CN109546904B - Rotor position detection method of double three-phase permanent magnet synchronous motor - Google Patents

Rotor position detection method of double three-phase permanent magnet synchronous motor Download PDF

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CN109546904B
CN109546904B CN201811379903.XA CN201811379903A CN109546904B CN 109546904 B CN109546904 B CN 109546904B CN 201811379903 A CN201811379903 A CN 201811379903A CN 109546904 B CN109546904 B CN 109546904B
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double
permanent magnet
synchronous motor
magnet synchronous
rotor
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CN109546904A (en
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高强
朱昊越
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Shanghai Jiaotong University
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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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/34—Modelling or simulation for control purposes
    • 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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • 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
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

Abstract

The invention provides a rotor position detection method of a double three-phase permanent magnet synchronous motor, which comprises the following steps: constructing a mathematical model of the double three-phase permanent magnet synchronous motor; carrying out spatial decoupling transformation on a mathematical model of the double three-phase permanent magnet synchronous motor to obtain mathematical models under X and Y planes; simplifying mathematical models under X and Y planes to obtain a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor; in a pulse width modulation period, simultaneously establishing a voltage-current transient relation equation at any two control moments to calculate the cosine and sine of the electrical angle of the double-frequency rotor; and estimating the rotor position of the double three-phase permanent magnet synchronous motor according to the cosine and sine of the double-frequency rotor electrical angle. In the process, rotor position (or speed) measuring hardware (such as an encoder) is omitted, interference caused by various hardware during measurement of a position (or speed) sensor can be eliminated, the reliability of the double three-phase permanent magnet synchronous motor is improved, and the system cost is reduced.

Description

Rotor position detection method of double three-phase permanent magnet synchronous motor
Technical Field
The invention relates to the technical field of motors, in particular to a rotor position detection method of a double three-phase permanent magnet synchronous motor.
Background
The permanent magnet synchronous motor has the advantages of no need of exciting current and stator current, and low copper loss and rotor loss; the double three-phase permanent magnet synchronous motor has higher fault-tolerant capability, larger torque density and smaller torque pulsation, and is convenient for realizing high-power output.
The traditional speed sensorless algorithm adopted by the double three-phase permanent magnet synchronous motor directly or indirectly estimates the rotor electrical angle by utilizing the rotor electrical angle information contained in the back electromotive force. Since the back electromotive force is directly proportional to the rotation speed, when the motor is running at low speed, the signal-to-noise ratio of the useful signal is very low, so that the sampling is usually difficult and the error of the estimated electrical angle is large.
Through retrieval, document Yanhui He, et al, speed and position sensor control for dual-phase PMSM drivers [ C ]. IEEE Applied Power electronics and exposure 24th Annual Conference (APEC),2009 provides a position estimation algorithm based on the counter electromotive force third harmonic, two sets of windings at different neutral points are spatially different from each other by 30 degrees, in a double d-q change, the counter electromotive force third harmonic in two-phase stationary coordinate systems contains rotor electrical angle information and is orthogonal, and the rotor electrical angle can be estimated. Since the back emf is directly proportional to the rotational speed, the signal-to-noise ratio of the useful signal will be low and it is often difficult to sample at low motor speeds. Documents a.h. almarhoon, y.ren and z.q.zhu.sensory switching-table-based direct control for dual-phase PMSM drivers [ C ].17th international conference on Electrical Machines and Systems (ICEMS),2014 use the Popov hyperstability theory as a basis to convert information containing rotor speed to a state matrix by vector space transformation and Park transformation. However, under the condition of low speed of the motor, the Id and the Iq are very small, the sampling signal-to-noise ratio is very low, and the accuracy and the stability of the self-adaptive model are seriously influenced. Document z.zhu, a.alert on and p.xu.improved Rotor Position Estimation by rotation Carrier signalling extraction Zero-Sequence Carrier Voltage for Dual Three-phase PMSM [ J ]. IEEE Transactions on Industrial Electronics,2016, vol. pp, No.99, pp.1-1 injects high-frequency Voltage signals with certain phase difference on two sets of Three-phase windings, and then performs Position detection by detecting Zero-Sequence high-frequency Voltage between two central points of the motor. The method can realize low-speed and zero-speed operation of the double three-phase motor, but needs to inject high-frequency signals.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a rotor position detection method of a double three-phase permanent magnet synchronous motor.
