CN103904978A - Linear induction motor drive characteristic analysis equivalent circuit and analysis method - Google Patents

Abstract

The invention discloses a linear induction motor drive characteristic analysis equivalent circuit and an analysis method. A Maxwell equation is combined with a winding function method, and a primary winding function, a secondary fundamental wave winding function and a secondary end effect wave winding function of a linear induction motor are obtained in terms of distribution of an actual primary winding of the linear induction motor. According to a winding function basic theory, equivalent inductance and the motion potential coefficient of the linear induction motor are analyzed and calculated, a voltage and flux linkage equation of the linear induction motor is built, and further, a novel equivalent circuit model of the linear induction motor is built. By means of the novel equivalent circuit mode, steady-mode and dynamic characteristics of the linear induction motor are analyzed. On the basis of the distribution situation of actual windings of the motor, influences of a transverse edge effect, a longitudinal edge effect and a primary semi-filled groove of the linear inductance motor on motor inductance and secondary resistance are reasonably considered, and drive characteristics of the linear induction motor are accurately and effectively analyzed.

Description

Line inductance electromotor drive characteristic analyzing equivalent circuit and analytical method

Technical field

The invention belongs to line inductance electromotor field, more specifically, relate to a kind of line inductance electromotor drive characteristic analyzing equivalent circuit and analytical method.

Background technology

The core component driving as straight line trailer system, line inductance electromotor (Linear Induction Machine is called for short LIM) is being brought into play very important effect.But, because cut-off at the elementary longitudinal magnetic circuit of line inductance electromotor two ends, primary and secondary air gap is larger, there is following features: (1) even can produce asymmetrical three-phase current under symmetrical external voltage effect, they will produce positive sequence forward magnetic field, backward opposing magnetic field and zero sequence impulsive magnetic field in air gap, wherein, backward and zero sequence magnetic field are static or in service at motor, will produce resistance and increase supplementary load loss, thereby affecting power energy characteristic and the operating efficiency of line inductance electromotor.(2) transverse magnetic flux density distribution is inhomogeneous, and secondary conductor plate equivalent resistivity increases, and air gap effective magnetic field is entering end weakening, go out end and strengthen, make its tractive effort produce pulsation, Electric Machine Control difficulty increases, traction coeficient reduces, and can aggravate three-phase current unbalance and produce larger resistance when serious.(3) after magnetic circuit cut-offs, the end number of windings is middle half, and variation has occurred for longitudinal magnetic flux density and current density, affects motor equivalent parameters and pulling figure.

Therefore, LIM equivalent parameters has stronger intercoupling property and nonlinearity, current, and the method for analyzing LIM mainly comprises Electromagnetic Calculation method (field) and equivalent-circuit technique (road).Electromagnetic Calculation method comprises analytic method and Finite Element, need very large mesh generation region, maybe need to adopt special dynamic grid subdivision technology, its Electromagnetic Calculation is consuming time very long, data processing is very loaded down with trivial details, and under different operating modes, boundary condition is set and mesh generation is all worthy of careful study, if arrange unreasonablely, be difficult to rationally be separated.Equivalent-circuit technique mainly comprises series and parallel connections circuit model method, and definite conception is simple, but supposes numerously in calculating, and precision is poor.

Summary of the invention

For above defect or the Improvement requirement of prior art, the invention provides a kind of line inductance electromotor drive characteristic analyzing equivalent circuit and analytical method, this equivalent electric circuit can be widely used in line inductance electromotor stable state and the dynamic driving specificity analysis under different operating modes, the method can be analyzed accurately and effectively to the drive characteristic of line inductance electromotor, and method is simple, can further be applied in the associated drives control strategy of line inductance electromotor.

For achieving the above object, according to one aspect of the present invention, provide a kind of line inductance electromotor drive characteristic analyzing equivalent circuit, it is characterized in that, comprised α axle equivalent electric circuit and β axle equivalent electric circuit; α axle equivalent electric circuit comprises the first branch road, the second branch road and the 3rd branch road, after the second branch road and the 3rd branch circuit parallel connection, connects with the first branch road, and the node of three branch roads is designated as A, first elementary phase resistance R of route _s, elementary phase leakage inductance L _lswith the first voltage source e _{α st}be in series, the first voltage source e _{α st}positive pole near node A, second secondary phase resistance R of route _r, secondary phase leakage inductance L _lrwith second voltage source e _{α r}be in series, second voltage source e _{α r}positive pole near node A, the 3rd route air gap equivalence mutual inductance L _mwith tertiary voltage source e _{α t}be in series, tertiary voltage source e _{α t}positive pole near node A; β axle equivalent electric circuit comprises the 4th branch road, the 5th branch road and the 6th branch road, after the 5th branch road and the 6th branch circuit parallel connection, connects with the 4th branch road, and the node of three branch roads is designated as B, the 4th the elementary phase resistance R of route _s, elementary phase leakage inductance L _lswith the 4th voltage source e _{β st}be in series, the 4th voltage source e _{β st}positive pole near Node B, the 5th the secondary phase resistance R of route _r, secondary phase leakage inductance L _lrwith the 5th voltage source e _{β r}be in series, the 5th voltage source e _{β r}positive pole near Node B, the 6th route air gap equivalence mutual inductance L _mwith the 6th voltage source e _{β t}be in series, the 6th voltage source e _{β t}positive pole near Node B;

Described the first voltage source e _{α st}voltage be e _{α st}=-pL _{α s β s}i _{β s}, wherein, p is differential operator d/dt, t is the time, L _{α s β s}for the mutual inductance between α axle armature winding and β axle armature winding, i _{β s}for β axle primary winding current; Described second voltage source e _{α r}voltage be e _{α r}=v (π/τ) λ _{β r}, wherein, v is the motor speed of service, τ is armature winding pole span, λ _{β r}for the secondary first-harmonic winding of β axle magnetic linkage; Described tertiary voltage source e _{α t}voltage be e _{α t}=p[L' _{α s α re}i _{α re}+ L' _{α s β re}i _{β re}], wherein, L' _{α s α re}=-KL _{α s α re}, L' _{α s β re}=-KL _{α s β re}, L _{α s α re}for the mutual inductance between α axle armature winding and α axle secondary side end effect wave winding, L _{α s β re}for the mutual inductance between α axle armature winding and β axle secondary side end effect wave winding, i _{α re}for α axle secondary side end effect wave winding electric current, i _{β re}for β axle secondary side end effect wave winding electric current; Described the 4th voltage source e _{β st}voltage be e _{β st}=-pL _{α s β s}i _{α s}, wherein, i _{α s}for α axle primary winding current; Described the 5th voltage source e _{β r}voltage e _{β r}=-v (π/τ) λ _{α r}, wherein, λ _{α r}for the secondary first-harmonic winding of α axle magnetic linkage; Described the 6th voltage source e _{β t}voltage e _{β t}=p[L ' _{β s α re}i' _{α re}+ L ' _{β s β re}i' _{β re}], wherein, L' _{β s α re}=-KL _{β s α re}, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, L' _{β s β re}=-KL _{β s β re}, L _{β s β re}for the mutual inductance between β axle armature winding and β axle secondary side end effect wave winding, i' _{α re}=-Ki _{α re}, i' _{β re}=-Ki _{β re}; Wherein,

l _δfor elementary phase length, L _rfor secondary phase inductance.

According to another aspect of the present invention, a kind of line inductance electromotor stable state drive characteristic analytical method is provided, it is characterized in that, comprise the steps: that (1) obtains motor speed of service v and three-phase primary windings electric current, three-phase primary windings electric current is carried out to changes in coordinates, obtain α axle primary winding current i _{α s}with β axle primary winding current i _{β s}; (2) utilize α axle primary winding current i _{α s}with β axle primary winding current i _{β s}, according to armature winding voltage equation and secondary first-harmonic winding voltage equation, try to achieve the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}; Described armature winding voltage equation is:

$\left\{\begin{array}{c}{u}_{\mathrm{\αs}}=[R_s-{\mathrm{\ω}}_e(L_{\mathrm{\αs\βs}}+L_{\mathrm{\βs\αre}}^{\′})]i_{\mathrm{\αs}}-{\mathrm{\ω}}_e(L_{\mathrm{ls}}+L_m+L_{\mathrm{\βs\βre}}^{\′})i_{\mathrm{\βs}}-{\mathrm{\ω}}_e(L_{\mathrm{\βs\αr}}+L_{\mathrm{\βs\αre}}^{\′})i_{\mathrm{\αr}}-{\mathrm{\ω}}_e(L_m+L_{\mathrm{\βs\βre}}^{\′})i_{\mathrm{\βr}}\\ u_{\mathrm{\βs}}={\mathrm{\ω}}_e(L_{\mathrm{ls}}+L_m+L_{\mathrm{\αs\αre}}^{\′})i_{\mathrm{\αs}}+[R_s++{\mathrm{\ω}}_e(L_{\mathrm{\αs\βs}}+L_{\mathrm{\αs\βre}}^{\′})]i_{\mathrm{\βs}}+{\mathrm{\ω}}_e(L_m+L_{\mathrm{\αs\αre}}^{\′})i_{\mathrm{\αr}}+{\mathrm{\ω}}_e(L_{\mathrm{\αs\βr}}+L_{\mathrm{\αs\βre}}^{\′})i_{\mathrm{\βr}}+\end{array},;\right.=$

Wherein, R _sfor elementary phase resistance, ω _efor elementary angular frequency, L _{α s β s}for the mutual inductance between α axle armature winding and β axle armature winding, L' _{β s α re}=-KL _{β s α re}, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, L _lsfor elementary phase leakage inductance, L _mfor air gap equivalence mutual inductance, L' _{β s β re}=-KL _{β s β re}, L _{β s β re}for the mutual inductance between β axle armature winding and β axle secondary side end effect wave winding, L _{β s α r}for the mutual inductance between β axle armature winding and the secondary first-harmonic winding of α axle, L' _{α s α re}=-KL _{α s α re}, L _{α s α re}for the mutual inductance between α axle armature winding and α axle secondary side end effect wave winding, L' _{α s β re}=-KL _{α s β re}, L _{α s β re}for the mutual inductance between α axle armature winding and β axle secondary side end effect wave winding, L _{α s β r}for the mutual inductance between α axle armature winding and the secondary first-harmonic winding of β axle,

l _δfor elementary phase length, L _rfor secondary phase inductance; Described secondary first-harmonic winding voltage equation is:

$\left\{\begin{array}{c}0=[-{\mathrm{\&omega;}}_e(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;s}}+[-{\mathrm{\&omega;}}_e\left(L_{m+}{L}_{\mathrm{\&beta;r\&beta;re}}^{\&prime;}\right)+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;s}}\\ +[R_r-{\mathrm{\&omega;}}_e(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;r}}+[-{\mathrm{\&omega;}}_e(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;<figure-callout\; id="0"\; label="r"\; filenames="HDA0000486050040000021.png"\; state="\{\{state\}\}">r</figure-callout>}}\\ 0=[{\mathrm{\&omega;}}_e(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;s}}+[{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;s}}\\ +[{\mathrm{\&omega;}}_e(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;r}}+[R_r+{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;r}}\end{array}\right.;$

Wherein, L _{β r α s}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle armature winding, L' _{β r α re}=-KL _{β r α re}, L _{β r α re}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle secondary side end effect wave winding, τ is armature winding pole span, L' _{β r β re}=-KL _{β r β re}, L _{β r β re}for the mutual inductance between the secondary first-harmonic winding of β axle and β axle secondary side end effect wave winding, R _rfor secondary phase resistance, L _{β r α r}for the mutual inductance between the secondary first-harmonic winding of β axle and the secondary first-harmonic winding of α axle, L _lrfor secondary phase leakage inductance, L' _{α r α re}=-KL _{α r α re}, L _{α r α re}for the mutual inductance between the secondary first-harmonic winding of α axle and α axle secondary side end effect wave winding, L _{α r β s}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle armature winding, L' _{α r β re}=-KL _{α r β re}, L _{α r β re}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle secondary side end effect wave winding, L _{α r β r}for the mutual inductance between the secondary first-harmonic winding of α axle and the secondary first-harmonic winding of β axle; (3) utilize α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}, try to achieve the characteristic variable of line inductance electromotor, realize the analysis of stable state drive characteristic; The characteristic variable of described line inductance electromotor comprises motor magnetic linkage, motor thrust F _x, at least one in motor input active power, motor input reactive power, motor thrust output, motor active power of output, motor power factor and electric efficiency.

Preferably, described motor magnetic linkage comprises α axle armature winding magnetic linkage λ _{α s}, β axle armature winding magnetic linkage λ _{β s}, the secondary first-harmonic winding of α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of β axle magnetic linkage λ _{β r};

Described α axle armature winding magnetic linkage λ _{α s}for:

λ _αs＝(L _ls+L _m+L' _αsαre)i _αs+(L _αsβs+L' _αsβre)i _βs+(L _m+L' _αsαre)i _αr+(L _αsβr+L' _αsβre)i _βr；

Described β axle armature winding magnetic linkage λ _{β s}for:

λ _βs＝(L _αsβs+L' _βsαre)i _αs+(L _ls+L _m+L' _βsβre)i _βs+(L _βsαr+L' _βsαre)i _αr+(L _m+L' _βsβre)i _βr；

The secondary first-harmonic winding of described α axle magnetic linkage λ _{α r}for:

λ _αr＝(L _m+L' _αrαre)i _αs+(L _αrβs+L' _αrβre)i _βs+(L _lr+L _m+L' _αrαre)i _αr+(L _αrβr+L' _αrβre)i _βr；

The secondary first-harmonic winding of described β axle magnetic linkage λ _{β r}for:

λ _βr＝(L _βrαs+L' _βrαre)i _αs+(L _m+L' _βrβre)i _βs+(L _βrαr+L' _βrαre)i _αr+(L _lr+L _m+L' _βrβre)i _βr；

Described motor thrust F _xfor:

F _x＝(3π/2τ)[L _m(i _αri _βs-i _βri _αs)+i _αs(i _αr+i _αs)G' _αsαre+i _αs(i _βr+i _βs)G' _αsβre+i _βs(i _αr+i _αs)G' _βsαre+i _βs(i _βr+i _βs)G' _βsβre]；

Wherein, G' _{α s α re}=-KG _{α s α re}, G' _{α s β re}=-KG _{α s β re}, G' _{β s α re}=-KG _{β s α re}, G' _{β s β re}=-KG _{β s β re}, G _{α s α re}=L _{β s α re}, G _{α s β re}=L _{β s β re}, G _{β s α re}=-L _{α s α re}, G _{β s β re}=-L _{α s β re}.

