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CN110112965B - A method for observing the back electromotive force of a permanent magnet synchronous motor - Google Patents

A method for observing the back electromotive force of a permanent magnet synchronous motor Download PDF

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CN110112965B
CN110112965B CN201910376079.0A CN201910376079A CN110112965B CN 110112965 B CN110112965 B CN 110112965B CN 201910376079 A CN201910376079 A CN 201910376079A CN 110112965 B CN110112965 B CN 110112965B
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CN110112965A (en
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郭磊磊
金楠
秦世耀
王瑞明
代林旺
罗魁
曹玲芝
李琰琰
武洁
吴振军
窦智峰
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China Electric Power Research Institute Co Ltd CEPRI
Zhengzhou University of Light Industry
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Zhengzhou University of Light Industry
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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
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings

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Abstract

本发明提出一种永磁同步电机反电动势观测方法，其步骤为：首先采样计算得到电机定子电压和定子电流均在静止

Figure DEST_PATH_IMAGE001
坐标系下的电压分量和电流分量；其次，根据电压分量和电流分量计算得到估计的定子电流及高频滑模信号；再将高频滑模信号分别经过两次低通滤波得到估计的实际转子位置角及电机的反电动势幅值；最后，根据估计的实际转子位置角和电机的反电动势幅值计算得到估计的电机反电动势。本发明采用双低通滤波器法，根据第二个低通滤波器对反电动势相位和幅值的影响补偿由第一个低通滤波器引起的反电动势相位延迟和幅值衰减问题，能够实现反电动势的准确观测，本发明无需使用电机的转速信息，能够提高电机反电动势的观测精度，提高电机的动态性能。

Figure 201910376079

The invention provides a method for observing the back electromotive force of a permanent magnet synchronous motor.

Figure DEST_PATH_IMAGE001
The voltage component and current component in the coordinate system; secondly, the estimated stator current and high-frequency sliding mode signal are calculated according to the voltage component and current component; then the high-frequency sliding mode signal is subjected to two low-pass filtering to obtain the estimated actual rotor. position angle and the back-EMF amplitude of the motor; finally, the estimated back-EMF of the motor is calculated according to the estimated actual rotor position angle and the back-EMF amplitude of the motor. The invention adopts the double low-pass filter method to compensate the phase delay and amplitude attenuation problems of the back-EMF caused by the first low-pass filter according to the influence of the second low-pass filter on the phase and amplitude of the back-EMF, and can realize For the accurate observation of the back electromotive force, the present invention does not need to use the rotational speed information of the motor, which can improve the observation precision of the back electromotive force of the motor and improve the dynamic performance of the motor.

Figure 201910376079

Description

一种永磁同步电机反电动势观测方法A method for observing the back electromotive force of a permanent magnet synchronous motor

技术领域technical field

本发明涉及电力电子领域，特别是指一种永磁同步电机反电动势观测方法。The invention relates to the field of power electronics, in particular to a method for observing the back electromotive force of a permanent magnet synchronous motor.

背景技术Background technique

近年来，随着能源危机的不断加剧，光伏发电技术、风力发电技术和新能源电动汽车技术都得到了蓬勃发展。永磁同步电机因具有功率密度大、效率高等诸多优点，在风力发电系统和新能源电动汽车驱动系统中得到了广泛应用。然而，在运行环境较恶劣，振动、潮湿、低温等环境因素下，往往会导致速度传感器出现断线、脉冲信号丢失等故障，进而导致控制系统运行失败。因此，为了提高永磁同步电机控制系统的运行可靠性，无速度传感器控制技术在近年来得到广泛研究。在传统的基于二阶滑模观测器的永磁同步电机无速度传感器控制中，常采用计算的方法得到电机的反电动势，且计算过程中需要使用到电机的转速信息，但在电机的无速度传感器控制中，估算的电机转速常常带有一定的转速误差，从而造成计算所得的电机反电动势中也不可避免的具有误差。In recent years, with the continuous intensification of the energy crisis, photovoltaic power generation technology, wind power generation technology and new energy electric vehicle technology have all developed vigorously. Permanent magnet synchronous motors have been widely used in wind power generation systems and new energy electric vehicle drive systems due to their high power density and high efficiency. However, under the harsh operating environment, vibration, humidity, low temperature and other environmental factors, the speed sensor is often disconnected, the pulse signal is lost and other faults, which in turn lead to the failure of the control system. Therefore, in order to improve the operation reliability of the PMSM control system, the speed sensorless control technology has been widely studied in recent years. In the traditional sensorless control of permanent magnet synchronous motor based on the second-order sliding mode observer, the calculation method is often used to obtain the back EMF of the motor, and the speed information of the motor needs to be used in the calculation process. In sensor control, the estimated motor speed often has a certain speed error, resulting in inevitable errors in the calculated back EMF of the motor.