The invention provides a rotor position detection method of a double three-phase permanent magnet synchronous motor, which comprises the following steps:
constructing a mathematical model of the double three-phase permanent magnet synchronous motor;
carrying out spatial decoupling transformation on the mathematical model of the double three-phase permanent magnet synchronous motor to obtain mathematical models under X and Y planes;
simplifying the mathematical model under the X and Y planes to obtain a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor;
in a pulse width modulation period, simultaneously establishing a voltage-current transient relation equation at any two control moments to obtain cosine and sine of a double-frequency rotor electric angle;
and estimating the rotor position of the double three-phase permanent magnet synchronous motor according to the cosine and sine of the electrical angle of the double frequency rotor.
Optionally, the constructing a mathematical model of the double three-phase permanent magnet synchronous motor includes:
under a six-phase static coordinate system, defining a mathematical model of the double three-phase permanent magnet synchronous motor as follows:
Figure BDA0001871621060000021
Figure BDA0001871621060000022
wherein u issAs a stator voltage vector matrix, RsIs a stator resistance matrix, IsIs a stator current vector matrix, LsIs a matrix of stator inductances which are,
Figure BDA0001871621060000023
is the rotor permanent magnet flux linkage, t is time, and theta is the rotor angle.
Optionally, performing spatial decoupling transformation on the mathematical model of the dual three-phase permanent magnet synchronous motor to obtain mathematical models under X and Y planes, including:
obtaining an inductance matrix in the X and Y planes
Figure BDA0001871621060000031
And inverse matrix
Figure BDA0001871621060000032
Figure BDA0001871621060000033
Figure BDA0001871621060000034
Wherein:
Figure BDA0001871621060000036
Figure BDA0001871621060000037
wherein: theta is the rotor angle, La0For exciting the amplitude of the DC component of the inductor, La1Is the amplitude of the self-leakage inductance direct current quantity, La2For mutual leakage inductance of the amplitude of the direct currentg0For self-inductive sine magnitude, Lg1The amplitude of the sine quantity of the mutual inductance between the windings is 30 degrees and 150 degreesg2The amplitude of the mutual inductance sine quantity between the windings is 120 degrees and 240 degrees; l is1And L2Is the intermediate variable of the conversion;
according to the inductance matrix under the X and Y planes
Figure BDA0001871621060000038
And inverse matrix
Figure BDA0001871621060000039
Carrying out spatial decoupling transformation on the mathematical model of the double three-phase permanent magnet synchronous motor to obtain the following mathematical models under X and Y planes:
Figure BDA00018716210600000310
wherein u isxyIs an xy plane voltage vector, RsIs a stator resistance matrix, IxyThe stator current matrix, t is time.
Optionally, the obtaining of the voltage-current transient relation equation of the dual three-phase permanent magnet synchronous motor by simplifying the mathematical model under the X and Y planes includes:
neglecting in mathematical models in said X and Y plane
Figure BDA00018716210600000311
And obtaining a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor through transformation as follows:
Figure BDA00018716210600000312
wherein: i isxIs the x-axis current component, IyIs a y-axis current component, uyIs a y-axis current component, uxIs the x-axis current component, uαis an α axis voltage component, uβis an β axis voltage component.
Optionally, in a pulse width modulation period, simultaneously establishing a voltage-current transient relation equation at any two control times to obtain a cosine and a sine of the double frequency rotor electrical angle, including:
keeping the rotor angle theta unchanged in a pulse width modulation period, and controlling the time t by any two1And t2Calculating cosine cos2 theta and sine sin2 theta of the double-frequency rotor electrical angle;
the cosine of the electrical angle of the double frequency rotor cos2 θ is as follows:
Figure BDA0001871621060000041
the sine of the second harmonic rotor electrical angle, sin2 θ, is as follows:
Figure BDA0001871621060000042
wherein: u. ofx1Is the x-axis component, u, of the first voltage vectory1Is the y-axis component of the first voltage vector, ux2Is the x-axis component, u, of the second voltage vectory2Is the y-axis component of the second voltage vector, Iy1Is the y-axis component of the first current vector, Iy2The y-axis component of the second current vector. Optionally, estimating a rotor position of the double three-phase permanent magnet synchronous motor according to the cosine and the sine of the electrical angle of the double-frequency rotor includes:
cosine and sine of the double-frequency rotor electrical angle are used as input of a two-phase orthogonal phase-locked loop to obtain a double-frequency rotor electrical angle 2 theta;
setting the phase-locked loop error to sin (2 theta-2 theta)*) Obtaining an estimated angle of the rotor position of the double three-phase permanent magnet synchronous motor; wherein the phase-locked loop closed-loop transfer function G(s) is as follows:
Figure BDA0001871621060000043
wherein: s is Laplace operator, kpIs a proportionality coefficient, kiAs an integral coefficient, θ*The estimated angle of the rotor position of the double three-phase permanent magnet synchronous motor is shown, and theta is the rotor angle.
