| Structurally, the line-start permanent magnet synchronous motor (LSPMSM) can be seen as an induction motor with interior permanent magnets, and it has self-starting ability, by means of the asynchronous torque generated by the rotor cage. Compared with induction motor, LSPMSM has the advantages of high efficiency, high power factor and wide range of economic operation, etc. Under the global trend of energy conservation and emissions reduction, the advantages of LSPMSM will be further highlighted and LSPMSM will have broad prospects of development. In recent years, scholars have further studied LSPMSM, and established the foundation for the design, manufacture and widespread use of LSPMSM. But there are still some problems in the practical application of LSPMSM. This is mainly due to the lack of systematic study of three major problems of LSPMSM, that is, the demagnetization of permanent magnets, cogging torque, and electromagnetic vibration. Based on the National Natural Science Foundation of China "Study on Several Difficult Problems of Line-start Permanent Magnet Synchronous Motor" (51177089), this paper studied the three difficult problems, and the main contents are as follows.1. The demagnetization characteristics of LSPMSM during the starting process and under different fault conditionsIn order to better reflect the demagnetization state of permanent magnets, magnets’ minimum operating point is calculated on the basis of finite element simulation results. It can reflect not only the demagnetization state of the whole permanent magnets, but also whether the local irreversible demagnetization occurs. In this paper, a 22 kW 6-pole LSPMSM is taken as the prototype motor. The demagnetization characteristics of LSPMSM during the starting process and under some fault conditions, including unbalanced supply voltages, out-of-step, supersynchronous and reverse rotation, are studied by finite element method (FEM). For illustrative purposes, the concepts of magnets’ local largest demagnetization point and magnets’ global largest demagnetization point are defined. Magnets’ local largest demagnetization point is the minimum value of magnets’ minimum operating point curve during one transient process. Magnets’global largest demagnetization point under one condition is permanent magnets’ minimum operating point when the motor encounters the severest demagnetization field of the condition.The demagnetization effects of the magnetomotive forces of stator and rotor windings on permanent magnets during the starting process are analyzed. It is found that the direct-axis compound fundamental magnetomotive force of stator and rotor windings can accurately reflect the demagnetization state of permanent magnets, the variation trend of which agrees well with that of magnets’minimum operating point curve. As for the controversy that when the severest demagnetization field occurs during the starting process of LSPMSM, this paper further analyzes the effects of the moment of inertia, load torque and initial rotor position on magnets’ local largest demagnetization point. It is found that when the load condition and the initial rotor position are different, magnets’ local largest demagnetization point may appear at any speed. But with the increase of load torque and the moment of inertia, the probability that the motor speed when magnets’ local largest demagnetization point occurs is close to the synchronous speed increases. When the motor speed at the moment magnets’ local largest demagnetization point occurs is closer to the synchronous speed, the probability that magnets’ local largest demagnetization point is low will be higher.The demagnetization characteristics of LSPMSM under fault conditions of unbalanced supply voltages, out-of-step, supersynchronous and sudden reverse rotation are further studied. The effects of load condition and other factors on the demagnetization of permanent magnets are analyzed, and the rules that the largest demagnetization field occurs are obtained.In addition, this paper establishes the analytical calculation model of magnets’ average operating point during the starting process of LSPMSM, by combining the dynamic mathematical model and magnetic circuit model of LSPMSM. The stator and rotor currents at the each moment of the starting process are calculated by the dynamic mathematical model, and the corresponding demagnetization magnetomotive force of permanent magnets can be calculated. Importing the demagnetization magnetomotive force into the magnetic circuit model, we can calculate the corresponding average operating point of permanent magnets. The correctness of the proposed analytical calculation model is verified by the finite element simulation.2. The analytical analysis and reduction of cogging torque in LSPMSMExisting studies on the cogging torque of permanent magnet machines are almost confined to permanent magnet machines with one-sided slots. The cogging torque of LSPMSM lacks of effective analytical analysis and reduction methods. Because of the slots on both stator and rotor sides of