According to another aspect of the present invention, line inductance electromotor stable state drive characteristic analytical method is provided, it is characterized in that, comprise the steps: that (1) obtains motor speed of service v, elementary angular frequency _eand three-phase primary windings voltage, three-phase primary windings voltage is carried out to changes in coordinates, obtain α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}; (2) utilize α axle armature winding voltage u _{α s}, β axle armature winding voltage u _{β s}, motor speed of service v and elementary angular frequency _e, calculate α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}; (3) utilize α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}, try to achieve the characteristic variable of line inductance electromotor, realize the analysis of stable state drive characteristic; The characteristic variable of described line inductance electromotor comprises motor magnetic linkage, motor thrust F _x, at least one in motor input active power, motor input reactive power, motor thrust output, motor active power of output, motor power factor and electric efficiency.

According to another aspect of the present invention, a kind of line inductance electromotor dynamic driving characteristic analysis method is provided, it is characterized in that, comprise the steps: that (1) obtains as front motor speed of service v, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}; (2) obtain three-phase primary windings electric current, three-phase primary windings electric current is carried out to changes in coordinates, obtain α axle primary winding current i _{α s}with β axle primary winding current i _{β s}; (3) utilize α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, try to achieve the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}be respectively:

$\begin{array}{c}{i}_{\mathrm{\&alpha;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]\end{array}$ With

$\begin{array}{c}{i}_{\mathrm{\&beta;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]\end{array};$

Wherein, L _mfor air gap equivalence mutual inductance, L' _{α r α re}=-KL _{α r α re}, L _{α r α re}for the mutual inductance between the secondary first-harmonic winding of α axle and α axle secondary side end effect wave winding, L _{α r β s}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle armature winding, L' _{α r β re}=-KL _{α r β re}, L _{α r β re}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle secondary side end effect wave winding, L _lrfor secondary phase leakage inductance, L' _{β r β re}=-KL _{β r β re}, L _{β r β re}for the mutual inductance between the secondary first-harmonic winding of β axle and β axle secondary side end effect wave winding, L _{β r α s}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle armature winding, L' _{β r α re}=-KL _{β r α re}, L _{β r α re}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle secondary side end effect wave winding, L _{α r β r}for the mutual inductance between the secondary first-harmonic winding of α axle and the secondary first-harmonic winding of β axle, L _{β r α r}for the mutual inductance between the secondary first-harmonic winding of β axle and the secondary first-harmonic winding of α axle,

l _δfor elementary phase length, L _rfor secondary phase inductance, R _rfor secondary phase resistance; (4) utilize α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}, calculate motor thrust F _xand/or other characteristic variable of line inductance electromotor; Other characteristic variable of described line inductance electromotor comprises at least one in armature winding magnetic linkage, motor input active power, motor input reactive power, motor thrust output, motor active power of output, motor power factor and electric efficiency; (5) according to working as front motor speed of service v, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}, calculate α axle secondary first-harmonic winding magnetic linkage increment and the secondary first-harmonic winding of β axle magnetic linkage increment, further integration obtains the secondary first-harmonic winding of the α axle magnetic linkage λ ' in next moment _{α r}with the secondary first-harmonic winding of β axle magnetic linkage λ ' _{β r}, make the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}=λ ' _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}=λ ' _{β r}; (6) according to motor thrust F _x, obtaining the motor speed of service v' in next moment, order is as front motor speed of service v=v'; (7) circulation is carried out described step (2) to (6), realizes the analysis of dynamic driving characteristic.

Preferably, described motor thrust F _xfor:

F _x＝(3π/2τ)[L _m(i _αri _βs-i _βri _αs)+i _αs(i _αr+i _αs)G' _αsαre+i _αs(i _βr+i _βs)G' _αsβre+i _βs(i _αr+i _αs)G' _βsαre+i _βs(i _βr+i _βs)G' _βsβre]；

Wherein, τ is armature winding pole span, G' _{α s α re}=-KG _{α s α re}, G' _{α s β re}=-KG _{α s β re}, G' _{β s α re}=-KG _{β s α re}, G' _{β s β re}=-KG _{β s β re}, G _{α s α re}=L _{β s α re}, G _{α s β re}=L _{β s β re}, G _{β s α re}=-L _{α s α re}, G _{β s β re}=-L _{α s β re}, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, L _{β s β re}for the mutual inductance between β axle armature winding and β axle secondary side end effect wave winding, L _{α s α re}for the mutual inductance between α axle armature winding and α axle secondary side end effect wave winding, L _{α s β re}for the mutual inductance between α axle armature winding and β axle secondary side end effect wave winding.

Preferably, described armature winding magnetic linkage comprises α axle armature winding magnetic linkage λ _{α s}with β axle armature winding magnetic linkage λ _{β s}; Described α axle armature winding magnetic linkage λ _{α s}for:

λ _αs＝(L _ls+L _m+L' _αsαre)i _αs+(L _αsβs+L' _αsβre)i _βs+(L _m+L' _αsαre)i _αr+(L _αsβr+L' _αsβre)i _βr；

Described β axle armature winding magnetic linkage λ _{β s}for:

λ _βs＝(L _αsβs+L' _βsαre)i _αs+(L _ls+L _m+L' _βsβre)i _βs+(L _βsαr+L' _βsαre)i _αr+(L _m+L' _βsβre)i _βr；

Wherein, L _lselementary phase leakage inductance, L _{α s β s}for the mutual inductance between α axle armature winding and β axle armature winding, L' _{α s β re}=-KL _{α s β re}, L _{α s β re}for the mutual inductance between α axle armature winding and β axle secondary side end effect wave winding, L _{α s β r}for the mutual inductance between α axle armature winding and the secondary first-harmonic winding of β axle, L' _{β s α re}=-KL _{β s α re}, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, L' _{β s β re}=-KL _{β s β re}, L _{β s β re}for the mutual inductance between β axle armature winding and β axle secondary side end effect wave winding, L _{β s α r}for the mutual inductance between β axle armature winding and the secondary first-harmonic winding of α axle.

According to another aspect of the present invention, a kind of line inductance electromotor dynamic driving characteristic analysis method is provided, it is characterized in that, comprise the steps: that (1) obtains as front motor speed of service v, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, current α axle primary winding current i _{α s}with current β axle primary winding current i _{β s}; (2) obtain three-phase primary windings voltage, three-phase primary windings voltage is carried out to changes in coordinates, obtain α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}; (3) utilize the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, current α axle primary winding current i _{α s}with current β axle primary winding current i _{β s}, try to achieve the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}be respectively:

$\begin{array}{c}{i}_{\mathrm{\&alpha;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]\end{array}$ With

$\begin{array}{c}{i}_{\mathrm{\&beta;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]\end{array};$

Wherein, L _mfor air gap equivalence mutual inductance, L' _{α r α re}=-KL _{α r α re}, L _{α r α re}for the mutual inductance between the secondary first-harmonic winding of α axle and α axle secondary side end effect wave winding, L _{α r β s}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle armature winding, L' _{α r β re}=-KL _{α r β re}, L _{α r β re}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle secondary side end effect wave winding, L _lrfor secondary phase leakage inductance, L' _{β r β re}=-KL _{β r β re}, L _{β r β re}for the mutual inductance between the secondary first-harmonic winding of β axle and β axle secondary side end effect wave winding, L _{β r α s}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle armature winding, L' _{β r α re}=-KL _{β r α re}, L _{β r α re}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle secondary side end effect wave winding, L _{α r β r}for the mutual inductance between the secondary first-harmonic winding of α axle and the secondary first-harmonic winding of β axle, L _{β r α r}for the mutual inductance between the secondary first-harmonic winding of β axle and the secondary first-harmonic winding of α axle,

l _δfor elementary phase length, L _rfor secondary phase inductance, R _rfor secondary phase resistance; (4) utilize current α axle primary winding current i _{α s}, current β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}, calculate motor thrust F _xand/or other characteristic variable of line inductance electromotor; Other characteristic variable of described line inductance electromotor comprises at least one in armature winding magnetic linkage, motor input active power, motor input reactive power, motor thrust output, motor active power of output, motor power factor and electric efficiency; (5) according to working as front motor speed of service v, current α axle primary winding current i _{α s}, current β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, calculate α axle primary winding current increment, β axle primary winding current increment, the secondary first-harmonic winding of α axle magnetic linkage increment and the secondary first-harmonic winding of β axle magnetic linkage increment, further integration obtains the α axle primary winding current i' in next moment _{α s}, β axle primary winding current i' _{β s}, the secondary first-harmonic winding of α axle magnetic linkage λ ' _{α r}with the secondary first-harmonic winding of β axle magnetic linkage λ ' _{β r}, make current α axle primary winding current i _{α s}=i' _{α s}, current β axle primary winding current i _{β s}=i' _{β s}, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}=λ ' _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}=λ ' _{β r}; (6) according to motor thrust F _x, obtaining the motor speed of service v' in next moment, order is as front motor speed of service v=v'; (7) circulation is carried out described step (2) to (6), realizes the analysis of dynamic driving characteristic.

In general, the above technical scheme of conceiving by the present invention compared with prior art, adopt the analysis thinking of Chang He road combination, Maxwell equation and winding function method are combined, from the distribution of the elementary actual winding of line inductance electromotor, obtain the armature winding function of line inductance electromotor, secondary first-harmonic winding function and secondary side end effect wave winding function.Then according to winding function basic theories, analysis meter calculates equivalent inductance, the motion coefficient of potential of line inductance electromotor, and sets up voltage and the flux-linkage equations of line inductance electromotor.Further set up the novel equivalent-circuit model of line inductance electromotor, meanwhile, according to the energy relationship of primary and secondary, derive the energy index expression formulas such as thrust, power factor and the efficiency of line inductance electromotor.Utilize novel equivalent-circuit model, stable state and dynamic characteristic to line inductance electromotor are analyzed.The present invention is from the actual winding distribution situation of motor, reasonable consideration the transverse edge effect of line inductance electromotor, longitudinal edge effect and the impact of elementary half filling slot on motor inductance and secondary resistance, can analyze accurately and effectively the drive characteristic of line inductance electromotor, and method is simple, can further be applied in the associated drives control strategy of line inductance electromotor.

Accompanying drawing explanation

Fig. 1 is the one-dimentional structure analytical model of line inductance electromotor;

Fig. 2 is the alpha-beta axle equivalent circuit while considering limit end effect and half filling slot;

Fig. 3 is the variation diagram of line inductance electromotor stable state thrust with the motor speed of service;

Fig. 4 is line inductance electromotor dynamic thrust variation diagram.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.In addition,, in each execution mode of described the present invention, involved technical characterictic just can combine mutually as long as do not form each other conflict.

Below in conjunction with accompanying drawing, concrete analysis of the present invention and implementation process are elaborated.

1, the foundation of one dimension simplified model

The one-dimentional structure analytical model of model line inductance electromotor, (wherein x axle is longitudinally, i.e. elementary length and the direction of motion specifically as shown in Figure 1; Z axle is laterally, i.e. elementary Width).Elementaryly formed by unshakable in one's determination and winding, the elementary initial end in the direction of motion be elementary enter end, leave end and go out to hold for elementary; The elementary single layer winding (i.e. half filling slot, its number is the span of motor winding) that enters end and go out end to exist some, all the other are two layer winding.Secondary by conductor plate (being generally aluminium sheet or copper coin) and backboard (being generally iron block) formation.For convenience of analysis below, first do following hypothesis: (1) elementary lamination and secondary backboard magnetic permeability are for infinitely great, and coordinate system is placed on elementary upper, and armature winding is defined as effective district; (2) the magnetic flux density B of y direction size is the same, and travelling-magnetic-field and electric motor primary are only moved along X-direction; (3) secondary current only flows along z direction, and elementary half filling slot can be by selecting suitable armature winding function to solve.

2, the foundation of winding function

According to winding function correlation theory, winding function N (x) can obtain by the calculating of simple number of conductor, and it is a circuit concept, and a character is closely connected.Calculating conductor number from left to right successively, when outside current direction paper, N (x) increases; In current direction paper, N (x) reduces.According to this rule, to closed loop A1A2A3A4A1 with Ampere circuit law can be in the hope of motor-field intensity:

$H\left(x\right)=\frac{i}{g_e}N\left(x\right)---\left(1\right)$

I is winding current, g _efor equivalent electric magnetic air gap.Winding function N (x) equals, by the normalized magnetomotive force MMF of winding current, not to be subject to motor excitation current affects, only with the geometry Size dependence of motor.

