CN101420157B - Magnetic circuit designing method for non-sine power supply multi-phase induction motor - Google Patents

Abstract

The invention relates to a method for designing a magnetic circuit of a polyphase induction motor with nonsine power supply. The method uses fundamental wave magnetic potential and harmonic wave magnetic potential satisfying superposition principle as theoretic foundation, carries out uniformly-spaced circumferential blocking in half polar range of a motor, obtains each node magnetic density along the central line of a circumferential air gap by iterative computation, obtains fundamental wave magnetic density and harmonic wave magnetic density by Fourier decomposition, further calculates fundamental wave inductive kick and harmonic wave inductive kick, and finally obtains magnetizing reactance. The method does not need amplitude factor or joke part correction factor, and is applicable to sine or non-sine nonlinear magnetic circuit design. The method combines the advantages of two analyzing methods of magnetic field and magnetic circuit together, not only avoids huge amount of calculation of the magnetic field analyzing method, but also improves the precision of the traditional magnetic circuit calculation method, and breaks through restriction to sine of magnetic potential in the traditional method.

Description

The magnetic circuit design method of non-sine power supply multi-phase induction motor

Technical field

The invention belongs to the analysis design field of induction machine, relate in particular to a kind of magnetic circuit design method of non-sine power supply multi-phase induction motor.

Background technology

The inverter supply multiphase induction motor has characteristics such as high reliability and high torque density, has become the electric propulsion field emphasis of research both at home and abroad at present.Because invalid harmonic magnetic potential reduces in a large number in the multiphase induction motor; Stator can adopt whole apart from concentrating winding and supplying power with non-sinusoidal voltage; Its purpose is to improve the core material utilance and improves the motor performance index, and Electromagnetic Design is the basis of developing non-sine power supply multi-phase induction motor.In traditional design method, during known revolutional slip induction machine to be carried out design demand and carry out two-layer iteration, external iteration is a pressure-drop coefficient, the nexine iteration is a saturation coefficient.The two-layer iteration of in the traditional design method this is summed up as magnetic Circuit Design, and its essence is to confirm to take into account saturated excitatory reactance.Under the situation of known excitatory reactance and other parameter of rotor, just available equivalent circuit carries out Performance Calculation to induction machine.Owing to relate to double iteration, it is consuming time too much to carry out non-linear magnetic circuit design meeting with FInite Element, especially more difficult use the in the optimal design process.

Magnetic Circuit Design in the traditional design method is under the situation that computational tools such as slide ruler, calculator fall behind, to grow up; Wherein relate to tabling look-up of wave amplitude coefficient, yoke portion correction coefficient; And yoke portion correction coefficient and motor pole number, yoke portion maximum magnetic flux is close, yoke portion height is relevant with pole span ratio; Look-up method is not only inaccurate but also pretty troublesome with Computer Processing, and this computational methods can only obtain air gap flux density, tooth portion magnetic is close and yoke portion magnetic is close maximum.For remedy existing magnetic circuit method on the computational accuracy with comfort level on deficiency, according to the actual conditions that computer data disposal ability and arithmetic speed significantly improve, can rethink magnetic circuit design method from the physical essence that motor moves.Particularly importantly; Non-sine power supply multi-phase induction motor rotor composite magnetic power is a non-sine distribution magnetic potential; Mmf wave approaches flat-topped wave, and the existing magnetic circuit design method that is the basis with sinusoidal magnetic potential can't use, and this is the basic reason that magnetic Circuit Design must adopt new method.

Summary of the invention

The object of the present invention is to provide a kind of magnetic circuit design method of non-sine power supply multi-phase induction motor, to overcome existing deficiency in the prior art.

