CN101604347A - Modeling method of double three-phase asynchronous motor based on winding complex conversion - Google Patents

Abstract

The invention discloses a modeling method of a double-three-phase asynchronous motor based on complex transformation of windings. The method is based on the principle that magnetomotive force and power remain unchanged. A two-phase winding is equivalently transformed into a two-phase winding. Then, using the mature mathematical model in the two-phase static coordinate system, the mathematical model of the double-three-phase asynchronous motor in the α-β coordinate system and the simulation model based on Matlab/Simulink are established. The method is relatively simple and the physical concept is clear. Comparing the simulation results with the corresponding test data, the maximum error between the two is within 2%.

Description

Modeling method of double three-phase asynchronous motor based on winding complex conversion

Technical field:

The invention relates to a modeling method of an asynchronous motor, in particular to a modeling method of a double-three-phase asynchronous motor based on winding complex conversion.

Background technique:

The dual three-phase motor system has obvious advantages in performance over the three-phase motor system:

(1) The dual three-phase motor system has the ability to use low-voltage standard power devices to achieve high-voltage and high-power processing;

(2) The dual three-phase motor system has the advantages of increasing the number of space harmonics that have a greater impact, and the amplitude decreases, and the torque ripple decreases;

(3) Double three-phase motor system, its magnetomotive force waveform is improved, which can improve motor efficiency and reduce motor noise;

(4) The dual-three-phase motor system adopts a multi-phase redundant structure speed control system, which greatly improves the reliability of the system level.

In recent years, relevant technical personnel have carried out relevant research on the modeling and operation of multi-phase asynchronous motors. Among the modeling methods of multi-phase motors provided by the prior art, the main method used is: using the orthogonal transformation matrix Project the voltage and current space vectors of the dual-three-phase asynchronous motor into three mutually orthogonal two-dimensional subspaces, and then eliminate the rotor rotation angle through the rotation transformation matrix to transform the rotor variables into the stator static coordinate system to obtain the cage Simplified model of rotor double three-phase asynchronous motor in stationary coordinate system.

The above-mentioned modeling method has complex design and cumbersome implementation steps in actual operation, which limits its practicability.

Invention content:

The present invention provides a new modeling and simulation method for a dual-three-phase asynchronous motor aiming at the defects in the prior art in the modeling of the dual-three-phase motor system, which is relatively simple and has clear physical concepts.

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

A modeling method for a dual three-phase asynchronous motor based on winding complex transformation, the method includes the following steps:

(1) First, the dual three-phase windings of the dual three-phase asynchronous motor are equivalently transformed into dual two-phase windings;

(2) The dual two-phase winding is then equivalently transformed into a two-phase winding;

(3) Based on the two-phase winding obtained in step (2), the mathematical model of the dual-three-phase asynchronous motor in the two-phase stationary coordinate system is established.

The step (1) performs equivalent transformation based on the principle of constant magnetomotive force and power, and uses an equivalent transformation method from a three-phase stationary coordinate system to a two-phase stationary coordinate system to perform equivalent transformation.

When described step (1) carries out equivalent transformation, the transformation matrix that adopts is:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}}\left[\begin{array}{cccccc}\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; .</span>$

The step (2) performs an equivalent transformation based on the principle that the magnetomotive force and power are constant to obtain a two-phase stationary winding, and the transformation matrix used is:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; .</span>$

Obtained according to the above technical solution, the present invention first converts the dual three-phase winding into a dual two-phase equivalent winding, and then further transforms it into an equivalent two-phase winding. Therefore, the mathematical model of the dual three-phase asynchronous motor in the two-phase stationary coordinate system is established, and a simulation model based on Matlab/Simulink can be constructed.

The method is relatively simple and the physical concept is clear. Comparing the simulation results with the corresponding test data, the maximum error between the two is within 2%. The method based on winding complex conversion proposed by the invention is implementable, and the mathematical model and simulation model of the double-three-phase asynchronous motor established based on the method are correct and effective.

Description of drawings:

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

Figure 1 is a schematic diagram of the stator winding of a dual three-phase asynchronous motor.

Fig. 2 is a schematic diagram of the magnetomotive force space vector of the two-phase and two-phase coordinate system.

Figure 3 is the simulation model of the dual three-phase asynchronous motor.

Fig. 4A is a diagram of torque variation of a simulated dual three-phase asynchronous motor.

Fig. 4B is a diagram of the rotational speed change of the simulated dual three-phase asynchronous motor.

