CN107124128A - A kind of control method of the double winding heavy-duty motor drive system based on IEGT - Google Patents

A kind of control method of the double winding heavy-duty motor drive system based on IEGT Download PDF

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Publication number
CN107124128A
CN107124128A CN201710295824.XA CN201710295824A CN107124128A CN 107124128 A CN107124128 A CN 107124128A CN 201710295824 A CN201710295824 A CN 201710295824A CN 107124128 A CN107124128 A CN 107124128A
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mrow
msub
winding
double winding
double
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CN107124128B (en
Inventor
王鑫
张然
王文龙
张瑜
宇文达
周志军
牛颖
郭晋
刘昱
张海涛
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Rongxin Huike Electric Co.,Ltd.
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Rong \/ Electric Technology LLC
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13Observer control, e.g. using Luenberger observers or Kalman filters
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/141Flux estimation
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18Estimation of position or speed
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22Current control, e.g. using a current control loop
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)

Abstract

The present invention provides a kind of control method of the double winding heavy-duty motor drive system based on IEGT, comprises the following steps:Der Geschwindigkeitkreis use Active Disturbance Rejection Control, calculate the reference value of double winding T shaft current average values;Magnetic linkage ring calculates the reference value of double winding M shaft current average values through P adjusters;Respective M axles and T shaft currents are calculated under the synchronized rotating coordinate system of the phase current of double winding six, and then calculate double winding M axles and the respective average value of T shaft currents and difference, double winding M axles and the average value and difference of T shaft currents calculate the amplitude of reference voltage vector through pi regulator, and rotated coordinate system obtains reference voltage vector;Using nine level conversion carrier modulation algorithms, the six-phase voltage needed for double-winding motor is obtained.Double winding MT shaft current ring average values and difference control, it is to avoid current imbalance problem caused by winding parameter is inconsistent, a kind of new thinking is provided for double-winding motor control.

Description

A kind of control method of the double winding heavy-duty motor drive system based on IEGT
Technical field
The present invention relates to high-power frequency conversion ac speed control technology field, the big work(of more particularly to a kind of double winding based on IEGT The control method of rate motor driven systems.
Background technology
Medium Voltage VF Technology realizes high-power transmission by improving the voltage class of buncher, realizes powerful another One approach is polyphase machine transmission system.Compared with conventional three-phase electric system, polyphase machine is in high-power and high-reliability Conjunction has prominent advantage, it is more suitable for the fields such as ship's electrical propulsion, track traffic, Aero-Space, wind tunnel test.As wind The occasions such as hole experiment have harsh control requirement to the wind speed of test section, it is desirable to which wind speed adjustable range is wide, and precision index is high, regulation Speed is fast, and Flow Field in Wind Tunnel control system is by inverter control motor rotating speed, so being proposed to Frequency Converter Control performance Higher requirement.
The inconsistent of parameter can cause the disequilibrium of double winding electric current between double-winding motor winding, and then can cause A set of winding longtime running is then operated in light load situation, on the one hand limits motor belt motor in high load capacity situation, another set of winding Loading capability, on the other hand affects the service life of motor, it is impossible to meet the control requirement of high performance motor drive system.
Current double-winding motor control is main using double d, q (or double M, T) shaft current independent controls, the d axles of double winding (or T axles) electric current tracks the regulation output of der Geschwindigkeitkreis closed loop respectively, and q axles (or M axles) electric current of double winding tracks common respectively Reference value, to reach that double-winding current is balanced.Motor double winding is completely the same in terms of electric parameter in theory, actually electric Machine double winding there is some difference property, and there is also certain coupling, script double winding for induction reactance between double winding Independent d (or q) shaft current introduces coupling between controlling to adjust device mutually, causes double d, q shaft currents in practice independently to be controlled The pi regulator parameter tuning of system brings certain difficulty.
The content of the invention
In order to overcome the deficiencies in the prior art, the present invention provides a kind of double winding heavy-duty motor drivetrain based on IEGT The control method of system, can solve the problem that high-power double-winding motor drive system double winding current-unbalance problem, and double wrap Pi regulator parameter tuning difficult problem during group M, T shaft current independent control.
