CN107994824A - A kind of asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation - Google Patents
A kind of asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation Download PDFInfo
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- CN107994824A CN107994824A CN201711351406.4A CN201711351406A CN107994824A CN 107994824 A CN107994824 A CN 107994824A CN 201711351406 A CN201711351406 A CN 201711351406A CN 107994824 A CN107994824 A CN 107994824A
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/22—Current control, e.g. using a current control loop
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Abstract
The invention discloses a kind of asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, including step：Primary Calculation electric machine frequency f and stator line voltage V under constant voltage constant frequency control strategy, calculates modulation depth M；Gather the three-phase current i of motorsa、isbAnd isc, and carry out coordinate and be transformed into rotating coordinate system obtaining electric current isdWith isq；Reactive current i under rotating coordinate system is extracted according to self-adaptive routingsqSteady-state value isq *, and with not having filtered reactive current isqIt is poor to make, and difference is adjusted after PI is controlled to the modulation depth M under corresponding modulator approach, calculates the modulation depth M after adjusting*Value；By the i of collectionsa、isbAnd iscLow-pass filtering is carried out, by the judgement to current polarity, determines the compensation time t to inverter non-linear factor；Compensation time t is added in control algolithm and carries out real-Time Compensation.This invention removes asynchronous machine under unloaded or underloading the unstable phenomenon of system, the electric current as caused by inverter non-linear factor, torque harmonic wave are reduced, so as to reduce the vibration on motor surface.
Description
Technical field
The present invention relates to motor frequency conversion control technology, more particularly to it is a kind of low with the asynchronous machine of compensation based on current closed-loop
Frequency oscillation suppression method.
Background technology
Continuous with energy crisis is deepened, and the electric automobile of energy-saving and emission-reduction becomes domestic and international major motor corporation and scientific research
The research hotspot of universities and colleges.Critical component of the motor as drive system of electric automobile is driven, its correlation properties is related to vehicle
Service life and other many performances.The control strategy used at present include Direct Torque Control (DTC), vector controlled (VC),
Constant voltage constant frequency control (V/F) etc., at present, V/F still occupies most market in frequency conversion speed-adjusting system, accordingly, it is capable to it
The research for carrying out some operating modes and performance is necessary, and the control method will be caused to be more widely applied.
The phenomenon of low-frequency oscillation occurs in low frequency at light load for some motors, and the at this moment fluctuation of motor speed and torque is very
Greatly, work under such conditions for a long time and most likely result in shaft coupling and axis infringement or fracture.The reason for causing low-frequency oscillation master
If between motor-field, rotor caused by energy exchange, and the non-linear factor of inverter also can cause very big shadow to vibration
Ring, the harmonic distortion that can not only reduce the signals such as electric current, rotating speed, torque is compensated to it, moreover it is possible to rise to a certain extent
Influence to suppression non-linear factor to low-frequency oscillation.
Modulator approach for existing low-frequency oscillation suppression method just for SVPWM, and most of is all adjustment stator
Voltage magnitude.This method is adjusted the value of modulation depth and non-thread to inverter using a simple electric current loop feedback
Sexual factor compensates so that inhibition is quick, obvious and be easily achieved, and can be applicable in more modulation method.
The content of the invention
The purpose of the present invention is the deficiency for prior art, there is provided one kind based on current closed-loop and inverter it is non-linear because
The asynchronous machine low-frequency oscillation suppression method of element compensation, can realize so that this method can be wider under different modulating strategy
Apply to generally in engineering, improve motor stationarity.
To achieve these goals, technical scheme is as follows：
A kind of asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, including step：
Step S1, according to actual condition primary Calculation under constant voltage constant frequency control strategy (V/f) electric machine frequency f and stator line
Voltage V, the value of M is calculated by the relation of modulation depth M and stator line voltage V；
Step S2, gathers the three-phase current i under motor operation operating modesa、isbAnd isc, and carry out coordinate and be transformed into rotation seat
Mark system electric current isdWith isq；
Step S3, the reactive current i under rotating coordinate system is extracted according to self-adaptive routingsqSteady-state value isq *, and with not having
Filtered reactive current isqIt is poor to make, this difference is adjusted after PI is controlled to the modulation depth M under corresponding modulator approach,
Calculate the modulation depth M after adjustment*Value；
Step S4, by the motor threephase stator electric current i of collectionsa、isbAnd iscLow-pass filtering is carried out, by current polarity
Judgement, determine compensation time t to inverter non-linear factor；
Step S5, compensation time t is added in control algolithm, and the width for changing control signal carries out real-Time Compensation.