Utilize Maxwell fundamental equation, the air gap flux linkage density equation of deriving line inductance electromotor is:

$\frac{{\&PartialD;}^2{B}_y}{\&PartialD;x^2}-\frac{{\mathrm{\&mu;}}_0{\mathrm{\&sigma;}}_{e}v}{g_e}\frac{{\&PartialD;B}_y}{\&PartialD;x}-\frac{{\mathrm{\&mu;}}_0{\mathrm{\&sigma;}}_e}{g_e}\frac{{\&PartialD;B}_y}{\&PartialD;t}=\frac{{\mathrm{\&mu;}}_0}{g_e}\frac{{\&PartialD;J}_s}{\&PartialD;x}---\left(2\right)$

In above formula, B _yfor air-gap flux gross density, comprise the magnetic linkage density B that primary current produces _s, the magnetic linkage density B that secondary current produces _r, v is the motor speed of service, μ ₀for air permeability, σ _efor secondary conductor plate equivalent conductivity.Wherein, B _swith stator current density J _smeet following relational expression:

$J_s=\frac{g_e}{{\mathrm{\&mu;}}_0}\frac{{\&PartialD;B}_s}{\&PartialD;x}---\left(3\right)$

Convolution (2) and (3) can be simplified and obtained:

$\frac{{\&PartialD;}^2{B}_r}{\&PartialD;x^2}-\frac{{\mathrm{\&mu;}}_0{\mathrm{\&sigma;}}_{e}v}{g_e}\frac{{\&PartialD;B}_r}{\&PartialD;x}-\frac{{\mathrm{\&mu;}}_0{\mathrm{\&sigma;}}_e}{g_e}\frac{{\&PartialD;B}_r}{\&PartialD;t}=\frac{{\mathrm{\&mu;}}_0{\mathrm{\&sigma;}}_{e}v}{g_e}\frac{{\&PartialD;B}_s}{\&PartialD;x}+\frac{{\mathrm{\&mu;}}_0{\mathrm{\&sigma;}}_e}{g_e}\frac{{\&PartialD;B}_s}{\&PartialD;t}---\left(4\right)$

On the basis of formula (4), the elementary first-harmonic winding function of the further Derivation of the present invention, secondary first-harmonic winding function and secondary side end effect wave winding function, detailed process is as follows.

Ignore the impact of high order harmonic component, only consider the fundametal compoment of winding function, suppose that near the winding function on lamination border be c phase, according to line inductance electromotor winding distribution situation, the expression formula that can obtain elementary three-phase winding function is:

$N_{\mathrm{as}}\left(x\right)=\frac{N_s}{2}\cos (\mathrm{\&pi;x}/\mathrm{\&tau;}+\mathrm{\&pi;})---\left(5\right)$

$N_{\mathrm{bs}}\left(x\right)=\frac{N_s}{2}\cos (\mathrm{\&pi;x}/\mathrm{\&tau;}+\mathrm{\&pi;}/3)---\left(6\right)$

$N_{\mathrm{cs}}\left(x\right)=\frac{N_s}{2}\cos (\mathrm{\&pi;x}/\mathrm{\&tau;}-\mathrm{\&pi;}/3)---\left(7\right)$

Wherein, N _sfor elementary every phase winding effective turn, τ is armature winding pole span.According to principle of coordinate transformation in Electrical Motor, three-phase winding function is transformed to (wherein two phase coordinate systems are fixed on elementary going up, and β axle and a coincide) in two-phase alpha-beta coordinate system.Because magnetic field is conservation law, in conversion process, the constant in energy in the whole magnetic field of motor internal, derive and show that the mathematic(al) representation of armature winding function is:

$N_{\mathrm{\&alpha;s}}\left(x\right)=\frac{3}{2}\frac{N_s}{2}\sin (\mathrm{\&pi;x}/\mathrm{\&tau;})---\left(8\right)$

$N_{\mathrm{\&beta;s}}\left(x\right)=-\frac{3}{2}\frac{N_s}{2}\cos (\mathrm{\&pi;x}/\mathrm{\&tau;})---\left(9\right)$

Due to the existence of elementary end half filling slot, the distribution of armature winding function is brought to certain influence, the present invention trades off by the original position of selecting corresponding β and α axle, specifically supposes that β axle lags behind half pole span of α axle in motor direction of advance.

Do not have actual winding to distribute because line inductance electromotor is secondary, associated winding function can be derived and be tried to achieve by Theory of Electromagnetic Field.Air gap flux linkage density B _sthe universal expression of (x, t) and winding function N (x) is:

$B(x,t)=\frac{{\mathrm{\&mu;}}_0}{g_e}N\left(x\right)i\left(t\right)---\left(10\right)$

Formula (10) is applicable to elementary first-harmonic winding function, secondary first-harmonic winding function and secondary side end effect wave winding function simultaneously.For elementary first-harmonic winding function, the magnetic linkage density B in air gap _s(x, t) is by primary current i _sproduce, its expression formula is:

$B_s(x,t)=\frac{-3{\mathrm{\&mu;}}_0}{4g_e}{N}_s{I}_s\exp ({\mathrm{j\&omega;}}_{e}t-\mathrm{\&pi;x}/\mathrm{\&tau;})---\left(11\right)$

Wherein, j is the imaginary part of symbol, and ω is elementary angular frequency.According to the basic functional principle of line inductance electromotor, the present invention sets secondary winding function and comprises two isolated components, i.e. fundametal compoment N _rsand edge effect component N (x) _re(x).Two components are independent electric, and variation is separately independent of each other, but can produce coupling in the calculation of parameter of the elementary alpha-beta circuit of motor.

The present invention supposes that the close fundametal compoment of the secondary magnetic of line inductance electromotor is B _rs(x, t), according to the transient state equation of formula (4) and dependent field magnitude relation formula, can derive B _rsthe expression formula of (x, t) is:

$B_{\mathrm{rs}}(x,t)=\frac{({3\mathrm{\&mu;}}_0/4g_e)N_s}{\sqrt{1+{(1/s{G}_e)}^2}}{I}_s\exp \left[j({\mathrm{\&omega;}}_{e}t-\mathrm{\&pi;x}/\mathrm{\&tau;}+{\mathrm{\&theta;}}_s)\right]---\left(12\right)$

Wherein, G _efor the quality factor of line inductance electromotor, its size is

i _sfor primary current effective value, θ _sfor the angle of secondary branch current hysteresis primary current, be expressed as

meanwhile, according to the T-shaped equivalent electric circuit of motor and one dimension field theory, can try to achieve secondary first-harmonic equivalent current amplitude I _rs(t) be:

$\begin{array}{c}{I}_{\mathrm{rs}}=I_s\frac{-j{X}_m}{j{X}_m+\frac{R_r}{s}}=I_s\frac{-j{X}_m}{j{X}_m+\frac{R_r}{s}}\exp \left(j{\mathrm{\&omega;}}_{e}t\right)=-I_s\frac{1}{1-j\frac{1}{s{G}_e}}\exp \left({\mathrm{j\&omega;}}_{e}t\right)\\ =\frac{-I_s}{\sqrt{1+{(1/s{G}_e)}^2}}\exp \left[j({\mathrm{\&omega;}}_{e}t+{\mathrm{\&theta;}}_s)\right]\end{array}---\left(13\right)$

Due to secondary fundamental flux density B _rs(x, t), secondary first-harmonic winding function N _rsand secondary fundamental current I (x) _rs(t) meet following relational expression:

$B_{\mathrm{rs}}(x,t)=\frac{{\mathrm{\&mu;}}_0}{g_e}{N}_{\mathrm{rs}}\left(x\right)I_{\mathrm{rs}}\left(t\right)---\left(14\right)$

Wushu (12) and (13) are brought formula (14) into, can obtain N _rs(x) expression formula is:

$N_{\mathrm{rs}}\left(x\right)=\frac{-3}{4}{N}_s\exp (-j\mathrm{\&pi;x}/\mathrm{\&tau;})---\left(15\right)$

Further decompose after alpha-beta coordinate system, the expression formula that can obtain secondary winding function fundametal compoment is:

$N_{\mathrm{\&alpha;rs}}\left(x\right)=\frac{3}{4}{N}_s\sin (\mathrm{\&pi;x}/\mathrm{\&tau;})---\left(16\right)$

$N_{\mathrm{\&beta;rs}}\left(x\right)=\frac{-3}{4}{N}_s\cos (\mathrm{\&pi;x}/\mathrm{\&tau;})---\left(17\right)$

According to the principle that solves secondary winding function fundametal compoment, the expression formula that the present invention further solves the secondary side end effect wave winding function of motor is:

$N_{\mathrm{\&alpha;re}}\left(x\right)=-\frac{N_c}{K}\exp (-x/{\mathrm{\&alpha;}}_2)\sin (\mathrm{\&pi;x}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)---\left(18\right)$

$N_{\mathrm{\&beta;re}}\left(x\right)=\frac{N_c}{K}\exp (-x/{\mathrm{\&alpha;}}_2)\cos (\mathrm{\&pi;x}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)---\left(19\right)$

In formula,

l _δfor elementary phase length, L _rfor secondary phase inductance, R _rfor secondary phase resistance, τ _efor limit end effect ripple pole span, N _cand θ _ebe respectively the variable relevant to motor operating state, $N_c=\frac{-3N_s}{4}\frac{\sqrt{{(\frac{1}{{\mathrm{\&alpha;}}_2}+s{G}_e\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}})}^2+{\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)}^2}}{\sqrt{{(\frac{1}{{\mathrm{\&alpha;}}_1}+\frac{1}{{\mathrm{\&alpha;}}_2})}^2+{\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)}^2}},{\mathrm{\&theta;}}_e={\tan }^{-1}\frac{\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA0000486050040000012.png,HDA0000486050040000022.png"\; state="\{\{state\}\}">e</figure-callout>}}}}{\frac{1}{{\mathrm{\&alpha;}}_2}+s{G}_e\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}}-{\tan }^{-1}\frac{\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA0000486050040000012.png,HDA0000486050040000022.png"\; state="\{\{state\}\}">e</figure-callout>}}}}{\frac{1}{{\mathrm{\&alpha;}}_1}+\frac{1}{{\mathrm{\&alpha;}}_2}},$ Wherein, α ₁enter to hold air gap flux density attenuation coefficient, α for elementary ₂go out to hold air gap flux density attenuation coefficient for elementary.

3, the derivation of equivalent parameters

According to derive three groups of winding functions, the present invention utilizes winding function correlation theory, further solves mutual inductance, self-induction and the velocity voltage correction coefficient of motor, for the foundation of line inductance electromotor equivalent electric circuit equation and model below lays the first stone.

First,, according to winding function theory, derive two mutual inductance L between winding ₁₂calculating formula be:

$L_{12}=\frac{{\mathrm{\&mu;}}_0{l}_{\mathrm{\&delta;}}}{g_e}\underset{0}{\overset{p_e\mathrm{\&tau;}}{\&Integral;}}{N}_1\left(x\right)N_2\left(x\right)\mathrm{dx}---\left(20\right)$

In above formula, N ₁and N (x) ₂(x) be two different winding function mathematic(al) representations, l _δfor the width of elementary lamination, p _efor motor pole number, Integration Solving limited range is limited in armature winding effective length.In the time solving motor self-induction, N ₁and N (x) ₂(x) mathematic(al) representation is identical.According to 3 groups of winding functions, the present invention solves 36 inductance value altogether, and the concrete form of its inductance matrix is as follows:

$\left[L\right]=\left[\begin{array}{cccccc}{L}_{\mathrm{\&alpha;s\&alpha;s}}& L_{\mathrm{\&alpha;s\&beta;s}}& L_{\mathrm{\&alpha;s\&alpha;r}}& L_{\mathrm{\&alpha;s\&beta;r}}& L_{\mathrm{\&alpha;s\&alpha;re}}& L_{\mathrm{\&alpha;s\&beta;re}}\\ L_{\mathrm{\&beta;s\&alpha;s}}& L_{\mathrm{\&beta;s\&beta;s}}& L_{\mathrm{\&beta;s\&alpha;r}}& L_{\mathrm{\&beta;s\&beta;r}}& L_{\mathrm{\&beta;s\&alpha;re}}& L_{\mathrm{\&beta;s\&beta;re}}\\ L_{\mathrm{\&alpha;r\&alpha;s}}& L_{\mathrm{\&alpha;r\&beta;s}}& L_{\mathrm{\&alpha;r\&alpha;r}}& L_{\mathrm{\&alpha;r\&beta;r}}& L_{\mathrm{\&alpha;r\&alpha;re}}& L_{\mathrm{\&alpha;r\&beta;re}}\\ L_{\mathrm{\&beta;r\&alpha;s}}& L_{\mathrm{\&beta;r\&beta;s}}& L_{\mathrm{\&beta;r\&alpha;r}}& L_{\mathrm{\&beta;r\&beta;r}}& L_{\mathrm{\&beta;r\&alpha;re}}& L_{\mathrm{\&beta;r\&beta;re}}\\ L_{\mathrm{\&alpha;re\&alpha;s}}& L_{\mathrm{\&alpha;re\&beta;s}}& L_{\mathrm{\&alpha;re\&alpha;e}}& L_{\mathrm{\&alpha;re\&beta;r}}& L_{\mathrm{\&alpha;re\&alpha;re}}& L_{\mathrm{\&alpha;re\&beta;re}}\\ L_{\mathrm{\&beta;re\&alpha;s}}& L_{\mathrm{\&beta;re\&beta;s}}& L_{\mathrm{\&beta;re\&alpha;r}}& L_{\mathrm{\&beta;re\&beta;r}}& L_{\mathrm{\&beta;re\&alpha;re}}& L_{\mathrm{\&beta;re\&beta;re}}\end{array}\right]---\left(21\right)$

Below the subscript of above-mentioned 36 inductance is explained as follows.α s and β s represent respectively α axle and β axle armature winding, and α r and β r represent respectively α axle and the secondary first-harmonic winding of β axle, and α re and β re represent respectively secondary side end effect wave winding.Hence one can see that, L _{α s β s}for the mutual inductance between α axle armature winding and β axle armature winding, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, the rest may be inferred for the implication of other inductance, do not repeat them here.

Independent variable is got and is comprised the above part of diagonal, amounts to 18, and in inductance solution procedure, integral operation bound all will be limited in the effective range of electric motor primary.