目前已存在永磁同步电机的无速度传感器控制技术的方法，比如，申请号为201610631269.9，发明名称为一种基于滑模观测器的无速度传感器控制方法，提出了采用低通滤波器观测反电动势及补偿电机相移角度的方法，并且实现了电机的无速度传感器控制，但是该方法只对产生的角度相移进行了补偿，获得了准确的电机角度，而没有考虑对电机反电动势幅值造成的衰减进行补偿。因此，控制系统中使用的电机反电动势存在误差。文献[压缩机用内置式永磁同步电机无位置传感器控制[J].电工技术学报，2013，28(5)：182-187]提出了一种采用低通滤波器串联的方式来实时获得反电动势信息，对低通滤波器引起的相移进行补偿获得准确的电机角度的方法，从而实现电机的无速度传感器控制。然而该方法仅仅对角度进行了相移补偿，没有考虑到滤波器对电机反电动势幅值造成的衰减。文献[王高林,杨荣峰,于泳等.内置式永磁同步电机无位置传感器控制[J].中国电机工程学报，2010，30(30)：93-98.]提出了基于二阶滑模观测器的永磁同步电机无速度传感器控制方法，该方法仅对反电动势的相位延迟进行了补偿，且补偿算法需要使用估计的转速。在电机的无速度传感器控制中，估算的电机转速常常带有一定的转速误差，从而造成计算所得的电机反电动势中不可避免的具有较大的误差。At present, there are methods for the speed sensorless control technology of permanent magnet synchronous motors. For example, the application number is 201610631269.9, and the name of the invention is a speed sensorless control method based on a sliding mode observer. It is proposed to use a low-pass filter to observe the back electromotive force. And the method of compensating the motor phase shift angle, and the speed sensorless control of the motor is realized, but this method only compensates the generated angle phase shift, and obtains the accurate motor angle, without considering the motor back EMF amplitude. to compensate for the attenuation. Therefore, there is an error in the motor back EMF used in the control system. Literature [The position sensorless control of built-in permanent magnet synchronous motor for compressors [J]. Journal of Electrotechnical Technology, 2013, 28(5): 182-187] proposes a method of using low-pass filters in series to obtain the feedback in real time. The electromotive force information, the method of compensating the phase shift caused by the low-pass filter to obtain the accurate motor angle, so as to realize the speed sensorless control of the motor. However, this method only compensates the phase shift of the angle, and does not take into account the attenuation of the back EMF amplitude of the motor caused by the filter. Reference [Wang Gaolin, Yang Rongfeng, Yu Yong, et al. Sensorless control of built-in permanent magnet synchronous motor [J]. Chinese Journal of Electrical Engineering, 2010, 30(30): 93-98.] proposed a method based on second-order sliding mode observation This method only compensates the phase delay of the back EMF, and the compensation algorithm needs to use the estimated speed. In the sensorless control of the motor, the estimated motor speed often has a certain speed error, which inevitably causes a large error in the calculated back EMF of the motor.

发明内容SUMMARY OF THE INVENTION

针对现有的永磁同步电机的反电动势的计算方法存在未补偿反电动势的幅值造成电机反电动势的误差较大的技术问题，本发明提出了一种永磁同步电机反电动势观测方法，采用双低通滤波器法对电机反电动势的幅值和相位进行补偿，且该方法无需使用电机的转速信息，从而可以获得更为准确的电机反电动势，提高电机的动态性能。Aiming at the technical problem that the back-EMF calculation method of the existing permanent magnet synchronous motor has the technical problem that the amplitude of the back-EMF is not compensated, resulting in a large error in the back-EMF of the motor, the present invention proposes a method for observing the back-EMF of a permanent-magnet synchronous motor. The double low-pass filter method compensates the amplitude and phase of the motor back-EMF, and this method does not need to use the motor speed information, so that a more accurate motor back-EMF can be obtained and the dynamic performance of the motor can be improved.

本发明的技术方案是这样实现的：The technical scheme of the present invention is realized as follows:

一种永磁同步电机反电动势观测方法，其步骤如下：A method for observing the back electromotive force of a permanent magnet synchronous motor, the steps of which are as follows:

步骤一、利用电压传感器对电机定子电压进行采样得到电机定子电压uAB和uBC，计算电机的三相相电压uA、uB和uC，并将三相电压uA、uB和uC通过坐标变换得到静止α-β坐标系下的电压uα和电压uβ；Step 1. Use the voltage sensor to sample the motor stator voltage to obtain the motor stator voltages u AB and u BC , calculate the three-phase phase voltages u A , u B and u C of the motor, and calculate the three-phase voltages u A , u B and u C obtains the voltage u α and the voltage u β in the stationary α-β coordinate system through coordinate transformation;

步骤二、利用电流传感器对电机定子三相电流进行采样得到电机定子电流iA、iB和iC，并通过坐标变换得到静止α-β坐标系下的电流iα和电流iβ；Step 2, using the current sensor to sample the three-phase current of the motor stator to obtain the motor stator currents i A , i B and i C , and obtain the current i α and the current i β in the static α-β coordinate system through coordinate transformation;

步骤三、初始化电机的电流

Figure BDA0002051709770000021
和电流
Figure BDA0002051709770000022
计算电流
Figure BDA0002051709770000023
与步骤二得到的电流iα的差值，计算电流
Figure BDA0002051709770000024
和步骤二得到的电流iβ的差值，并通过符号函数计算得到高频滑模信号sα和高频滑模信号sβ；Step 3. Initialize the current of the motor
Figure BDA0002051709770000021
and current
Figure BDA0002051709770000022
Calculate current
Figure BDA0002051709770000023
The difference with the current i α obtained in step 2, calculate the current
Figure BDA0002051709770000024
The difference between the current i β and the current i β obtained in step 2, and the high-frequency sliding mode signal s α and the high-frequency sliding mode signal s β are obtained by calculating the sign function;

步骤四、利用步骤一得到的电压uα减去步骤三得到的高频滑模信号sα得到第一组中间变量E1α，利用步骤一得到的电压uβ减去步骤三得到的高频滑模信号sβ得到第一组中间变量E1β；Step 4: Use the voltage u α obtained in step 1 to subtract the high-frequency sliding mode signal s α obtained in step 3 to obtain the first group of intermediate variables E 1α , and use the voltage u β obtained in step 1 to subtract the high-frequency sliding mode signal obtained in step 3. The modulo signal s β obtains the first group of intermediate variables E 1β ;

步骤五、根据步骤四得到的第一组中间变量E1α、E1β和电机q轴电感计算得到第二组中间变量E2α、E2β；Step 5: Calculate and obtain the second group of intermediate variables E 2α and E 2β according to the first group of intermediate variables E 1α and E 1β obtained in step 4 and the q-axis inductance of the motor;