Further, in the step S1, under constant voltage constant frequency control strategy, electric machine frequency f and stator line voltage V into than
Example relation, can change voltage in the case where inverter direct-current power supply voltage is constant by varying modulation depth M.
Further, in the step S1, motor stator frequency f is determined by operating mode, according to the relation curve of constant voltage and frequency ratio
The amplitude of stator line voltage V is calculated, the value of modulation depth M is calculated according to the relation curve of modulation depth M and stator line voltage V,
The value of corresponding modulation system corresponding modulating depth M is determined by following formula：
Wherein h be corresponding modulation system linear modulationra, UdcFor the voltage of DC power supply before inversion, under each modulation system
Calculating process it is similar, simply linear modulationra h it is different.
Further, the modulation system includes modulation system, the modulation system of SVPWM and the SPWM injection of SPWM three times
Harmonic modulation mode.
Further, when modulation system is the modulation system of SPWM, the value of the linear modulationra h is 0.866；
When modulation system is the modulation system of SVPWM, the value of the linear modulationra h is 1；When modulation system is injected for SPWM
During triple-frequency harmonics modulation system, the value of the linear modulationra h is 1.
Further, the step S2 is specifically included：
Gather motor threephase stator electric current isa、isbAnd isc, i is transformed into by ClarkαAnd iβ, i is determined by following formulaαWith
iβValue：
Two-phase static coordinate is converted to by two cordic phase rotator i by following formulasdAnd isq：
Further, in the step S3, the steady-state value of reactive current is extracted according to sef-adapting filterIt is described adaptive
Wave filter is answered to be used as input, i using constantsqAs expectation, i is extractedsqDC component, that is, extract reactive current steady-state value
Further, in the step S3, by isqWithMake the undulate quantity that the difference after difference reflects motor low-frequency oscillation,
This difference is controlled by PI, is then used for adjusting the modulation depth M under corresponding modulator approach；Determined finally by following formula
Modulation depth M after the adjustment of power oscillation damping method*Value：
Further, in the step S4, when being compensated to the non-linear factor of inverter, the non-linear factor bag
Include dead time, pressure drop, switch time；The compensation is the compensation based on pulse, i.e., compensates in time non-thread by inverter
Error caused by sexual factor, low-pass filtering is carried out by three-phase current, by the judgement to current polarity, is determined non-thread to inverter
The compensation time of sexual factor, it is added in control algolithm and carries out real-Time Compensation.
Further, in the step S4, the compensation time t of each phase of motor is determined especially by following formula：
Wherein, tdFor dead time；vdFor IGBT pressure drops；vfFor diode drop；tonAnd toffFor IGBT switch times；T
For carrier cycle；I is stator phase currents, and value when i corresponds to each phase is respectively isa、isbAnd isc；UdcFor the electricity of dc-battery
Pressure.
Compared with prior art, the beneficial effects of the invention are as follows：
(1) this method can preferably suppress asynchronous machine low-frequency oscillation, allow electric current, rotating speed and torque all relatively to stablize；
(2) this method can suppress influence of the inverter non-linear factor to low-frequency oscillation, and can be eliminated after compensating and have these
The distortion of the signals such as electric current caused by factor；
(3) this method can be directed to more modulation method, such as the pulsewidth tune such as SVPWM, SPWM, SPWM injection triple-frequency harmonics
System, application surface is extensive, has filled up blank of the existing low-frequency oscillation suppression method just for SVPWM modulation strategies.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, attached drawing forms the part of the application, but is only to embody inventive concept with diagram
Some inventions non-limiting examples, rather than for making any restrictions.
Fig. 1 is the flow chart of method described in the specific embodiment of the invention.
Fig. 2 is the asynchronous machine low-frequency oscillation suppression side that the present invention is compensated based on current closed-loop and inverter non-linear factor
Method schematic diagram.
Fig. 3 (a) is that asynchronous machine dead-beat in 20Hz suppresses and no-ningerse transformer non-linear factor compensates.
Fig. 3 (b) is the waveform time domain that asynchronous machine has vibration to suppress in 20Hz and has inverter non-linear factor to compensate
Figure.
Fig. 3 (c) is the waveform time domain that asynchronous machine has that vibration suppresses but no-ningerse transformer non-linear factor is compensated in 20Hz
Figure.
Fig. 4 (a) is the waveform frequency domain that asynchronous machine has vibration to suppress in 20Hz and has inverter non-linear factor to compensate
Figure.