To achieve these goals, the method that the present invention adopted comprises following steps:

First step: getting half pole span of induction machine is the analytical calculation zone; Write out magnetic potential expression formula separately by first-harmonic exciting curent and harmonic wave exciting curent; The stack magnetic potential of any location point equals the algebraical sum of this fundamental magnetic potential and harmonic magnetic potential on the space, and linear relationship is satisfied in the magnetic potential stack;

Second step: in half pole span model of induction machine, carry out magnetic circuit and analyze subregion, being divided into is 5 districts: wherein I is the air gap district, and II and III are respectively stator teeth district and yoke portion district, and IV and V are respectively rotor tooth portion district and yoke portion district; Make many through the center of circle and ray that adjacent two folded central angles are equated, along the circumferential direction uniformly-spaced be divided into some with half pole span analytical calculation of these bundle of rays motors zone;

Third step: think that the magnetic flux density waveforms of each node is similar with mmf wave in the air gap, confirm the air gap flux density initial value with this;

The 4th step:, calculate that each node place stator teeth magnetic is close, rotor tooth portion magnetic is close, stator yoke portion magnetic is close, rotor yoke magnetic is close according to the principle of continuity of magnetic flux;

The 5th step: the stator teeth magnetic by each node place is close, rotor tooth portion magnetic is close, stator yoke portion magnetic is close, the close iron core magnetization curve of looking into of rotor yoke magnetic obtains corresponding magnetic field intensity;

The 6th step: under the situation of known magnetic field intensity, calculate the magnetic pressure in each air gap district, node place, stator teeth district, stator yoke portion district, rotor tooth portion district, rotor yoke district and fall, the magnetic pressure in these 5 districts is fallen and is added up to total magnetic pressure and fall;

The 7th step: the magnetic potential that all will equal this node place falls in the total magnetic pressure of closed magnetic circuit through each node on the air gap center line; If this condition does not satisfy; Again confirm the initial value of each node air gap flux density on the air gap center line; Repeat the process of above-mentioned the 4th step to the six steps, fall relative error quadratic sum with magnetic potential less than given accuracy up to each node place magnetic pressure, the magnetic that finally obtains each node place is close;

The 8th step: open up the scope of finding the solution to territory, a pair of polar region from half pole span, obtain the air gap flux density value of each node on the air gap center line, carry out fourier decomposition and obtain the close amplitude of air gap first-harmonic magnetic close amplitude harmonic magnetic according to strange, even symmetry property;

The 9th step: obtain first-harmonic induced potential harmonic induced potential by the close amplitude of air gap first-harmonic magnetic close amplitude harmonic magnetic, induced potential is excitatory reactance with the ratio of exciting curent, obtains then magnetic Circuit Design end of excitatory reactance.

The present invention is in the same place the advantages of the two kinds of analytical methods in magnetic field and magnetic circuit, both avoided the huge amount of calculation of magnetic field analysis method, has improved the precision of traditional magnetic circuit computing method again and has broken through in the conventional method the sinusoidal restriction of magnetic potential.Important difference of the present invention and existing magnetic circuit design method is, analyzes design and not only obtains the air gap flux density maximum, but can obtain each node air gap flux density value on the air gap center line, and this lays a good foundation for fourier decomposition.The present invention measures excitatory reactance through no load test and compares with calculated value, more consistent validity of the present invention and the accuracy explained of result.

Description of drawings

Fig. 1 is half pole span magnetic circuit model of induction machine of the present invention and block plan radially.

Fig. 2 is circumferential piecemeal of half pole span magnetic circuit of induction machine of the present invention solving model and magnetic potential closed-loop path figure.

Fig. 3 is multiphase induction motor fundamental magnetic potential of the present invention and 3 subharmonic magnetic potential overlaid waveforms figure.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is made further detailed description.

Existing is example with one 15 phase induction machine, this motor rated power P _NBe 45kW; Number of pole-pairs p is 2; The specified phase voltage U of first-harmonic ₁Be 140V; The specified phase current I of first-harmonic ₁Be 25A; Rated speed n is 600r/min, and the stator winding total number of turns W that whenever is in series is 48.

