CN101604347B - Method for building model of dual three-phase asynchronous motor based on winding complex transformation - Google Patents

Abstract

The invention discloses a method based on winding complex transformation for building a model of a dual three-phase asynchronous motor. The method is based on the principle of invariability of magnetic motive force and power, a dual three-phase winding is equivalently converted into a dual two-phase winding, and then the dual two-phase winding is converted into a two-phase winding. A mathematical model in a mature two-phase stationary coordinate system is used for building the mathematical model of the dual three-phase asynchronous motor under an alpha-beta coordinate system and a simulation model based on Matlab /Simulink. The method is comparatively simple, and the physical conception is clear. Indicated by the result of comparison between a simulation result and corresponding experiment data, the maximum error between the two is within 2 percent.

Description

Modeling method based on the double triphase asynchronous motor of winding complex transformation

Technical field:

The present invention relates to a kind of modeling method of asynchronous motor, particularly a kind of modeling method of the double triphase asynchronous motor based on the winding complex transformation.

Background technology:

Two three phase electric machine system has remarkable advantages than three phase electric machine system on performance:

(1) two three phase electric machine system has and can adopt the low-voltage standards power device to realize the ability that high-power is handled;

(2) number of times of two three phase electric machine system with the bigger space harmonics of influence increases, and amplitude descends degradation advantage under the torque pulsation;

(3) two three phase electric machine system, its mmf waveform improves, and can improve electric efficiency, reduces noise of motor;

(4) two three phase electric machine system adopts the governing system of heterogeneous redundancy structure to improve system-level reliability greatly.

In recent years, relevant technician has carried out relevant research to the modeling of polyphase asynchronous motor with operation, prior art provide the modeling method of polyphase machine in, the main method that adopts is: utilize orthogonal transform matrix that the voltage and current space vector of double triphase asynchronous motor is projected in three two mutually orthogonal n-dimensional subspace ns and go, by rotational transform matrix cancellation rotor rotation angle the rotor change of variable is arrived under the stator rest frame again, obtain the simplified model of cage-type rotor double triphase asynchronous motor under rest frame.

Above-mentioned this modeling method in practical operation, exists design complicated, and performing step is loaded down with trivial details, thereby has limited its practicality.

Summary of the invention:

The present invention is directed to above-mentioned prior art existing defective in two three phase electric machine system modellings, and a kind of new modeling and simulating method that is used for double triphase asynchronous motor is provided, this method is simple relatively, clear physics conception.

In order to achieve the above object, the technical solution adopted in the present invention is as follows:

Based on the modeling method of the double triphase asynchronous motor of winding complex transformation, this method may further comprise the steps:

(1) be pair two phase windings at first with two three phase winding equivalent transformations of double triphase asynchronous motor;

(2) be two phase windings with two two phase winding equivalent transformations again;

(3) two phase windings that obtain based on step (2) are set up the mathematical model of double triphase asynchronous motor under the two-phase rest frame.

Described step (1) is carried out equivalent transformation based on mmf and the constant principle of power, and the equivalent transformation method that adopts the three phase static coordinate to be tied to the two-phase rest frame is carried out equivalent transformation.

When described step (1) was carried out equivalent transformation, the transformation matrix of employing was:

$C_{6/4}=\sqrt{\frac{2}{3}}\left[\begin{array}{cccccc}1& -\frac{1}{2}& -\frac{1}{2}& 0& 0& 0\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}& 0& 0& 0\\ 0& 0& 0& 1& -\frac{1}{2}& -\frac{1}{2}\\ 0& 0& 0& 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right].$

Described step (2) is carried out the static winding that equivalent transformation obtains two-phase based on mmf and the constant principle of power, and the transformation matrix of employing is:

${\mathrm{<figure-callout\; id="4"\; label="C"\; filenames="H2009100495179E00012.png"\; state="\{\{state\}\}">C</figure-callout>}}_{4/2}=\frac{\sqrt{2}}{2}\left[\begin{array}{cccc}1& 0& \frac{\sqrt{3}}{2}& -\frac{1}{2}\\ 0& 1& \frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right].$

Obtain the present invention according to technique scheme and at first two three phase winding equivalent transformations are two two phase windings, again it further is transformed to two phase windings of equivalence.Set up the mathematical model of double triphase asynchronous motor under the two-phase rest frame thus, and can make up realistic model based on Matlab/Simulink.

This method is simple relatively, clear physics conception.Contrast simulation result and corresponding experiment data, maximum error is in 2% between the two.The method based on the winding complex transformation that the present invention proposes is enforceable, and the mathematical model and the realistic model thereof of the double triphase asynchronous motor of setting up based on this method are effectively correct.

