WO1988007287A1 - Improved control method of an ac induction motor and device therefor - Google Patents
Improved control method of an ac induction motor and device therefor Download PDFInfo
- Publication number
- WO1988007287A1 WO1988007287A1 PCT/SE1988/000124 SE8800124W WO8807287A1 WO 1988007287 A1 WO1988007287 A1 WO 1988007287A1 SE 8800124 W SE8800124 W SE 8800124W WO 8807287 A1 WO8807287 A1 WO 8807287A1
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- WO
- WIPO (PCT)
- Prior art keywords
- signal
- voltage
- stator
- rotor
- motor
- Prior art date
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Classifications
-
- 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
- H02P29/00—Arrangements for regulating or controlling electric motors, appropriate for both AC and DC motors
- H02P29/50—Reduction of harmonics
Definitions
- the present invention relates to an improved method for voltage control of an AC induction motor.
- the invention also relates to an electronic circuit for performing said method.
- the invention is based on the disclosure of Swedish Patent No. 8000118-3 (equivalent to US-A-4,458,193) which is incorporated herein by reference.
- the Swedish Patent is based on an idealized motor model with linear magnetic properties and neglectable leakage inductances.
- the present invention is an improvement thereof. It eliminates the torque ripple caused by the nonlinear iron magnetization curve, especially at low speed.
- the leakage inductances have been added to the motor model with the corresponding additions to the control system. Thus, two major differences between the idealized motor model for the control system and the real motor have been eliminated.
- the present invention relates to more advanced systems, which make it possible to control the AC induction motor in all kinds of drives, also in servo drives having fast dynamic response to control signals. In the following primarily such advanced drives are considered.
- the AC induction motor has a very complicated mathematical model. In modern literature, for example the book "Control of Electric Drives” by professor Werner Leonhard (Springer Verlag, 1985), a theoretical motor model, "tailored to the needs of controlled drives", is given. The voltages and currents are described by complex two-dimensional vectors. The motor model results in one complex differential equation for the stator and one complex differential equation for the rotor, plus one complex differential equation for the torque calculation. No analytical solution of the non-linear equations exists, according to professor Leonhard.
- the mathematical treatment is different in the case of voltage control and current control of the induction motor.
- Current control is normally preferred. However, there are some problems associated with current control.
- the Swedish Patent No. 8000118-3 discloses an AC induction motor control system based on the use of a voltage control vector, composed of two orthogonal signals. This control vector is modulated with the sine and cosine of a modulating frequency before connection to the motor stator windings.
- This system is based on a simplified and linear model of the AC induction motor and is simple and fulfils almost all essential demands on such a system.
- the non-linear magnetization curve of the iron is an unwanted error source in the motor. So are the leakage inductances. They represent approximately 5 % of the total inductance. They are parasitic elements without any contribution to the torque generation. They should be made as small as possible in modern motor designs. However, since they cannot be completely eliminated, it is important to include them in the motor model and in the control system design.
- DISCLOSURE OF THE INVENTION It is an object of the present invention to provide a method of controlling an AC induction motor for controlling or compensating the feed voltage so that the magnetizing part of said voltage is sine shaped.
- Another object of this invention is to provide a method of controlling an AC induction motor for compensating for torque ripple due to a nonlinear magnetization curve of the iron.
- a further object of this invention is to disclose a control method and an electronic circuit that takes into account the leakage inductances of the stator and the rotor.
- This invention may be used together with the Swedish Patent No. 8000118-3 (US-A-4,458,193) mentioned above, and together with all similar control systems for the AC induction motor.
- Fig. 1 is a schematic diagram of a two-phase induction motor according to Fig. 3 of the above-mentioned Swedish Patent No. 8000118-3.
- Fig. 2 is a schematic diagram of the equivalent circuit of one phase in the induction motor, according to Fig. 4 of the above-mentioned Swedish Patent No. 8000118-3.
- Fig. 3 is a phasor diagram showing voltages and currents in one phase of the induction motor, according to Fig. 5 of the above-mentioned Swedish Patent No. 8000118-3.