In order to achieve the above object, the present invention is realized using following technical scheme:
A kind of control method of the double winding heavy-duty motor drive system based on IEGT, comprises the following steps:
Step 1: obtaining the phase current information i of double winding six by current detecting and Rotating speed measringsa1、isb1、isc1、isa2、 isb2、isc2, rotational speed omegafWith rotor position angle λ, magnetic linkage ψ is obtained through flux observerδWith magnetic linkage angular position theta information;
Step 2: according to the tachometer value ω of settingrefWith the feedback tachometer value ω of detectionfTo the Active Disturbance Rejection Control of der Geschwindigkeitkreis Calculated, obtain the reference value i of double winding T shaft current average valuessT_mean_ref
Step 3: magnetic linkage ring calculates the reference value i of M shaft current average values through P adjusterssM_mean_refWith through pi regulator Calculate exciting current reference value ifdref1, wherein exciting current reference value reach excitation system carry out PI regulations, output excitation electricity Press ufd
Step 4: the reference value of T shaft current difference adjusters and M shaft current difference adjusters is set into 0;
Step 5: it is each that the synchronized rotating coordinate system of the phase current of double winding six that current detecting is obtained is conversed into double winding From M shaft currents isM1、isM2With T shaft currents isT1、isT2
Step 6: calculating double winding M axles and the respective average value of T shaft currents and difference:
T shaft currents mean value calculation is isT_mean=(isT1+isT2)*0.5
M shaft currents mean value calculation is isM_mean=(isM1+isM2)*0.5
T shaft currents mathematic interpolation is isT_dif=isT1-isT2
M shaft currents mathematic interpolation is isM_dif=isM1-isM2
Step 7: using double winding T axles and the average value and difference of M shaft currents as value of feedback, respectively with Step 2: step Rapid three and the reference value of the T shaft currents that provide of step 4 and the reference value of M shaft current average values, T shaft currents and M shaft current differences Difference operation is done, calculating the T axles of double winding, M shaft currents average value respectively through 4 road pi regulators adjusts through PI closed loops and export Value isT_mean_PIout、isM_mean_PIoutT axles, M shaft currents difference with double winding adjust output valve i through PI closed loopssT_dif_PIout、 isM_dif_PIout
Step 8: the control of double winding MT shaft currents average value and difference based on electric voltage feed forward are controlled under M, T axle of generation The amplitude of double winding reference voltage vector be represented by:
Wherein:uMdc1、uTdc1、uMdc2、uTdc2For M, T shaft voltage feedforward amount of double winding;
Step 9: rotated coordinate system inverse transformation obtains six phase reference voltage vector usa1、usb1、usc1、usa2、usb2、usc2, Using nine level conversion carrier modulation algorithms, the six-phase voltage needed for double-winding motor is obtained.
Der Geschwindigkeitkreis in described step two use Active Disturbance Rejection Control (ADRC) so that the control of double-winding motor rotating speed has Eliminated in the features such as non-overshoot, interference rejection ability are strong, reliability is high, der Geschwindigkeitkreis automatic disturbance rejection controller in traditional Active Disturbance Rejection Control TD links.
The MT shaft voltage feedforward amounts u of double winding in described step eightMdc1、uTdc1、uMdc2、uTdc2Computational methods are:
R in formulasFor stator winding resistance, LslFor stator leakage inductance, ω is rotor velocity, and ψ is air gap flux linkage.
Compared with prior art, the beneficial effects of the invention are as follows:
1st, a kind of control method of double winding heavy-duty motor drive system based on IEGT proposed by the present invention, is different from Double M, T shaft current ring independent controls, introduce the current average control and difference control of double winding.First, by adjusting The parameter of electric current loop difference pi regulator so that the current differential between double winding is as small as possible, it is ensured that double winding Uniformity (or synchronism);Again, the parameter of setting current ring average value P I regulator so that the average current pair of double winding The tracking of set-point.
2nd, the control method of a kind of double winding heavy-duty motor drive system based on IEGT proposed by the present invention, using double Winding MT shaft currents average value and difference control, double-winding current disequilibrium is directly suppressed, can avoid two sets around The problem of inconsistent electric current brought of group parameter, Voltage unbalance, a kind of new thinking is provided for double-winding motor control.