15 phase induction machines adopt the main purpose of non-sine power supply to reduce the fundamental magnetic potential peak value through 3 subharmonic magnetic potentials exactly in the present embodiment; Thereby make the local degree of saturation of iron core reduce to improve the utilance of ferromagnetic material; If the stack magnetic potential is maximum than fundamental magnetic potential decline degree; Then the negative amplitude position of fundamental magnetic potential true amplitude position and 3 subharmonic magnetic potentials should be positioned at space same point (Fig. 3), and this moment, the expression formula of composite magnetic power was:

F(α)＝F _1m?cosα-F _3m?cos3α

Wherein, fundamental magnetic potential amplitude F _1mWith first-harmonic exciting curent effective value I _M1Be directly proportional; 3 subharmonic magnetic potential amplitude F _3mWith 3 subharmonic current effective value I _M3Be directly proportional.

The same with conventional method, the present invention analyzes design and in half pole span zone, carries out, and from 0 to pi/2 (Fig. 1), and establishing fundamental magnetic potential amplitude position and 3 subharmonic magnetic potential amplitude positions, to be in α together be 0 point corresponding to electrical degree α for half pole span.Whole magnetic circuit analysis design is divided into 5 districts by conventional method, and wherein I is the air gap district, and II and III are respectively stator teeth district and yoke portion district, and IV and V are respectively rotor tooth portion district and yoke portion district.

In half pole span model of induction machine, make many through the center of circle ray and make adjacent two folded central angles of ray equate that half pole span analytical calculation of these bundle of rays motors zone along the circumferential direction uniformly-spaced has been divided into some (Fig. 2).

If in half pole span along circumferentially evenly being divided into the N piece, then corresponding N+1 node uniformly-spaced on the air gap center line, in polar coordinate system, i node polar radius r (i) and polar angle ρ (i) are:

$r\left(i\right)=\frac{D_{i1}+D_2}{2}$

$\mathrm{\ρ}\left(i\right)=\frac{i-1}{N}\frac{\mathrm{\π}}{2}$

Wherein: D _I1With D ₂Be respectively motor stator internal diameter and rotor diameter.

I node magnetic potential is:

$F\left(i\right)=\frac{15\sqrt{2}}{\mathrm{\&pi;}}\frac{W}{p}[I_{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="H2008102366411E00012.png,H2008102366411E00021.png"\; state="\{\{state\}\}">m</figure-callout>}1}\cos \left(\frac{i-1}{N}\frac{\mathrm{\&pi;}}{2}\right)-\frac{1}{3}{I}_{\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="H2008102366411E00021.png"\; state="\{\{state\}\}">m</figure-callout>}3}\cos \left(\frac{i-1}{\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="H2008102366411E00021.png"\; state="\{\{state\}\}">N</figure-callout>}}\frac{3\mathrm{\&pi;}}{2}\right)]$

Under the known situation of each node magnetic potential, can think during beginning that the magnetic flux density waveforms of each node is similar with mmf wave on the air gap center line.The air gap flux density B of i node place _g(i) be:

$B_g\left(i\right)=\frac{{\mathrm{\&mu;}}_{0}F\left(i\right)}{g_{\mathrm{ef}}{k}_{\mathrm{st}}}$

Wherein: μ ₀Be air permeability; g _EfBe the effective air gap length after the consideration slot effect; k _StBe the saturation coefficient of looking ahead, this is an empirical coefficient, generally get 1 and 1.5 between a certain constant.

Set air-gap flux and all from tooth, pass through, according to the principle of continuity of magnetic flux, the close B of i node place stator and rotor tooth portion magnetic _T1(i), B _T2(i) be respectively:

$B_{t1}\left(i\right)=B_g\left(i\right)\frac{l{\mathrm{\&tau;}}_{t1}}{l_{\mathrm{fe}1}{\mathrm{<figure-callout\; id="1"\; label="b\; t"\; filenames="H2008102366411E00012.png,H2008102366411E00021.png"\; state="\{\{state\}\}">b</figure-callout>}}_t}$

$B_{t2}\left(i\right)=B_g\left(i\right)\frac{l{\mathrm{\&tau;}}_{t2}}{l_{\mathrm{fe}2}{b}_{t2}}$

Wherein: l is the axial effective length of motor magnetic circuit; l _Fe1, l _Fe2Be respectively and consider stator core axial length behind stacking factor and the radial ventilation ditch, rotor core axial length; τ _T1, τ _T2Be respectively stator tooth distance, the rotor slot-pitch of air gap center; b _T1, b _T2Be respectively the stator facewidth, the rotor facewidth of calculating place.