步骤六、根据步骤三估计的电流

Figure BDA0002051709770000025
电流
Figure BDA0002051709770000026
和电机定子电阻及q轴电感计算得到第三组中间变量E3α、E3β；Step 6. Current estimated according to Step 3
Figure BDA0002051709770000025
current
Figure BDA0002051709770000026
Calculate the third group of intermediate variables E 3α and E 3β with the motor stator resistance and q-axis inductance;

步骤七、利用步骤五得到的第二组中间变量E2α减去步骤六得到的第三组中间变量E3α得到第四组中间变量E4α，利用步骤五得到的第二组中间变量E2β减去步骤六得到的第三组中间变量E3β得到第四组中间变量E4β；Step 7: Use the second group of intermediate variables E 2α obtained in step 5 to subtract the third group of intermediate variables E 3α obtained in step 6 to obtain the fourth group of intermediate variables E 4α , and use the second group of intermediate variables E 2β obtained in step 5 to subtract. Go to the third group of intermediate variables E 3β obtained in step 6 to obtain the fourth group of intermediate variables E 4β ;

步骤八、根据步骤七得到的第四组中间变量E4α、E4β更新步骤三中的电流

Figure BDA0002051709770000027
和电流
Figure BDA0002051709770000028
进而更新高频滑模信号sα和高频滑模信号sβ；Step 8. Update the current in Step 3 according to the fourth group of intermediate variables E 4α and E 4β obtained in Step 7
Figure BDA0002051709770000027
and current
Figure BDA0002051709770000028
Then update the high-frequency sliding mode signal s α and the high-frequency sliding mode signal s β ;

步骤九、将更新后的高频滑模信号sα和高频滑模信号sβ通过第一低通滤波器进行低通滤波分别得到第五组中间变量s1α、s1β；Step 9. Perform low-pass filtering on the updated high-frequency sliding mode signal s α and the high-frequency sliding mode signal s β through the first low-pass filter to obtain the fifth group of intermediate variables s 1α and s 1β respectively;

步骤十、将步骤九得到的第五组中间变量s1α、s1β通过第二低通滤波器进行低通滤波分别得到第六组中间变量s2α、s2β；Step 10. Perform low-pass filtering on the fifth group of intermediate variables s 1α and s 1β obtained in step 9 through the second low-pass filter to obtain the sixth group of intermediate variables s 2α and s 2β respectively;

步骤十一、据据步骤九得到的第五组中间变量s1α、s1β计算有效反电动势q轴偏差

Figure BDA0002051709770000031
Step 11: Calculate the effective back EMF q-axis deviation according to the fifth group of intermediate variables s 1α and s 1β obtained in step 9
Figure BDA0002051709770000031

步骤十二、将步骤十一得到的有效反电动势q轴偏差

Figure BDA0002051709770000032
通过比例积分器计算得到估计的转速
Figure BDA0002051709770000033
Step 12, offset the effective back EMF q-axis obtained in step 11
Figure BDA0002051709770000032
Estimated speed calculated by proportional integrator
Figure BDA0002051709770000033

步骤十三、将步骤十二得到的转速

Figure BDA0002051709770000034
通过积分调节得到经过第一个低通滤波器产生一次相位延迟后的转子位置角θ1；Step 13, the speed obtained in step 12
Figure BDA0002051709770000034
The rotor position angle θ 1 after the first phase delay is generated by the first low-pass filter is obtained by integral adjustment;

步骤十四、根据步骤十得到的第六组中间变量s2α、s2β计算得到经过了第一低通滤波器和第二低通滤波器产生两次相位延迟之后的转子位置角θ2；Step 14: Calculate the rotor position angle θ 2 after two phase delays are generated by the first low-pass filter and the second low-pass filter according to the sixth group of intermediate variables s 2α and s 2β obtained in step 10;

步骤十五、根据步骤十三得到的转子位置角θ1减去步骤十四得到的转子位置角θ2得到延迟角度Δθ，再根据转子位置角θ1和延迟角度Δθ计算得到估计的实际转子位置角θ；Step 15: Subtract the rotor position angle θ 1 obtained in step 13 from the rotor position angle θ 2 obtained in step 14 to obtain the delay angle Δθ, and then calculate the estimated actual rotor position according to the rotor position angle θ 1 and the delay angle Δθ. angle θ;

步骤十六、根据步骤九得到的第五组中间变量s1α、s1β和步骤十得到的第六组中间变量s2α、s2β计算得到第一低通滤波器和第二低通滤波器对电机反电动势幅值产生的衰减比k；Step 16: According to the fifth group of intermediate variables s 1α and s 1β obtained in step 9 and the sixth group of intermediate variables s 2α and s 2β obtained in step 10, the first low-pass filter and the second low-pass filter pair are obtained by calculating The attenuation ratio k generated by the amplitude of the back EMF of the motor;

步骤十七、根据步骤九得到的第五组中间变量s1α、s1β和步骤十六得到的衰减比k计算得到电机的反电动势幅值em；Step 17: Calculate the back EMF amplitude em of the motor according to the fifth group of intermediate variables s 1α and s 1β obtained in step 9 and the attenuation ratio k obtained in step 16;

步骤十八、根据步骤十七得到的反电动势幅值em和步骤十五得到的实际转子位置角θ计算得到估计的电机反电动势

Figure BDA0002051709770000035
和
Figure BDA0002051709770000036
Step 18: Calculate the estimated back EMF of the motor according to the back EMF amplitude em obtained in Step 17 and the actual rotor position angle θ obtained in Step 15.
Figure BDA0002051709770000035
and
Figure BDA0002051709770000036

优选地，所述步骤一中的三相电压uA、uB和uC通过坐标变换得到静止α-β坐标系下的电压uα和电压uβ的方法为：

Figure BDA0002051709770000037
其中，
Figure BDA0002051709770000038
uAB和uBC为电机定子电压。Preferably, the method for obtaining the voltage u α and the voltage u β in the static α-β coordinate system through the coordinate transformation of the three-phase voltages u A , u B and u C in the first step is:
Figure BDA0002051709770000037
in,
Figure BDA0002051709770000038
u AB and u BC are the motor stator voltages.