The each self-corresponding mutual inductance of elementary α axle and β axle is:

$L_{\mathrm{\&alpha;s\&alpha;s}}=L_{\mathrm{\&beta;s\&beta;s}}=\frac{3{\mathrm{\&mu;}}_0{l}_{\mathrm{\&delta;}}{p}_e\mathrm{\&tau;}}{16g_e}{N}_s^2=L_m---\left(22\right)$

Line inductance electromotor armature winding is L at α axle and β axle self-induction separately _{α s}=L _{β s}=L _m+ L _ls, wherein, L _lsfor electric motor primary leakage inductance, can obtain by conventional motors correlation theory.Similarly, the mutual inductance size further solving between line inductance electromotor α axle armature winding and β axle armature winding is:

$L_{\mathrm{\&alpha;s\&beta;s}}=\frac{1}{4\mathrm{\&pi;}}\frac{3{\mathrm{\&mu;}}_0{l}_{\mathrm{\&delta;}}{p}_e\mathrm{\&tau;}}{16g_e}{N}_s^2=\frac{1}{4\mathrm{\&pi;}}{L}_m---\left(23\right)$

Above formula shows, because elementary longitudinal magnetic circuit cut-offs impact, its armature winding front-end and back-end exist the relation that intercouples, and cause L _{α s β s}be not 0, further obtain L _{α s α re}, L _{α s β re}, L _{β s α re}and L _{β s β re}.

$\begin{array}{c}{L}_{\mathrm{\&alpha;s\&alpha;re}}=\frac{\frac{1}{2}{l}_{\mathrm{\&delta;}}{N}_s{N}_c\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)/K}{[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}+\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e})}^2][{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}-\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e})}^2]}\&times;\\ \left\{\right[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)}^2-{\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)}^2]\&times;[\exp (-p_e\mathrm{\&tau;}/{\mathrm{\&alpha;}}_2)\sin (p_e\mathrm{\&pi;\&tau;}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)+\sin {{\mathrm{\&theta;}}_e]}_{}\\ +\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)\left(\frac{2\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)[\exp (-p_e\mathrm{\&tau;}/{\mathrm{\&alpha;}}_2)\cos (p_e\mathrm{\&pi;\&tau;}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)-\cos {\mathrm{\&theta;}}_e]\}\end{array}---\left(24\right)$

$\begin{array}{c}{L}_{\mathrm{\&alpha;s\&beta;re}}=\frac{\frac{1}{2}{l}_{\mathrm{\&delta;}}{N}_s{N}_c\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)/K}{[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}+\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e})}^2][{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}-\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e})}^2]}\\ \&times;\left\{\right[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)}^2-{\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)}^2]\&times;[-\exp (-p_e\mathrm{\&tau;}/{\mathrm{\&alpha;}}_2)\cos (p_e\mathrm{\&pi;\&tau;}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)+\cos {{\mathrm{\&theta;}}_e]}_{}\\ +\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)\left(\frac{2\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)[\exp (-p_e\mathrm{\&tau;}/{\mathrm{\&alpha;}}_2)\sin (p_e\mathrm{\&pi;\&tau;}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)-\sin {\mathrm{\&theta;}}_e]\}\end{array}---\left(25\right)$

$\begin{array}{c}{L}_{\mathrm{\&beta;s\&beta;re}}=\frac{\frac{1}{2}{l}_{\mathrm{\&delta;}}{N}_s{N}_2\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)/K}{[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}+\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e})}^2][{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}-\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e})}^2]}\\ \&times;\left\{\right[-{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)}^2-{\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)}^2]\&times;[\exp (-p_e\mathrm{\&tau;}/{\mathrm{\&alpha;}}_2)\sin (p_e\mathrm{\&pi;\&tau;}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)+\sin {{\mathrm{\&theta;}}_e]}_{}\\ +\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)}^2+{\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)}^2][\exp (-p_e\mathrm{\&tau;}/{\mathrm{\&alpha;}}_2)\sin (p_e\mathrm{\&pi;\&tau;}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)-\sin {\mathrm{\&theta;}}_e]\}\end{array}---\left(26\right)$

$\begin{array}{c}{L}_{\mathrm{\&beta;s\&alpha;re}}=\frac{\frac{1}{2}{l}_{\mathrm{\&delta;}}{N}_s{N}_2\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)/K}{[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}+\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e})}^2][{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}-\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e})}^2]}\\ \&times;\left\{\frac{\mathrm{\&tau;}}{{\mathrm{\&tau;}}_e}\right[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)}^2-{\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)}^2]\&times;[-\exp (-p_e\mathrm{\&tau;}/{\mathrm{\&alpha;}}_2)\cos (p_e\mathrm{\&pi;\&tau;}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)+\cos {{\mathrm{\&theta;}}_e]}_{}\\ +\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)[{\left(\frac{1}{{\mathrm{\&alpha;}}_2}\right)}^2+{\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right)}^2+{\left(\frac{\mathrm{\&pi;}}{{\mathrm{\&tau;}}_e}\right)}^2]\left[\exp (-p_e\mathrm{\&tau;}/{\mathrm{\&alpha;}}_2)\sin (p_e\mathrm{\&pi;\&tau;}/{\mathrm{\&tau;}}_e-{\mathrm{\&theta;}}_e)+\sin {\mathrm{\&theta;}}_e\right]\}\end{array}---\left(27\right)$

Further, the present invention solves and obtains other 11 inductance parameters and be:

L _αrαr＝L _m，L _βrβr＝L _m，L _αrβr＝0，L _αsαr＝L _m，L _αsβr＝0，L _βsβr＝L _m，L _βsαr＝0，L _αrαre＝L _αsαre，L _αrβre＝L _αsβre，L _βrαre＝L _βsαre，L _βrβre＝L _βsβre。

Secondary first-harmonic is L in the total inductance of α axle and β axle _{α r}=L _{β r}=L _m+ L _lr, L _lrbe secondary leakage inductance, can adopt the correlation technique of traditional rotary inductive motor to solve or measuring.

Line inductance electromotor is in the time of operation, and armature winding can produce velocity voltage in secondary winding.The present invention supposes velocity voltage e ₁₂for circuit 2 senses the induced voltage in circuit 1, its expression formula is:

$e_{12}=\left(\frac{\mathrm{\&pi;v}}{\mathrm{\&tau;}}\right)i_2\left(\frac{\mathrm{\&tau;}}{\mathrm{\&pi;}}\frac{{\&PartialD;L}_{12}}{\&PartialD;x}\right)---\left(28\right)$

According to above formula, the present invention defines velocity voltage correction coefficient and is:

$G_{12}=\frac{\mathrm{\&tau;}}{\mathrm{\&pi;}}\frac{{\&PartialD;L}_{12}}{\&PartialD;x}=\frac{\mathrm{\&tau;}}{\mathrm{\&pi;}}\frac{{\mathrm{\&mu;}}_0{l}_{\mathrm{\&delta;}}}{g_e}{\&Integral;}_0^{p_e\mathrm{\&tau;}}{N}_1\left(x\right)\frac{\&PartialD;N_2(x+y)}{\&PartialD;y}{|}_{y=0}\mathrm{dx}---\left(29\right)$

Formula (29) is expressed and is solved velocity voltage correction coefficient with the form of winding function, and the present invention, before carrying out integration, first will carry out partial derivative computing, introduces variable y and distinguishes concrete differential and integral operation operation.According to 3 groups of winding functions, try to achieve 6 effective velocity voltage correction coefficient:

G _αrβs＝-G _βrαs＝L _m （30）

G _αrβr＝-G _βrαr＝L _m+L _lr （31）

G _αrαre＝L _βsαre （32）

G _αrβre＝L _βsβre （33）

G _βrαre＝-L _αsαre （34）

G _βrβre＝-L _αsβre （35）

According to line inductance electromotor one dimension Theory of Electromagnetic Field, secondary resistance is affected by quality factor, and it and excitation reactance meet following relational expression: $R_r=\frac{X_m}{G_e}---\left(36\right)$

4, the foundation of equivalent electric circuit

According to Electrical Motor basic theories, on the basis of the above-mentioned parameter of electric machine, the voltage equation of the different windings of three groups of models of the present invention, three groups of different magnetic linkage equations of winding and the velocity voltage equation of three groups of different windings.Then,, according to the restriction relation between line inductance electromotor voltage, electric current, back-emf, magnetic linkage, the present invention derives and sets up Type Equivalent Circuit Model.Detailed process is summarized as follows.

Armature winding voltage equation:

$\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;s}}=R_s{i}_{\mathrm{\&alpha;s}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}}{\mathrm{dt}}+e_{\mathrm{\&alpha;s}}\\ u_{\mathrm{\&beta;s}}=R_s{i}_{\mathrm{\&beta;s}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}}{\mathrm{dt}}+e_{\mathrm{\&beta;s}}\end{array}\right.---\left(37\right)$

Secondary first-harmonic winding voltage equation:

$\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;r}}=0=R_r{i}_{\mathrm{\&alpha;r}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}}{\mathrm{dt}}+e_{\mathrm{\&alpha;r}}\\ u_{\mathrm{\&beta;r}}=0=R_r{i}_{\mathrm{\&beta;r}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}}{\mathrm{dt}}+e_{\mathrm{\&beta;r}}\end{array}\right.---\left(38\right)$

Secondary side end effect winding voltage equation:

$\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;re}}=R_{\mathrm{\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&alpha;re}}}{\mathrm{dt}}+e_{\mathrm{\&alpha;re}}\\ u_{\mathrm{\&beta;re}}=R_{\mathrm{\&beta;re}}{i}_{\mathrm{\&beta;re}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&beta;re}}}{\mathrm{dt}}+e_{\mathrm{\&beta;re}}\end{array}\right.---\left(39\right)$

Armature winding magnetic linkage equation:

$\left\{\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}=L_{\mathrm{\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+L_{\mathrm{\&alpha;s\&beta;s}}{i}_{\mathrm{\&beta;s}}+L_{\mathrm{\&alpha;s\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+L_{\mathrm{\&alpha;s\&beta;r}}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&alpha;s\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&alpha;s\&beta;re}}{i}_{\mathrm{\&beta;re}}\\ =(L_{\mathrm{ls}}+L_m)i_{\mathrm{\&alpha;s}}+L_{\mathrm{\&alpha;s\&beta;s}}{i}_{\mathrm{\&beta;s}}+L_m{i}_{\mathrm{\&alpha;r}}+L_{\mathrm{\&alpha;s\&beta;r}}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&alpha;s\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&alpha;s\&beta;re}}{i}_{\mathrm{\&beta;re}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}=L_{\mathrm{\&beta;s\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+L_{\mathrm{\&beta;s}}{i}_{\mathrm{\&beta;s}}+L_{\mathrm{\&beta;s\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+L_{\mathrm{\&beta;s\&beta;r}}^{\&prime;}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&beta;s\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&beta;s\&beta;re}}{i}_{\mathrm{\&beta;re}}\\ =L_{\mathrm{\&beta;s\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+(L_{\mathrm{ls}}+L_m)i_{\mathrm{\&beta;s}}+L_{\mathrm{\&beta;s\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+L_m{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&beta;s\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&beta;s\&beta;re}}{i}_{\mathrm{\&beta;re}}\end{array}\right.---\left(40\right)$

Secondary first-harmonic winding magnetic linkage equation:

$\left\{\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}=L_{\mathrm{\&alpha;r\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+L_{\mathrm{\&alpha;r\&beta;s}}{i}_{\mathrm{\&beta;s}}+L_{\mathrm{\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+L_{\mathrm{\&alpha;r\&beta;r}}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&alpha;r\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&alpha;r\&beta;re}}{i}_{\mathrm{\&beta;re}}\\ =L_m{i}_{\mathrm{\&alpha;s}}+L_{\mathrm{\&alpha;r\&beta;s}}{i}_{\mathrm{\&beta;s}}+{\left(}_{L_{\mathrm{lr}}+L_m}{i}_{\mathrm{\&alpha;r}}+L_{\mathrm{\&alpha;r\&beta;r}}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&alpha;r\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&alpha;r\&beta;re}}{i}_{\mathrm{\&beta;re}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}=L_{\mathrm{\&beta;r\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+L_{\mathrm{\&beta;r\&beta;s}}{i}_{\mathrm{\&beta;s}}+L_{\mathrm{\&beta;r\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+L_{\mathrm{\&beta;r}}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&beta;r\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&beta;r\&beta;re}}{i}_{\mathrm{\&beta;re}}\\ =L_{\mathrm{\&beta;r\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+L_m{i}_{\mathrm{\&beta;s}}+L_{\mathrm{\&beta;r\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+{\left(}_{L_{\mathrm{lr}}+L_m}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&beta;r\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&beta;r\&beta;re}}{i}_{\mathrm{\&beta;re}}\end{array}\right.---\left(41\right)$

Secondary side end effect wave winding magnetic linkage equation:

$\left\{\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;re}}=L_{\mathrm{\&alpha;re\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+L_{\mathrm{\&alpha;re\&beta;s}}{i}_{\mathrm{\&beta;s}}+L_{\mathrm{\&alpha;re\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+L_{\mathrm{\&alpha;re\&beta;r}}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&alpha;re\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&alpha;re\&beta;re}}{i}_{\mathrm{\&beta;re}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;re}}=L_{\mathrm{\&beta;re\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+L_{\mathrm{\&beta;re\&beta;s}}{i}_{\mathrm{\&beta;s}}+L_{\mathrm{\&beta;re\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+L_{\mathrm{\&beta;re\&beta;r}}{i}_{\mathrm{\&beta;r}}+L_{\mathrm{\&beta;re\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&beta;re\&beta;re}}{i}_{\mathrm{\&beta;re}}\end{array}\right.---\left(42\right)$

Armature winding velocity voltage equation: $\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;s}}=0\\ e_{\mathrm{\&beta;s}}=0\end{array}\right.---\left(43\right)$