Can know according to the principle of continuity of magnetic flux that equally the radial flux between the 1st node and i node on the air gap median plane equals the circumferential magnetic flux on the i node place yoke portion cross section.If represent numerical integration with trapezoid formula, the close B of i node place stator and rotor yoke portion magnetic then _C1(i), B _C2(i) be respectively:

$B_{c1}\left(i\right)=\left\{\begin{array}{cc}0& i=1\\ \frac{\underset{k=2}{\overset{i}{\mathrm{\&Sigma;}}}\frac{B_g(k-1)+B_g\left(k\right)}{2}\frac{\mathrm{\&tau;}}{2N}l}{l_{\mathrm{fe}1}{h}_{c1}}& i>1\end{array}\right.$

$B_{c2}\left(i\right)=\left\{\begin{array}{cc}0& i=1\\ \frac{\underset{k=2}{\overset{i}{\mathrm{\&Sigma;}}}\frac{B_g(k-1)+B_g\left(k\right)}{2}\frac{\mathrm{\&tau;}}{2N}l}{l_{\mathrm{fe}2}{h}_{c2}}& i>1\end{array}\right.$

Wherein: τ is the motor pole span of air gap center; h _C1, h _C2Be respectively stator yoke height, rotor yoke height.

If the close B of each node magnetic on the air gap center line _g(i) (i=1,2,3 ... N+1) be known quantity, then can obtain the B at all node places _T1(i), B _T2(i) and B _C1(i), B _C2(i).

The close B of stator and rotor tooth portion magnetic according to i node place _T1(i), B _T2(i) and the close B of stator and rotor yoke portion magnetic _C1(i), B _C2(i) look into magnetization curve unshakable in one's determination and obtain corresponding magnetic field intensity H _T1(i), H _T2(i) and H _C1(i), H _C2(i).

Closed path among Fig. 2 shown in the heavy line is thought the magnetic loop through i node place, and the closed-loop path magnetic pressure is fallen and comprised that in fact F falls in i node place air gap magnetic pressure _g(i), F falls in i node place stator teeth magnetic pressure _T1(i), F falls in i node place rotor tooth portion magnetic pressure _T2(i), F falls in stator yoke portion magnetic pressure between i node to the N+1 node _C1(i) F falls in the rotor yoke magnetic pressure and between i node to the N+1 node _C2(i).

The formula that embodies that the each part mentioned above magnetic pressure is fallen is respectively:

$F_g\left(i\right)=\frac{B_g\left(i\right)}{{\mathrm{\&mu;}}_0}{g}_{\mathrm{ef}}$

F _t1(i)＝B _t1(i)h _t1

F _t2(i)＝B _t2(i)h _t2

$F_{c1}\left(i\right)=\underset{k=i}{\overset{N}{\mathrm{\&Sigma;}}}\frac{B_{c1}\left(k\right)+B_{c1}(k+1)}{2}\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; c"\; filenames="H2008102366411E00012.png,H2008102366411E00021.png"\; state="\{\{state\}\}">l</figure-callout>}}_c}{2N}$

$F_{c2}\left(i\right)=\underset{k=i}{\overset{N}{\mathrm{\&Sigma;}}}\frac{B_{c2}\left(k\right)+B_{c2}(k+1)}{2}\frac{l_{c2}}{2N}$

Above-listed various in, h _T1, h _T2Be respectively stator tooth depth, rotor tooth depth; l _C1, l _C2Being respectively one of stator extremely descends yoke minister degree, one of rotor extremely to descend yoke minister degree.

