap magnetomotive force and the phase current amplitude I and the air gap magnetomotive force satisfy the following relation:
normal travelling wave induced electromotive force of motor
Comprises the following steps:
the normal magnetic flux density traveling wave impedance can be obtained according to ohm's law as follows:
wherein the air gap reactance XmThe expression of (a) is:
fundamental wave electromagnetic thrust Fe0Can be solved by the relative flux density and current density as:
wherein the primary length Lp=2P τ, motor running speed v and motor synchronous speed vsIs v = (1-s) vs. The mechanical power of the motor is thus:
due to the straight lineThe secondary of the induction motor is a metal conductor plate, so that the leakage inductance of the secondary is very small and is not considered for the moment, and meanwhile, the influence of iron loss resistance is ignored (the working frequency is lower). Therefore, the normal traveling wave impedance in equation (31)
Can be regarded as an air gap reactance XmAnd an equivalent resistance r2The/s is formed by connecting in parallel, as shown in FIG. 5, namely:
in combination with the formulas (23) and (34), the secondary resistance r can be derived2The expression is as follows:
(5-2) calculating the magnetic density reflected wave impedance of the input end
Inputting total electromagnetic power P of magnetic flux reflected wavem1Can be solved as:
the input end has magnetic density reflection wave impedance of
By simplifying the obtained correction coefficient
Comprises the following steps:
electromagnetic thrust F of incoming magnetic density reflected wavee1And total electromagnetic output power Pm1In relation to each other, similar to equation (33), we obtain:
corresponding effective electromagnetic power P of incoming-end magnetic secret reflected wavee1Comprises the following steps:
the effective impedance of the magnetic flux density reflected wave thrust at the input end is
Wherein the correction coefficient
Comprises the following steps:
from the equations (37) and (40), the input end magnetic density reflection leakage reactance is
(5-3) calculating the end magnetic density reflected wave impedance
Total electromagnetic power P of outgoing magnetic flux density reflected wavem2Can be solved as:
that is, the magnetic density reflected wave impedance at the output end is
By simplifying the obtained correction coefficient
Comprises the following steps:
the electromagnetic thrust of the outgoing end magnetic density reflected wave is as follows:
the corresponding effective electromagnetic power of the outgoing end magnetic flux density reflected wave is as follows:
that is, the effective impedance of the magnetic flux density reflected wave thrust at the outlet end is
Wherein the correction coefficient
Comprises the following steps:
from the equations (42) and (44), the magnetic flux density reflection leakage reactance at the output end is
(6) Impedance of normal magnetic flux density traveling wave
Impedance of input end magnetic density reflection wave
And output end magnetic density reflected wave impedanceCalculating to obtain the total impedance of the single-phase circuit of the linear induction motor
Comprises the following steps:
wherein the primary phase resistance r0=ρwLavw1/swPrimary phase leakage reactance
For a correct normal flux density traveling wave impedance,
for corrected longitudinal side-end effect impedance, where pwIs primary winding resistivity, LavFor each turn of winding length, w1Number of coils, s, connected in series for each phase windingwIs the cross-sectional area of each turn of the coil, WpriFor the width of the primary lamination, q is the number of slots per phase of the motor, λs、λt、λeAnd λdThe magnetic leakage conductivity of the primary slot, the magnetic leakage conductivity of the primary tooth part, the magnetic leakage conductivity of the end part of the primary winding and the harmonic magnetic permeability of the primary winding are respectively.