- Fig. 4 is a block diagram according to Fig. 8 of the above-mentioned Swedish Patent No. 8000118-3.
- Fig. 5 is a typical magnetization curve for iron.
- Fig. 6 is a block diagram of an apparatus for control of an induction motor, including compensation for the nonlinear iron magnetization curve, according to the invention.
- Fig. 7 is a block diagram similar to Fig. 6 but including another compensation circuit.
- Fig. 8 is a schematic diagram of a two-phase resolver.
- Fig. 9 is a schematic diagram of a three-phase resolver.
- Fig. 10 is a block diagram similar to Fig. 6 comprising a three-phase resolver.
- Fig. 11 is a coordinate transformation scheme.
- Fig. 12 is a phasor diagram similar to Fig. 3 comprising the complete model of the induction motor.
- Fig. 13 is a schematic diagram similar to Fig. 2 of the equivalent circuit of one phase of the induction motor.
- Fig. 14 is a block diagram similar to Fig. 4 of the complete circuit.
- Fig. 15 is a schematic diagram of the magnetizing current distorted according to the invention. DETAILED DESCRIPTION OF THE THEORY AND OF THE EMBODIMENTS
- Fig. 2 is a schematic diagram of the equivalent circuit of one phase of the induction motor.
- the circuit includes only the primary components of the theoretical model.
- the broken lines represent the air-gap between stator and rotor. Components to the left of the broken lines represent the stator, and components to the right represent the rotor.
- Stator resistance is R S
- stator inductance is L 0
- rotor resistance is R R .
- Supply voltage is u S .
- Total current on the stator side is i S .
- Inductive stator current is i M and rotor current is i R .
- the magnetizing voltage V L is transformed from the stator to the rotor through the airgap.
- a counter-electromotive voltage U is induced in the rotor winding. U is proportional to rotor speed.
- the transformation ratio between the stator and rotor windings is assumed to be "1". Any real motor parameters can be converted to this transformation ratio.
- the stator and rotor leakage inductances are neglected.
- Fig. 3 is a phasor diagram showing voltages in one phase of the induction motor.
- the inductive current i M is used as a reference phasor, pointing to the right in the diagram.
- the resistive current in is 90 ahead, pointing upwards in the diagram.
- Fig. 4 is a block diagram of an electronic circuit constructed according to the phasor diagram of Fig. 3 and according to Swedish Patent No. 8000118-3.
- the total supply voltage vector u S to the motor is composed of two orthogonal components S 1 and S 2 , where S 2 is substantially a constant voltage, compensating for the resistive stator voltage drop caused by the inductive stator current and S 1 is the sum of the magnetizing voltage V L plus the resistive stator voltage drop caused by the rotor current. If any of these components (S 1 and S 2 ) are incorrect, the total supply voltage vector u S will be affected and hence all parts of the system. Thus, it is important that both components are correct.
- Both the magnetic field strength B and the rotor current i R must be modulated with undistorted sine and cosine waveforms. Both these quantities depend directly on the magnetizing voltage V L .
- the magnetizing voltage V L is of vital importance for the motor function, since it is the common supply voltage for the stator inductance as well as for the rotor circuit.
- the rotor current i R is resistive, and if V L is a sine signal, the rotor current will also be a sine signal.
- the application of a well-known electromagnetic law reveals an interesting fact about the stator magnetic field, and this is the very heart of the present invention.
- the magnetizing voltage V L is equal to the time derivative of the total magnetic flux linkage, and thus of the total magnetic field strength B.
- V L (dB / dt) x C where C is a constant
- FIG. 5 shows a typical magnetization curve for iron (the hysteresis effect has been neglected) and if the magnetic field strength B is known, the corresponding inductive current iM can be obtained. The curve is not linear, and at higher field strength, the current increases faster than the field strength.
- the magnetic field should be controlled by a voltage (V L ) although it is created by a current.