Secondary winding fundametal compoment velocity voltage equation:

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;r}}=v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}[G_{\mathrm{\&alpha;r\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+G_{\mathrm{\&alpha;r\&beta;s}}{i}_{\mathrm{\&beta;s}}+G_{\mathrm{\&alpha;r\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+G_{\mathrm{\&alpha;r\&beta;r}}{i}_{\mathrm{\&beta;r}}+G_{\mathrm{\&alpha;r\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+G_{\mathrm{\&alpha;r\&beta;re}}{i}_{\mathrm{\&beta;re}}]=v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\\ e_{\mathrm{\&beta;r}}=v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}[G_{\mathrm{\&beta;r\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+G_{\mathrm{\&beta;r\&beta;s}}{i}_{\mathrm{\&beta;s}}+G_{\mathrm{\&beta;r\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+G_{\mathrm{\&beta;r\&beta;r}}{i}_{\mathrm{\&beta;r}}+G_{\mathrm{\&beta;r\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+G_{\mathrm{\&beta;r\&beta;re}}{i}_{\mathrm{\&beta;re}}]=-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\end{array}\right.---\left(44\right)$

Secondary winding edge effect component velocity voltage equation,

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;re}}=v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}[G_{\mathrm{\&alpha;re\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+G_{\mathrm{\&alpha;re\&beta;s}}{i}_{\mathrm{\&beta;s}}+G_{\mathrm{\&alpha;re\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+G_{\mathrm{\&alpha;re\&beta;r}}{i}_{\mathrm{\&beta;r}}+G_{\mathrm{\&alpha;re\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+G_{\mathrm{\&alpha;re\&beta;re}}{i}_{\mathrm{\&beta;re}}]\\ e_{\mathrm{\&beta;re}}=v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}[G_{\mathrm{\&beta;re\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+G_{\mathrm{\&beta;re\&beta;s}}{i}_{\mathrm{\&beta;s}}+G_{\mathrm{\&beta;re\&alpha;r}}{i}_{\mathrm{\&alpha;r}}+G_{\mathrm{\&beta;re\&beta;r}}{i}_{\mathrm{\&beta;r}}+G_{\mathrm{\&beta;re\&alpha;re}}{i}_{\mathrm{\&alpha;re}}+G_{\mathrm{\&beta;re\&beta;re}}{i}_{\mathrm{\&beta;re}}]\end{array}\right.---\left(45\right)$

According to motor one dimension field theory, Derivation of the present invention goes out in α β axle, and the pass of secondary side edge effect electric current and primary current and secondary fundamental current is:

$\left\{\begin{array}{c}{i}_{\mathrm{\&alpha;re}}=-K(i_{\mathrm{\&alpha;s}}+i_{\mathrm{\&alpha;r}})\\ i_{\mathrm{\&beta;re}}=-K(i_{\mathrm{\&beta;s}}+i_{\mathrm{\&beta;r}})\end{array}\right.---\left(46\right)$

The present invention supposes that the mutual inductance of line inductance electromotor has following relation, L' _{α s α re}=-KL _{α s α re}, L' _{α s β re}=-KL _{α s β re}, L' _{α r α re}=-KL _{α r α re}, L' _{α r β re}=-KL _{α r β re}, L' _{β s α re}=-KL _{β s α re}, L' _{β s β re}=-KL _{β s β re}, L' _{β r α re}=-KL _{β r α re}, L' _{β r β re}=-KL _{β r β re}.Similar, the present invention further obtains the simplification relation of speed voltage coefficient, G' _{α s α re}=-KG _{α s α re}, G' _{α s β re}=-KG _{α s β re}, G' _{α r α re}=-KG _{α r α re}, G' _{α r β re}=-KG _{α r β re}, G' _{β s α re}=-KG _{β s α re}, G' _{β s β re}=-KG _{β s β re}, G' _{β r α re}=-KG _{β r α re}, G' _{β r β re}=-KG _{β r β re}.

In conjunction with formula (37)～(46), the present invention with the voltage of the armature winding of line inductance electromotor, secondary winding and magnetic linkage equation for solving object, using the voltage of secondary side end effect winding and magnetic linkage as intermediate variable, the voltage and the magnetic linkage equation that obtain armature winding, secondary winding by mathematical derivation are as follows.

Armature winding voltage equation is: $\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;s}}=R_s{i}_{\mathrm{\&alpha;s}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}}{\mathrm{dt}}\\ u_{\mathrm{\&beta;s}}=R_s{i}_{\mathrm{\&beta;s}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}}{\mathrm{dt}}\end{array}\right.---\left(47\right)$

Secondary first-harmonic winding voltage equation is: $\left\{\begin{array}{c}0=R_r{i}_{\mathrm{\&alpha;r}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}}{\mathrm{dt}}+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}{\mathrm{\&lambda;}}_{\mathrm{\&beta;<figure-callout\; id="0"\; label="r"\; filenames="HDA0000486050040000021.png"\; state="\{\{state\}\}">r</figure-callout>}}\\ 0=R_r{i}_{\mathrm{\&beta;r}}+\frac{d{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}}{\mathrm{dt}}-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\end{array}\right.---\left(48\right)$

Armature winding magnetic linkage equation is:

$\left\{\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}=\left({L_{\mathrm{ls}}+L_m+L}_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}\right)i_{\mathrm{\&alpha;s}}+(L_{\mathrm{\&alpha;s\&beta;s}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}+(L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;r}}+{(L_{\mathrm{\&alpha;s\&beta;r}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;})i}_{\mathrm{\&beta;r}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}=(L_{\mathrm{\&alpha;s\&beta;s}}+L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}+(L_{\mathrm{ls}}+L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}+(L_{\mathrm{\&beta;s\&alpha;r}}+L_{\mathrm{\&beta;s\&alpha;r}}^{\&prime;})i_{\mathrm{\&alpha;r}}+(L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;r}}\end{array}\right.---\left(49\right)$

Secondary first-harmonic winding magnetic linkage equation is:

$\left\{\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}=\left({L_m+L}_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;}\right)i_{\mathrm{\&alpha;s}}+(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}+(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;r}}+{(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i}_{\mathrm{\&beta;r}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}=(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}+(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}+(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;r}}^{\&prime;})i_{\mathrm{\&alpha;r}}+(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;r}}\end{array}\right.---\left(50\right)$

Adopt voltage and the magnetic linkage the Representation Equation of matrix form to armature winding, secondary first-harmonic winding to be:

$\stackrel{\&RightArrow;}{u}=\left[R\right]\stackrel{\&RightArrow;}{i}+\frac{\mathrm{d\&lambda;}}{\mathrm{dt}}+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\left[U\right]\stackrel{\&RightArrow;}{\mathrm{\&lambda;}}---\left(51\right)$

$\stackrel{\&RightArrow;}{u}={[v_{\mathrm{\&alpha;s}},v_{\mathrm{\&beta;s}},\mathrm{0,0}]}^T---\left(52\right)$

$\stackrel{\&RightArrow;}{i}={[i_{\mathrm{\&alpha;s}},i_{\mathrm{\&beta;s}},i_{\mathrm{\&alpha;r}}^{\&prime;},i_{\mathrm{\&beta;r}}^{\&prime;}]}^T---\left(53\right)$

$\left[R\right]=\left[\begin{array}{cccc}{R}_s& 0& 0& 0\\ 0& {\mathrm{<figure-callout\; id="0"\; label="R\; s"\; filenames="HDA0000486050040000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_s& 0& 0\\ 0& 0& R_r^{\&prime;}& 0\\ 0& 0& 0& R_r^{\&prime;}\end{array}\right]---\left(54\right)$

$\left[L\right]=\left[\begin{array}{cccc}{l}_s+L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}& L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;}+L_{\mathrm{\&alpha;s\&beta;s}}& L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}& L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;}\\ L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;}+L_{\mathrm{\&alpha;s\&beta;s}}& l_s+L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;}& L_{\mathrm{\&beta;s\&alpha;re}}& L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;}\\ L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;}& L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;}& l_r^{\&prime;}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;}& L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;}\\ L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;}& L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;}& L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;}& l_r^{\&prime;}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;}\end{array}\right]---\left(55\right)$

$\left[U\right]=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 1\\ 0& 0& -1& 0\end{array}\right]---\left(57\right)$

According to the equivalent voltage equation of the armature winding derived above, the equivalent voltage equation of secondary first-harmonic winding, armature winding magnetic linkage equation and secondary first-harmonic winding magnetic linkage equation, the present invention concludes and obtains the pass of primary and secondary winding magnetic linkage and primary and secondary electric current under alpha-beta axle and be:

$\left[\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\end{array}\right]=\left[\begin{array}{cccc}{L}_{\mathrm{ls}}+L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}& L_{\mathrm{\&alpha;s\&beta;s}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;}& L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}& L_{\mathrm{\&alpha;s\&beta;r}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;}\\ L_{\mathrm{\&alpha;s\&beta;s}}+L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;}& L_{\mathrm{ls}}+L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;}& L_{\mathrm{\&beta;s\&alpha;r}}+L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;}& L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;}\\ L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;}& L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;}& L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;}& L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;}\\ L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;}& L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;}& L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;}& L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\&alpha;s}}\\ i_{\mathrm{\&beta;s}}\\ i_{\mathrm{\&alpha;r}}\\ i_{\mathrm{\&beta;r}}\end{array}\right]---\left(58\right)$

Above formula shows, affects because the present invention has taken into full account the elementary end of line inductance electromotor half filling slot, and motor mutual inductance exists certain coupling, i.e. L at alpha-beta between centers _{α s β s}≠ 0.Eddy current in secondary guide plate produces impact in various degree to elementary magnetic linkage and secondary magnetic linkage, each magnetic linkage equation all with four current i _{α s}, i _{β s}, i _{α r}and i _{β r}relevant.By in formula (49) and (50) substitution formula (47) and (48), and hypothesis:

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;t}}=p[L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;}{i}_{\mathrm{\&beta;re}}]\\ e_{\mathrm{\&beta;t}}=p[L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;}{i}_{\mathrm{\&alpha;re}}^{\&prime;}+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;}{i}_{\mathrm{\&beta;re}}^{\&prime;}]\end{array}\right.---\left(59\right)$

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;st}}=-p{L}_{\mathrm{\&alpha;s\&beta;s}}{i}_{\mathrm{\&beta;s}}\\ e_{\mathrm{\&beta;st}}=-p{L}_{\mathrm{\&alpha;s\&beta;s}}{i}_{\mathrm{\&alpha;s}}\end{array}\right.---\left(60\right)$

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;r}}=v(\mathrm{\&pi;}/\mathrm{\&tau;}){\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\\ e_{\mathrm{\&beta;r}}=-v(\mathrm{\&pi;}/\mathrm{\&tau;}){\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\end{array}\right.---\left(61\right)$

P is differential operator d/dt, and t is the time, voltage source e _{α t}, e _{β t}, e _{α st}and e _{β st}for considering 4 induced potentials after the end effect effect of limit, they are all inductance differentiation functions.E _{α r}and e _{β r}for secondary reduction is to elementary speed voltage, all relevant to the motor speed of service.Simplify the equivalent voltage equation that obtains armature winding and secondary first-harmonic winding.

Armature winding voltage equation is:

$\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;s}}=R_s{i}_{\mathrm{\&alpha;s}}+L_{\mathrm{ls}}p{i}_{\mathrm{\&alpha;s}}+L_{m}p(i_{\mathrm{\&alpha;s}}+i_{\mathrm{\&alpha;r}})+e_{\mathrm{\&alpha;t}}-e_{\mathrm{\&alpha;st}}\\ u_{\mathrm{\&beta;s}}=R_s{i}_{\mathrm{\&beta;s}}+L_{\mathrm{ls}}{\mathrm{pi}}_{\mathrm{\&beta;s}}+L_{m}p(i_{\mathrm{\&beta;s}}+i_{\mathrm{\&beta;r}})+e_{\mathrm{\&beta;t}}-e_{\mathrm{\&beta;st}}\end{array}\right.---\left(62\right)$

Secondary first-harmonic winding voltage equation is:

$\left\{\begin{array}{c}0=e_{\mathrm{\&alpha;t}}+L_{m}p(i_{\mathrm{\&alpha;s}}+i_{\mathrm{\&alpha;r}})+L_{\mathrm{lr}}{\mathrm{pi}}_{\mathrm{\&alpha;r}}+i_{\mathrm{\&alpha;r}}{R}_r+e_{\mathrm{\&alpha;<figure-callout\; id="0"\; label="r"\; filenames="HDA0000486050040000021.png"\; state="\{\{state\}\}">r</figure-callout>}}\\ 0=e_{\mathrm{\&beta;t}}+L_{m}p(i_{\mathrm{\&beta;s}}+i_{\mathrm{\&beta;r}})+L_{\mathrm{lr}}{\mathrm{pi}}_{\mathrm{\&beta;r}}{+i}_{\mathrm{\&beta;r}}{R}_r+e_{\mathrm{\&beta;r}}\end{array}\right.---\left(63\right)$

According to formula (62) and (63), the present invention sets up the Type Equivalent Circuit Model of line inductance electromotor under alpha-beta axle, specifically as shown in Figure 2.Comprise α axle equivalent electric circuit and β axle equivalent electric circuit.

α axle equivalent electric circuit comprises the first branch road, the second branch road and the 3rd branch road, after the second branch road and the 3rd branch circuit parallel connection, connects with the first branch road, and the node of three branch roads is designated as A, first elementary phase resistance R of route _s, elementary phase leakage inductance L _lswith the first voltage source e _{α st}be in series, the first voltage source e _{α st}positive pole near node A, second secondary phase resistance R of route _r, secondary phase leakage inductance L _lrwith second voltage source e _{α r}be in series, second voltage source e _{α r}positive pole near node A, the 3rd route air gap equivalence mutual inductance L _mwith tertiary voltage source e _{α t}be in series, tertiary voltage source e _{α t}positive pole near node A.