FIG. 4C is a waveform diagram of phase A1 current of a simulated dual three-phase asynchronous motor.

Fig. 4D is a diagram of torque variation of a simulated dual three-phase asynchronous motor.

Fig. 4E is a diagram of the speed change of the simulated dual three-phase asynchronous motor.

FIG. 4F is a waveform diagram of phase A1 current of a simulated dual-three-phase asynchronous motor.

Figure 5 is a diagram of the test system for a dual three-phase asynchronous motor.

Detailed ways:

In order to make the technical means, creative features, goals and effects achieved by the present invention easy to understand, the present invention will be further described below in conjunction with specific illustrations.

The present invention proposes a new mathematical modeling method for a double-three-phase asynchronous motor in order to solve the defects existing in the modeling of the double-three-phase motor system in the prior art.

This method is based on the principle that the magnetomotive force and power remain unchanged. First, the double three-phase winding is equivalently transformed into a double two-phase winding, and then the double two-phase winding is equivalently transformed into a two-phase winding. Then, using the mature mathematical model in the two-phase static coordinate system, the mathematical model of the double-three-phase asynchronous motor in the α-β coordinate system and the simulation model based on Matlab/Simulink are established.

Based on above-mentioned design principle, the present invention is concretely implemented as follows:

The first step is the conversion of dual three-phase windings to dual two-phase windings

For the convenience of analysis, under the condition that the accuracy requirements required by the actual engineering are met, this embodiment enables the dual three-phase windings of the dual three-phase permanent magnet synchronous motor to have the following characteristics, as shown in Figure 1:

1) The two sets of stator windings A ₁ B ₁ C ₁ and A ₂ B ₂ C ₂ are exactly the same, and they are staggered in space by 30° electrical angle. Each set of three-phase windings is symmetrical in space, that is, the number of turns of each phase winding is the same, and the phase windings are separated by 120° space electrical angle. The surface of the stator and rotor is smooth, without cogging effect, and the air gap is uniform.

2) Ferromagnetic saturation, hysteresis, eddy current influence and conductor skin effect are not considered.

3) The air gap magnetic field is sinusoidally distributed, ignoring the influence of higher harmonics of the magnetic field.

In this step, apply the equivalent transformation from the three-phase stationary coordinate system to the two-phase stationary coordinate system, transform the A ₁ B ₁ C ₁ winding into α ₁ β ₁ winding, and transform the A ₂ B ₂ C ₂ winding into α ₂ β ₂ windings (as shown in Figure 1). During the transformation, the magnetomotive force and total power synthesized before and after the transformation must be kept unchanged, then the transformation matrix from the dual three-phase coordinate system to the dual two-phase coordinate system is:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}}\left[\begin{array}{cccccc}\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

After this transformation, the double three-phase winding is equivalent to a double two-phase winding. Equation (1) is not only the current transformation matrix, but also the voltage and flux linkage transformation matrix. The relationship before and after the stator current transformation is:

i _αβ12 = C _6/4 i _ABC12 (2)

In 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

In this step, the transformation matrix from the dual two-phase coordinate system to the dual three-phase coordinate system is:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}}\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In this embodiment, the rotor windings of the dual three-phase windings have been converted to the stator side. Define the resistance and leakage inductance of each phase of the stator and rotor windings as R _s , L _lS and R _r , L _lr respectively, and the maximum mutual inductance between the two-phase windings is L _ms . It can be seen from the flux linkage conversion relationship that the resistance and leakage inductance of each phase of the stator and rotor windings of the converted dual-phase winding will remain unchanged, and the maximum mutual inductance will become 3/2 times of the original.

The second step is the conversion of dual two-phase windings to two-phase windings

This step is also based on the principle that the magnetomotive force and power remain unchanged, and the double two-phase winding can be equivalently transformed into a two-phase winding. As shown in Figure 2, in order to make the transformed two-phase winding equivalent to the dual two-phase winding, the magnetomotive force relationship must satisfy:

In this formula, N ₂ and N ₄ are the effective number of turns per phase of the two-phase winding and the dual two-phase winding in series connection respectively. Define C _4/2 and C _2/4 as transformation matrices from double-two-phase to two-phase and two-phase to double-two-phase coordinate system respectively. Under the condition that the total power remains unchanged before and after transformation, it can be proved that the turns ratio is

$\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="N"\; filenames="A2009100495170011H2.png"\; state="\{\{state\}\}">N</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

The transformation matrices obtained from equations (4) and (5) are:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="C"\; filenames="A2009100495170011H2.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}& \frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

After this transformation, compared with the dual two-phase winding, the resistance and leakage inductance of each phase winding of the stator and rotor of the two-phase winding remain unchanged, and the maximum mutual inductance between the two-phase windings is twice that of the dual two-phase winding. Right now

${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ms</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ms</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

The third step is to establish a mathematical model of the dual-three-phase asynchronous motor in the two-phase stationary coordinate system (this modeling method is a prior art, and will not be repeated here).

