考虑磁桥非线性的内置式永磁同步电机空载电磁性能通用解析模型

General Analytical Model of No-Load Electromagnetic Performance of Interior Permanent Magnet Synchronous Motors Considering Nonlinearity of Magnetic Bridges

该文提出一种将子域法及等效磁路法相结合的新型解析模型,可在计及磁桥饱和的情况下,计算具有任意极槽配合的V型/U型/一字型内置式永磁电机的空载电磁性能。建模时首先根据转子结构将永磁体进行等效,以便于各子域的建立;为了考虑转子磁桥处的饱和,采用等效磁路法来计算磁桥处的磁导率,以便于相应子域边界条件方程的建立。电机无槽时的空载气隙磁通密度分布可以通过求解各子域交界面处边界条件方程组得到,然后通过保角映射的方法可考虑定子开槽的影响。该文所提模型可用于计算内置电机的空载气隙磁通密度分布、反电动势及齿槽转矩。将模型计算结果与实验测试及有限元计算结果进行对比,验证了所提出模型的有效性。与有限元法相比,该文所提模型具有建模速度快、耗时短,同时可达到近似精度的优点,这为相关电机的初始设计及优化带来了方便。

Interior permanent magnet(IPM)motors,due to the high power/torque density and wide speed range,are widely used in industrial applications and smart homes.Considerable computation time is one of the major issues faced by designers due to the changeable rotor configurations.The finite element analysis(FEA)is widely used in motor design due to its ability to consider saturation and complex geometries.However,the need for high-precision mesh is time-consuming.The analytical method has acceptable accuracy and fast calculation,which is regarded as an effective tool by designers.However,the existing analytical models are not universal.Therefore,this paper proposes a novel general analytical model to predict the no-load performance of IPM motors with different topologies.Firstly,the magnets with different topologies are equivalent according to the principle that the total flux produced by the magnets is constant,facilitating the establishment of subdomains.Secondly,based on the boundary conditions between different subdomains,the field governing equations can be obtained to solve the undetermined coefficients.Thirdly,the magnetic equivalent circuit(MEC)method is employed to obtain the permeability of magnetic bridges to consider the effect of saturation and improve the calculation accuracy.Finally,the influence of slotting is considered based on the conformal mapping method to obtain the air-gap magnetic field of slotted motors.The proposed general model is suitable for V-shape,U-shape,and straight-shape IPM motors with any slot-pole combination.The computation time is greatly shortened compared with FEA because the equations to be solved are linear.The calculated no-load air-gap flux density waveforms,back electromotive force(EMF),and cogging torque by the proposed model are in good agreement with those of FEA results.For the V-shape motor,the fundamental amplitudes of back EMF obtained by FEA,analytical model and experiment are 85.5 V,86.2 V,and 84.8 V,respectively;the corresponding total harmonic distortions(THDs)are 2.57%,1.95%,and 3.02%,respectively.For the U-shape motor,the fundamental amplitudes of back EMF obtained by FEA and analytical model are 213.7 V and 215.9 V,respectively;the THDs are 4.98%and 4.7%,respectively.For the straight-shape motor,the fundamental amplitudes of back EMF obtained by FEA,analytical model and experiment are 318.7 V,325.3 V,and 320.4 V,respectively;the THDs are 1.09%,1.62%,and 1.55%,respectively.The amplitudes of cogging torque for the V-shape motor calculated by FEA and analytical model are 368 mN·m and 403 mN·m,the calculation error is 9.5%.The amplitudes of cogging torque for the U-shape motor are 609 mN·m and 584 mN·m,and the calculation error is 4.1%.The amplitudes of cogging torque for the straight-shape motor are 57 mN·m and 51 mN·m,the calculation error is 10.5%.The above results show that the model can effectively calculate the no-load performance of IPM motors with different rotor structures.The following conclusions can be drawn from the above analysis:(1)Compared with FEA,the proposed general model can significantly reduce the computational cost since the calculation is based on linear equations rather than numerical iteration.(2)The proposed model has higher precision,and the errors between calculated and FEA results are within the allowable range of the engineering.(3)The proposed magnet equivalence method provides ideas for the analytical derivation of other types of IPM motors with irregular magnets arrangement,which brings convenience to the design and optimization of related types of motors.