LSPMSM, the distribution of effective air-gap length is very complex when the relative position of stator and rotor changes. This greatly increases the difficulty to analytically calculate the cogging torque of LSPMSM. In order to reduce the difficulty to analytically calculate the distribution of effective air-gap length, the effect of the whole rotor (including rotor slots) is equivalent to the distribution of air-gap magnetomotive force. Thus the distribution of effective air-gap length is only related to the distribution of the stator slots. Using energy method, we deduce the analytical expression of the cogging torque of LSPMSM. It should be noticed that the purpose of the analytical calculation method is to establish clear relationship between cogging torque and motor parameters, instead of accurate calculation of cogging torque.Using the above analytical expression of cogging torque, we analyze the effects of the combination of pole-number and slot-number, stator skewing and non-uniform air-gap on the cogging torque of LSPMSM. It is found that by appling non-uniform air-gap and appropriate combination of pole-number and slot-number, low cogging torque can be obtained. The cogging torque of LSPMSM can be eliminated by selecting appropriate stator skewing number.In addition, this paper further studies methods to reduce the cogging torque of LSPMSM. The analytical expressions of cogging torque with changing the stator tooth width, stator teeth pairing, stator slots pairing, changing the rotor tooth width, rotor teeth pairing, rotor slots pairing and poles shifting are deduced. The corresponding methods to calculate the motor parameters that can effectively reduce the cogging torque are given. The effectiveness of these methods and their effects on the motor performance are analyzed by FEM. The results show that the proposed methods can effectively reduce the cogging torque of LSPMSM, and will not significantly affect the motor performance.3. The analytical analysis of electromagnetic force and the suppression methods of electromagnetic vibration in LSPMSMThe Electromagnetic vibration is caused by the time evolution electromagnetic force that acts on the stator core. There is no reference that establishes the analytical calculation model of the electromagnetic force of LSPMSM at present. This is mainly due to the slots on both stator and rotor sides of LSPMSM, which greatly increases the difficulty to analytically calculate its electromagnetic force. We adopt the equivalence method of rotor in the study of cogging torque, thus the difficulty to analytically calculate the electromagnetic force of LSPMSM is reduced. The analytical expression of the no-load electromagnetic force is deduced by the Maxwell stress tensor method. It should be noticed that the purpose of the analytical expression is to establish clear relationship between motor parameters and the electromagnetic force with different orders and frequencies, instead of accurate calculation of the electromagnetic force.This paper takes a 1.5kW 4-pole LSPMSM as the prototype motor, and calculates its no-load distributions of air-gap flux density and electromagnetic force by FEM. The sound power level spectrum generated by the main low-order electromagnetic force is calculated by the method of mechanical impedance. From the spectrum, we find the order number and frequency of the main electromagnetic force that needs to be suppressed. Using the above analytical calculation method of electromagnetic force, we deduce the analytical expressions of no-load electromagnetic force with changing the rotor tooth width,changing the stator tooth width, stator teeth pairing and stator slots pairing. The corresponding methods to calculate the motor parameters that can effectively suppress the main electromagnetic force are obtained. The effectiveness of these methods and their effects on the motor performance are analyzed by FEM. The results show that the proposed methods can effectively suppress both the main electromagnetic force and the no-load electromagnetic vibration of LSPMSM, and will have little effects on the motor performance.Using the analytical analysis model of the electromagnetic force, we further study the effects of rotor static eccentricity and dynamic eccentricity on the frequency component of electromagnetic force. Results show that the main frequencies of the electromagnetic force without rotor eccentricity and with rotor static eccentricity include the even multiples of power frequency. Except the frequencies of the electromagnetic force without rotor eccentricity, those with rotor dynamic eccentricity also include the odd multiples of half power frequency and odd multiples of power frequency. In addition, the no-load vibration spectrum of the 1.5kW LSPMSM is measured, and its main frequency component agrees well with the result of analytical analysis. That further verifies that the proposed analytical analysis model can reflect the main frequency component of electromagnetic force of LSPMSM. |
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