| Permanent magnet synchronous machines(PMSM)are widely used in energy conversion,power generation,electrified transportation,industrial automation because of their high-power density,high efficiency,and reliable operation,and are important and basic components involved in modernization and national defense construction.Currently,the optimization of PMSM has become an important topic in electric machine research and industrial applications,with specific objectives including improving torque density,reducing torque pulsation,weakening cogging torque,and suppressing vibration noise.At the root,the above negative performances are mainly caused by the complex temporal and spatial harmonics of PMSMs.However,the traditional electric machine theory is based on the fundamental magnetic field model,so there are limitations in analyzing and solving the above problems.Based on this,this paper is devoted to studying the sources and existence of various harmonics in PMSMs,analyzing the interaction laws between harmonics and their effects on PMSM performance,and exploring optimization methods for motor design and control considering the harmonic effects.The main work of this paper is summarized as follows.Firstly,the sources and existence forms of PMSM harmonics are discussed,including rotor flux harmonics,stator winding harmonics,and inverter voltage harmonics.The harmonic analysis of rotor flux includes the surface-mounted and interior PM rotors,as well as the harmonic characteristics under the conditions of magnetic saturation,asymmetric pole,unequal air-gap,and stator slotting.The harmonic analysis of stator winding includes electromotive force and magnetomotive force(MMF)of different winding topologies,as well as the stator magnetic harmonics under the conditions of multi-phase winding,asymmetric current,fractional-slot concentrated-winding,and salient-pole rotor.The harmonic analysis of inverter voltage includes classical pulse-width modulation methods,as well as inverter nonlinear characteristics such as dead time,parasitic effect,and zero-current clamp effect.Therefore,the coexistence of temporal and spatial harmonics of PMSM is obtained.Further,the analytical model of the harmonic action is developed based on the harmonic forms,specifically the synchronous torque and its pulsation generated by the harmonic action of the stator and rotor fluxes,the reluctance torque and its pulsation generated by the harmonic action of the stator MMF and the rotor reluctance,the cogging torque generated by the action of the rotor MMF and the airgap reluctance slot harmonics,and the radial electromagnetic(EM)force generated by the action of the stator and rotor MMFs and the airgap reluctance slot harmonic.Thus,the harmonic characteristics and the influencing factors that cause the undesirable performances of PMSM are obtained.Moreover,this paper has carried out accurate modeling research on the cogging torque,and the proposed cogging torque harmonic action model(HAM)has been verified by finite-element method(FEM)to calculate cogging torque accurately with faster solving speed,thus verifying the effectiveness of the proposed analytical HAM.Then,based on the HAM of PMSM,this paper proposes:1)the design method of torque pulsation reduction based on rotor reluctance harmonics construction,which constructs the rotor reluctance harmonics by designing the rotor profile to change the 6n±1th rotor airgap flux density harmonic composition,the FEM and experiment verify that the proposed method can effectively weaken the overall EM torque pulsation;2)the design method of cogging torque reduction based on airgap reluctance slot harmonics construction,which can reduce the cogging torque by designing the stator dummy slot to increase the fundamental frequency of the airgap reluctance slot harmonic and the rotor MMF order with which it acts;3)the multi-objective design optimization of EM characteristics of PMSM,which replaces the finite-element model with the metamodel and uses stochastic algorithms to achieve fast design optimization for several key EM properties,including improving torque density,decreasing torque pulsation,and reducing vibration noise,and the effectiveness of the proposed multiobjective design optimization is verified by FEM and experiment.In addition,considering that the traditional vector control model is difficult to consider the complex field harmonics and the resulting EM torque pulsation,this paper establishes a harmonic vector model(HVM)of PMSM,which analyzes the vector expression of the stator and rotor magnetic harmonics and the torque pulsation law.Moreover,this paper proposes a dynamic simulation method of PMSM system based on HVM with code as the framework,and verifies by FEM that harmonic vector simulation can effectively simulate the synchronous torque pulsation of PMSM,so as to make up for the deficiency of the traditional vector simulation which cannot calculate the inherent torque pulsation,and make the simulation more consistent with the actual motor control,and lay the theoretical foundation for the vector control optimization.Finally,based on the HVM of PMSM,this paper proposes:1)EM torque pulsation suppression control,which generates 6n synchronous torque pulsations by injecting 6n+1 current harmonics,and the generated synchronous torque pulsations are opposite to the inherent EM torque pulsations,so as to achieve mutual offset of torque pulsations;2)Harmonic torque utilization control,which proposes an EM design method for the coexistence of full-order odd spatial magnetic field harmonics in PMSMs,and proposes to make full use of the magnetic field harmonics by injecting 2n+1th current harmonics to produce maximum harmonic torque without increasing the current amplitude;3)Optimal harmonic torque control,which is a method to effectively reduce torque pulsation while significantly increasing the average torque by integrating the current harmonics injected with torque pulsation suppression and harmonic torque utilization,and the FEM verifies the effectiveness of the proposed current injection method. |
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