Description of drawings:

Further specify the present invention below in conjunction with the drawings and specific embodiments.

Fig. 1 is a double triphase asynchronous motor stator winding synoptic diagram.

Fig. 2 is two two-phases and two phase coordinate system mmf space vector synoptic diagram.

Fig. 3 is the realistic model of double triphase asynchronous motor.

Fig. 4 A is the torque variation diagram of emulation double triphase asynchronous motor.

Fig. 4 B is the rotation speed change figure of emulation double triphase asynchronous motor.

Fig. 4 C is the A1 phase current waveform figure of emulation double triphase asynchronous motor.

Fig. 4 D is the torque variation diagram of emulation double triphase asynchronous motor.

The rotation speed change figure of Fig. 4 E emulation double triphase asynchronous motor.

Fig. 4 F is the A1 phase current waveform figure of emulation double triphase asynchronous motor.

Fig. 5 is the double triphase asynchronous motor measurement system diagram.

Embodiment:

For technological means, creation characteristic that the present invention is realized, reach purpose and effect is easy to understand, below in conjunction with concrete diagram, further set forth the present invention.

The present invention is in order to solve prior art existing defective in two three phase electric machine system modellings, and proposed a kind of mathematical modeling new method of double triphase asynchronous motor.

This method is two two phase windings with two three phase winding equivalent transformations earlier based on mmf and the constant principle of power, is two phase windings with two two phase winding equivalent transformations again.Then use the mathematical model under the ripe two-phase rest frame, set up double triphase asynchronous motor under the alpha-beta coordinate system mathematical model and based on the realistic model of Matlab/Simulink.

Based on above-mentioned design concept, the present invention specifically implements as follows:

The first step, two three phase windings are to the conversion of two two phase windings

Analyze for convenient, satisfying under the actual required accuracy requirement of engineering, present embodiment makes two three phase windings of double three-phase permanent-magnetic synchronous motors have following characteristics, as shown in Figure 1:

1) two cover stator winding A ₁B ₁C ₁And A ₂B ₂C ₂Identical, 30 ° of electrical angles spatially stagger.Every cover three phase windings are symmetry spatially, and promptly every phase winding number of turn wire gauge is identical, and phase winding is 120 ° of space electrical angles at interval.Stator, rotor surface are smooth, no slot effect, and air gap is even.

2) disregard ferromagnetic saturated, magnetic hysteresis, vortes interference and conductor skin effect.

3) air-gap field Sine distribution is ignored the influence of magnetic field higher hamonic wave.

In this step, use the equivalent transformation that the three phase static coordinate is tied to the two-phase rest frame, with A ₁B ₁C ₁Winding transforms to α ₁β ₁Winding is with A ₂B ₂C ₂Winding transforms to α ₂β ₂Winding (as shown in Figure 1).When carrying out conversion, must keep conversion front and back synthetic mmf and general power constant, then two three phase coordinate systems to the transformation matrix of two two phase coordinate systems are:

$C_{6/4}=\sqrt{\frac{2}{3}}\left[\begin{array}{cccccc}1& -\frac{1}{2}& -\frac{1}{2}& 0& 0& 0\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}& 0& 0& 0\\ 0& 0& 0& 1& -\frac{1}{2}& -\frac{1}{2}\\ 0& 0& 0& 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]---\left(1\right)$

After this conversion, two three phase windings are become two two phase windings by equivalence.Formula (1) is the current transformation matrix, also is voltage and magnetic linkage transformation matrix simultaneously.Wherein the pass before and after the stator current conversion is:

i _αβ12＝C _6/4·i _ABC12 (2)

In the formula (2)

i _ABC12＝[i _A1?i _B1?i _C1?i _A2?i _B2?i _C2] ^T，i _αβ12＝[i _α1?i _β1?i _α2?i _β2] ^T

Two two phase coordinate systems to the transformation matrix of two three phase coordinate systems are in this step:

${\mathrm{<figure-callout\; id="4"\; label="C"\; filenames="H2009100495179E00012.png"\; state="\{\{state\}\}">C</figure-callout>}}_{4/6}=\sqrt{\frac{2}{3}}\left[\begin{array}{cccc}1& 0& 0& 0\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}& 0& 0\\ -\frac{1}{2}& -\frac{\sqrt{3}}{2}& 0& 0\\ 0& 0& 1& 0\\ 0& 0& -\frac{1}{2}& \frac{\sqrt{3}}{2}\\ 0& 0& -\frac{1}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]---\left(3\right)$

In the present embodiment, the rotor winding of two three phase windings has been converted stator side.The every phase resistance of definition stator and rotor winding, leakage inductance are respectively R _s, L _1SAnd R _r, L _1r, the mutual inductance maximal value is L between two phase windings _MsEvery phase resistance, the leakage inductance of the stator and rotor winding of two two phase windings after then being changed as can be known by the magnetic linkage transformational relation will remain unchanged, and the mutual inductance maximal value becomes original 3/2 times.