Reduce to top 5 part magnetic pressure through the total magnetic pressure in the closed-loop path of i node and fall sum, be expressed as:

F _Σ(i)＝F _g(i)+F _t1(i)+F _t2(i)+F _c1(i)+F _c2(i)

Can know that by Ampere circuit law total magnetic pressure degradation is in magnetic potential in the closed magnetic circuit, if the corresponding closed magnetic circuit of each node (except N+1 the node), as far as all closed magnetic circuits, total magnetic pressure is fallen all and will be equaled magnetic potential.In numerical computations, available relative error quadratic sum representes that less than given accuracy ε magnetic potential equates, promptly

$\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left[\frac{F\left(i\right)-F_{\mathrm{\&Sigma;}}\left(i\right)}{F_{\left(i\right)}}\right]}^2<\mathrm{\&epsiv;}$

If following formula does not satisfy, it is close then to provide on the air gap center line each node magnetic again, wherein i (the close B of the new magnetic of node of i ≠ N+1) _g(i) ' be:

$B_g\left(i\right)\&prime;=B_g\left(i\right)[1+k_B\frac{F\left(i\right)-F_{\mathrm{\&Sigma;}}\left(i\right)}{F\left(i\right)}]$

In the formula, k _BBe empirical coefficient, can get big value and possibly disperse that the iterations that gets the small value increases, will weigh consideration during concrete value 0.05 to 0.5 value.

Use B _g(i) ' and magnetic circuit computational process above repeating, till precision meets the demands, then obtain N+1 the air gap flux density value on the node.

Open up to a pair of pole span from half pole span finding the solution scope earlier before adopting fourier decomposition; On the air gap center line; Total 4N node in a pair of pole span after the continuation; Can obtain 4N the air gap flux density value on the node according to strange, even symmetry property, carry out to obtain the close amplitude B of air gap first-harmonic magnetic after the fourier decomposition _G1mWith the close amplitude B of 3 subharmonic magnetic _G3m

Can know that according to the computing formula of induced potential fundamental frequency is f ₁The time first-harmonic induced potential effective value E ₁With 3 subharmonic induced potential effective value E ₃, promptly

${\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="H2008102366411E00012.png,H2008102366411E00021.png"\; state="\{\{state\}\}">E</figure-callout>}}_1=\sqrt{2}\mathrm{\&pi;}{f}_{1}W{\mathrm{\&Phi;}}_{1m}$

${\mathrm{<figure-callout\; id="3"\; label="E"\; filenames="H2008102366411E00021.png"\; state="\{\{state\}\}">E</figure-callout>}}_3=\sqrt{2}\mathrm{\&pi;}\left(3f_1\right)W{\mathrm{\&Phi;}}_{3m}$

Wherein, the every utmost point magnetic flux of first-harmonic maximum Φ _1mWith the every utmost point magnetic flux of 3 subharmonic maximum Φ _3mBe respectively:

${\mathrm{\&Phi;}}_{1m}=\frac{2}{\mathrm{\&pi;}}{B}_{g1m}\mathrm{\&tau;l}$

${\mathrm{\&Phi;}}_{3m}=\frac{2}{\mathrm{\&pi;}}{B}_{g3m}\frac{\mathrm{\&tau;}}{3}l$

Because I _M1With I _M3For known quantity, be that the front analytic process is to provide I _M1With I _M3Situation under the E that obtains ₁With E ₃, the excitatory reactance X of first-harmonic then _M1, the excitatory reactance X of 3 subharmonic _M3Be respectively E ₁With I _M1Ratio, E ₃With I _M3Ratio.

Excitatory reactance of first-harmonic and the excitatory reactance of 3 subharmonic when mmf wave is non-sine under 15 phase induction machine fundamental magnetic potentials and the 3 subharmonic magnetic potential actings in conjunction at last calculated with the present invention; And measure the excitatory reactance of first-harmonic with no load test and the excitatory reactance of 3 subharmonic compares, to verify correctness of the present invention and order of accuarcy.The every phase fundamental voltage of stator effective value U ₁Be 140.6V, 3 subharmonic voltage effective value U ₃Be 23.23V, the excitatory reactance calculated value of first-harmonic is 23.35 Ω, and measured value is 23.45 Ω, error-0.43%; The excitatory reactance calculated value of 3 subharmonic is 8.461 Ω, and measured value is 8.851 Ω, error-4.41%.