3rd, the control method of a kind of double winding heavy-duty motor drive system based on IEGT proposed by the present invention, in double wrap Electric voltage feed forward is introduced respectively in the calculating of the M axles of group and the reference voltage of T axles, counteracts phase of the electromotive force between M axles and T axles Mutual coupling.
4th, a kind of control method of double winding heavy-duty motor drive system based on IEGT proposed by the present invention, double winding Motor may operate in be carried at full speed, entirely, full speed, semi-load, Half Speed, semi-load, is exceeded the speed limit, is carried isotype entirely, improve the reliable of system Property.
Brief description of the drawings
Fig. 1 is the System control structures schematic diagram of the present invention;
Fig. 2 is the der Geschwindigkeitkreis Active Disturbance Rejection Control structural representation of the present invention;
Fig. 3 is the double winding M shaft currents average value and difference control structure schematic diagram of the present invention;
Fig. 4 is the double winding T shaft currents average value and difference control structure schematic diagram of the present invention.
Wherein:The mark of each part is as follows in Fig. 3 and Fig. 4:
1、isT1、isT1- winding 1 and the corresponding T shaft currents of winding 2;
2、isM1、isM2- winding 1 and the corresponding M shaft currents of winding 2;
3、isT_mean_ref、isT_meanThe reference value and calculated value of-double winding T shaft current average values;
4、isM_mean_ref、isM_meanThe reference value and calculated value of-double winding M shaft current average values;
5、isT_difThe difference of-double winding T shaft currents;
6、isM_difThe difference of-double winding M shaft currents;
7、usM1_ref、usT1_refThe M axles of-winding 1 and the amplitude of T axle reference voltage vectors;
8、usM2_ref、usT2_refThe M axles of-winding 2 and the amplitude of T axle reference voltage vectors;
9、uMdc1、uTdc1The M axles and T shaft voltage feedforward values of-winding 1;
10、uMdc2、uTdc2The M axles and T shaft voltage feedforward values of-winding 2;
11、isT_mean_PIoutThe T shaft currents average value of-double winding adjusts output valve through PI closed loops;
12、isM_mean_PIoutThe M shaft currents average value of-double winding adjusts output valve through PI closed loops;
13、isT_dif_PIoutThe T shaft currents difference of-double winding adjusts output valve through PI closed loops;
14、isM_dif_PIoutThe M shaft currents difference of-double winding adjusts output valve through PI closed loops.
Embodiment
The embodiment provided below in conjunction with accompanying drawing the present invention is described in detail.
As Figure 1-4, a kind of control method of the double winding heavy-duty motor drive system based on IEGT, including following Step:
Step 1: obtaining the phase current information i of double winding six by current detecting and Rotating speed measringsa1、isb1、isc1、isa2、 isb2、isc2, rotational speed omegafWith rotor position angle λ, magnetic linkage ψ is obtained through flux observerδWith magnetic linkage angular position theta information;
Step 2: according to the tachometer value ω of settingrefWith the feedback tachometer value ω of detectionfTo the Active Disturbance Rejection Control of der Geschwindigkeitkreis Calculated, obtain the reference value i of double winding T shaft current average valuessT_mean_ref
Step 3: magnetic linkage ring calculates the reference value i of M shaft current average values through P adjusterssM_mean_refWith through pi regulator Calculate exciting current reference value ifdref1, wherein exciting current reference value reach excitation system carry out PI regulations, output excitation electricity Press ufd
Step 4: the reference value of T shaft current difference adjusters and M shaft current difference adjusters is set into 0;
Step 5: it is each that the synchronized rotating coordinate system of the phase current of double winding six that current detecting is obtained is conversed into double winding From M shaft currents isM1、isM2With T shaft currents isT1、isT2
Step 6: calculating double winding M axles and the respective average value of T shaft currents and difference:
T shaft currents mean value calculation is isT_mean=(isT1+isT2)*0.5
M shaft currents mean value calculation is isM_mean=(isM1+isM2)*0.5
T shaft currents mathematic interpolation is isT_dif=isT1-isT2
M shaft currents mathematic interpolation is isM_dif=isM1-isM2
Step 7: using double winding T axles and the average value and difference of M shaft currents as value of feedback, respectively with Step 2: step Rapid three and the reference value of the T shaft currents that provide of step 4 and the reference value of M shaft current average values, T shaft currents and M shaft current differences Difference operation is done, calculating the T axles of double winding, M shaft currents average value respectively through 4 road pi regulators adjusts through PI closed loops and export Value isT_mean_PIout、isM_mean_PIoutT axles, M shaft currents difference with double winding adjust output valve i through PI closed loopssT_dif_PIout、 isM_dif_PIout
Step 8: the control of double winding MT shaft currents average value and difference based on electric voltage feed forward are controlled under M, T axle of generation Double winding reference voltage vector amplitude;
Step 9: rotated coordinate system inverse transformation obtains six phase reference voltage vector usa1、usb1、usc1、usa2、usb2、usc2, Using nine level conversion carrier modulation algorithms, the six-phase voltage needed for double-winding motor is obtained.