Compared with the prior art, the invention has the following beneficial effects:
the rotor position detection method of the double three-phase permanent magnet synchronous motor provided by the invention comprises the steps of constructing a mathematical model of the double three-phase permanent magnet synchronous motor; carrying out spatial decoupling transformation on the mathematical model of the double three-phase permanent magnet synchronous motor to obtain mathematical models under X and Y planes; simplifying the mathematical model under the X and Y planes to obtain a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor; in a pulse width modulation period, simultaneously establishing a voltage-current transient relation equation at any two control moments to obtain cosine and sine of a double-frequency rotor electric angle; and estimating the rotor position of the double three-phase permanent magnet synchronous motor according to the cosine and sine of the electrical angle of the double frequency rotor. Therefore, the non-speed sensor is adopted to estimate the position of the rotor, the position (or speed) measuring hardware (such as an encoder) of the rotor is omitted in the process, the interference caused by various hardware during the measurement of the position (or speed) sensor can be eliminated, the reliability of the double three-phase permanent magnet synchronous motor is improved, the system cost is reduced, and meanwhile, the connecting wires can be reduced, so that the system is miniaturized and lightened.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
fig. 1 is a flowchart of a rotor position detection method of a double three-phase permanent magnet synchronous motor according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a two-phase quadrature phase-locked loop;
FIG. 3(a) is a diagram illustrating the simulation result of the estimation error when the motor speed is stabilized at 10 rpm;
FIG. 3(b) is a diagram illustrating simulation results of the estimated electrical angle when the motor speed is stabilized at 10 rpm;
FIG. 3(c) is a diagram showing simulation results of sine 2 θ and cosine cos2 θ of the double frequency rotor electrical angle when the motor speed is stabilized at 10 rpm;
FIG. 4(a) is a diagram illustrating the simulation result of the estimation error when the motor speed is stabilized at 300 rpm;
FIG. 4(b) is a diagram illustrating simulation results of the estimated electrical angle when the motor speed is stabilized at 300 rpm;
FIG. 4(c) is a diagram showing simulation results of sine 2 θ and cosine cos2 θ of the double frequency rotor electrical angle when the motor speed is stabilized at 300 rpm;
FIG. 5(a) is a diagram illustrating the simulation result of the estimated error when the motor speed is stabilized at 1000 rpm;
FIG. 5(b) is a diagram illustrating simulation results of the estimated electrical angle when the motor speed is stabilized at 1000 rpm;
FIG. 5(c) is a diagram showing simulation results of sine 2 θ and cosine cos2 θ of the double frequency rotor electrical angle when the motor speed is stabilized at 1000 rpm;
FIG. 6(a) is a diagram illustrating simulation results of load estimation electrical angles when the motor rotation speed dynamically changes;
FIG. 6(b) is a diagram illustrating simulation results of load estimation errors when the motor rotation speed dynamically changes;
FIG. 6(c) is a diagram showing simulation results of the load A-phase current when the motor rotation speed is dynamically changed;
FIG. 6(d) is a diagram illustrating simulation results of motor load when the motor speed is dynamically changed;
FIG. 7(a) is a diagram illustrating a simulation result of the rotational speed estimation electrical angle when the motor load torque is subjected to a step change;
FIG. 7(b) is a diagram illustrating simulation results of the error of the rotational speed estimation when the motor load torque is changed in steps;
fig. 7(c) is a diagram showing a simulation result of the rotation speed of the load motor when the load torque of the motor is changed in a step manner.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Fig. 1 is a flowchart of a method for detecting a rotor position of a dual three-phase permanent magnet synchronous motor according to an embodiment of the present invention, and as shown in fig. 1, the method in this embodiment may include:
s101, constructing a mathematical model of the double three-phase permanent magnet synchronous motor.