When method of the present invention is applicable to sinusoidal wave supply power voltage too in the magnetic Circuit Design of multiphase induction motor.

Method of the present invention is called the distribution Magnetic Circuit Method.

The present invention describes through the drawings in detail of most preferred embodiment.Ripely can derive many variations and needn't deviate from category of the present invention from most preferred embodiment in these those skilled in the art.Therefore, the unlikely restriction of most preferred embodiment category of the present invention.

The content of not doing in this specification to describe in detail belongs to this area professional and technical personnel's known prior art.

Claims (2)

1. the magnetic circuit design method of a non-sine power supply multi-phase induction motor, its concrete steps are:

First step: getting half pole span of induction machine is the analytical calculation zone; Write out magnetic potential expression formula separately by first-harmonic exciting curent and harmonic wave exciting curent; The stack magnetic potential of any location point equals the algebraical sum of this fundamental magnetic potential and harmonic magnetic potential on the space, and linear relationship is satisfied in the magnetic potential stack;

Second step: in half pole span model of induction machine, carry out magnetic circuit and analyze subregion, being divided into is 5 districts: wherein I is the air gap district, and II and III are respectively stator teeth district and yoke portion district, and IV and V are respectively rotor tooth portion district and yoke portion district; Make many through the center of circle and ray that adjacent two folded central angles are equated, along the circumferential direction uniformly-spaced be divided into some with half pole span analytical calculation of these bundle of rays motors zone;

Third step: think that the magnetic flux density waveforms of each node is similar with mmf wave in the air gap district, confirm the air gap flux density initial value with this;

The 4th step:, calculate that each node place stator teeth magnetic is close, rotor tooth portion magnetic is close, stator yoke portion magnetic is close, rotor yoke magnetic is close according to the principle of continuity of magnetic flux;

The 5th step: the stator teeth magnetic by each node place is close, rotor tooth portion magnetic is close, stator yoke portion magnetic is close, the close iron core magnetization curve of looking into of rotor yoke magnetic obtains corresponding magnetic field intensity;

The 6th step: under the situation of known magnetic field intensity, calculate the magnetic pressure in each air gap district, node place, stator teeth district, stator yoke portion district, rotor tooth portion district, rotor yoke district and fall, the magnetic pressure in these 5 districts is fallen and is added up to total magnetic pressure and fall;

The 7th step: the magnetic potential that all will equal this node place falls in the total magnetic pressure of closed magnetic circuit through each node on the air gap center line; If this condition does not satisfy; Again confirm the initial value of each node air gap flux density on the air gap center line; Repeat the process of above-mentioned the 4th step to the six steps, fall relative error quadratic sum with magnetic potential less than given accuracy up to each node place magnetic pressure, the magnetic that finally obtains each node place is close;

The 8th step: open up the scope of finding the solution to territory, a pair of polar region from half pole span, obtain the air gap flux density value of each node on the air gap center line, carry out fourier decomposition and obtain the close amplitude of air gap first-harmonic magnetic close amplitude harmonic magnetic according to strange, even symmetry property;

The 9th step: obtain first-harmonic induced potential harmonic induced potential by the close amplitude of air gap first-harmonic magnetic close amplitude harmonic magnetic; The first-harmonic induced potential is the excitatory reactance of first-harmonic with the ratio of first-harmonic exciting curent; The harmonic wave induced potential is the excitatory reactance of harmonic wave with the ratio of harmonic wave exciting curent, obtains then magnetic Circuit Design end of excitatory reactance.

2. according to the magnetic circuit design method of the said non-sine power supply multi-phase induction motor of claim 1, it is characterized in that: said multiphase induction motor supply power voltage is a non-sinusoidal waveform voltage, and magnetic potential of air gap is the non-sine magnetic potential.

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