The method specifically comprises the following steps:
(6-1) correction of coefficient by transverse magnetic flux density distortion
Longitudinal magnetic flux density distortion correction coefficientAnd a primary half-filled trench correction factor KpFor normal magnetic close traveling wave impedance
Correcting to obtain corrected normal magnetic density traveling wave impedance <math>
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as a function of the motor configuration and operating conditions,
In order to ensure the safe operation of the linear induction motor, the transverse width (z axis) of the primary is usually larger than that of the secondary, as shown in fig. 6, thereby exerting a certain influence on the magnetic flux density of the transverse air gap, and the distortion correction coefficient of the transverse magnetic flux density can be used
And (6) carrying out correction. Because the air gap of the linear motor is larger, the flux density of the air gap generates certain distortion on the x axis, and the coefficient can be corrected by using the distortion of the longitudinal flux density
And (6) correcting. Because the primary magnetic circuit is broken, a half-filled slot exists at the end part, namely the equivalent current density of the coil in the span range of the end part is half of that of other full-filled slots, the structure has certain influence on the equivalent magnetic density of an air gap, and the coefficient K can be corrected by using the primary half-filled slotpAnd (6) carrying out correction.
Comprehensively considering the longitudinal edge effect, transverse edge effect, half-filled slot and air gap distortion effect of the linear induction motor to obtain the corrected normal magnetic density traveling wave impedance
(6-2) magnetic density reflection wave impedance from input endMagnetic density reflected wave impedance at output end
And corrected normal flux density traveling wave impedance
Obtaining corrected longitudinal side-end effect impedance
Further analysis by equations (38), (41), (43), and (46) yields the following relationships:
the formula (48) shows that the magnetic flux density reflected wave at the input end and the magnetic flux density reflected wave at the output end of the linear induction motor correspond to the leakage reactance
I.e. the whole secondary input power
Term and mechanical output power
The terms are equal. The invention assumes the longitudinal side effect impedance of the linear induction motor
Comprises the following steps:
wherein,and the correction coefficient is the longitudinal side effect of the linear induction motor. The corrected longitudinal side effect impedance of the linear induction motor can be obtained according to the formula (49)
(6-3) by corrected normal flux density traveling wave impedance
And corrected longitudinal side-effect impedance
Obtaining the total impedance of the single-phase circuit of the linear induction motor
Based on the derivation, the total impedance of the single-phase circuit of the linear induction motor is obtainedAs shown in the formula (47),
comprising a primary phase resistance r0Primary phase leakage reactance x0Corrected normal flux density traveling wave impedance
And corrected longitudinal side-effect impedance
Corrected longitudinal edge effect impedance
Including a corrected ingress end magnetic density reflected wave impedance and a corrected egress end magnetic density reflected wave impedance, the corrected ingress end magnetic density reflected wave impedance further including a corrected effective impedance of an ingress end reflected wave thrust
Corrected input end reflected wave leakage reactance
The corrected outgoing magneto-resistive reflected wave impedance further comprises a corrected effective impedance of the outgoing reflected wave thrust
And corrected output reflected wave leakage reactance
As shown in fig. 7.
(7) Total impedance of single-phase circuit of linear induction motorAnd analyzing the performance parameters of the linear induction motor under different stable states.
Total impedance of single-phase circuit of linear induction motor using embodiment of the invention
Parameters such as thrust, power factor, efficiency and the like of the linear induction motor under different stable states such as constant-voltage constant-frequency driving (called constant-voltage constant-frequency for short, and the like in the following) constant-current constant-frequency driving, variable-voltage variable-frequency driving, variable-current variable-frequency driving and the like can be analyzed. In particular, the total impedance of the single-phase circuit from the linear induction motorCan obtain the thrust of the linear induction motor under the steady state operation
Power factor
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The special properties of the linear induction motor, including longitudinal edge effect, transverse edge effect, primary end half-filled slot, air gap x-axis magnetic flux density distortion and the like, are embodied in relevant correction coefficients
KpAndin a variation of (2). Under different operating states, the transmission speed and the attenuation range of the reflected wave at the inlet end and the reflected wave at the outlet end of the air gap field of the linear induction motor are different, and the related change conditions can be determined by the corresponding attenuation coefficient alpha1And alpha2Half wavelength τeAnd correction coefficient
And
and (6) carrying out analysis.