β axle equivalent electric circuit comprises the 4th branch road, the 5th branch road and the 6th branch road, after the 5th branch road and the 6th branch circuit parallel connection, connects with the 4th branch road, and the node of three branch roads is designated as B, the 4th the elementary phase resistance R of route _s, elementary phase leakage inductance L _lswith the 4th voltage source e _{β st}be in series, the 4th voltage source e _{β st}positive pole near Node B, the 5th the secondary phase resistance R of route _r, secondary phase leakage inductance L _lrwith the 5th voltage source e _{β r}be in series, the 5th voltage source e _{β r}positive pole near Node B, the 6th route air gap equivalence mutual inductance L _mwith the 6th voltage source e _{β t}be in series, the 6th voltage source e _{β t}positive pole near Node B.

This novel equivalent electric circuit can be described limit end effect and the impact of elementary half filling slot on line inductance electromotor characteristic flexibly effectively, is embodied in:

(1) consider limit end effect, consider the impact of elementary half filling slot

Limit end effect is larger on the impact of motor self-induction, is mainly reflected in four limit end effect mutual inductance L _{α s α re}, L _{α s β re}, L _{β s α re}, L _{β s β re}variation in, and strengthen with the speed of service of motor; Voltage source e simultaneously _{α t}and e _{β t}for the induced potential relevant to limit end effect.Affected by elementary end half filling slot, motor is non-vanishing in the mutual inductance of α axle and β between centers, voltage source e _{α st}and e _{β st}also relevant to half filling slot.

(2) do not consider limit end effect, consider the impact of elementary half filling slot

In the inductance parameters matrix of formula (58), all variablees relevant to limit end effect are zero (but mutual inductance L _{α s β s}≠ 0), thus the magnetic linkage equation matrix form that is simplified of the present invention be:

$\left[\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\end{array}\right]=\left[\begin{array}{cccc}{L}_{\mathrm{ls}}+L_m& L_{\mathrm{\&alpha;s\&beta;s}}& L_m& L_{\mathrm{\&alpha;s\&beta;r}}\\ L_{\mathrm{\&alpha;s\&beta;s}}& L_{\mathrm{ls}}+L_m& L_{\mathrm{\&beta;s\&alpha;r}}& L_m\\ L_m& L_{\mathrm{\&alpha;r\&beta;s}}& L_{\mathrm{lr}}+L_m& L_{\mathrm{\&alpha;r\&beta;r}}\\ L_{\mathrm{\&beta;r\&alpha;s}}& L_m& L_{\mathrm{\&beta;r\&alpha;r}}& L_{\mathrm{lr}}+L_m\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\&alpha;s}}\\ i_{\mathrm{\&beta;s}}\\ i_{\mathrm{\&alpha;r}}\\ i_{\mathrm{\&beta;r}}\end{array}\right]---\left(64\right)$

Voltage source e simultaneously _{α t}, e _{β t}, e _{α st}, e _{β st}, e _{α r}and e _{β r}abbreviation is:

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;t}}=0\\ e_{\mathrm{\&beta;t}}=0\end{array}\right.---\left(65\right)$

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;st}}=-p{L}_{\mathrm{\&alpha;s\&beta;s}}{i}_{\mathrm{\&beta;s}}\\ e_{\mathrm{\&beta;st}}=-p{L}_{\mathrm{\&alpha;s\&beta;s}}{i}_{\mathrm{\&alpha;s}}\end{array}\right.---\left(66\right)$

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;r}}=v(\mathrm{\&pi;}/\mathrm{\&tau;}){\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\\ e_{\mathrm{\&beta;r}}=-v(\mathrm{\&pi;}/\mathrm{\&tau;}){\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\end{array}\right.---\left(67\right)$

(3) do not consider limit end effect, consider the impact of elementary half filling slot

Now motor mutual inductance L _{α s β s}=0, again ask for other inductance values, there is L' _{α s β re}=0; L' _{β s α re}=0; L' _{α r β re}=0; L' _{β r α re}=0.The matrix equation of magnetic linkage is:

$\left[\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\end{array}\right]=\left[\begin{array}{cccc}{L}_{\mathrm{ls}}+L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}& 0& L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}& 0\\ 0& L_{\mathrm{ls}}+L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;}& 0& L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;}\\ L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;}& 0& L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;}& 0\\ 0& L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;}& 0& L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\&alpha;s}}\\ i_{\mathrm{\&beta;s}}\\ i_{\mathrm{\&alpha;r}}\\ i_{\mathrm{\&beta;r}}\end{array}\right]---\left(68\right)$

Similarly, voltage source e _{α t}, e _{β t}, e _{α st}, e _{β st}, e _{α r}and e _{β r}can be reduced to:

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;t}}=p[L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;}{i}_{\mathrm{\&alpha;re}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;}{i}_{\mathrm{\&beta;re}}]\\ e_{\mathrm{\&beta;t}}=p[L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;}{i}_{\mathrm{\&alpha;re}}^{\&prime;}+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;}{i}_{\mathrm{\&beta;re}}^{\&prime;}]\end{array}\right.---\left(69\right)$

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;st}}=0\\ e_{\mathrm{\&beta;st}}=0\end{array}\right.---\left(70\right)$

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;r}}=v(\mathrm{\&pi;}/\mathrm{\&tau;}){\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\\ e_{\mathrm{\&beta;r}}=-v(\mathrm{\&pi;}/\mathrm{\&tau;}){\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\end{array}\right.---\left(71\right)$

(4) do not consider limit end effect, consider the impact of elementary half filling slot

In this case, seemingly, the inductance parameters relevant to limit end effect is zero for the inductance parameters of line inductance electromotor and traditional rotary inductive electric machinery, motor mutual inductance L _{α s β s}=0.Derive through relevant, the reduced form that the present invention obtains magnetic linkage matrix is:

$\left[\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\\ {\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\end{array}\right]=\left[\begin{array}{cccc}{L}_{\mathrm{ls}}+L_m& 0& {\mathrm{<figure-callout\; id="0"\; label="L\; m"\; filenames="HDA0000486050040000021.png"\; state="\{\{state\}\}">L</figure-callout>}}_m& 0\\ 0& L_{\mathrm{ls}}+L_m& 0& L_m\\ L_m& 0& L_{\mathrm{lr}}+{\mathrm{<figure-callout\; id="0"\; label="L\; m"\; filenames="HDA0000486050040000021.png"\; state="\{\{state\}\}">L</figure-callout>}}_m& 0\\ 0& L_m& 0& L_{\mathrm{lr}}+L_m\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\&alpha;s}}\\ i_{\mathrm{\&beta;s}}\\ i_{\mathrm{\&alpha;r}}\\ i_{\mathrm{\&beta;r}}\end{array}\right]---\left(72\right)$

Correspondingly, six voltage source e _{α t}, e _{β t}, e _{α st}, e _{β st}, e _{α r}and e _{β r}can be reduced to

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;t}}=0\\ e_{\mathrm{\&beta;t}}=0\end{array}\right.---\left(73\right)$

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;st}}=0\\ e_{\mathrm{\&beta;st}}=0\end{array}\right.---\left(74\right)$

$\left\{\begin{array}{c}{e}_{\mathrm{\&alpha;r}}=v(\mathrm{\&pi;}/\mathrm{\&tau;}){\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}={\mathrm{\&omega;}}_r{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}\\ e_{\mathrm{\&beta;r}}=-v(\mathrm{\&pi;}/\mathrm{\&tau;}){\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}={-\mathrm{\&omega;}}_r{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\end{array}\right.---\left(75\right)$

Wherein, ω _rfor the electric angle speed of secondary operation.Further, the equivalent-circuit model obtaining in this situation shows, in the time not considering the affecting of limit end effect and half filling slot, the line inductance electromotor equivalent-circuit model that the present invention derives according to winding function theory is identical with traditional rotary inductive motor.By formula (58)～(63), the present invention has described limit end effect and the impact of half filling slot on linear electric motors parameter and correlation properties well, the property of line inductance electromotor is embodied in the expression formula of limit end effect inductance, mutual inductance and motion electromotive force, they are all functions of electric machine structure parameter, slippage, elementary frequency and speed, can be different under different operating modes.

5, the derivation of power energy parameter and drive characteristic analysis

According to the motor electric parameter and the equivalent-circuit model that obtain above, the present invention further derives the power energy parameter (mainly comprising thrust, input power, power output, efficiency and power factor) of motor, for the driveability analysis of line inductance electromotor lays the first stone.

According to line inductance electromotor primary and secondary conservation of energy principle, the motor thrust of first deriving F _xfor:

F _x＝(3π/2τ)[i ₁] ^T[G][i ₁] （76）

In formula, [i ₁] be current matrix, comprise end effect electric current in limit in secondary guide plate, expression formula is:

[i ₁]＝[i _αs,i _βs,i _αr,i _βr,-K(i _αs+i _αr),-K(i _βs+i _βr)] ^T （77）

In formula (76), [G] is speed voltage correction matrix, and its expression formula is:

$\left[G\right]=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& G_{\mathrm{\&alpha;r\&beta;s}}& 0& G_{\mathrm{\&alpha;r\&beta;r}}& G_{\mathrm{\&alpha;r\&alpha;re}}& G_{\mathrm{\&alpha;r\&beta;re}}\\ G_{\mathrm{\&beta;r\&alpha;s}}& 0& G_{\mathrm{\&beta;r\&alpha;r}}& 0& G_{\mathrm{\&beta;r\&alpha;re}}& G_{\mathrm{\&beta;r\&beta;re}}\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]---\left(78\right)$

Convolution (30)～(35) and formula (76)～(78), and consider the impact of COEFFICIENT K on motion electromotive force, the present invention is after to the further abbreviation of motor thrust:

F _x＝(3π/2τ)[L _m(i _αri _βs-i _βri _αs)+i _αs(i _αr+i _αs)G ^' _αsαre+i _αs(i _βr+i _βs)G' _αsβre+i _βs(i _αr+i _αs)G' _βsαre+i _βs(i _βr+i _βs)G' _βsβre] （79）

According to Electrical Motor knowledge, the input that the present invention further tries to achieve motor is gained merit and is:

$p_{\mathrm{in}}=\frac{3}{2}(u_{\mathrm{\&alpha;s}}{i}_{\mathrm{\&alpha;s}}+u_{\mathrm{\&beta;s}}+i_{\mathrm{\&beta;s}})---\left(80\right)$

The input reactive power of motor is: $q_{\mathrm{in}}=\frac{3}{2}(u_{\mathrm{\&beta;s}}{i}_{\mathrm{\&alpha;s}}-u_{\mathrm{\&alpha;s}}{i}_{\mathrm{\&beta;s}})---\left(81\right)$

The thrust output of motor is: F _out=F _x-F _r-F _l(82)

In formula, F _rfor the suffered resistance of motor, comprise frictional resistance, air drag etc., F _lfor load force.

The active power of output of motor is: p _out=F _xv (83)

The power factor of motor is:

The efficiency of motor is: η=p _outp _in(85)

The present invention utilizes winding function theory, sets up elementary actual winding distribution function, then utilizes a road analysis principle, and Derivation goes out secondary first-harmonic winding function and secondary side end effect wave winding function.The present invention has taken into account the accuracy of electromagnetic field analysis and the rapidity of concentrated circuit method in whole derivation, the equivalent electric circuit equation and the equivalent-circuit model that obtain, can the Steady state and transient state drive characteristic of line inductance electromotor be carried out reasonably prediction and be analyzed, specific as follows.

When the present invention analyzes motor steady-state characteristic, suppose d/dt=j ω in formula (47) and (48) _e, (wherein ω _efor elementary angular speed), derive following voltage equation.

Armature winding voltage equation is: $\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;s}}=R_s{i}_{\mathrm{\&alpha;s}}-{\mathrm{\&omega;}}_e{\mathrm{\&lambda;}}_{\mathrm{\&beta;s}}\\ u_{\mathrm{\&beta;s}}=R_s{i}_{\mathrm{\&beta;s}}+{\mathrm{\&omega;}}_e{\mathrm{\&lambda;}}_{\mathrm{\&alpha;s}}\end{array}\right.---\left(86\right)$

Secondary first-harmonic winding voltage equation is: $\left\{\begin{array}{c}0=R_r{i}_{\mathrm{\&alpha;r}}-{\mathrm{\&omega;}}_e{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}{\mathrm{\&lambda;}}_{\mathrm{\&beta;<figure-callout\; id="0"\; label="r"\; filenames="HDA0000486050040000021.png"\; state="\{\{state\}\}">r</figure-callout>}}\\ 0=R_r{i}_{\mathrm{\&beta;r}}+{\mathrm{\&omega;}}_e{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}\end{array}\right.---\left(48\right)$

Magnetic linkage expression formula λ in wushu (49) and (50) _{α s}, λ _{β s}, λ _{α r}, λ _{β r}be updated in formula (86) and (87), obtain new armature winding voltage equation and secondary first-harmonic winding voltage equation.