- Fig. 6 is a block diagram of a preferred embodiment of a complete circuit for voltage control of an AC induction motor, with compensation for the nonlinear magnetizing current according to the present invention.
- This block diagram is identical to that in the Swedish Patent No. 8000118-3 (US-A-4,458,193), except for the nonlinear compensation.
- Block 5 in the Swedish Patent has been replaced by the blocks 6 - 10 in Fig. 6.
- An external control voltage vector S 1 , S 2 is generated according to the phasor diagram. This is a stationary vector (not rotating). In the circuit, the vector is modulated by sine and cosine signals in four multipliers 1. The four multiplier outputs are added respectively subtracted in the adders 2. The four multipliers and the two adders together form a so called “resolver” or vector rotator. The rotating output vector is then fed to the power circuits 3, which control the motor 4.
- the modulating frequency w is calculated according to the Swedish Patent No. 8000118-3 (US-A-4,458,193), or any other suitable method.
- Block 6 is a so called "modulo-2 ⁇ " integrator, which integrates the input frequency w and delivers the output angle. At the angle (2 ⁇ ) the integration resumes from zero. Integration can be performed forward and backwards.
- Block 7 is a sine table, delivering the sine of the input angle to the multiplier 1.
- Block 8 is a cosine table.
- Block 9 is a sine table, modified according to the desired waveform of the magnetizing current.
- Block 10 is a cosine table, modified according to the desired waveform of the magnetizing current.
- Such a "modulo-2 ⁇ " integrator can easily be made as a counter in digital technique.
- the counter counts incoming pulses up to its upper limit, which corresponds to the angle 2 ⁇ , and the next pulse will overflow the counter, which now shows zero.
- the output signal from the counter will be an angle which is input to the tables 7 - 10.
- the modulating frequency w is obtained by addition of two different signals, one proportional to the motor speed (or counter emf) and one proportional to the signal S 1 . If an incremental position encoder is connected to the motor shaft, the pulse train from this encoder has a frequency which is proportional to the motor speed. This pulse train can be used as input signal to the "modulo-2 ⁇ " counter in block 6.
- signal S 1 is convenient to make also signal S 1 as a pulse train, which can be added to the pulse train from the position encoder and integrated in the counter. It is observed that this principle is very easy to implement in a microprocessor-controlled system. Also, if the control system is integrated into an "application specific integrated circuit" ASIC, it is preferred to use this "digital" approach.
- the voltage S 2 can be about 20V, while the voltage S 1 can vary between +380V and -380V.
- S 1 When the motor is standing still, S 1 will be zero and the component S 2 will dominate, but at medium speed and maximum speed, S 1 dominates.
- both components are important, each one in its specific speed area (S 1 at high and medium speeds and S 2 at low speeds).
- the improvement according to the present invention will be most important at low speeds and zero speed.
- the modulation with sine and cosine waveforms does not mean that the waveforms to the motor always are sine shaped.
- the control signal S 1 comes from the outer control loop, and may change very quickly. This has direct influence on the motor voltages.
- Fig. 7 shows how the invention can be adapted to different magnetization fields B 0 .
- the blocks 9 and 10 of Fig. 6 are replaced by two blocks 11 in Fig. 7.
- Block 11 comprises a sine or cosine table 12, the input signal of which being the control signal ⁇ .
- the output of block 12 is fed to a multiplier 13 for multiplication with a constant B 0 .
- the output from block 13 is fed to another table comprising the nonlinear magnetization curve of the iron and the output from block 14 will be the magnetizing current i M .
- equations 1 and 2 are the same as given in the above-mentioned book "Control of Electric Drives” by professor Werner Leonhard, chapter 10, equations 10.38 and 10.39. These equations are the starting point for the following analysis. The calculations are based on stator coordinates, rotor coordinates and field coordinates. The relationship between these coordinates appears from Fig. 11.
- Equation 3 defines the magnetizing current.
- the currents i M , i R and i S are converted to field coordinates and inserted in equations 1 and 2 resulting in equations 8 and 9, where the stator current is eliminated.
