Loss Optimization Control Of Permanent-Magnet Synchronous Motor With Electromagnetic Torque Ripple Suppression

In aerospace applications,due to limited power energy and difficulties of heat transfer in high altitudes,a permanent-magnet synchronous motor（PMSM）of servo systems is expected to operate with stator loss and rotor loss as little as possible.In addition,shapes of back EMFs of the motor are ideally sinusoidal in time domain.In practice,due to the factors of unideal magnetization of magnets and application of concentrated windings,the back EMFs appear to be non-sinusoidal.When sine-wave currents are injected into the motor,a problem is suffered that significant electromagnetic torque ripple is produced with lower harmonics.To address the problems of torque ripple and losses,loss-optimization control methods with electromagnetic torque ripple suppression are proposed for the PMSM with non-sinusoidal back EMFs.By optimizing the current waveform under a constraint of zero torque harmonics,and precisely controlling the harmonic currents,torque ripple is suppressed and simulaneously one or more of the winding copper loss,stator loss and rotor eddy-current loss are minimized,so that more energy is saved.Electromagnetic torque performance and thermal situation of the motor are also improved.Contributions and novel ideas of this research are as follows.（1）An improved method of determining copper-loss-optimization current vector is proposed,which not only suppresses the electromagnetic torque ripple and copper loss,but also compensates the torque generation error caused by eddy-current and hysteresis effects of the stator core.The research shows that the effects may reduce the torque in steady state,and the reduction becomes greater with higher rotor speeds and lower loads.To address the problem,a new formula of the torque is deduced with the effects and non-sinusoidal back EMFs considered.Based on the formula,the traditional optimal current vector is improved by properly expanding the amplitude and leading the phase,so as to reduce the torque generation error.Considering that there are 6^th and 12^th harmonic components contained in the optimal currents,which tend to cause a control delay and introduce an electromagnetic torque ripple again,this paper proposes a compensation strategy based on delay characteristics of the current loop,to achieve a precise control of the harmonic currents.An experiment based on a 0.95-k W,3000-rpm PMSM was done to verify performances of the improved method and compensation strategy.The toque generaton error was reduced from 27%to less than 5%.（2）A method of stator-loss-optimization control with electromagnetic torque ripple suppre-ssion is proposed to realize a better tracking of minimal-loss points and a higher efficiency of a PMSM by calculating the stator loss more precisely based on multiple synchronous rotational（MSR）transformation theory.Traditional methods suffer a problem that the calculated stator iron loss does not match the actual iron loss when the PMSM has non-sinusoidal back EMFs.Then optimization errors of the stator loss are resulted in.To address the problem,this paper develops a new mathematic model of PMSM in MSR frames,based on which the calculated iron loss matches well with the actual one.Then a tangent-point strategy is presented to determine the optimal current solution under a constraint of ripple-free torque.By injecting the current solution into a 3.8-k W,12000-rpm PMSM,testing results showed that the electro-magnetic torque ripple was suppressed effectively.Compared with the traditional stator-loss-optimization method,the proposed one could track the minimal-loss points at various speeds more accurately.Under rated operation of the motor,the stator loss was reduced by 9%and the motor efficiency is enhanced by 0.7%when compared with the above method of copper-loss-optimization control.（3）In aerospace applications,if lower harmonic currents are injected into the motor to suppress the torque ripple,additional rotor eddy-current loss is induced,leading to a higher temperature of the magnets.To address the problem,a new method is proposed to reduce the loss by optimizing amplitudes of the harmonic currents.If traditional models of eddy-current loss are used in the method,it is difficult to determine an analytical current solution with a high precision.Therefore,a new loss model is developed with a quadric-form expression,so that the analytical solution can be obtained by the Lagrangian Multiplier Method.Coefficients of the model are determined by finite-element simulations to improve the model precision.Based on the model,the optimal harmonic amplitudes are solved under a constraint of zero 6^thharmonic torque.The solution can be easily implemented online with a proportion to the torque command.A comparison experiment with the copper-loss-optimization control was carried out based on the 3.8-k W PMSM,which showed that the eddy-current loss was reduced by at least 37.8%.Therefore,complicated manufactures such as sleeve slotting and copper cladding on the rotor can be avoided.（4）A method of electromagnetic torque ripple suppression and total-loss-optimization control is proposed to improve thermal situation of the motor by adjusting two weight coefficients of the optimal current solution.A total loss model including copper loss,stator iron loss and rotor eddy-current loss is developed with two weight coefficients,and then minimized under a constraint of zero 6^th harmonic torque to determine the optimal current solution,which can be used to reduce any of the losses.The proposed method can realize smooth switchinges between different current waveforms with the electromagnetic torque ripple suppressed.As a result,the thermal situation of the motor is changed to meet complex energy and cooling requirements in aerospace applications.Based on the 3.8-k W motor platform,the laws of loss variations with different weight coefficients were validated.A switching between the stator-loss-optimization and eddy-current-loss-optimization currents was realized within two seconds,and the electromagnetic torque ripple was suppressed effectively in the process.