As shown in Fig. 2 the der Geschwindigkeitkreis in described step two use Active Disturbance Rejection Control (ADRC) so that double-winding motor turns It is certainly anti-that tradition is eliminated in the features such as speed control has non-overshoot, interference rejection ability is strong, reliability is high, der Geschwindigkeitkreis automatic disturbance rejection controller Disturb the TD links in control.
The circular of the amplitude of double winding reference voltage vector in described step eight is:
Voltage equation such as formula (1) institute of double-winding motor under MT axle rotating coordinate systems is obtained in Air-gap-flux orientated theory Show:
R in formulasFor stator winding resistance, LslFor stator leakage inductance, ω is rotor velocity, and ψ is air gap flux linkage.
M axles in double-winding current ring and electric voltage feed forward is introduced respectively in the given voltage of T axles, counteract electromotive force and exist Intercoupling between M axles and T axles, the electric voltage feed forward amount u in Fig. 3 and Fig. 4Mdc1、uTdc1、uMdc2、uTdc2, as shown in formula (2):
Formula (2) and formula (3) are together substituted into formula (1), formula (1), which can be arranged, is:
Double M, T shaft current ring independent controls based on electric voltage feed forward can be obtained based on formula (4), i.e.,:
In formula:
1、usM1_ref、usT1_refThe M axles of-winding 1 and the amplitude of T axle reference voltage vectors;
2、usM2_ref、usT2_refThe M axles of-winding 2 and the amplitude of T axle reference voltage vectors;
3、isM1_PIout、isT1_PIoutM axles and T shaft current rings the pi regulator output of-winding 1;
4、isM2_PIout、isT2_PIoutM axles and T shaft current rings the pi regulator output of-winding 2.
Different from double M, T shaft current ring independent controls, the double winding heavy-duty motor drivetrain of the invention based on IEGT The control method of system, introduces the current average control and difference control of double winding.First, setting current ring difference is passed through The parameter of pi regulator so that the current differential between double winding is as small as possible, it is ensured that the uniformity of double winding is (or same Step property);Again, the parameter of setting current ring average value P I regulator so that the average current of double winding to set-point with Track.
Such as formula (6), and shown in reference picture 3 and Fig. 4, double winding MT shaft currents average value control based on electric voltage feed forward and The amplitude of double winding reference voltage vector under M, T axle of difference control generation is represented by:
In the present invention, controlled using double winding MT shaft currents average value and difference, double-winding current disequilibrium is entered Row directly suppresses, and the problem of can avoiding the inconsistent electric current brought of double winding parameter, Voltage unbalance, is double-winding motor Control provides a kind of new thinking.
Above example is implemented lower premised on technical solution of the present invention, gives detailed embodiment and tool The operating process of body, but protection scope of the present invention is not limited to the above embodiments.Method therefor is such as without spy in above-described embodiment It is conventional method not mentionlet alone bright.