优选地，所述步骤二中的电机定子电流iA、iB和iC通过坐标变换得到静止α-β坐标系下的电流iα和电流iβ的方法为：

Figure BDA0002051709770000039
Preferably, the method for obtaining the current i α and the current i β in the static α-β coordinate system through the coordinate transformation of the motor stator currents i A , i B and i C in the second step is:
Figure BDA0002051709770000039

优选地，所述步骤三中的高频滑模信号sα和高频滑模信号sβ的获得方法为：

Figure BDA0002051709770000041
其中，M为滑模增益，sgn()为符号函数。Preferably, the method for obtaining the high-frequency sliding mode signal s α and the high-frequency sliding mode signal s β in the step 3 is:
Figure BDA0002051709770000041
Among them, M is the sliding mode gain, and sgn() is the sign function.

优选地，所述第一组中间变量E1α、E1β的获得方法为：

Figure BDA0002051709770000042
Preferably, the method for obtaining the first group of intermediate variables E 1α and E 1β is:
Figure BDA0002051709770000042

所述第二组中间变量E2α、E2β的获得方法为：

Figure BDA0002051709770000043
其中，Lq为电机q轴电感；The method for obtaining the second group of intermediate variables E 2α and E 2β is:
Figure BDA0002051709770000043
Among them, L q is the q-axis inductance of the motor;

所述第三组中间变量E3α、E3β的获得方法为：

Figure BDA0002051709770000044
其中，Rs为电机定子电阻；The method for obtaining the third group of intermediate variables E 3α and E 3β is:
Figure BDA0002051709770000044
Among them, R s is the motor stator resistance;

所述第四组中间变量E4α、E4β的获得方法为：

Figure BDA0002051709770000045
The method for obtaining the fourth group of intermediate variables E 4α and E 4β is:
Figure BDA0002051709770000045

优选地，所述步骤八中的电流

Figure BDA0002051709770000046
和电流
Figure BDA0002051709770000047
的更新方法为：
Figure BDA0002051709770000048
其中，Ts为采样周期。Preferably, the current in the eighth step
Figure BDA0002051709770000046
and current
Figure BDA0002051709770000047
The update method is:
Figure BDA0002051709770000048
Among them, T s is the sampling period.

优选地，所述第五组中间变量s1α、s1β的获得方法为：

Figure BDA0002051709770000049
其中，ωc是第一低通滤波器和第二低通滤波器的截止频率，s为拉普拉斯算子；Preferably, the method for obtaining the fifth group of intermediate variables s 1α and s 1β is:
Figure BDA0002051709770000049
Among them, ω c is the cutoff frequency of the first low-pass filter and the second low-pass filter, and s is the Laplace operator;

所述第六组中间变量s2α、s2β的获得方法为：

Figure BDA00020517097700000410
The method for obtaining the sixth group of intermediate variables s 2α and s 2β is:
Figure BDA00020517097700000410

优选地，所述有效反电动势q轴偏差

Figure BDA00020517097700000411
的获得方法为：
Figure BDA00020517097700000412
其中，θ1为转子位置角；Preferably, the effective back EMF q-axis deviation
Figure BDA00020517097700000411
The method of obtaining is:
Figure BDA00020517097700000412
Among them, θ 1 is the rotor position angle;

所述估计的转速

Figure BDA00020517097700000413
的获得方法为：
Figure BDA00020517097700000414
kp为比例系数，ki为积分系数；the estimated rotational speed
Figure BDA00020517097700000413
The method of obtaining is:
Figure BDA00020517097700000414
k p is the proportional coefficient, ki is the integral coefficient;

所述转子位置角θ1的更新方法为：

Figure BDA00020517097700000415
The update method of the rotor position angle θ 1 is:
Figure BDA00020517097700000415

所述转子位置角θ2的获得方法为：θ2＝arctan(-s2α/s2β)；The method for obtaining the rotor position angle θ 2 is: θ 2 =arctan(-s 2α /s 2β );

所述延迟角度Δθ的获得方法为：Δθ＝θ1-θ2；The method for obtaining the delay angle Δθ is: Δθ=θ 1 −θ 2 ;

所述估计的实际转子位置角θ的获得方法为：θ＝θ1+Δθ。The method for obtaining the estimated actual rotor position angle θ is: θ=θ 1 +Δθ.

优选地，所述低通滤波器对电机反电动势幅值产生的衰减比k为：

Figure BDA0002051709770000051
Preferably, the attenuation ratio k generated by the low-pass filter to the back EMF amplitude of the motor is:
Figure BDA0002051709770000051

所述电机的反电动势幅值em的获得方法为：

Figure BDA0002051709770000052
The method for obtaining the back EMF amplitude em of the motor is:
Figure BDA0002051709770000052

优选地，所述步骤十八中的估计的电机反电动势

Figure BDA0002051709770000053
和
Figure BDA0002051709770000054
的获得方法为：
Figure BDA0002051709770000055
Preferably, the estimated motor back EMF in the step eighteen
Figure BDA0002051709770000053
and
Figure BDA0002051709770000054
The method of obtaining is:
Figure BDA0002051709770000055

本技术方案能产生的有益效果：采用二阶滑模观测器对永磁同步电机的反电动势进行滚侧，并设计了一种采用双低通滤波器法对反电动势的幅值和相位进行补偿，从而克服了反电动势相位和幅值补偿受转速估计误差影响的问题，提高了反电动势的观测精度。The beneficial effects that this technical solution can produce: the second-order sliding mode observer is used to roll the back electromotive force of the permanent magnet synchronous motor, and a double low-pass filter method is designed to compensate the amplitude and phase of the back electromotive force. , so as to overcome the problem that the phase and amplitude compensation of the back EMF is affected by the speed estimation error, and improve the observation accuracy of the back EMF.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

图1为本发明电流iα观测器框图。Fig. 1 is a block diagram of the current i α observer of the present invention.