Fig. 8 is a comparison graph of the steady-state torque variation of the simulated linear induction motor at different speeds by the analysis method of the embodiment of the invention and the actual test result. As can be seen from fig. 8, the maximum error between the calculated value and the actual measured value of the equivalent circuit according to the embodiment of the present invention is 7.8%, the minimum error is 2.2%, and the average error is 4.7%, which satisfies the requirements of engineering application.
The analysis method can be further applied to electromagnetic optimization design of the linear induction motor and motor steady-state characteristic analysis under different control strategies, including scalar control, space vector control, direct torque control and the like.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A steady state characteristic analysis method of a linear induction motor is characterized by comprising the following steps:
(1) establishing a one-dimensional flux density distribution model of the linear induction motor, wherein the primary mechanical motion direction is taken as an x axis, the effective flux density direction of an air gap is taken as a y axis, and the one-dimensional flux density distribution model meets the following conditions:
(A) the primary windings are distributed in a limited area, and the magnetic permeability of the primary iron core lamination and the secondary iron yoke is infinite;
(B) the air gap magnetic field only contains y-axis components and is irrelevant to y-axis coordinates, the traveling wave magnetic field and the motor running direction are along the x-axis, all electromagnetic field parameters are sine functions of the x-axis coordinates x and time t, only the fundamental component of each field quantity is considered, and the influence of space harmonics and time harmonics is ignored;
(C) the secondary skin effect is not considered, and the secondary end electrical parameters are all reduced to the primary;
(2) calculating y-axis magnetic flux density according to one-dimensional magnetic flux density distribution model
Wherein,
and
the amplitudes of the normal flux density traveling wave, the input flux density reflected wave and the output flux density reflected wave are in complex forms, tau is the half wavelength of the normal flux density traveling wave, tau is the amplitude of the normal flux density traveling wave, and tau is the amplitude of the normal flux density traveling waveeIs a half wavelength, alpha, of the incident-end magnetic flux density reflected wave and the emergent-end magnetic flux density reflected wave1For inputting the attenuation coefficient of magnetic density reflected wave, alpha2The attenuation coefficient of the outgoing magnetic flux density reflected wave is shown, and omega is the primary angular frequency;
(3) two end faces in the primary x-axis direction are used as magnetic barrier faces, and the following characteristics of the magnetic barrier faces are utilized: (A) all field quantities of the linear induction motor are distributed between the magnetic barrier surfaces; (B) the magnetic flux density outside the area between the magnetic barrier surfaces is zero, and the component of each field quantity between the magnetic barrier surfaces, which is vertical to the two end surfaces, is zero; (C) the sum of the area integrals of the air gap flux density between the magnetic barrier surfaces is zero; (D) the electric field intensity outside the region between the magnetic barrier surfaces is zero, and the area of the electric field intensity between the magnetic barrier surfaces is zero; magnetic flux density b from y-axisyIs expressed to obtain the electric field intensity ezAnd the complex form of the amplitude of the normal flux density traveling wave back emf
Input end magnetic density reflection wave back-reflection electricityComplex form of magnitude of potential
And the complex form of the amplitude of the magnetic density reflected wave counter potential at the output end
(4) According to the principle of the rotating electrical machine, obtaining the complex form of the amplitude of the normal magnetic flux density traveling waveAccording to the one-dimensional magnetic flux density distribution model and the magnetic barrier surface characteristics, the magnetic flux density b is measured from the y-axisyThe expression of (a) obtains the complex form of the amplitude of the incoming magnetic flux density reflected wave
And the complex form of the amplitude of the outgoing magnetic dense reflected wave
(5) Based on the equality of the primary and secondary complex powers and conservation of energy, the complex form of the amplitude of the normal flux density traveling wave
And the complex form of the amplitude of the normal flux density traveling wave back emfObtaining normal magnetic density traveling wave impedance
The complex form of the amplitude of the magnetic flux density reflected wave from the input end
And the complex form of the amplitude of the counter potential of the magnetic density reflected wave at the input endObtaining the impedance of the input end magnetic density reflected wave
Wherein,
the impedance correction coefficient of the magnetic density reflection wave at the input end; complex form of amplitude of magnetic dense reflected wave from output end
And the complex form of the amplitude of the magnetic density reflected wave counter potential at the output end
Obtaining the magnetic density reflected wave impedance of the output end
Wherein,the impedance correction coefficient of the outgoing end magnetic density reflected wave;
(6) impedance of normal magnetic flux density traveling wave
Impedance of input end magnetic density reflection wave
And output end magnetic density reflected wave impedance
Calculating to obtain the total impedance of the single-phase circuit of the linear induction motor
Wherein r is0And x0Respectively primary phase resistance and primary phase leakage reactance, corrected normal magnetic flux density traveling wave impedance <math>
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And KpRespectively a transverse flux density distortion correction coefficient, a longitudinal flux density distortion correction coefficient and a primary half-filled slot correction coefficient;
(7) total impedance of single-phase circuit of linear induction motor
And analyzing the performance parameters of the linear induction motor under different stable states.
