Introduction to the measurement method of permanent magnet synchronous motor

    1. Summary

    In permanent magnet synchronous motor control, whether it is sensored FOC or sensorless FOC, obtaining accurate motor parameters can improve the performance of the controller and observer. In modern control theory, establishing a mathematical model of the system is a crucial link, especially the observer in sensorless FOC. In theory, the physical quantities in the voltage equation, flux equation and torque equation can be accurately measured. If a model is established, the motor performance can be greatly optimized, including electrical parameters such as rotor pole pair number (p), stator resistance (R), DQ axis inductance (L), back electromotive force coefficient (Kv), permanent magnet flux and mechanical parameters such as moment of inertia (J), torque constant, friction coefficient, etc. Among them, mechanical parameters are often difficult to measure and are usually determined during the debugging process. This article mainly introduces the most commonly used and simplest measurement methods for electrical parameters.

    2. Mathematical Model

    The voltage equation, flux equation and torque equation of the permanent magnet synchronous motor are shown in Figure 1.

    3. Number of rotor pole pairs (p)

    The number of rotor pole pairs of a permanent magnet synchronous motor refers to the number of rotor magnetic poles, which is the ratio of the electrical angle to the mechanical angle. As shown in Figure 2, the permanent magnet synchronous motor a has three pairs of poles, and b has four pairs of poles.

    Measurement method:

    Connect the motor's A phase to the positive pole of the power supply, the B phase to the negative pole of the power supply, and the C phase can be left floating. Note that the power supply current limit point can be set to about 0.2A. Do not set it too high, otherwise it may damage the motor.

    Manually rotate the motor rotor and mark each stable rotor position;

    After the rotor rotates one circle, the number of rotor pole pairs is equal to the number of stable rotor positions;

    4. Stator resistance (R) and DQ axis inductance (L)

    The three-phase coil of a permanent magnet synchronous motor can be regarded as a series model of resistance R and inductance L. The resistance R is usually in the milliohm level, and the inductance L is usually in the microhenry level. The accuracy of a multimeter is far from enough, and it is usually necessary to use a bridge or inverter for measurement.

    Measurement method 1: Use a bridge to measure. When using a bridge to test the stator resistance, it is best to set the measurement frequency to 100HZ. When measuring the DQ axis inductance, it is best to set the measurement frequency to 1kHZ or 10kHZ.

    When measuring the internal resistance, connect any two phases of the motor with a bridge, and the stator resistance is half of the measured value.

    When measuring inductance, use a bridge to connect any two phases of the motor, slowly rotate the motor rotor, and read the bridge measurement results after the rotor stabilizes. The D-axis inductance is half of the smaller value, and the Q-axis inductance is half of the larger value. The DQ-axis inductance values ​​of most surface-mount permanent magnet synchronous motors are approximately equal.

    Measurement method 2: In the absence of a bridge, the stator resistance (R) and DQ-axis inductance (L) can also be measured with the help of a motor driver.

    Apply a voltage vector ud=constant, uq=0 in the (d, q) coordinate system that overlaps the alfa axis in the two-phase coordinate system to the inverter. In steady state, the motor is stationary, the electrical angular velocity in the voltage equation is 0, and the current differential is also 0. Measure the current id at this time, and the stator phase resistance can be obtained according to the voltage equation. In fact, in order to eliminate the influence of the dead zone and the conduction voltage drop of the power device, a differential algorithm is often used to identify the resistance. The specific method is to apply two sets of voltage vectors with different amplitudes to the inverter: ud1=constant, uq1=0, ud2=constant, uq2=0, and then measure two sets of currents id1 and id2. Finally, the calculation formula of the phase resistance can be obtained:

    When differentially identifying resistance, the given voltage must be selected carefully. It is best if the linear relationship of the current is consistent with the linear relationship of the voltage. For example, if the given voltage is 2 times, then the current should also be roughly 2 times. If the deviation is too large, it means that the selected given voltage is not appropriate.

    When the voltage vector ud=constant and uq=0 is applied to the inverter in the (d, q) coordinate system, the motor rotor will not rotate. At this time, the motor d-axis is a first-order inertia link with a time constant of L/R. Record the rising curve of the d-axis current i at this time. According to the properties of the first-order inertia link, when the d-axis current rises from 0 to 63.2% of the steady-state value, the time t is exactly equal to the time constant L/R. After obtaining the stator resistance (R) value, the inductance (L) value can be obtained according to the time constant t:

    5. Back EMF coefficient and permanent magnet flux

    The back-EMF coefficient and permanent magnet flux actually represent the same concept, which refers to the proportional relationship between the electromotive force generated by the flux and the speed when the motor rotates. The unit of the back-EMF coefficient kv is Vs/rad, and the unit of the permanent magnet flux is Wb. The two units can be converted into each other.

    Measurement method: When measuring the back electromotive force coefficient, an oscilloscope is required.

    Connect any two phases of the motor with an oscilloscope probe to measure the line voltage of the back EMF;

    Because the back EMF value is generally small, try to rotate the motor at a faster speed and then capture the back EMF waveform at this time;

    Calculate the back electromotive force coefficient of the motor according to the formula;

    6. Summary

    When a regular motor manufacturer sends a motor out of the factory, it will be equipped with a specification sheet with detailed parameters. However, most motors on the market do not have corresponding specifications. In order to obtain better control performance, it is necessary to measure the motor parameters. Whether it is the parameters measured by the bridge (affected by the accuracy of the measuring equipment) or the parameters measured by the inverter (affected by the nonlinearity of the inverter, sampling accuracy, etc.), the measured parameters may have certain errors. During the motor debugging process, do not be superstitious about the measured parameters. If necessary, they need to be constantly corrected.