Fig. 4 (b) is the waveform frequency domain that asynchronous machine has that vibration suppresses but no-ningerse transformer non-linear factor is compensated in 20Hz
Figure.
Fig. 5 is that asynchronous machine has vibration to suppress and has the compensation of inverter non-linear factor in 20Hz-27Hz boosting velocity procedures
Waveform time domain figure.
Embodiment
With reference to specification drawings and specific embodiments, the invention will be further described, for verification method at the same time
Feasibility and accuracy, embodiment are realized in emulation.
The asynchronous machine low-frequency oscillation compensated as shown in Figure 1 for the present invention based on current closed-loop and inverter non-linear factor
Suppressing method flow chart is emulated, Fig. 2 is schematic diagram, and referring to Figures 1 and 2, embodiment of the invention comprises the following steps：
Battery is built in Simulink first and is reverse into three-phase electric drive motor model, drives the control strategy of inverter bridge
For constant voltage and frequency ratio, for SPWM, (exemplified by this sentences SPWM, SVPWM, SPWM inject the pulse duration modulation methods such as triple-frequency harmonics to modulation system
Same method can be used), and dead time t is added in control methodd, IGBT pressure drops vd, diode drop vf, switch when
Between tonAnd toffDeng non-linear factor, emulation is allowed to be more nearly reality；
Motor stator frequency f is determined by operating mode, stator line voltage amplitude V is calculated according to the relation curve of constant voltage and frequency ratio；
A kind of asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, including step：
Step S1, according to actual condition primary Calculation under constant voltage constant frequency control strategy (V/f) electric machine frequency f and stator line
Voltage V, calculates the value of modulation depth M, i.e., according to modulation depth M and stator line by the relation of modulation depth M and stator line voltage V
The relation curve of voltage V calculates the value of modulation depth M, and the relational expression of different modulation is different, only lists SPWM herein
Modulation system, the modulation system such as SVPWM is similar therewith, and simply linear modulationra is different；
The value of the modulation depth M of SPWM is determined by formula (1)：
Wherein 0.866 be SPWM linear modulationra, UdcFor the voltage of DC power supply before inversion.
Step S2, gathers the three-phase current i under motor operation operating modesa、isbAnd isc, i is transformed into by ClarkαAnd iβ；It is logical
Cross formula (2) and determine iαAnd iβValue：
Two-phase static coordinate is converted to by two cordic phase rotator i by formula (3)sdAnd isq：
Step S3, the steady-state value of reactive current is extracted according to sef-adapting filterThe sef-adapting filter is with constant
As input, isqAs expectation, i is extractedsqDC component, that is, extract reactive current steady-state valueBy isqWithIt is poor to make,
This difference reflects the undulate quantity of motor low-frequency oscillation, this difference is controlled by PI, then is used for adjusting accordingly adjusting
Modulation depth M under method processed；The modulation depth M after the adjustment of power oscillation damping method is determined finally by formula (4)*Value：
Step S4, when being compensated to the non-linear factor of inverter, the non-linear factor includes dead time, pressure
Drop, switch time；The compensation is the compensation based on pulse, i.e., compensates in time as caused by inverter non-linear factor by mistake
Difference, low-pass filtering is carried out by three-phase current, by the judgement to current polarity, when determining the compensation to inverter non-linear factor
Between, it is added in control algolithm and carries out real-Time Compensation；The compensation time t of each phase of motor is determined especially by formula (5)：
Wherein, tdFor dead time；vdFor IGBT pressure drops；vfFor diode drop；tonAnd toffFor IGBT switch times；T
For carrier cycle；I is stator phase currents, and value when corresponding to each phase is respectively isa、isbAnd isc；UdcFor the voltage of dc-battery；
By taking A phase currents as an example, compensation time t is determined by formula (6)：
By taking B phase currents as an example, compensation time t is determined by formula (7)：
By taking C phase currents as an example, compensation time t is determined by formula (8)：
Step S5, compensation time t is added in control algolithm, and the width for changing control signal carries out real-Time Compensation, mends
During repaying, analysis stator current, rotor speed, the undulate quantity of torque and spectrogram.
In order to verify the correctness of the method for the present invention and accuracy, emulated on a certain step motor.Fig. 3 (a) is
Time-domain diagram, motor and related inverter when certain asynchronous machine dead-beat under 20HZ suppresses and no-ningerse transformer non-linear factor compensates
Parameter refer to table 1.From Fig. 3 (a), low-frequency oscillation occurs under the operating mode for motor, stator three-phase current undulate quantity it is big and
Generation Severe distortion, rotating speed and torque ripple are very big, this will have hardware very big infringement.