Armature winding voltage equation is updated to:

$\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;s}}=[R_s-{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;s\&beta;s}}+L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;s}}-{\mathrm{\&omega;}}_e(L_{\mathrm{ls}}+L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}\\ -{\mathrm{\&omega;}}_e(L_{\mathrm{\&beta;s\&alpha;r}}+L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;r}}-{\mathrm{\&omega;}}_e(L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;r}}\\ u_{\mathrm{\&beta;s}}={\mathrm{\&omega;}}_e(L_{\mathrm{ls}}+L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}+[R_s++{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;s\&beta;s}}+L_{\mathrm{\&alpha;\&beta;}}^{\&prime;})]i_{\mathrm{\&beta;s}}\\ +{\mathrm{\&omega;}}_e(L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;r}}+{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;s\&beta;r}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;r}}\end{array}\right.---\left(88\right)$

Secondary first-harmonic winding voltage equation is updated to:

$\left\{\begin{array}{c}0=[-{\mathrm{\&omega;}}_e(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;s}}+[-{\mathrm{\&omega;}}_e\left(L_{m+}{L}_{\mathrm{\&beta;r\&beta;re}}^{\&prime;}\right)+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;s}}\\ +[R_r-{\mathrm{\&omega;}}_e(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;r}}+[-{\mathrm{\&omega;}}_e(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;r}}\\ 0=[{\mathrm{\&omega;}}_e(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;s}}+[{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;s}}\\ +[{\mathrm{\&omega;}}_e(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;r}}+[R_r+{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;r}}\end{array}\right.---\left(89\right)$

When primary current is during as input variable, line inductance electromotor stable state drive characteristic analytical method comprises the steps: that (1) obtains motor speed of service v and three-phase primary windings electric current, three-phase primary windings electric current is carried out to changes in coordinates, obtain α axle primary winding current i _{α s}with β axle primary winding current i _{β s}; (2), according to formula (88) and (89), try to achieve the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}; (3) try to achieve the characteristic variable of line inductance electromotor, realize the analysis of stable state drive characteristic.

When primary voltage is during as input variable, line inductance electromotor stable state drive characteristic analytical method comprises the steps: that (1) obtains motor speed of service v, elementary angular frequency _eand three-phase primary windings voltage, three-phase primary windings voltage is carried out to changes in coordinates, obtain α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}; (2) calculate α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}; (3) try to achieve the characteristic variable of line inductance electromotor, realize the analysis of stable state drive characteristic.

Fig. 3 is the thrust F of line inductance electromotor under different steady operation speed _xchange curve.As seen from the figure, below 40km/h, motor is subject to constant current driven, and due to the impact of limit end effect, thrust slightly declines; More than 40km/h, motor is driven by constant voltage, and too fast in order to suppress thrust reduction, in this interval, linearity increases slip-frequency conventionally.Whole service interval, motor thrust output F _xmeasured value and calculated value mean error be 4.9%, meet the requirement of Practical Project.

The dynamic characteristic of line inductance electromotor mainly comprises the situation of change of the characteristic quantities such as current of electric under different operating modes (as load variations, rotation speed change etc.), magnetic linkage, thrust, speed, acceleration.The novel equivalent electric circuit that the present invention proposes, can, according to Current Control or voltage-controlled difference, analyze the dynamic characteristic of line inductance electromotor.

After known elementary three-phase current, obtain primary current i under α β coordinate system by changes in coordinates _{α s}and i _{β s}.The present invention is out of shape (supposing p=d/dt) to formula (48) and obtains:

$\left\{\begin{array}{c}p{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}=-v\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right){\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-R_r{i}_{\mathrm{\&alpha;r}}\\ p{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}=-v\left(\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}\right){\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-R_r{i}_{\mathrm{\&beta;r}}\end{array}\right.---\left(90\right)$

According to formula (50), available primary current i _{α s}and i _{β s}calculate secondary first-harmonic equivalent current i _{α r}and i _{β r}:

$\begin{array}{c}{i}_{\mathrm{\&alpha;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]\end{array}---\left(91\right)$

$\begin{array}{c}{i}_{\mathrm{\&beta;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]\end{array}---\left(92\right)$

In dynamic changing process, the thrust same available formula of size (79) of line inductance electromotor calculates, and wherein the speed differential equation of line inductance electromotor meets:

$M\frac{\mathrm{dv}}{\mathrm{dt}}=F_x-F_r-F_l---\left(93\right)$

Wherein, the elementary weight that M is line inductance electromotor.

When primary current is during as input variable, line inductance electromotor dynamic driving characteristic analysis method comprises the steps: that (1) obtains as front motor speed of service v, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}; (2) obtain three-phase primary windings electric current, three-phase primary windings electric current is carried out to changes in coordinates, obtain α axle primary winding current i _{α s}with β axle primary winding current i _{β s}; (3) calculate the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}; (4) calculate motor thrust F _xand/or other characteristic variable of line inductance electromotor; (5) calculate α axle secondary first-harmonic winding magnetic linkage increment and the secondary first-harmonic winding of β axle magnetic linkage increment, further integration obtains the secondary first-harmonic winding of the α axle magnetic linkage λ ' in next moment _{α r}with the secondary first-harmonic winding of β axle magnetic linkage λ ' _{β r}, make the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}=λ ' _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}=λ ' _{β r}; (6) according to motor thrust F _x, obtaining the motor speed of service v' in next moment, order is as front motor speed of service v=v'; (7) circulation is carried out described step (2) to (6), realizes the analysis of dynamic driving characteristic.

When primary voltage is during as input variable, line inductance electromotor dynamic driving characteristic analysis method comprises the steps: that (1) obtains as front motor speed of service v, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, current α axle primary winding current i _{α s}with current β axle primary winding current i _{β s}; (2) obtain three-phase primary windings voltage, three-phase primary windings voltage is carried out to changes in coordinates, obtain α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}; (3) calculate the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}; (4) calculate motor thrust F _xand/or other characteristic variable of line inductance electromotor; (5) calculate α axle primary winding current increment, β axle primary winding current increment, the secondary first-harmonic winding of α axle magnetic linkage increment and the secondary first-harmonic winding of β axle magnetic linkage increment, further integration obtains the α axle primary winding current i' in next moment _{α s}, β axle primary winding current i' _{β s}, the secondary first-harmonic winding of α axle magnetic linkage λ ' _{α r}with the secondary first-harmonic winding of β axle magnetic linkage λ ' _{β r}, make current α axle primary winding current i _{α s}=i' _{α s}, current β axle primary winding current i _{β s}=i' _{β s}, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}=λ ' _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}=λ ' _{β r}; (6) according to motor thrust F _x, obtaining the motor speed of service v' in next moment, order is as front motor speed of service v=v'; (7) circulation is carried out described step (2) to (6), realizes the analysis of dynamic driving characteristic.

Fig. 4 is the dynamic thrust F in line inductance electromotor motion process _xcalculated value and measured value, as seen from the figure, thrust error large (12%) during the 11st second, all the other run duration measured values and calculated value are all in 5%.As can be seen here, new model and analytical method that the present invention proposes, can assess the variation of line inductance electromotor dynamic thrust and forces associated energy parameter effectively.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any modifications of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.

Claims (8)

1. a line inductance electromotor drive characteristic analyzing equivalent circuit, is characterized in that, comprises α axle equivalent electric circuit and β axle equivalent electric circuit;

α axle equivalent electric circuit comprises the first branch road, the second branch road and the 3rd branch road, after the second branch road and the 3rd branch circuit parallel connection, connects with the first branch road, and the node of three branch roads is designated as A, first elementary phase resistance R of route _s, elementary phase leakage inductance L _lswith the first voltage source e _{α st}be in series, the first voltage source e _{α st}positive pole near node A, second secondary phase resistance R of route _r, secondary phase leakage inductance L _lrwith second voltage source e _{α r}be in series, second voltage source e _{α r}positive pole near node A, the 3rd route air gap equivalence mutual inductance L _mwith tertiary voltage source e _{α t}be in series, tertiary voltage source e _{α t}positive pole near node A;

β axle equivalent electric circuit comprises the 4th branch road, the 5th branch road and the 6th branch road, after the 5th branch road and the 6th branch circuit parallel connection, connects with the 4th branch road, and the node of three branch roads is designated as B, the 4th the elementary phase resistance R of route _s, elementary phase leakage inductance L _lswith the 4th voltage source e _{β st}be in series, the 4th voltage source e _{β st}positive pole near Node B, the 5th the secondary phase resistance R of route _r, secondary phase leakage inductance L _lrwith the 5th voltage source e _{β r}be in series, the 5th voltage source e _{β r}positive pole near Node B, the 6th route air gap equivalence mutual inductance L _mwith the 6th voltage source e _{β t}be in series, the 6th voltage source e _{β t}positive pole near Node B;

Described the first voltage source e _{α st}voltage be e _{α st}=-pL _{α s β s}i _{β s}, wherein, p is differential operator d/dt, t is the time, L _{α s β s}for the mutual inductance between α axle armature winding and β axle armature winding, i _{β s}for β axle primary winding current; Described second voltage source e _{α r}voltage be e _{α r}=v (π/τ) λ _{β r}, wherein, v is the motor speed of service, τ is armature winding pole span, λ _{β r}for the secondary first-harmonic winding of β axle magnetic linkage; Described tertiary voltage source e _{α t}voltage be e _{α t}=p[L' _{α s α re}i _{α re}+ L' _{α s β re}i _{β re}], wherein, L' _{α s α re}=-KL _{α s α re}, L' _{α s β re}=-KL _{α s β re}, L _{α s α re}for the mutual inductance between α axle armature winding and α axle secondary side end effect wave winding, L _{α s β re}for the mutual inductance between α axle armature winding and β axle secondary side end effect wave winding, i _{α re}for α axle secondary side end effect wave winding electric current, i _{β re}for β axle secondary side end effect wave winding electric current;

Described the 4th voltage source e _{β st}voltage be e _{β st}=-pL _{α s β s}i _{α s}, wherein, i _{α s}for α axle primary winding current; Described the 5th voltage source e _{β r}voltage e _{β r}=-v (π/τ) λ _{α r}, wherein, λ _{α r}for the secondary first-harmonic winding of α axle magnetic linkage; Described the 6th voltage source e _{β t}voltage e _{β t}=p[L ' _{β s α re}i' _{α re}+ L ' _{β s β re}i' _{β re}], wherein, L' _{β s α re}=-KL _{β s α re}, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, L' _{β s β re}=-KL _{β s β re}, L _{β s β re}for the mutual inductance between β axle armature winding and β axle secondary side end effect wave winding, i' _{α re}=-Ki _{α re}, i' _{β re}=-Ki _{β re};

Wherein, l _δfor elementary phase length, L _rfor secondary phase inductance.

2. a line inductance electromotor stable state drive characteristic analytical method, is characterized in that, comprises the steps:

(1) obtain motor speed of service v and three-phase primary windings electric current, three-phase primary windings electric current is carried out to changes in coordinates, obtain α axle primary winding current i _{α s}with β axle primary winding current i _{β s};

(2) utilize α axle primary winding current i _{α s}with β axle primary winding current i _{β s}, according to armature winding voltage equation and secondary first-harmonic winding voltage equation, try to achieve the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s};

Described armature winding voltage equation is:

$\left\{\begin{array}{c}{u}_{\mathrm{\&alpha;s}}=[R_s-{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;s\&beta;s}}+L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;s}}-{\mathrm{\&omega;}}_e(L_{\mathrm{ls}}+L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}\\ -{\mathrm{\&omega;}}_e(L_{\mathrm{\&beta;s\&alpha;r}}+L_{\mathrm{\&beta;s\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;r}}-{\mathrm{\&omega;}}_e(L_m+L_{\mathrm{\&beta;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;r}}\\ u_{\mathrm{\&beta;s}}={\mathrm{\&omega;}}_e(L_{\mathrm{ls}}+L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}+[R_s++{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;s\&beta;s}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;s}}\\ +{\mathrm{\&omega;}}_e(L_m+L_{\mathrm{\&alpha;s\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;r}}+{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;s\&beta;r}}+L_{\mathrm{\&alpha;s\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;r}}\end{array}\right.;$

Wherein, R _sfor elementary phase resistance, ω _efor elementary angular frequency, L _{α s β s}for the mutual inductance between α axle armature winding and β axle armature winding, L' _{β s α re}=-KL _{β s α re}, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, L _lsfor elementary phase leakage inductance, L _mfor air gap equivalence mutual inductance, L' _{β s β re}=-KL _{β s β re}, L _{β s β re}for the mutual inductance between β axle armature winding and β axle secondary side end effect wave winding, L _{β s α r}for the mutual inductance between β axle armature winding and the secondary first-harmonic winding of α axle, L' _{α s α re}=-KL _{α s α re}, L _{α s α re}for the mutual inductance between α axle armature winding and α axle secondary side end effect wave winding, L' _{α s β re}=-KL _{α s β re}, L _{α s β re}for the mutual inductance between α axle armature winding and β axle secondary side end effect wave winding, L _{α s β r}for the mutual inductance between α axle armature winding and the secondary first-harmonic winding of β axle,

l _δfor elementary phase length, L _rfor secondary phase inductance;

Described secondary first-harmonic winding voltage equation is:

$\left\{\begin{array}{c}0=[-{\mathrm{\&omega;}}_e(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;s}}\\ +[-{\mathrm{\&omega;}}_e(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;s}}\\ +[R_r-{\mathrm{\&omega;}}_e(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;r}}\\ +[-{\mathrm{\&omega;}}_e(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})+v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;r}}\\ 0=[{\mathrm{\&omega;}}_e(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;s}}\\ +[{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;s}}\\ +[{\mathrm{\&omega;}}_e(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})]i_{\mathrm{\&alpha;r}}\\ +[R_r+{\mathrm{\&omega;}}_e(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})-v\frac{\mathrm{\&pi;}}{\mathrm{\&tau;}}(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]i_{\mathrm{\&beta;r}}\end{array}\right.;$

Wherein, L _{β r α s}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle armature winding, L' _{β r α re}=-KL _{β r α re}, L _{β r α re}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle secondary side end effect wave winding, τ is armature winding pole span, L' _{β r β re}=-KL _{β r β re}, L _{β r β re}for the mutual inductance between the secondary first-harmonic winding of β axle and β axle secondary side end effect wave winding, R _rfor secondary phase resistance, L _{β r α r}for the mutual inductance between the secondary first-harmonic winding of β axle and the secondary first-harmonic winding of α axle, L _lrfor secondary phase leakage inductance, L' _{α r α re}=-KL _{α r α re}, L _{α r α re}for the mutual inductance between the secondary first-harmonic winding of α axle and α axle secondary side end effect wave winding, L _{α r β s}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle armature winding, L' _{α r β re}=-KL _{α r β re}, L _{α r β re}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle secondary side end effect wave winding, L _{α r β r}for the mutual inductance between the secondary first-harmonic winding of α axle and the secondary first-harmonic winding of β axle;

(3) utilize α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}, try to achieve the characteristic variable of line inductance electromotor, realize the analysis of stable state drive characteristic;

The characteristic variable of described line inductance electromotor comprises motor magnetic linkage, motor thrust F _x, at least one in motor input active power, motor input reactive power, motor thrust output, motor active power of output, motor power factor and electric efficiency.