图2为本发明电流iβ观测器框图。FIG. 2 is a block diagram of the current i β observer of the present invention.

图3为本发明的整体框图。FIG. 3 is an overall block diagram of the present invention.

图4为本发明所得的反电动势和实际反电动势的关系曲线；eα和eβ为实际的电机反电动势，

Figure BDA0002051709770000056
和
Figure BDA0002051709770000057
为本发明所得的电机反电动势。Fig. 4 is the relation curve of the back EMF obtained by the present invention and the actual back EMF; e α and e β are the actual motor back EMF,
Figure BDA0002051709770000056
and
Figure BDA0002051709770000057
is the back electromotive force of the motor obtained by the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有付出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

如图3所示，本发明提出了一种永磁同步电机反电动势观测方法，首先，采样计算得到电机定子电压和定子电流均在静止α-β坐标系下的电压分量和电流分量；其次，根据电压分量和电流分量计算得到估计的定子电流及高频滑模信号；再将高频滑模信号分别经过两次低通滤波得到估计的实际转子位置角及电机的反电动势幅值；最后，根据估计的实际转子位置角和电机的反电动势幅值计算得到估计的电机反电动势。具体步骤如下：As shown in Figure 3, the present invention proposes a method for observing the back electromotive force of a permanent magnet synchronous motor. First, the voltage and current components of the stator voltage and stator current of the motor in the static α-β coordinate system are obtained by sampling and calculation; secondly, The estimated stator current and high-frequency sliding mode signal are calculated according to the voltage component and current component; then the high-frequency sliding mode signal is subjected to two low-pass filtering to obtain the estimated actual rotor position angle and the back EMF amplitude of the motor; finally, The estimated back-EMF of the motor is calculated from the estimated actual rotor position angle and the back-EMF amplitude of the motor. Specific steps are as follows:

步骤一、利用电压传感器对电机定子电压进行采样得到电机定子电压uAB和uBC，根据公式(1)计算电机的三相相电压uA、uB和uC：Step 1: Use the voltage sensor to sample the motor stator voltage to obtain the motor stator voltages u AB and u BC , and calculate the three-phase phase voltages u A , u B and u C of the motor according to formula (1):

Figure BDA0002051709770000061
Figure BDA0002051709770000061

再根据公式(2)将三相电压uA、uB和uC通过坐标变换得到静止α-β坐标系下的电压uα和电压uβ；Then according to formula (2), the three-phase voltages u A , u B and u C are obtained by coordinate transformation to obtain the voltage u α and the voltage u β in the static α-β coordinate system;

Figure BDA0002051709770000062
Figure BDA0002051709770000062

步骤二、利用电流传感器对电机定子三相电流进行采样得到电机定子电流iA、iB和iC，并通过公式(3)的坐标变换得到静止α-β坐标系下的电流iα和电流iβ：Step 2: Use the current sensor to sample the three-phase current of the motor stator to obtain the motor stator currents i A , i B and i C , and obtain the current i α and the current in the static α-β coordinate system through the coordinate transformation of formula (3). i β :

Figure BDA0002051709770000063
Figure BDA0002051709770000063

步骤三、初始化电机的电流

Figure BDA0002051709770000064
和电流
Figure BDA0002051709770000065
如图1和图2所示，计算电流
Figure BDA0002051709770000066
与步骤二得到的电流iα以及电流
Figure BDA0002051709770000067
与步骤二得到的电流iβ的差值，再根据公式(4)通过符号函数计算得到高频滑模信号sα和高频滑模信号sβ：Step 3. Initialize the current of the motor
Figure BDA0002051709770000064
and current
Figure BDA0002051709770000065
As shown in Figures 1 and 2, calculate the current
Figure BDA0002051709770000066
with the current i α obtained in step 2 and the current
Figure BDA0002051709770000067
The difference between the current i β and the current i β obtained in step 2, and then calculate the high-frequency sliding mode signal s α and the high-frequency sliding mode signal s β through the sign function according to formula (4):

Figure BDA0002051709770000068
Figure BDA0002051709770000068

其中，M为滑模增益，电流

Figure BDA0002051709770000069
和电流
Figure BDA00020517097700000610
的初始值均为0，sgn()为符号函数。Among them, M is the sliding mode gain, the current
Figure BDA0002051709770000069
and current
Figure BDA00020517097700000610
The initial value of is 0, and sgn() is a sign function.

步骤四、利用步骤一得到的电压uα减去步骤三得到的高频滑模信号sα得到第一组中间变量E1α，利用步骤一得到的电压uβ减去步骤三得到的高频滑模信号sα和高频滑模信号sβ得到第一组中间变量E1β，如公式(5)所示：Step 4: Use the voltage u α obtained in step 1 to subtract the high-frequency sliding mode signal s α obtained in step 3 to obtain the first group of intermediate variables E 1α , and use the voltage u β obtained in step 1 to subtract the high-frequency sliding mode signal obtained in step 3. The first group of intermediate variables E 1β is obtained from the mode signal s α and the high-frequency sliding mode signal s β , as shown in formula (5):

Figure BDA00020517097700000611
Figure BDA00020517097700000611

步骤五、根据步骤四得到的第一组中间变量E1α、E1β和电机q轴电感计算得到第二组中间变量E2α、E2β，如公式(6)所示：Step 5. Calculate and obtain the second group of intermediate variables E 2α and E 2β according to the first group of intermediate variables E 1α and E 1β obtained in step 4 and the q-axis inductance of the motor, as shown in formula (6):

Figure BDA0002051709770000071
Figure BDA0002051709770000071

其中，Lq为电机q轴电感。Among them, L q is the q-axis inductance of the motor.