In this embodiment, under a six-phase stationary coordinate system, a mathematical model of a dual three-phase permanent magnet synchronous motor is defined as:
Figure BDA0001871621060000061
Figure BDA0001871621060000062
wherein: wherein u issAs a stator voltage vector matrix, RsIs a stator resistance matrix, IsIs a stator current vector matrix, LsIs a matrix of stator inductances which are,
Figure BDA0001871621060000063
is the rotor permanent magnet flux linkage, t is time, and theta is the rotor angle.
S102, performing spatial decoupling transformation on the mathematical model of the double three-phase permanent magnet synchronous motor to obtain the mathematical model under the X and Y planes.
In this embodiment, first, the inductance matrix under the X and Y planes is obtained
Figure BDA0001871621060000064
And inverse matrix
Figure BDA0001871621060000065
Figure BDA0001871621060000066
Figure BDA0001871621060000071
Wherein:
Figure BDA0001871621060000072
Figure BDA0001871621060000073
wherein: theta is the rotor angle, La0For exciting the amplitude of the DC component of the inductor, La1Is the amplitude of the self-leakage inductance direct current quantity, La2For mutual leakage inductance of the amplitude of the direct currentg0For self-inductive sine magnitude, Lg1The amplitude of the sine quantity of the mutual inductance between the windings is 30 degrees and 150 degreesg2The amplitude of the mutual inductance sine quantity between the windings is 120 degrees and 240 degrees; l is1And L2Is the intermediate variable of the conversion;
according to the inductance matrix in the X and Y plane
Figure BDA0001871621060000074
And inverse matrix
Figure BDA0001871621060000075
Carrying out spatial decoupling transformation on a mathematical model of the double three-phase permanent magnet synchronous motor to obtain the following mathematical model under X and Y planes:
Figure BDA0001871621060000076
wherein u isxyIs an xy plane voltage vector, RsIs a stator resistance matrix, IxyThe stator current matrix, t is time.
S103, simplifying mathematical models under the X and Y planes to obtain a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor.
In this exampleDue to RsIs small and therefore can be neglected in mathematical models in the X and Y planes
Figure BDA0001871621060000077
And then obtaining a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor through conversion:
Figure BDA0001871621060000078
wherein: i isxIs the x-axis current component, IyIs a y-axis current component, uyIs a y-axis current component, uxIs the x-axis current component, uαis an α axis voltage component, uβis an β axis voltage component.
And S104, in a pulse width modulation period, simultaneously establishing a voltage-current transient relation equation at any two control moments to obtain the cosine and sine of the double-frequency rotor electrical angle.
In this embodiment, the rotor position, i.e., the rotor electrical angle θ, can be approximately considered to be constant within one Pulse Width Modulation (PWM) period. At any two control times t1And t2Calculating cosine cos2 theta and sine sin2 theta of the double-frequency rotor electrical angle;
the cosine of the electrical angle of the double frequency rotor cos2 θ is as follows:
Figure BDA0001871621060000081
the sine of the second harmonic rotor electrical angle, sin2 θ, is as follows:
Figure BDA0001871621060000082
wherein: u. ofx1Is the x-axis component, u, of the first voltage vectory1Is the y-axis component of the first voltage vector, ux2Is the x-axis component, u, of the second voltage vectory2Is the y-axis component of the second voltage vector, Iy1Is the y-axis component of the first current vector, Iy2The y-axis component of the second current vector.
And S105, estimating the rotor position of the double three-phase permanent magnet synchronous motor according to the cosine and sine of the double-frequency rotor electrical angle.
FIG. 2 is a schematic diagram of a two-phase quadrature phase-locked loop; as shown in fig. 2, the cosine and sine of the double frequency rotor electrical angle can be used as the input of the two-phase orthogonal phase-locked loop to obtain the double frequency rotor electrical angle 2 θ. The phase-locked loop error is then set to sin (2 theta-2 theta)*) Obtaining an estimated angle of the rotor position of the double three-phase permanent magnet synchronous motor; wherein the phase-locked loop closed-loop transfer function G(s) is as follows:
Figure BDA0001871621060000083
wherein: s is Laplace operator, kpIs a proportionality coefficient, kiAs an integral coefficient, θ*The estimated angle of the rotor position of the double three-phase permanent magnet synchronous motor is shown, and theta is the rotor angle.