The voltage-current equation in this model:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; s\&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; s\&beta;</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; r\&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; r\&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; p</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="L\; m\; p"\; filenames="A2009100495170012H2.png,A2009100495170013H1.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="0"\; label="L\; m\; p"\; filenames="A2009100495170012H2.png,A2009100495170013H1.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; p</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; p</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; p</span>}\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; p</span>}& \mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; p</span>}& \mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}& {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; p</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; p</span>}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; s\&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; s\&beta;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r\&alpha;</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r\&beta;</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In this formula, L _s and L _r are the self-inductances of the stator and rotor equivalent two-phase stationary windings respectively:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ls</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ms</span>}}\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; lr</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; lr</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ms</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

The electromagnetic torque and equations of motion in this model:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; s\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r\&alpha;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; s\&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; s\&beta;</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; J</span>}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}\frac{\mathrm{<span\; class="notranslate">\; d\&omega;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In this formula, ω is the electrical angular velocity of the rotor rotation.

By formula (1), (3), (6), (7) and (9)-(11) the simulation model (this modeling method is prior art of the double three-phase asynchronous motor of construction on Matlab/simulink) will not be repeated here), as shown in Figure 3.

The input variables of the simulation model include double-three-phase voltage and load torque, and the output variables include electromagnetic torque, speed and phase current of double-three-phase stator windings.

Using the simulation model obtained from the design idea above, the actual double-three-phase asynchronous motor can be simulated. The main data of the double-three-phase asynchronous motor are: power 1.1kW, number of pole pairs n _P =2, phase voltage 190V, double-three-phase windings staggered by 30° space electrical angle.

Main data such as resistance and inductance: R _S = 3.8Ω, R _r = 3.0Ω, L _lS = 0.0107H, L _lr = 0.0177H, L _ms = 0.0805H, J = 0.01kg.m ² .

When utilizing the model that obtains according to the inventive method to carry out simulation to above-mentioned motor, after 0.4 seconds of given torque 1.96Nm starting, under the simulation condition that torque increases to 3.78Nm, the torque that simulation double three-phase asynchronous motor obtains, The results of the rotation speed and A1 _- phase current waveform are shown in Figures 4A, 4B, and 4C, respectively.

After starting for 0.4 seconds with a given torque of 5.66Nm, the torque increases to 7.52Nm under the simulation conditions. The results of the torque, speed and A1-phase current waveform obtained by simulating the double-three-phase asynchronous motor are shown in Figures 4D, 4E, and 4F. shown.

From the simulation results, the simulation data of the rotational speed current in the steady state can be obtained, as shown in Table 1:

Table 1 Simulation data of dual three-phase asynchronous motor

T ₂ in Table 1 is the output torque of the motor, which is equal to T _L after deducting the torque corresponding to the mechanical loss and additional loss. Among them, the mechanical loss is 18W based on experience, and the additional loss is about 1% of the input power.

Experimental tests are carried out on the above-mentioned dual three-phase asynchronous motors, and the motors are connected to the test system shown in Figure 5. The test results obtained are shown in Table 2:

Table 2 Relevant test data of double three-phase asynchronous motor

In the case of the same output torque, compare Table 1 and Table 2, analyze the speed and current of the motor, and the results are shown in Table 3. The second column in Table 3 is the speed test value, the third column is the error of the speed simulation value relative to the test value; the fourth column is the A ₁ phase current test value, and the fifth column is the error of the simulation value relative to the test value.

Table 3 Comparison of simulation and test errors

It can be concluded from Table 3 that the error between simulation and experiment is very small, and the maximum error is only 1.341%. It can be shown that the mathematical model and simulation model of the double-three-phase asynchronous motor are correct and can be implemented.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description only illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have Variations and improvements are possible, which fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims (4)

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.

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 and 2 is characterized in that when described step (1) was carried out equivalent transformation, the transformation matrix of employing was:

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

4, 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 (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:

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

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