3. line inductance electromotor stable state drive characteristic analytical method as claimed in claim 2, is characterized in that, described motor magnetic linkage comprises α axle armature winding magnetic linkage λ _{α s}, β axle armature winding magnetic linkage λ _{β s}, the secondary first-harmonic winding of α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of β axle magnetic linkage λ _{β r};

Described α axle armature winding magnetic linkage λ _{α s}for:

λ _αs＝(L _ls+L _m+L' _αsαre)i _αs+(L _αsβs+L' _αsβre)i _βs+(L _m+L' _αsαre)i _αr+(L _αsβr+L' _αsβre)i _βr；

Described β axle armature winding magnetic linkage λ _{β s}for:

λ _βs＝(L _αsβs+L' _βsαre)i _αs+(L _ls+L _m+L' _βsβre)i _βs+(L _βsαr+L' _βsαre)i _αr+(L _m+L' _βsβre)i _βr；

The secondary first-harmonic winding of described α axle magnetic linkage λ _{α r}for:

λ _αr＝(L _m+L' _αrαre)i _αs+(L _αrβs+L' _αrβre)i _βs+(L _lr+L _m+L' _αrαre)i _αr+(L _αrβr+L' _αrβre)i _βr；

The secondary first-harmonic winding of described β axle magnetic linkage λ _{β r}for:

λ _βr＝(L _βrαs+L' _βrαre)i _αs+(L _m+L' _βrβre)i _βs+(L _βrαr+L' _βrαre)i _αr+(L _lr+L _m+L' _βrβre)i _βr；

Described motor thrust F _xfor:

F _x＝(3π/2τ)[L _m(i _αri _βs-i _βri _αs)+i _αs(i _αr+i _αs)G' _αsαre+i _αs(i _βr+i _βs)G' _αsβre+i _βs(i _αr+i _αs)G' _βsαre+i _βs(i _βr+i _βs)G' _βsβre]；

Wherein, G' _{α s α re}=-KG _{α s α re}, G' _{α s β re}=-KG _{α s β re}, G' _{β s α re}=-KG _{β s α re}, G' _{β s β re}=-KG _{β s β re}, G _{α s α re}=L _{β s α re}, G _{α s β re}=L _{β s β re}, G _{β s α re}=-L _{α s α re}, G _{β s β re}=-L _{α s β re}.

4. a line inductance electromotor stable state drive characteristic analytical method, is characterized in that, comprises the steps:

(1) obtain motor speed of service v, elementary angular frequency _eand three-phase primary windings voltage, three-phase primary windings voltage is carried out to changes in coordinates, obtain α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s};

(2) utilize α axle armature winding voltage u _{α s}, β axle armature winding voltage u _{β s}, motor speed of service v and elementary angular frequency _e, calculate α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r};

(3) utilize α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s}, try to achieve the characteristic variable of line inductance electromotor, realize the analysis of stable state drive characteristic;

The characteristic variable of described line inductance electromotor comprises motor magnetic linkage, motor thrust F _x, at least one in motor input active power, motor input reactive power, motor thrust output, motor active power of output, motor power factor and electric efficiency.

5. a line inductance electromotor dynamic driving characteristic analysis method, is characterized in that, comprises the steps:

(1) obtain as front motor speed of service v, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r};

(2) obtain three-phase primary windings electric current, three-phase primary windings electric current is carried out to changes in coordinates, obtain α axle primary winding current i _{α s}with β axle primary winding current i _{β s};

(3) utilize α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, try to achieve the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}be respectively:

$\begin{array}{c}{i}_{\mathrm{\&alpha;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]\end{array}$ With

$\begin{array}{c}{i}_{\mathrm{\&beta;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]\end{array};$

Wherein, L _mfor air gap equivalence mutual inductance, L' _{α r α re}=-KL _{α r α re}, L _{α r α re}for the mutual inductance between the secondary first-harmonic winding of α axle and α axle secondary side end effect wave winding, L _{α r β s}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle armature winding, L' _{α r β re}=-KL _{α r β re}, L _{α r β re}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle secondary side end effect wave winding, L _lrfor secondary phase leakage inductance, L' _{β r β re}=-KL _{β r β re}, L _{β r β re}for the mutual inductance between the secondary first-harmonic winding of β axle and β axle secondary side end effect wave winding, L _{β r α s}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle armature winding, L' _{β r α re}=-KL _{β r α re}, L _{β r α re}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle secondary side end effect wave winding, L _{α r β r}for the mutual inductance between the secondary first-harmonic winding of α axle and the secondary first-harmonic winding of β axle, L _{β r α r}for the mutual inductance between the secondary first-harmonic winding of β axle and the secondary first-harmonic winding of α axle,

l _δfor elementary phase length, L _rfor secondary phase inductance, R _rfor secondary phase resistance;

(4) utilize α axle primary winding current i _{α s}, β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}, calculate motor thrust F _xand/or other characteristic variable of line inductance electromotor;

Other characteristic variable of described line inductance electromotor comprises at least one in armature winding magnetic linkage, motor input active power, motor input reactive power, motor thrust output, motor active power of output, motor power factor and electric efficiency;

(5) according to working as front motor speed of service v, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}, calculate α axle secondary first-harmonic winding magnetic linkage increment and the secondary first-harmonic winding of β axle magnetic linkage increment, further integration obtains the secondary first-harmonic winding of the α axle magnetic linkage λ ' in next moment _{α r}with the secondary first-harmonic winding of β axle magnetic linkage λ ' _{β r}, make the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}=λ ' _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}=λ ' _{β r};

(6) according to motor thrust F _x, obtaining the motor speed of service v' in next moment, order is as front motor speed of service v=v';

(7) circulation is carried out described step (2) to (6), realizes the analysis of dynamic driving characteristic.

6. line inductance electromotor dynamic driving characteristic analysis method as claimed in claim 5, is characterized in that, described motor thrust F _xfor:

F _x＝(3π/2τ)[L _m(i _αri _βs-i _βri _αs)+i _αs(i _αr+i _αs)G' _αsαre+i _αs(i _βr+i _βs)G' _αsβre+i _βs(i _αr+i _αs)G' _βsαre+i _βs(i _βr+i _βs)G' _βsβre]；

Wherein, τ is armature winding pole span, G' _{α s α re}=-KG _{α s α re}, G' _{α s β re}=-KG _{α s β re}, G' _{β s α re}=-KG _{β s α re}, G' _{β s β re}=-KG _{β s β re}, G _{α s α re}=L _{β s α re}, G _{α s β re}=L _{β s β re}, G _{β s α re}=-L _{α s α re}, G _{β s β re}=-L _{α s β re}, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, L _{β s β re}for the mutual inductance between β axle armature winding and β axle secondary side end effect wave winding, L _{α s α re}for the mutual inductance between α axle armature winding and α axle secondary side end effect wave winding, L _{α s β re}for the mutual inductance between α axle armature winding and β axle secondary side end effect wave winding.

7. the line inductance electromotor dynamic driving characteristic analysis method as described in claim 5 or 6, is characterized in that, described armature winding magnetic linkage comprises α axle armature winding magnetic linkage λ _{α s}with β axle armature winding magnetic linkage λ _{β s};

Described α axle armature winding magnetic linkage λ _{α s}for:

λ _αs＝(L _ls+L _m+L' _αsαre)i _αs+(L _αsβs+L' _αsβre)i _βs+(L _m+L' _αsαre)i _αr+(L _αsβr+L' _αsβre)i _βr；

Described β axle armature winding magnetic linkage λ _{β s}for:

λ _βs＝(L _αsβs+L' _βsαre)i _αs+(L _ls+L _m+L' _βsβre)i _βs+(L _βsαr+L' _βsαre)i _αr+(L _m+L' _βsβre)i _βr；

Wherein, L _lselementary phase leakage inductance, L _{α s β s}for the mutual inductance between α axle armature winding and β axle armature winding, L' _{α s β re}=-KL _{α s β re}, L _{α s β re}for the mutual inductance between α axle armature winding and β axle secondary side end effect wave winding, L _{α s β r}for the mutual inductance between α axle armature winding and the secondary first-harmonic winding of β axle, L' _{β s α re}=-KL _{β s α re}, L _{β s α re}for the mutual inductance between β axle armature winding and α axle secondary side end effect wave winding, L' _{β s β re}=-KL _{β s β re}, L _{β s β re}for the mutual inductance between β axle armature winding and β axle secondary side end effect wave winding, L _{β s α r}for the mutual inductance between β axle armature winding and the secondary first-harmonic winding of α axle.

8. a line inductance electromotor dynamic driving characteristic analysis method, is characterized in that, comprises the steps:

(1) obtain as front motor speed of service v, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, current α axle primary winding current i _{α s}with current β axle primary winding current i _{β s};

(2) obtain three-phase primary windings voltage, three-phase primary windings voltage is carried out to changes in coordinates, obtain α axle armature winding voltage u _{α s}with β axle armature winding voltage u _{β s};

(3) utilize the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}, the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, current α axle primary winding current i _{α s}with current β axle primary winding current i _{β s}, try to achieve the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}be respectively:

$\begin{array}{c}{i}_{\mathrm{\&alpha;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})]\end{array}$ With

$\begin{array}{c}{i}_{\mathrm{\&beta;r}}=\left\{\begin{array}{c}[{\mathrm{\&lambda;}}_{\mathrm{\&beta;r}}-(L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}-(L_{\mathrm{\&beta;r\&alpha;s}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}](L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})\\ -[{\mathrm{\&lambda;}}_{\mathrm{\&alpha;r}}-(L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})i_{\mathrm{\&alpha;s}}-(L_{\mathrm{\&alpha;r\&beta;s}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})i_{\mathrm{\&beta;s}}](L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})\end{array}\right\}/\\ [(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&alpha;r\&alpha;re}}^{\&prime;})(L_{\mathrm{lr}}+L_m+L_{\mathrm{\&beta;r\&beta;re}}^{\&prime;})-(L_{\mathrm{\&alpha;r\&beta;r}}+L_{\mathrm{\&alpha;r\&beta;re}}^{\&prime;})(L_{\mathrm{\&beta;r\&alpha;r}}+L_{\mathrm{\&beta;r\&alpha;re}}^{\&prime;})]\end{array};$

Wherein, L _mfor air gap equivalence mutual inductance, L' _{α r α re}=-KL _{α r α re}, L _{α r α re}for the mutual inductance between the secondary first-harmonic winding of α axle and α axle secondary side end effect wave winding, L _{α r β s}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle armature winding, L' _{α r β re}=-KL _{α r β re}, L _{α r β re}for the mutual inductance between the secondary first-harmonic winding of α axle and β axle secondary side end effect wave winding, L _lrfor secondary phase leakage inductance, L' _{β r β re}=-KL _{β r β re}, L _{β r β re}for the mutual inductance between the secondary first-harmonic winding of β axle and β axle secondary side end effect wave winding, L _{β r α s}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle armature winding, L' _{β r α re}=-KL _{β r α re}, L _{β r α re}for the mutual inductance between the secondary first-harmonic winding of β axle and α axle secondary side end effect wave winding, L _{α r β r}for the mutual inductance between the secondary first-harmonic winding of α axle and the secondary first-harmonic winding of β axle, L _{β r α r}for the mutual inductance between the secondary first-harmonic winding of β axle and the secondary first-harmonic winding of α axle,

l _δfor elementary phase length, L _rfor secondary phase inductance, R _rfor secondary phase resistance;

(4) utilize current α axle primary winding current i _{α s}, current β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}with the secondary first-harmonic winding current of β axle i _{β r}, calculate motor thrust F _xand/or other characteristic variable of line inductance electromotor;

Other characteristic variable of described line inductance electromotor comprises at least one in armature winding magnetic linkage, motor input active power, motor input reactive power, motor thrust output, motor active power of output, motor power factor and electric efficiency;

(5) according to working as front motor speed of service v, current α axle primary winding current i _{α s}, current β axle primary winding current i _{β s}, the secondary first-harmonic winding current of α axle i _{α r}, the secondary first-harmonic winding current of β axle i _{β r}, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}, calculate α axle primary winding current increment, β axle primary winding current increment, the secondary first-harmonic winding of α axle magnetic linkage increment and the secondary first-harmonic winding of β axle magnetic linkage increment, further integration obtains the α axle primary winding current i' in next moment _{α s}, β axle primary winding current i' _{β s}, the secondary first-harmonic winding of α axle magnetic linkage λ ' _{α r}with the secondary first-harmonic winding of β axle magnetic linkage λ ' _{β r}, make current α axle primary winding current i _{α s}=i' _{α s}, current β axle primary winding current i _{β s}=i' _{β s}, the secondary first-harmonic winding of current α axle magnetic linkage λ _{α r}=λ ' _{α r}with the secondary first-harmonic winding of current β axle magnetic linkage λ _{β r}=λ ' _{β r};

(6) according to motor thrust F _x, obtaining the motor speed of service v' in next moment, order is as front motor speed of service v=v';

(7) circulation is carried out described step (2) to (6), realizes the analysis of dynamic driving characteristic.

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