Claims (3)

1. a kind of control method of the double winding heavy-duty motor drive system based on IEGT, it is characterised in that including following step Suddenly:
Step 1: obtaining the phase current information i of double winding six by current detecting and Rotating speed measringsa1、isb1、isc1、isa2、isb2、 isc2, rotational speed omegafWith rotor position angle λ, magnetic linkage ψ is obtained through flux observerδWith magnetic linkage angular position theta information;
Step 2: according to the tachometer value ω of settingrefWith the feedback tachometer value ω of detectionfActive Disturbance Rejection Control to der Geschwindigkeitkreis is counted Calculate, obtain the reference value i of double winding T shaft current average valuessT_mean_ref
Step 3: magnetic linkage ring calculates the reference value i of M shaft current average values through P adjusterssM_mean_refCalculated with through pi regulator Go out exciting current reference value ifdref1, wherein exciting current reference value reach excitation system carry out PI regulations, export excitation voltage ufd
Step 4: the reference value of T shaft current difference adjusters and M shaft current difference adjusters is set into 0;
Step 5: it is respective that the synchronized rotating coordinate system of the phase current of double winding six that current detecting is obtained is conversed into double winding M shaft currents isM1、isM2With T shaft currents isT1、isT2
Step 6: calculating double winding M axles and the respective average value of T shaft currents and difference:
T shaft currents mean value calculation is isT_mean=(isT1+isT2)*0.5
M shaft currents mean value calculation is isM_mean=(isM1+isM2)*0.5
T shaft currents mathematic interpolation is isT_dif=isT1-isT2
M shaft currents mathematic interpolation is isM_dif=isM1-isM2
Step 7: using double winding T axles and the average value and difference of M shaft currents as value of feedback, respectively with Step 2: step 3 The reference value of the T shaft currents and the reference value of M shaft current average values, T shaft currents and the M shaft current differences that are provided with step 4 makes the difference It is worth computing, calculating the T axles of double winding, M shaft currents average value respectively through PI closed loops through 4 road pi regulators adjusts output valve isT_mean_PIout、isM_mean_PIoutT axles, M shaft currents difference with double winding adjust output valve i through PI closed loopssT_dif_PIout、 isM_dif_PIout
Step 8: the control of double winding MT shaft currents average value and difference based on electric voltage feed forward control two under M, T axle of generation The amplitude of set winding reference voltage vector is represented by:
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Wherein:uMdc1、uTdc1、uMdc2、uTdc2For M, T shaft voltage feedforward amount of double winding;
Step 9: rotated coordinate system inverse transformation obtains six phase reference voltage vector usa1、usb1、usc1、usa2、usb2、usc2, use Nine level conversion carrier modulation algorithms, obtain the six-phase voltage needed for double-winding motor.
2. a kind of control method of double winding heavy-duty motor drive system based on IEGT according to claim 1, its It is characterised by, the der Geschwindigkeitkreis in described step two use Active Disturbance Rejection Control (ADRC) so that double-winding motor rotating speed control tool Have in the features such as non-overshoot, interference rejection ability are strong, reliability is high, der Geschwindigkeitkreis automatic disturbance rejection controller and eliminate in traditional Active Disturbance Rejection Control TD links.
3. a kind of control method of double winding heavy-duty motor drive system based on IEGT according to claim 1, its It is characterised by, the MT shaft voltage feedforward amounts u of the double winding in described step eightMdc1、uTdc1、uMdc2、uTdc2Computational methods For:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>M</mi> <mi>d</mi> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&amp;omega;L</mi> <mrow> <mi>s</mi> <mi>l</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>T</mi> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>T</mi> <mi>d</mi> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;omega;L</mi> <mrow> <mi>s</mi> <mi>l</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>M</mi> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>&amp;omega;</mi> <mi>&amp;Psi;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>M</mi> <mi>d</mi> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&amp;omega;L</mi> <mrow> <mi>s</mi> <mi>l</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>T</mi> <mn>2</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>T</mi> <mi>d</mi> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;omega;L</mi> <mrow> <mi>s</mi> <mi>l</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>s</mi> <mi>M</mi> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi>&amp;omega;</mi> <mi>&amp;Psi;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>
R in formulasFor stator winding resistance, LslFor stator leakage inductance, ω is rotor velocity, and ψ is air gap flux linkage.
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