Abstract: When high dynamic performance is required for asynchronous motors driven by frequency converters, vector control is typically employed. The dynamic performance of vector control and the speed estimation accuracy in sensorless vector control both depend on the detailed parameters of the motor. This paper analyzes the equivalent circuit and mathematical model of the motor and proposes a scheme for automatic motor parameter identification using a frequency converter. Simulation and experimental results demonstrate that this method is simple to implement, and the identification results meet the requirements for vector control and speed estimation applications, showing strong practicality.
1 Introduction
In AC asynchronous motor speed control systems, vector control can decouple the excitation current and torque current of the AC motor, thereby achieving speed regulation performance similar to that of a DC separately excited motor speed control system. However, this current decoupling requires the motor's stator and rotor resistance, stator and rotor leakage inductance, and mutual inductance parameters. For general-purpose frequency converters, the parameters of motors in the engineering field are unpredictable, and it is even more difficult to measure parameters using conventional locked-rotor and no-load tests. Furthermore, for the same motor, long-term aging and environmental influences can cause changes in motor parameters. Therefore, it is necessary to utilize the frequency converter itself to automatically identify motor parameters before operation. This paper, based on this requirement, relies on the frequency converter itself, without adding any additional circuitry or changing the motor wiring, and uses the principle of frequency converter pulse modulation to identify motor parameters through DC tests, single-phase AC locked-rotor tests, and no-load tests.
2. Parameter Identification Principle
In an asynchronous motor vector control system, the main motor parameters required include: stator resistance, rotor resistance, stator-rotor mutual inductance, stator leakage inductance, and rotor leakage inductance. Figure 1 shows a typical connection between a voltage-source inverter and a three-phase asynchronous motor. The three arms A, B, and C of the inverter are connected to the three-phase windings a, b, and c of the asynchronous motor, respectively.
Figure 1. Main circuit structure of frequency converter and motor
Fig.1 Main circuit structure of inverter and motor
Figure 2 shows the single-phase T-shaped equivalent circuit of an asynchronous motor.
Figure 2. Single-phase T-shaped equivalent circuit of an asynchronous motor.
Fig.2 The T equivalent circuit of induction motor
2.1 Stator Resistance Identification
Identification via DC experiment (i.e., the volt-ampere method) requires injecting DC current into the motor stator windings through an inverter. This is achieved by making the control signals for phases B and C of the bridge arm in Figure 1 identical, i.e., short-circuiting phases b and c of the motor, and applying a DC pulse voltage to the motor. Within each switching cycle, the energy of the inductor's charging and discharging is equal; therefore, the average value of the sampled current is the DC current in the experiment. The equivalent circuit is simplified as shown in Figure 3.
Figure 3 Equivalent circuit for DC experiment
Fig.3TheTequivalentcircuitofDCexperiment
According to Figure 3, assuming the average actual voltage applied to the motor is and the average actual current of phase a is , the stator resistance can be calculated as shown in equation (1):
(1)
In practical applications, using the sampled current as the actual current while maintaining a suitable current (but not a large value) results in a smaller error. However, the duty cycle of the actual output DC voltage is extremely small, leading to a large error in the actual applied voltage detection. Using the voltage value sent by the frequency converter for calculation also introduces the effects of dead zone and switching transistor voltage drop, resulting in further errors. Therefore, a slope calculation method is used to eliminate the effects of dead zone and switching transistor voltage drop. The specific implementation is as follows:
The target currents are given sequentially, and the average value of the A-phase current is sampled as feedback. The difference between the two currents is used by a PI regulator to output the duty cycle of a DC pulse voltage. After the closed-loop output stabilizes, the average values of the currents and the voltage duty cycles are recorded. Let the actual average voltages at the two recorded times be and , respectively, then:
(2)
Subtracting the two equations, we obtain the stator resistance calculation as shown in equation (3).
(3)
2.2 Identification of stator and rotor leakage inductance and rotor resistance
A single-phase test is used instead of the traditional three-phase locked-rotor test to identify stator and rotor leakage inductance and rotor resistance. When a single-phase sinusoidal voltage is applied to the motor windings, no electromagnetic torque is generated, and its electromagnetic phenomena are basically similar to those of a three-phase locked-rotor test.
The specific implementation method for generating a single-phase sinusoidal voltage is similar to the DC voltage generation method described in 2.1. The control signals for bridge arms B and C are identical. The amplitude of the A-phase current is used as a feedback signal, and the difference between this signal and the current control target is output as the required voltage amplitude via a PI regulator. A sinusoidal voltage at the motor's rated frequency is then applied to the motor according to this amplitude. The equivalent circuit is shown in Figure 4(a). Under a rated frequency sinusoidal AC voltage, the leakage reactance and resistance of the stator and rotor of the asynchronous motor are very small relative to the inductive reactance of the mutual inductance. Therefore, Figure 4(a) can be further simplified to Figure 4(b). To reduce the complexity of identification, the stator leakage inductance and rotor leakage inductance are generally considered to be approximately equal.