- These equations are differentiated resulting in equations 10 and 11, and converted to field coordinates in equation 13 and 14.
- Equations 13 and 14 are exact and are the basis for the following synthesis.
- the motor is controlled by the voltage vector S, which is field oriented.
- the control vector S is defined in equation 12 and is calculated mathematically exact as shown below. The only condition is that the rotor flux should be constant. In practice even this condition is not absolutely necessary. It is well-known that unwanted crosscoupling is eliminated by having the rotor flux constant.
- Equations 15 - 18 define the magnetic flux. Equations 19 and 20 are obtained from equation 18. Equation 20 is true only if the rotor flux is constant. Equations 15 - 20 are inserted in equations 13 and 14 resulting in equations 21 and 22. Equation 23 is obtained from equation 22 and the Laplace operator s is introduced in equation 24. The stator equation 25 is obtained from equations 21 - 24. The present control system is based on stator equation 25. Equation 26 defines the rotor flux as reference and equation 27 defines the control vector S. The stator equation 25 is split into its real and imaginary parts by means of equations 26 and 27 resulting in equations 28 and 29. The rotor current i Rf is defined in equation 30 according to equation 23. Equations 31 and 32 are the same as equations 28 and 29 but inserting the rotor current. Equation 33 calculates the field angle frequency from equation 29.
- Equations 31 and 32 are shown graphically in Fig. 12.
- the influence of the added leakage inductances are shown in the extended block diagram of an apparatus for control of an induction motor shown in Fig. 14 which is based on equations 28 and 33.
- This block diagram is essentially the same as shown in Fig. 4, but the scaling factors for frequency calculation have been extended to include the leakage inductances.
- a new term has been added to the control voltage S 2 as shown in Fig. 14.
- the stator frequency w is multiplied in block 21 with the difference between the stator frequency and rotor speed from block 22.
- the result is multiplied in block 23 with a constant and subtracted in block 24 from the original S 2 signal.
- Fig. 8 shows a resolver symbol for a two-phase resolver according to Fig. 6.
- Fig. 9 shows a resolver symbol for a three-phase resolver including the angular relationship between the output signals.
- the present invention describes how the control system takes care of two different unwanted phenomena in the AC induction motor, namely the nonlinear iron magnetization curve and the leakage inductances.
- the two phenomena and their influences on the control system have been described separately, but of course it should be possible to include them in a common control system.
- Compensation for the nonlinear magnetization current was very easy to achieve, because the total signal S 2 was proportional to the nonlinear magnetizing current.
- the leakage inductances are added to the motor model and to the control system, there will be a new component in S 2 , proportional to the rotor current. Then the original S 2 component has to be modulated by a distorted sine wave and the new S 2 component has to be modulated by a normal sine wave.
- this is no problem in a modern digital system, but in practice one may prefer to simplify the system, depending on actual requirements and actual motor data.
- motors are designed with a quasi-continuous sinusoidal distribution of the stator windings, in order to obtain a spatial sinusoidal distribution of the magneto-motive force in the airgap, cf for example the book "Control of Electric Drives" page 146.
- the sinusoidal distribution in time is enough to guarantee a constant torque generation, without ripple.
- the stator magnetic field is described as the sum of two individual, orthogonal, pulsating magnetic fields, superimposed on each other. Possibly, the spatial sinusoidal distribution of the stator winding is unnecessary. Then a new motor design, with only two phases, and with each pole encircled by the whole phase winding, would permit a more efficient use of the material, both copper and iron.
- the AC induction motor is the most widely used motor today.
- the industrial standard motor is an excellent motor, and it is a great step forward that this motor now can be used with variable speed.
- the standard motor has to be improved in order to reduce the different sources of torque ripple, and only then the full value of this invention can be realized.
- the AC induction motor is originally designed for operation on the sine shaped 50 Hz or 60 Hz line voltage. Because of the nonlinear iron magnetization curve, the motor current is a slightly distorted sine shaped current. However, the motor torque is constant without ripple. Current control would generate a torque ripple.