In the embodiment, the phase-locked loop closed-loop transfer function G(s) is similar to a low-pass filter, so that after the phase-locked loop parameters are reasonably configured, the phase-locked loop can effectively filter high-frequency harmonics existing in a cosine sine of an actually measured double-frequency rotor electric angle in an experiment, and the estimated rotor electric angle can accurately and effectively track the actually measured rotor electric angle.
It should be noted that, in the present embodiment, the dual three-phase SMPMSM position sensorless algorithm that utilizes the saturation saliency under the X and Y subspaces. The method and the device can accurately estimate the position of the rotor in the low-speed or even zero-speed running state of the motor, and are also feasible in the high-speed running state of the motor.
In addition, the method of exciting the saliency effect in the present embodiment is not limited to SVPWM, and any other PWM or non-PWM current control method may be used. After the cosine and sine of the double-frequency rotor electrical angle are obtained, the position and the rotation speed and the rotor position can be estimated by using the phase-locked loop, and other filtering measures such as an observer and the like can be used for realizing the same function. The method in this embodiment is also applicable to a double three-phase induction motor, and by slight modification, can also be applied to other multi-phase (the number of phases is greater than 3, but not 6) alternating current induction motors or permanent magnet synchronous motors.
The invention is proved to be feasible through simulation verification. The motor and control system parameters in the simulation are shown in table 1.
TABLE 1 simulation System parameters
Figure BDA0001871621060000091
The simulation verification is divided into three parts: and (4) simulating results under the conditions of no-load rotating speed steady state, no-load rotating speed dynamic state and variable load rotating speed steady state, so as to verify the feasibility of the position estimation principle.
(1) Simulation result under no-load rotating speed steady state
Referring to fig. 3(a), fig. 4(a), and fig. 5(a), the simulation results of controlling the motor rotation speed to be stable at 10rpm, 300rpm, and 1000rpm under the no-load condition can be known: when the rotating speed of the motor is stabilized at 10rpm, 300rpm and 1000rpm, the error range can be stabilized within 5 degrees, and the estimation error of the rotor is small.
(2) Simulation result under rotation speed dynamic state
The rotation speed of the motor is controlled to change in steps under the condition of 5N × m load, the rotation speed change mode is 0 → 50rpm → 100rpm → 50rpm → 0, and the simulation result waveform is shown in fig. 6 (a). As can be seen from fig. 6(a), in the whole process of dynamic variation of the motor rotation speed, the estimation error is large at the moment of sudden change of the rotation speed, the error is within 10 °, and after the rotation speed is stabilized, the estimation error is within 2 °.
(3) Simulation result under variable load rotating speed steady state
Controlling the load torque of the motor to change in a step mode, wherein the torque change mode is as follows: 0 → 8N m → 16N m → 8N m → 0, the rotation speed is kept at 30rpm, and the waveform of the simulation result is shown in fig. 7 (a). As can be seen from fig. 7 (a): in the whole variable load process, the estimation error of the sudden change moment of the load torque is large and is within 10 degrees, and when the load torque is not changed, the estimation error is within 2 degrees.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (2)

1. A rotor position detection method of a double three-phase permanent magnet synchronous motor is characterized by comprising the following steps:
constructing a mathematical model of the double three-phase permanent magnet synchronous motor;
carrying out spatial decoupling transformation on the mathematical model of the double three-phase permanent magnet synchronous motor to obtain mathematical models under X and Y planes;
simplifying the mathematical model under the X and Y planes to obtain a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor;
in a pulse width modulation period, simultaneously establishing a voltage-current transient relation equation at any two control moments to obtain cosine and sine of a double-frequency rotor electric angle;
estimating the rotor position of the double three-phase permanent magnet synchronous motor according to the cosine and sine of the electrical angle of the double frequency rotor;
the mathematical model for constructing the double three-phase permanent magnet synchronous motor comprises the following steps:
under a six-phase static coordinate system, defining a mathematical model of the double three-phase permanent magnet synchronous motor as follows:
Figure FDA0002405397510000011
Figure FDA0002405397510000012
wherein: u. ofsAs a stator voltage vector matrix, RsIs a stator resistance matrix, IsIs a stator current vector matrix, LsIs a matrix of stator inductances which are,
Figure FDA0002405397510000013
a rotor permanent magnet flux linkage is formed, t is time, and theta is a rotor angle;
carrying out spatial decoupling transformation on the mathematical model of the double three-phase permanent magnet synchronous motor to obtain the mathematical model under X and Y planes, comprising the following steps:
obtaining an inductance matrix in the X and Y planes
Figure FDA0002405397510000014
And inverse matrix
Figure FDA0002405397510000015
Figure FDA0002405397510000021
Figure FDA0002405397510000022
Wherein:
Figure FDA0002405397510000023
Figure FDA0002405397510000024
wherein: theta is the rotor angle, La0For exciting the amplitude of the DC component of the inductor, La1Is the amplitude of the self-leakage inductance direct current quantity, La2For mutual leakage inductance of the amplitude of the direct currentg0For self-inductive sine magnitude, Lg1The amplitude of the sine quantity of the mutual inductance between the windings is 30 degrees and 150 degreesg2The amplitude of the mutual inductance sine quantity between the windings is 120 degrees and 240 degrees; l is1And L2Is the intermediate variable of the conversion;
according to the inductance matrix under the X and Y planes
Figure FDA0002405397510000025
And inverse matrix
Figure FDA0002405397510000026
Carrying out spatial decoupling transformation on the mathematical model of the double three-phase permanent magnet synchronous motor to obtain the following mathematical models under X and Y planes:
Figure FDA0002405397510000027
wherein u isxyIs an xy plane voltage vector, RsIs a stator resistance matrix, IxyIs a stator current matrix, t is time;
obtaining a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor by simplifying the mathematical model under the X and Y planes, wherein the equation comprises the following steps:
neglecting in mathematical models in said X and Y plane
Figure FDA0002405397510000028
And obtaining a voltage-current transient relation equation of the double three-phase permanent magnet synchronous motor through transformation as follows:
Figure FDA0002405397510000029
wherein: i isxIs the x-axis current component, IyIs a y-axis current component, uyIs a y-axis current component, uxIs the x-axis current component, uαis an α axis voltage component, uβis the beta axis voltage component;
estimating the rotor position of the double three-phase permanent magnet synchronous motor according to the cosine and sine of the electrical angle of the double frequency rotor, comprising:
cosine and sine of the double-frequency rotor electrical angle are used as input of a two-phase orthogonal phase-locked loop to obtain a double-frequency rotor electrical angle 2 theta;
setting the phase-locked loop error to sin (2 theta-2 theta)*) Obtaining an estimated angle of the rotor position of the double three-phase permanent magnet synchronous motor; wherein the phase-locked loop closed-loop transfer function G(s) is as follows:
Figure FDA0002405397510000031
wherein: s is Laplace operator, kpIs a proportionality coefficient, kiAs an integral coefficient, θ*The estimated angle of the rotor position of the double three-phase permanent magnet synchronous motor is shown, and theta is the rotor angle.
2. The method for detecting the rotor position of a double three-phase permanent magnet synchronous motor according to claim 1, wherein in a pulse width modulation period, simultaneous equations of voltage and current transient relations at any two control moments are obtained to obtain the cosine and sine of the electrical angle of the double-frequency rotor, and the method comprises the following steps:
keeping the rotor angle theta unchanged in a pulse width modulation period, and controlling the time t by any two1And t2Calculating cosine cos2 theta and sine sin2 theta of the double-frequency rotor electrical angle;
the cosine of the electrical angle of the double frequency rotor cos2 θ is as follows:
Figure FDA0002405397510000032
the sine of the second harmonic rotor electrical angle, sin2 θ, is as follows:
Figure FDA0002405397510000033
wherein: u. ofx1Is the x-axis component, u, of the first voltage vectory1Is the y-axis component of the first voltage vector, ux2Is the x-axis component, u, of the second voltage vectory2Is the y-axis component of the second voltage vector, Iy1Is the y-axis component of the first current vector, Iy2The y-axis component of the second current vector.
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