2. The steady state characteristic analysis method of a linear induction motor according to claim 1, wherein the step (2) comprises the substeps of:
(2-1) obtaining the following parameters according to a one-dimensional flux density distribution model by using an ampere loop law:
wherein j is1Is primary area current density, j2Is the secondary surface current density;
(2-2) obtaining an air gap magnetic field magnetic flux density equation according to the relationship among the current density, the resistivity and the air gap electric field:
wherein v is the running speed of the motor;
(2-3) simultaneously considering the influence of the normal flux density traveling wave, the incoming flux density reflected wave and the outgoing flux density reflected wave on the air gap flux linkage to obtain the y-axis flux density byIs described in (1).
3. The method for analyzing steady-state characteristics of a linear induction motor according to claim 1 or 2, wherein in the step (3), <math>
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Wherein v issThe synchronous speed of the motor.
4. The steady state characteristic analysis method of a linear induction motor according to claim 3, wherein in the step (4),wherein, mu0In order to have a magnetic permeability of air,
is the primary current density amplitude, g is the equivalent length of the electromagnetic air gap, s is the slip ratio of the motor, and the quality factor
And
respectively as follows:
wherein L ispIs the primary length.
5. The method of analyzing steady state characteristics of a linear induction motor according to claim 4, wherein the steady state characteristics of the linear induction motor are analyzed bySolving a figure of merit expression wherein LmIs mutual inductance of r2Is the secondary equivalent resistance.
6. The method for analyzing steady-state characteristics of a linear induction motor according to claim 4 or 5, wherein in the step (5),
wherein the air gap reactance
Secondary resistance
Wherein m is primaryNumber of winding phases, f primary excitation frequency, w1For each phase of the primary winding, Kw1Is the winding distribution coefficient, /)wThe width of the primary lamination, P is the actual pole pair number of the motor, and sigma is the conductivity of the secondary guide plate; <math>
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<mover>
<mi>K</mi>
<mo>‾</mo>
</mover>
<mn>2</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<msub>
<mi>α</mi>
<mn>2</mn>
</msub>
<mrow>
<mn>2</mn>
<mi>P</mi>
</mrow>
</mfrac>
<mfrac>
<msub>
<mi>τ</mi>
<mi>e</mi>
</msub>
<mrow>
<msub>
<mi>ττ</mi>
<mi>e</mi>
</msub>
<mo>+</mo>
<mi>j</mi>
<msub>
<mi>α</mi>
<mn>2</mn>
</msub>
<mi>π</mi>
<mrow>
<mo>(</mo>
<mi>τ</mi>
<mo>+</mo>
<msub>
<mi>τ</mi>
<mi>e</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>.</mo>
</mrow>
</math>
7. the method for analyzing steady-state characteristics of a linear induction motor according to any one of claims 1 to 6, wherein in the step (6), the transverse flux density distortion correction coefficientWherein G is the equivalent length of the electromagnetic air gap, s is the slip ratio of the motor, G is the quality factor,
for structural and operational conditions of the machineThe function, a, is half the width of the primary, <math>
<mrow>
<mover>
<mi>γ</mi>
<mo>‾</mo>