In second step, two two phase windings are to the conversion of two phase windings

This step can be two phase windings with two two phase winding equivalent transformations equally based on mmf and the constant principle of power.As shown in Figure 2, desire to make two phase windings and two two phase winding equivalences after the conversion, its mmf relation must satisfy:

In this formula, N ₂, N ₄Be respectively two phase windings and the two two phase windings effective turn that whenever is in series.Definition C _4/2And C _2/4Be respectively the transformation matrix of two two-phases, under the constant condition of conversion front and back general power, can prove that turn ratio is to two-phase and two-phase to two two phase coordinate systems

$\frac{N_4}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="H2009100495179E00011.png"\; state="\{\{state\}\}">N</figure-callout>}}_2}=\frac{\sqrt{2}}{2}---\left(5\right)$

Can try to achieve transformation matrix by formula (4) and (5) is respectively:

${\mathrm{<figure-callout\; id="4"\; label="C"\; filenames="H2009100495179E00012.png"\; state="\{\{state\}\}">C</figure-callout>}}_{4/2}=\frac{\sqrt{2}}{2}\left[\begin{array}{cccc}1& 0& \frac{\sqrt{3}}{2}& -\frac{1}{2}\\ 0& 1& \frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right]---\left(6\right)$

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="H2009100495179E00011.png"\; state="\{\{state\}\}">C</figure-callout>}}_{2/4}=\frac{\sqrt{2}}{2}\left[\begin{array}{cc}1& 0\\ 0& 1\\ \frac{\sqrt{3}}{2}& \frac{1}{2}\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right]---\left(7\right)$

After this conversion, to compare with two two phase windings, the resistance and the leakage inductance of the every phase winding of rotor of two phase windings still remain unchanged, and the mutual inductance maximal value is 2 times of two two phase windings between two phase windings.Promptly

$L_m=2\&CenterDot;\frac{3}{2}{L}_{\mathrm{ms}}=3L_{\mathrm{ms}}---\left(8\right)$

In the 3rd step, set up the mathematical model (this modeling method be prior art, herein do not given unnecessary details) of double triphase asynchronous motor under the two-phase rest frame.

Voltage-to-current equation in this model:

$\left[\begin{array}{c}{u}_{\mathrm{s\&alpha;}}\\ u_{\mathrm{s\&beta;}}\\ u_{\mathrm{r\&alpha;}}\\ u_{\mathrm{r\&beta;}}\end{array}\right]=\left[\begin{array}{cccc}{R}_s+L_{s}p& 0& {\mathrm{<figure-callout\; id="0"\; label="L\; m\; p"\; filenames="H2009100495179E00021.png,H2009100495179E00022.png"\; state="\{\{state\}\}">L</figure-callout>}}_{m}p& 0\\ 0& R_s+L_{s}p& 0& L_{m}p\\ L_{m}p& \mathrm{\&omega;}{L}_m& R_r+L_{r}p& \mathrm{\&omega;}{L}_r\\ -\mathrm{\&omega;}{L}_m& L_{m}p& -\mathrm{\&omega;}{L}_r& R_r+L_{r}p\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{s\&alpha;}}\\ i_{\mathrm{s\&beta;}}\\ i_{\mathrm{r\&alpha;}}\\ i_{\mathrm{r\&beta;}}\end{array}\right]---\left(9\right)$

L in this formula _sAnd L _rBe respectively the self-induction of the static winding of rotor equivalence two-phase:

$\left\{\begin{array}{c}{L}_s=L_{\mathrm{ls}}+L_m=L_{\mathrm{ls}}+3L_{\mathrm{ms}}\\ L_r=L_{\mathrm{lr}}+L_m=L_{\mathrm{lr}}+3L_{\mathrm{ms}}\end{array}\right.---\left(10\right)$

The electromagnetic torque in this model and the equation of motion:

$\left\{\begin{array}{c}{T}_e=n_p{L}_m(i_{\mathrm{s\&beta;}}{i}_{\mathrm{r\&alpha;}}-i_{\mathrm{s\&alpha;}}{i}_{\mathrm{r\&beta;}})\\ T_e=T_L+\frac{J}{n_p}\frac{\mathrm{d\&omega;}}{\mathrm{dt}}\end{array}\right.---\left(11\right)$

In this formula, ω is the electric angle speed of rotor rotation.