步骤六、根据步骤三估计的电流

Figure BDA0002051709770000072
电流
Figure BDA0002051709770000073
和电机定子电阻及q轴电感计算得到第三组中间变量E3α、E3β，如公式(7)所示：Step 6. Current estimated according to Step 3
Figure BDA0002051709770000072
current
Figure BDA0002051709770000073
And the motor stator resistance and q-axis inductance are calculated to obtain the third group of intermediate variables E 3α and E 3β , as shown in formula (7):

Figure BDA0002051709770000074
Figure BDA0002051709770000074

其中，Rs为电机定子电阻，Lq为电机q轴电感。Among them, R s is the stator resistance of the motor, and L q is the q-axis inductance of the motor.

步骤七、利用步骤五得到的第二组中间变量E2α减去步骤六得到的第三组中间变量E3α得到第四组中间变量E4α，利用步骤五得到的第二组中间变量E2β减去步骤六得到的第三组中间变量E3β得到第四组中间变量E4β，如公式(8)所示：Step 7: Use the second group of intermediate variables E 2α obtained in step 5 to subtract the third group of intermediate variables E 3α obtained in step 6 to obtain the fourth group of intermediate variables E 4α , and use the second group of intermediate variables E 2β obtained in step 5 to subtract. Go to the third group of intermediate variables E 3β obtained in step 6 to obtain the fourth group of intermediate variables E 4β , as shown in formula (8):

Figure BDA0002051709770000075
Figure BDA0002051709770000075

步骤八、根据步骤七得到的第四组中间变量E4α、E4β更新电流

Figure BDA0002051709770000076
和电流
Figure BDA0002051709770000077
如公式(9)所示：Step 8. Update the current according to the fourth group of intermediate variables E 4α and E 4β obtained in step 7
Figure BDA0002051709770000076
and current
Figure BDA0002051709770000077
As shown in formula (9):

Figure BDA0002051709770000078
Figure BDA0002051709770000078

其中，Ts为采样周期，电流

Figure BDA0002051709770000079
和电流
Figure BDA00020517097700000710
的初始值为0。Among them, T s is the sampling period, the current
Figure BDA0002051709770000079
and current
Figure BDA00020517097700000710
The initial value of is 0.

如图1和图2所示，根据电流iα观测器和电流iβ观测器的闭合回路，利用更新后的电流

Figure BDA00020517097700000711
和电流
Figure BDA00020517097700000712
进一步更新高频滑模信号sα、高频滑模信号sβ。As shown in Figure 1 and Figure 2, according to the closed loop of the current i α observer and the current i β observer, using the updated current
Figure BDA00020517097700000711
and current
Figure BDA00020517097700000712
The high-frequency sliding mode signal s α and the high-frequency sliding mode signal s β are further updated.

步骤九、将更新后的高频滑模信号sα和高频滑模信号sβ通过第一低通滤波器进行低通滤波分别得到第五组中间变量s1α、s1β，如公式(10)所示：Step 9. Perform low-pass filtering on the updated high-frequency sliding mode signal s α and high-frequency sliding mode signal s β through the first low-pass filter to obtain the fifth group of intermediate variables s 1α and s 1β respectively, as shown in formula (10 ) as shown:

Figure BDA00020517097700000713
Figure BDA00020517097700000713

其中，ωc为第一低通滤波器和第二低通滤波器的截止频率，s为拉普拉斯算子。Among them, ω c is the cutoff frequency of the first low-pass filter and the second low-pass filter, and s is the Laplace operator.

步骤十、将步骤九得到的第五组中间变量s1α、s1β通过第二低通滤波器进行第二次低通滤波分别得到第六组中间变量s2α、s2β，如公式(11)所示：Step 10. Perform the second low-pass filtering of the fifth group of intermediate variables s 1α and s 1β obtained in step 9 through the second low-pass filter to obtain the sixth group of intermediate variables s 2α and s 2β respectively, as shown in formula (11) shown:

Figure BDA0002051709770000081
Figure BDA0002051709770000081

其中，ωc为第一低通滤波器和第二低通滤波器的截止频率，s为拉普拉斯算子。Among them, ω c is the cutoff frequency of the first low-pass filter and the second low-pass filter, and s is the Laplace operator.

步骤十一、据据步骤九得到的第五组中间变量s1α、s1β计算有效反电动势q轴偏差

Figure BDA0002051709770000082
如公式(12)所示：Step 11: Calculate the effective back EMF q-axis deviation according to the fifth group of intermediate variables s 1α and s 1β obtained in step 9
Figure BDA0002051709770000082
As shown in formula (12):

Figure BDA0002051709770000083
Figure BDA0002051709770000083

其中，θ1为转子位置角，转子位置角θ1的初始值为0。Among them, θ 1 is the rotor position angle, and the initial value of the rotor position angle θ 1 is 0.

步骤十二、将步骤十一得到的有效反电动势q轴偏差

Figure BDA0002051709770000084
通过比例积分器计算得到估计的转速
Figure BDA0002051709770000085
如公式(13)所示：Step 12, offset the effective back EMF q-axis obtained in step 11
Figure BDA0002051709770000084
Estimated speed calculated by proportional integrator
Figure BDA0002051709770000085
As shown in formula (13):

Figure BDA0002051709770000086
Figure BDA0002051709770000086

其中，kp为比例系数，ki为积分系数，s为拉普拉斯算子。Among them, k p is the proportional coefficient, ki is the integral coefficient, and s is the Laplace operator.