</mover>
<mo>=</mo>
<msqrt>
<mn>1</mn>
<mo>+</mo>
<mi>jsG</mi>
</msqrt>
<mo>;</mo>
</mrow>
</math> longitudinal magnetic flux density distortion correction coefficient <math>
<mrow>
<mover>
<msub>
<mi>K</mi>
<mi>b</mi>
</msub>
<mo>‾</mo>
</mover>
<mo>=</mo>
<mfrac>
<mi>πg</mi>
<mrow>
<mn>2</mn>
<mi>τ</mi>
</mrow>
</mfrac>
<msqrt>
<mn>1</mn>
<mo>+</mo>
<mi>jsG</mi>
</msqrt>
<mo>/</mo>
<mi>th</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mi>π</mi>
<mi>τ</mi>
</mfrac>
<mfrac>
<mi>g</mi>
<mn>2</mn>
</mfrac>
<mo>·</mo>
<msqrt>
<mn>1</mn>
<mo>+</mo>
<mi>jsG</mi>
</msqrt>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
</math> Primary half-filled cell correction factor
Wherein, P is the actual pole pair number of the motor, y1The number of short-distance slots of the winding is shown, m is the number of phases of the primary winding, and q is the number of slots of each phase of the motor.
8. The method of analyzing steady state characteristics of a linear induction motor according to claim 7, wherein said motor structure and operating conditions are a function of
Comprises the following steps:
where c is half the difference between the primary and secondary widths.
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Cited By (5)
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| CN103904978A (en) * | 2014-04-02 | 2014-07-02 | 华中科技大学 | Linear induction motor drive characteristic analysis equivalent circuit and analysis method |
| CN109992874A (en) * | 2019-03-27 | 2019-07-09 | 湘潭大学 | A kind of unilateral composite secondary line inductance electromotor force characteristic modeling and analysis methods |
| CN110086318A (en) * | 2019-04-25 | 2019-08-02 | 江苏利得尔电机有限公司 | A kind of rail traffic line inductance electromotor W type secondary design method |
| CN112329293A (en) * | 2020-10-28 | 2021-02-05 | 郑州轻工业大学 | Method for calculating no-load back electromotive force and thrust of permanent magnet linear synchronous motor |
| CN117828244A (en) * | 2024-03-06 | 2024-04-05 | 华中科技大学 | Linear induction motor chain type equivalent circuit and characteristic analysis method |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103904978A (en) * | 2014-04-02 | 2014-07-02 | 华中科技大学 | Linear induction motor drive characteristic analysis equivalent circuit and analysis method |
| CN109992874A (en) * | 2019-03-27 | 2019-07-09 | 湘潭大学 | A kind of unilateral composite secondary line inductance electromotor force characteristic modeling and analysis methods |
| CN110086318A (en) * | 2019-04-25 | 2019-08-02 | 江苏利得尔电机有限公司 | A kind of rail traffic line inductance electromotor W type secondary design method |
| CN112329293A (en) * | 2020-10-28 | 2021-02-05 | 郑州轻工业大学 | Method for calculating no-load back electromotive force and thrust of permanent magnet linear synchronous motor |
| CN112329293B (en) * | 2020-10-28 | 2024-02-02 | 郑州轻工业大学 | Calculation method for no-load counter potential and thrust of permanent magnet linear synchronous motor |
| CN117828244A (en) * | 2024-03-06 | 2024-04-05 | 华中科技大学 | Linear induction motor chain type equivalent circuit and characteristic analysis method |
| CN117828244B (en) * | 2024-03-06 | 2024-05-14 | 华中科技大学 | Linear induction motor chain type equivalent circuit and characteristic analysis method |
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