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Team Introduction
Zhu SA, Ph.D., lecturer of School of energy and electrical engineering, Hehai University, postdoctoral of Daquan Group, IEEE member. Presided over one National Natural Science Youth Fund, one Jiangsu Natural Science Youth Fund, one general program of China Postdoctoral fund, and was selected into the "mass entrepreneurship and Innovation Program" of Jiangsu Province in 2019. He has published 11 SCI journal papers, applied for 5 invention patents and 5 software copyrights. At present, it is mainly committed to improve the calculation method of PWM harmonic loss of permanent magnet motor based on small signal analysis in frequency domain, and develop the multi physical field simulation design software of electrical equipment with independent intellectual property rights.
In the introduction, a new method is proposed to calculate the eddy current loss of permanent magnet in field modulated permanent magnet motor (pmpmpmm) powered by voltage source inverter, which combines ce-fea, small signal analysis in frequency domain and eddy current loss analysis model of rectangular permanent magnet.
Based on this method, only one step of static finite element calculation is needed to construct the main low-frequency alternating flux density components in permanent magnet; only four steps of time harmonic finite element calculation are needed to obtain the relationship between PWM harmonic voltage and high-frequency alternating flux density, and then the fast calculation of eddy current loss of permanent magnet is realized by combining with analytical model. Compared with the traditional time stepping finite element method, the relative error of the total loss calculated by this method is less than 4%, and the calculation speed is increased by hundreds of times.
DOI：10.19595/j.cnki.1000-6753.tces.191103
Research background
In order to control the torque and speed of the motor in real time, most permanent magnet motors are used with voltage source inverter. There are not only losses caused by fundamental current, but also PWM harmonic losses induced by PWM harmonic voltage in the permanent magnet motor powered by inverter. Accurate modeling and calculation of them is the premise to ensure the safe operation of the motor and realize the system level optimal design of the motor inverter.
The biggest disadvantage of the traditional method of calculating PWM harmonic loss based on the small step and long time step finite element method is that the time is too long, and the finite element model of the field modulated permanent magnet motor is larger than that of the ordinary permanent magnet motor, which makes the shortcomings of using the traditional method in this kind of motor more obvious. Therefore, it is necessary to study new methods that can effectively overcome this shortcoming.
Firstly, the method and innovation of this paper refer to ce-fea. According to the characteristics of large number of permanent magnets in the minimum symmetrical finite element model of the field modulated permanent magnet motor and the phase angle difference of the magnetic density change waveform in each permanent magnet, the phase-shifting transformation of the alternating magnetic density waveform in each permanent magnet calculated by several steps of finite element method can be used to build a permanent magnet alternating magnetic density waveform in a complete cycle.
For example, as shown in Figure 1, the flux density change waveform in 14 permanent magnets calculated by 5-step finite element method can be obtained through phase-shifting transformation. Then the main alternating components are obtained by Fourier decomposition. Finally, the low-frequency loss caused by fundamental current can be calculated by combining with the analytical loss model of permanent magnet.
The eddy current loss model of rectangular permanent magnet proposed by the author is given in the following formula:
formula
It has been proved that for the studied prototype, the main low-frequency alternating flux density component is included in the flux density waveform which is constructed by one-step finite element calculation. Based on this, the low-frequency eddy current loss in the permanent magnet can be calculated accurately.
Fig. 1 average magnetic density variation waveform through one cycle of PM1 is constructed by the calculation results of 5-step tsfea
In the calculation of PWM harmonic loss, based on the assumption that the amplitude of high-frequency harmonic current introduced by PWM harmonic voltage in the permanent magnet motor is very small, which is not enough to affect the saturation state of silicon steel sheet, we propose to use the frozen incremental permeability method to build the local linearization model of the permanent magnet motor. On this basis, we use the time harmonic finite element method with voltage source as input to study the high-frequency component and permanent magnet in PWM voltage Based on the function relationship between the medium and high frequency alternating magnetic density, the PWM voltage spectrum in the rotor coordinate system is used as the input to calculate the PWM harmonic loss in the permanent magnet rapidly.
The realization idea of this method is similar to the small signal analysis of analyzing the AC amplification characteristics of triode, so this analysis method is called the small signal analysis of permanent magnet motor in frequency domain, short for small signal analysis. The local linearization model realized by the frozen incremental permeability method is called the small signal model of permanent magnet motor. A complete flow chart of the proposed method is shown in Figure 2.
It has been proved that the traditional three-dimensional finite element method needs 1220min to complete the calculation task, which only needs 3.1min to complete, the total loss relative error is less than 4%, and the calculation time can be reduced by more than 400 times.
Figure 2 Calculation of total eddy current loss of permanent magnet under inverter power supply
Conclusion the low frequency eddy current loss in fcfmpm motor can be calculated quickly based on the combination of ce-fea and the eddy current loss analytical model of permanent magnet, and the PWM harmonic loss in permanent magnet can be calculated quickly based on the combination of small signal analysis and the analytical loss model. At least one step two-dimensional tsfea and four steps two-dimensional thfea are needed to calculate the eddy current loss of permanent magnet under inverter power supply. The relative calculation error of total loss is less than 4%, and the calculation time is shortened hundreds of times.
This paper proves that the method of fast calculation of PWM harmonic loss based on small signal analysis in frequency domain is also suitable for the field modulated permanent magnet motor, which lays a foundation for the fast optimization design of the integration of permanent magnet motor and inverter system. The method based on small signal analysis in frequency domain can also be used to calculate the PWM harmonic iron loss in silicon steel quickly, and this method is widely used in different types of permanent magnet motors, which will continue in our future research.
Zhu SA, Lu Zhipeng, Wang Weidong, Tian Jian, Wang Hao are cited in this paper. Based on ce-fea and small signal analysis, fast calculation of eddy current loss of permanent magnet in field modulation motor powered by inverter [J]. Journal of electrical technology, 2020, 35 (5): 963-971. Zhu SA, Lu Zhipeng, Wang Weidong, Tian Jian, Wang Hao. Fast Calculation of PM Eddy Current Loss in FCFMPM Machine under PWM VSI Supply Based on CE-FEA and Small-Signal Analysis. Transactions of China Electrotechnical Society, 2020, 35(5): 963-971.
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