Table 1 is asynchronous machine and inverter relevant parameter
| Rated power | 4KW | Mutual inductance | 0.1722H |
| Rated voltage | 400V | Direct current power source voltage | 689V |
| Rated frequency | 50Hz | Carrier frequency | 4950Hz |
| Number of poles | 2 | Dead time | 5μs |
| Stator resistance value | 1.405Ω | Switch time | 0.3μs |
| Stator leakage inductance | 0.005839H | IGBT pressure drops | 2V |
| Rotor resistance value | 1.395Ω | Diode drop | 3V |
| Rotor leakage inductance | 0.005839H |
Fig. 3 (b) is motor using after the suppressing method of low-frequency oscillation of the present invention and the compensation combination of inverter non-linear factor
Time-domain diagram, as can be seen from the figure motor stator electric current stablize, and current distortion rate reduce, torque and fluctuation of speed amount are significantly
Reduce, demonstrate the validity of control program of the present invention, Fig. 4 (a) is motor stator A phase currents and torque under its operating mode
Spectrogram.
Fig. 3 (c) is motor low-frequency oscillation method using the present invention, but non-linear without inverter using the present invention
Factor compensates, and as can be seen from the figure motor stator electric current is stablized, but current distortion rate is high, this is exactly non-linear by inverter
Distortion caused by factor.Torque and fluctuation of speed amount substantially reduce, but can see it is substantially more much bigger than Fig. 3 (b) undulate quantities,
Illustrate that the compensation to inverter non-linear factor is necessary, demonstrate control of the present invention to low-frequency oscillation and inverter
It is that can preferably control low-frequency oscillation and can reduce percent harmonic distortion that non-linear factor, which combines,.Fig. 4 (b) is the motor under its operating mode
Stator A phase currents and torque spectrogram, contrast spectrogram 4 (a) and Fig. 4 (b), it can be seen that compensation effect is obvious, allows by non-thread
Motor stator electric current caused by sexual factor and torque harmonic wave reduce very much, particularly electric current 100,140,220Hz and torque
120th, 240, at 360Hz, it is seen that compensation effect is fine.
Fig. 5 represent asynchronous machine from 20Hz to 26Hz during time domain beamformer, it is non-using inverter of the present invention
Linear factor compensates and motor low-frequency oscillation suppresses the method that combines, from the figure, it can be seen that motor is in boosting velocity procedure, without low
Frequency vibration is swung, and stability is preferable, and harmonic wave is also preferably suppressed, and illustrates that the method for the invention can not only fix frequency in motor
The stable state of rate plays the role of suppression, moreover it is possible to inhibitory action, wide application are played under the variable working condition of lifting speed.
To sum up, a kind of asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation of the present invention, energy
It is enough that following control effect is obtained at asynchronous machine low frequency：
1) this method can preferably suppress asynchronous machine low-frequency oscillation, allow electric current, rotating speed and torque all relatively to stablize；
2) this method can suppress influence of the inverter non-linear factor to low-frequency oscillation, and can be eliminated after compensating by these because
The distortion of the signals such as electric current caused by element；
3) this method can be directed to more modulation method, such as the pulsewidth modulation such as SVPWM, SPWM, SPWM injection triple-frequency harmonics,
Application surface is extensive.
The above embodiment of the present invention is only intended to clearly illustrate example of the present invention, and is not to the present invention
Embodiment restriction.For those of ordinary skill in the field, can also make on the basis of the above description
Other various forms of changes or variation.There is no necessity and possibility to exhaust all the enbodiments.It is all the present invention
All any modification, equivalent and improvement made within spirit and principle etc., should be included in the protection of the claims in the present invention
Within the scope of.
Claims (10)
1. a kind of asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, including step：
Step S1, according to actual condition primary Calculation under constant voltage constant frequency control strategy electric machine frequency f and stator line voltage V, by
The relation of modulation depth M and stator line voltage V calculates the value of M；
Step S2, gathers the three-phase current i under motor operation operating modesa、isbAnd isc, and carry out coordinate and be transformed into rotating coordinate system
Obtain electric current isdWith isq；
Step S3, the reactive current i under rotating coordinate system is extracted according to self-adaptive routingsqSteady-state value isq *, and with not passing through
The reactive current i of filteringsqIt is poor to make, this difference is adjusted after PI is controlled to the modulation depth M under corresponding modulator approach, calculating
Modulation depth M after adjustment*Value；
Step S4, by the motor threephase stator electric current i of collectionsa、isbAnd iscLow-pass filtering is carried out, by sentencing to current polarity
It is disconnected, determine the compensation time t to inverter non-linear factor；
Step S5, compensation time t is added in control algolithm, and the width for changing control signal carries out real-Time Compensation.
2. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 1
In：In the step S1, under constant voltage constant frequency control strategy, electric machine frequency f and the proportional relations of stator line voltage V, in inversion
It can change voltage by varying modulation depth M in the case that device direct current power source voltage is constant.
3. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 1
In：In the step S1, motor stator frequency f is determined by operating mode, stator line voltage V is calculated according to the relation curve of constant voltage and frequency ratio
Amplitude, the value of modulation depth M is calculated according to the relation curve of modulation depth M and stator line voltage V, is determined accordingly by following formula
The value of modulation system corresponding modulating depth M：
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4. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 3
In：The modulation system includes modulation system, the modulation system of SVPWM and SPWM the injection triple-frequency harmonics modulation system of SPWM.
5. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 4
In：When modulation system is the modulation system of SPWM, the value of the linear modulationra h is 0.866；When modulation system is
During the modulation system of SVPWM, the value of the linear modulationra h is 1；When modulation system injects triple-frequency harmonics modulation for SPWM
During mode, the value of the linear modulationra h is 1.
6. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 1
In：The step S2 is specifically included：
Gather motor threephase stator electric current isa、isbAnd isc, i is transformed into by ClarkαAnd iβ, i is determined by formula following formulaαAnd iβ's
Value：
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7. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 1
In：In the step S3, the steady-state value of reactive current is extracted according to sef-adapting filterThe sef-adapting filter is with constant
As input, isqAs expectation, i is extractedsqDC component, that is, extract reactive current steady-state value
8. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 1
In：In the step S3, by isqWithMake the undulate quantity that the difference after difference reflects motor low-frequency oscillation, this difference is passed through
PI is controlled, and is then used for adjusting the modulation depth M under corresponding modulator approach；Power oscillation damping side is determined finally by following formula
Modulation depth M after method adjustment*Value：
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<mi>&Delta;</mi>
<mi>M</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
9. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 1
In：In the step S4, when being compensated to the non-linear factor of inverter, the non-linear factor includes dead time, pressure
Drop, switch time；The compensation is the compensation based on pulse, i.e., compensates in time as caused by inverter non-linear factor by mistake
Difference, low-pass filtering is carried out by three-phase current, by the judgement to current polarity, when determining the compensation to inverter non-linear factor
Between, it is added in control algolithm and carries out real-Time Compensation.
10. the asynchronous machine low-frequency oscillation suppression method based on current closed-loop and compensation, its feature exist as claimed in claim 9
In：In the step S4, the compensation time t of each phase of motor is determined especially by following formula：
<mrow>
<mi>t</mi>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>d</mi>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mrow>
<mi>o</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>t</mi>
<mrow>
<mi>o</mi>
<mi>f</mi>
<mi>f</mi>
</mrow>
</msub>
<mo>+</mo>
<mn>0.5</mn>
<mo>(</mo>
<mrow>
<msub>
<mi>V</mi>
<mi>d</mi>
</msub>
<mo>+</mo>
<msub>
<mi>V</mi>
<mi>f</mi>
</msub>
</mrow>
<mo>)</mo>
<mi>T</mi>
<mo>/</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>d</mi>
<mi>c</mi>
</mrow>
</msub>
<mo>)</mo>
<mo>,</mo>
<mi>i</mi>
<mo>></mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>d</mi>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mrow>
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<mi>n</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>t</mi>
<mrow>
<mi>o</mi>
<mi>f</mi>
<mi>f</mi>
</mrow>
</msub>
<mo>+</mo>
<mn>0.5</mn>
<mo>(</mo>
<mrow>
<msub>
<mi>V</mi>
<mi>d</mi>
</msub>
<mo>+</mo>
<msub>
<mi>V</mi>
<mi>f</mi>
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</mrow>
<mo>)</mo>
<mi>T</mi>
<mo>/</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>d</mi>
<mi>c</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>i</mi>
<mo><</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein, tdFor dead time；vdFor IGBT pressure drops；vfFor diode drop；tonAnd toffFor IGBT switch times；T is load
Wave period；I is stator phase currents, and value when i corresponds to each phase is respectively isa、isbAnd isc；UdcFor the voltage of dc-battery.
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