步骤十三、将步骤十二得到的转速

Figure BDA0002051709770000087
通过积分调节得到经过第一个低通滤波器产生一次相位延迟后的转子位置角θ1，也即对转子位置角θ1进行更新，如公式(14)所示：Step 13, the speed obtained in step 12
Figure BDA0002051709770000087
Through integral adjustment, the rotor position angle θ 1 after the first phase delay is generated by the first low-pass filter is obtained, that is, the rotor position angle θ 1 is updated, as shown in formula (14):

Figure BDA0002051709770000088
Figure BDA0002051709770000088

其中，Ts为采样周期。Among them, T s is the sampling period.

步骤十四、根据步骤十得到的第六组中间变量s2α、s2β计算得到经过了第一低通滤波器和第二低通滤波器产生两次相位延迟之后的转子位置角θ2，如公式(15)所示：Step 14: Calculate the rotor position angle θ 2 after two phase delays generated by the first low-pass filter and the second low-pass filter according to the sixth group of intermediate variables s 2α and s 2β obtained in step 10, as Formula (15) shows:

θ2＝arctan(-s2α/s2β) (15)。θ 2 =arctan(−s 2α /s 2β ) (15).

步骤十五、根据公式(16)将步骤十三得到的转子位置角θ1减去步骤十四得到的转子位置角θ2得到延迟角度Δθ：Step 15. According to formula (16), subtract the rotor position angle θ 1 obtained in step 13 from the rotor position angle θ 2 obtained in step 14 to obtain the delay angle Δθ:

Δθ＝θ1-θ2 (16)；Δθ=θ 1 −θ 2 (16);

再根据公式(17)利用步骤十三得到的转子位置角θ1和延迟角度Δθ计算得到估计的实际转子位置角θ：Then according to formula (17), the estimated actual rotor position angle θ is obtained by using the rotor position angle θ 1 and the delay angle Δθ obtained in step 13:

θ＝θ1+Δθ (17)。θ=θ 1 +Δθ (17).

步骤十六、根据步骤九得到的第五组中间变量s1α、s1β和步骤十得到的第六组中间变量s2α、s2β计算得到第一低通滤波器和第二低通滤波器对电机反电动势幅值产生的衰减比k，如公式(18)所示：Step 16: According to the fifth group of intermediate variables s 1α and s 1β obtained in step 9 and the sixth group of intermediate variables s 2α and s 2β obtained in step 10, the first low-pass filter and the second low-pass filter pair are obtained by calculating The attenuation ratio k generated by the back EMF amplitude of the motor is shown in formula (18):

Figure BDA0002051709770000091
Figure BDA0002051709770000091

步骤十七、根据步骤九得到的第五组中间变量s1α、s1β和步骤十六得到的衰减比k计算得到电机的反电动势幅值em，如公式(19)所示：Step 17: Calculate the back EMF amplitude em of the motor according to the fifth group of intermediate variables s 1α and s 1β obtained in step 9 and the attenuation ratio k obtained in step 16, as shown in formula (19):

Figure BDA0002051709770000092
Figure BDA0002051709770000092

其中，k为衰减比。where k is the attenuation ratio.

步骤十八、根据步骤十七得到的反电动势幅值em和步骤十五得到的实际转子位置角θ计算得到估计的电机反电动势

Figure BDA0002051709770000093
和
Figure BDA0002051709770000094
如公式(20)所示：Step 18: Calculate the estimated back EMF of the motor according to the back EMF amplitude em obtained in Step 17 and the actual rotor position angle θ obtained in Step 15.
Figure BDA0002051709770000093
and
Figure BDA0002051709770000094
As shown in formula (20):

Figure BDA0002051709770000095
Figure BDA0002051709770000095

为了验证本发明的有效性，进行了仿真验证。仿真所用逆变器的直流侧电压Udc为400V，永磁同步电机的额定功率为6.6kW，磁链为0.35Wb，极对数为4，定子电感为12mH，定子电阻Rs为0.5Ω，额定频率为50Hz，额定电压为190V，采样频率为fs为10kHz。图4给出了本发明计算的反电动势

Figure BDA0002051709770000096
和实际的反电动势值eα、eβ的关系曲线图，对比可见，本发明在反电动势变化时，可以准确获得估计的反电动势，其幅值和相位均较准确。同时，由于本发明不需要电机的估计转速，因此其方法更加简单、精度更高。In order to verify the effectiveness of the present invention, simulation verification is carried out. The DC side voltage U dc of the inverter used in the simulation is 400V, the rated power of the permanent magnet synchronous motor is 6.6kW, the flux linkage is 0.35Wb, the number of pole pairs is 4, the stator inductance is 12mH, and the stator resistance R s is 0.5Ω, The rated frequency is 50Hz, the rated voltage is 190V, and the sampling frequency is f s is 10kHz. Figure 4 shows the back EMF calculated by the present invention
Figure BDA0002051709770000096
Compared with the actual back-EMF values e α , e β , it can be seen from the comparison that the present invention can accurately obtain the estimated back-EMF when the back-EMF changes, and its amplitude and phase are relatively accurate. At the same time, since the present invention does not require the estimated rotational speed of the motor, the method is simpler and more accurate.