By the realistic model (this modeling method is a prior art, is not given unnecessary details) of formula (1), (3), (6), (7) and (9)-double triphase asynchronous motor that (11) make up on Matlab/simulink herein, as shown in Figure 3.

This realistic model input variable has two three-phase voltages and load torque, and output variable has the phase current of electromagnetic torque, rotating speed and two threephase stator windings.

The realistic model that utilizes above-mentioned design philosophy to obtain can carry out emulation to actual double triphase asynchronous motor.The general data of this double triphase asynchronous motor is: power 1.1kW, number of pole-pairs n _P=2, phase voltage 190V, the two three phase windings 30 ° of space electrical angles that stagger.

General data: R such as resistance inductance _S=3.8 Ω, R _r=3.0 Ω, L _1S=0.0107H, L _1r=0.0177H, L _Ms=0.0805H, J=0.01kg.m ²

When the model that utilization obtains according to the inventive method carried out emulation to above-mentioned motor, after given torque 1.96Nm started for 0.4 second, torque was increased under the simulated conditions of 3.78Nm, the torque that the emulation double triphase asynchronous motor obtains, rotating speed and A ₁The result of phase current waveform is respectively shown in Fig. 4 A, 4B, 4C.

After given torque 5.66Nm started for 0.4 second, torque was increased under the simulated conditions of 7.52Nm, and the result of the torque that the emulation double triphase asynchronous motor obtains, rotating speed and A1 phase current waveform is shown in Fig. 4 D, 4E, 4F.

The emulated data of speed and current in the time of accessing stable state by simulation result, as shown in table 1:

Table 1 double triphase asynchronous motor emulated data

T in the table 1 ₂Be motor output torque, equal T _LGained after the torque of deduction mechanical loss and added losses correspondence.Wherein mechanical loss is got 18W by experience, and added losses are got about 1% of power input.

To the test that experimentizes of above-mentioned double triphase asynchronous motor, motor is inserted test macro shown in Figure 5.Its test result that obtains is as shown in table 2:

Table 2 double triphase asynchronous motor relevant test data

Under the identical situation of output torque, contrast table 1 and table 2 are analyzed rotating speed of motor and electric current, and the result is as shown in table 3.Second hurdle is the speed test value in the table 3, and third column is the error of rotating speed simulation value with respect to trial value; The 4th hurdle is A ₁Phase current trial value, the 5th hurdle are the error of simulation value with respect to trial value.

Table 3 emulation and test error contrast

Can be drawn by table 3, error is very little between emulation and the test, maximum error ability 1.341%.Mathematical model and realistic model that double triphase asynchronous motor can be described are correct, can implement.

More than show and described ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; that describes in the foregoing description and the instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.The claimed scope of the present invention is defined by appending claims and equivalent thereof.

Claims (3)

1. based on the modeling method of the double triphase asynchronous motor of winding complex transformation, it is characterized in that, said method comprising the steps of:

(1) be pair two phase windings at first with two three phase winding equivalent transformations of double triphase asynchronous motor;

(2) be two phase windings with two two phase winding equivalent transformations again;

(3) two phase windings that obtain based on step (2) are set up the mathematical model of double triphase asynchronous motor under the two-phase rest frame;

When described step (1) was carried out equivalent transformation, the transformation matrix of employing was:

$C_{6/4}=\sqrt{\frac{2}{3}}\left[\begin{array}{cccccc}1& -\frac{1}{2}& -\frac{1}{2}& 0& 0& 0\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}& 0& 0& 0\\ 0& 0& 0& 1& -\frac{1}{2}& -\frac{1}{2}\\ 0& 0& 0& 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right];$

When described step (2) was carried out equivalent transformation, the transformation matrix of employing was:

$C_{4/2}=\frac{\sqrt{2}}{2}\left[\begin{array}{cccc}1& 0& \frac{\sqrt{3}}{2}& -\frac{1}{2}\\ 0& 1& \frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right].$

2. the modeling method of the double triphase asynchronous motor based on the winding complex transformation according to claim 1, it is characterized in that, described step (1) is carried out equivalent transformation based on mmf and the constant principle of power, and the equivalent transformation method that adopts the three phase static coordinate to be tied to the two-phase rest frame is carried out equivalent transformation.

3. the modeling method of the double triphase asynchronous motor based on the winding complex transformation according to claim 1 is characterized in that, described step (2) is carried out equivalent transformation based on mmf and the constant principle of power and obtained the static winding of two-phase.

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