Figure 4. Equivalent circuit diagram of single-phase experiment
Fig.4Theequivalentcircuitofsinglephaseexperiment
As shown in Figure 4(b), the equivalent resistance in the circuit is:
(4)
The equivalent reactance is:
(5)
The rotor resistance is:
(6)
The stator and rotor leakage inductance are:
(7)
Where is the phase angle difference between voltage and current, is the synchronous angular frequency of voltage and current, and and are the corresponding voltage and current amplitudes.
For a single-phase sinusoidal signal, the signal can be used as a sample value. By differentiating the sampled values of the signal, an orthogonal signal can be constructed. The amplitude and phase angle of the single-phase sinusoidal signal can be obtained from the sampled values, as shown in equations (8) and (9). This method reduces the amount of computation compared to the FFT method and saves program running time.
(8)
(9)
2.3 Stator-rotor mutual inductance identification
The mutual inductance between the stator and rotor of the motor is identified through a no-load test. When the motor is unloaded, the motor speed is basically close to the synchronous speed, the slip is small, and the motor rotor circuit is equivalent to an open circuit. The single-phase equivalent circuit of the motor at this time is shown in Figure 5.
Figure 5 Equivalent circuit diagram of the idling experiment
Fig.5 The equivalent circuit of no-load experiment
As shown in Figure 5, the equivalent reactance is:
(10)
Mutual inductance is:
(11)
Where is the phase angle difference between voltage and current, is the synchronous angular frequency of voltage and current, and are the three-phase effective values of voltage and current, respectively. The angles and effective values of voltage and current can be obtained through three-phase coordinate transformation.
3. Simulation Verification
This paper verifies the proposed method using the Psim simulation platform. The relevant parameters of the motor model in the simulation are shown in Table 1.
Table 1 Motor parameter settings
Tab.1The set value of motor parameters
All calculations in the simulation use a per-unit system, with voltage base values, current base values, and a rated frequency of 50Hz.
For ease of comparison, both simulation and experiment used SVPWM to send pulses. When maintaining the calculated pulse angle, the pulse voltage and current waveforms obtained from the DC experiment are shown in Figure 6, where is the actual current of phase A, is the calculated average current, and is the modulation index required for the calculated pulse. The relationship between these values and the output voltage duty cycle is as follows:
The two current target values were set to 0.6 and 0.9 respectively. After the voltage and current stabilized, the voltage pulse duty cycle and the actual current were recorded respectively. The stator resistance per unit value was calculated according to formula (3) and converted into the actual value.
Figure 6. DC experimental voltage and current waveforms
Fig.6 The wave of DC simulation
In the single-phase experiment, a 50Hz single-phase current was applied to the motor, and the voltage and current waveforms were obtained as shown in Figure 7. The high-frequency harmonics can be filtered out by using the average value sampling method. The amplitude and phase angle are obtained according to the above method of constructing orthogonal signals. The rotor resistance and leakage inductance are obtained according to equations (4), (5), (6), and (7), and the per-unit values are converted into actual values.
Figure 7. Voltage and current waveforms in a single-phase stalled rotor experiment.
Fig.7 The wave of single phase simulation
The voltage and current waveforms obtained from the three-phase no-load test are shown in Figure 8. The high-frequency harmonics are filtered out by the average value sampling method. The required variables are obtained according to the three-phase coordinate transformation and the effective value calculation method of the three-phase AC signal. The mutual inductance between the stator and rotor is calculated according to formulas (10) and (11).
Figure 8. Waveforms of no-load test voltage and current
Fig.4 The wave of single phase simulation
The comparison between the parameter calculation results and the motor parameter settings is shown in Table 2:
Table 2 Motor parameter identification accuracy
Tab.2 Motor parameter identification precision
4. Experimental Verification
The experiment was conducted on an actual frequency converter and motor according to the method described in the text. The frequency converter used was a voltage-type two-level frequency converter with a current sampling accuracy of 12 bits, and the voltage was calculated from the transmitted voltage. The waveforms during the test were displayed on a host computer, as shown in Figures 9 and 10. In both figures, the output modulation index (modulate) and the detected current (Ia) are per-unit values. The waveform distortion is caused by fluctuations in the sampling period of the host computer.
Figure 9 DC experimental modulation and current waveform
Fig.9 The wave of DC experiment
Figure 10. Modulation and current waveform of single-phase locked rotor experiment.
Fig.10 The wave of single phase experiment
The traditional method involves testing and calculating according to electrical engineering test methods. The obtained parameter identification results are shown in Table 3.
Table 3 Comparison of parameter identification methods and traditional measurement methods
Tab.3 Parameter identification method with inverter compared with traditional measurement method
5. Conclusion
Simulation and experimental results demonstrate that the simulation results closely approximate the motor's set parameters. The experimental results are also close to those obtained through traditional measurements. While the stator and rotor resistance values exhibit significant errors due to variations in measurement time and ambient temperature, this aligns with actual motor characteristics. Other parameters show errors within 3%, meeting the requirements for high-performance speed control. This identification method is simple, easy to implement, and possesses high accuracy in identifying stator and rotor resistance, leakage inductance, and mutual inductance, making it widely applicable in general-purpose frequency converters.