以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (3)

1. A counter electromotive force observation method of a permanent magnet synchronous motor is characterized by comprising the following steps:
step one, sampling the motor stator voltage by using a voltage sensor to obtain the motor stator voltage uABAnd uBCCalculating the electricityThree-phase voltage u of machineA、uBAnd uCAnd the three-phase voltage u is converted intoA、uBAnd uCObtaining the voltage u under a static α - β coordinate system through coordinate transformationαAnd voltage uβ；
Step two, sampling the three-phase current of the motor stator by using a current sensor to obtain the current i of the motor statorA、iBAnd iCAnd obtaining the current i under a stationary α - β coordinate system through coordinate transformationαAnd current iβ；
Step three, initializing the current of the motor
Figure FDA0002564304500000011
And current
Figure FDA0002564304500000012
Calculating the current
Figure FDA0002564304500000013
With the current i obtained in step twoαIs calculated from the difference of (1), the current is calculated
Figure FDA0002564304500000014
And the current i obtained in step twoβAnd calculating by a sign function to obtain a high-frequency sliding mode signal sαAnd high frequency sliding mode signal sβ：
Figure FDA0002564304500000015
Wherein M is sliding mode gain, sgn () is a sign function;
step four, utilizing the voltage u obtained in the step oneαSubtracting the high-frequency sliding mode signal s obtained in the step threeαObtain a first set of intermediate variables E1αUsing the voltage u obtained in step oneβSubtracting the high-frequency sliding mode signal s obtained in the step threeβObtain a first set of intermediate variables E1β：
Figure FDA0002564304500000016
Step five, obtaining a first group of intermediate variables E according to the step four1α、E1βAnd the q-axis inductance of the motor is calculated to obtain a second group of intermediate variables E2α、E2β：
Figure FDA0002564304500000017
Wherein L isqIs a motor q-axis inductor;
step six, according to the current in the step three
Figure FDA0002564304500000018
Electric current
Figure FDA0002564304500000019
Calculating the resistance of the stator of the motor and the q-axis inductance to obtain a third group of intermediate variables E3α、E3β：
Figure FDA00025643045000000110
Wherein R issIs a motor stator resistor;
step seven, utilizing the second group of intermediate variables E obtained in the step five2αSubtracting the third group intermediate variable E obtained in the step six3αObtaining a fourth group of intermediate variables E4αUsing the second set of intermediate variables E obtained in step five2βSubtracting the third group intermediate variable E obtained in the step six3βObtaining a fourth group of intermediate variables E4β：
Figure FDA00025643045000000111
Step eight, obtaining a fourth group intermediate variable E according to the step seven4α、E4βUpdating the current in step three
Figure FDA00025643045000000112
And current
Figure FDA00025643045000000113
Figure FDA00025643045000000114
Further updating high-frequency sliding mode signal sαAnd high frequency sliding mode signal sβWherein, TsIs a sampling period;
step nine, updating the high-frequency sliding mode signal sαAnd high frequency sliding mode signal sβLow-pass filtering through the first low-pass filter to respectively obtain a fifth group of intermediate variables s1α、s1β：
Figure FDA0002564304500000021
Wherein, ω iscIs the cut-off frequency of the first low-pass filter and the second low-pass filter, s is the laplacian operator;
step ten, the fifth group of intermediate variables s obtained in the step nine1α、s1βLow-pass filtering through a second low-pass filter to respectively obtain a sixth group of intermediate variables s2α、s2β：
Figure FDA0002564304500000022
Step eleven, obtaining a fifth group of intermediate variables s according to the step nine1α、s1βCalculating effective back electromotive force q-axis deviation
Figure FDA0002564304500000023
Figure FDA0002564304500000024
Wherein, theta1Is the rotor position angle;
step twelve, the effective counter electromotive force q-axis deviation obtained in the step eleven
Figure FDA0002564304500000025
Calculating to obtain estimated rotating speed by a proportional integrator
Figure FDA0002564304500000026
Figure FDA0002564304500000027
kpIs a proportionality coefficient, kiIs an integral coefficient;
thirteen step, rotating speed obtained in the step twelve
Figure FDA0002564304500000028
The rotor position angle theta after primary phase delay generated by the first low-pass filter is obtained through integral adjustment1：
Figure FDA0002564304500000029
Step fourteen, obtaining a sixth group of intermediate variables s according to the step ten2α、s2βCalculating the rotor position angle theta after two phase delays generated by the first low-pass filter and the second low-pass filter2：θ2＝arctan(-s2α/s2β)；
Step fifteen, obtaining the rotor position angle theta according to the step thirteen1Subtracting the rotor position angle theta obtained in the step fourteen2The retardation angle △ theta, △ theta and theta are obtained1-θ2According to the rotor position angle theta1And delay angle △ theta to obtain an estimated actual rotor position angle
Figure FDA00025643045000000210
Figure FDA00025643045000000211
Sixthly, obtaining a fifth group of intermediate variables s according to the step nine1α、s1βAnd a sixth set of intermediate variables s obtained in step ten2α、s2βCalculating to obtain an attenuation ratio k of the first low-pass filter and the second low-pass filter to the back electromotive force amplitude of the motor:
Figure FDA00025643045000000212
seventhly, obtaining a fifth group of intermediate variables s according to the step nine1α、s1βAnd calculating the attenuation ratio k obtained in the step sixteen to obtain the back electromotive force amplitude e of the motorm：
Figure FDA00025643045000000213
Eighteen, obtaining the counter electromotive force amplitude e according to the seventeenth stepmAnd the actual rotor position angle obtained in step fifteen
Figure FDA0002564304500000037
Calculating to obtain estimated motor back electromotive force
Figure FDA0002564304500000031
And
Figure FDA0002564304500000032
Figure FDA0002564304500000033
2. method for observing back electromotive force of permanent magnet synchronous motor according to claim 1, wherein the three-phase voltage u in the first stepA、uBAnd uCObtaining the voltage u under a static α - β coordinate system through coordinate transformationαAnd voltage uβThe method comprises the following steps:
Figure FDA0002564304500000034
wherein,
Figure FDA0002564304500000035
uABand uBCIs the motor stator voltage.
3. Permanent magnet synchronous machine back-emf according to claim 1The method for observing the dynamic force is characterized in that the motor stator current i in the step twoA、iBAnd iCObtaining the current i under a stationary α - β coordinate system through coordinate transformationαAnd current iβThe method comprises the following steps:
Figure FDA0002564304500000036
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