- a further advantage of voltage control is that it automatically compensates for certain errors. As long as the magnetizing voltage V L is correct, the magnetic field B will be correct independent of errors like air-gap variations etc.
- the AC induction motor is originally and inherently a voltage control motor, and should be used as such.
- the control system according to the invention is useful not only for speed control, but also for torque control and position control, depending on the requirements.
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- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Control Of Ac Motors In General (AREA)
Abstract
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Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP88502596A JPH02502510A (en) | 1987-03-11 | 1988-03-11 | Improved control method for AC induction motor and device therefor |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
SE8701008-8 | 1987-03-11 | ||
SE8701008A SE8701008L (en) | 1987-03-11 | 1987-03-11 | IMPROVED CONTROL PROCEDURE FOR AN AC AC MOTOR AND DEVICE THEREOF |
Publications (1)
Publication Number | Publication Date |
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WO1988007287A1 true WO1988007287A1 (en) | 1988-09-22 |
Family
ID=20367830
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/SE1988/000124 WO1988007287A1 (en) | 1987-03-11 | 1988-03-11 | Improved control method of an ac induction motor and device therefor |
Country Status (5)
Country | Link |
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EP (1) | EP0349568A1 (en) |
JP (1) | JPH02502510A (en) |
AU (1) | AU1487788A (en) |
SE (1) | SE8701008L (en) |
WO (1) | WO1988007287A1 (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO1991012656A1 (en) * | 1990-02-12 | 1991-08-22 | Joensson Ragnar | Method and apparatus for controlling an ac induction motor by indirect measurement of the air-gap voltage |
US7592785B2 (en) | 2006-05-23 | 2009-09-22 | Denso Corporation | Output control apparatus and method for field winding type dynamo-electric machine |
Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
SE420141B (en) * | 1980-01-08 | 1981-09-14 | Ragnar Georg Jonsson | SET AND DEVICE FOR CONTROL OF AN AC POWER ASYNCHRONOUS MOTOR |
US4707651A (en) * | 1986-07-22 | 1987-11-17 | Westinghouse Electric Corp. | Voltage-controlled field-oriented induction motor control system |
-
1987
- 1987-03-11 SE SE8701008A patent/SE8701008L/en not_active Application Discontinuation
-
1988
- 1988-03-11 JP JP88502596A patent/JPH02502510A/en active Pending
- 1988-03-11 WO PCT/SE1988/000124 patent/WO1988007287A1/en not_active Application Discontinuation
- 1988-03-11 AU AU14877/88A patent/AU1487788A/en not_active Abandoned
- 1988-03-11 EP EP88902606A patent/EP0349568A1/en not_active Withdrawn
Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
SE420141B (en) * | 1980-01-08 | 1981-09-14 | Ragnar Georg Jonsson | SET AND DEVICE FOR CONTROL OF AN AC POWER ASYNCHRONOUS MOTOR |
US4707651A (en) * | 1986-07-22 | 1987-11-17 | Westinghouse Electric Corp. | Voltage-controlled field-oriented induction motor control system |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO1991012656A1 (en) * | 1990-02-12 | 1991-08-22 | Joensson Ragnar | Method and apparatus for controlling an ac induction motor by indirect measurement of the air-gap voltage |
US5294876A (en) * | 1990-02-12 | 1994-03-15 | Joensson Ragnar | Method and apparatus for controlling an AC induction motor by indirect measurement of the air-gap voltage |
US7592785B2 (en) | 2006-05-23 | 2009-09-22 | Denso Corporation | Output control apparatus and method for field winding type dynamo-electric machine |
Also Published As
Publication number | Publication date |
---|---|
SE8701008L (en) | 1988-09-12 |
JPH02502510A (en) | 1990-08-09 |
EP0349568A1 (en) | 1990-01-10 |
AU1487788A (en) | 1988-10-10 |
SE8701008D0 (en) | 1987-03-11 |
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