Parameter Calculation And Performance Analysis Of Line-Start Permanent Magnet Synchronous Motor With Composite Solid Rotor

Line-start permanent magnet synchronous motor(LSPMSM)is a type of permanent magnet synchronous motor with squirrel cage windings mounted on the outer surface of the rotor.When the stator windings are connected to the power supply,the LSPMSM is able to start directly due to the induction torque.When the starting process is over and the rotor speed rises to the synchronous speed,the LSPMSM enters the stable operation state.In this state,the working mechanism of LSPMSM is basically the same as that of the general permanent magnet synchronous motor,making the LSPMSM have high satisfactory working efficiency and power factor.The combination of self-starting ability and good steady-state working performance makes the LSPMSM an ideal alternative to induction motors in various applications,with which the energy saving and the consumption reduction can be realized and the economic benefits can be improved.However,in terms of starting performance,the LSPMSM usually does not have enough competitive advantages over induction motors of the same specification.Main reason for this phenomenon is stated as follows.The average electromagnetic torque of induction motor during the starting process contributes completely to the speed-rise of rotor,whereas the LSPMSM during the starting stage suffers also from the braking torque coming from interaction between permanent magnets and stator winding currents arising from the permanent magnet fluxes.The braking torque generally reaches its peak value when the slip is close to 1.When the braking torque is superposed with the induction torque,the synthetic average electromagnetic torque is significantly weakened and significantly concave at a low rotational speed,which makes it difficult for LSPMSM to obtain an ideal starting capability.Replacing the traditional cage rotor with solid rotor is an effective measure to enhance the starting performance of LSPMSM.The core part of the solid rotor is composed of solid ferromagnets with good electrical and magnetic conductivity,which can provide the flow path for rotor fluxes and rotor eddy currents simultaneously.The skin effect enables the solid-rotor LSPMSM to have large rotor resistance and high induction torque at initial starting process.However,compared with the conventional cage-rotor LSPMSM,the slope of the mechanical characteristic curve of the solid-rotor LSPMSM becomes smaller at small slips,due to which synchronization ability becomes worse.In order to solve the above-mentioned problem,a composite solid rotor combining the solid rotor with cage rotor is proposed by some researches.The LSPMSM with composite solid rotor can inherit the good starting performance of the solid-rotor LSPMSM,and can also obtain satisfactory synchronization ability through the reasonable design of cage winding.In recent years,there have been many scholars to discuss composite solid rotor LSPMSM,but some key questions concerned with the LSPMSM using composite solid rotor have not got in-depth researches.Among these questions requiring further researches,there are two outstanding ones.One of them is that accurate calculation method of electromagnetic parameters has not been established.The second is the lack of comprehensive analyses on electromagnetic vibration,rotor eddy-current loss,and rotor temperature rise.Therefore,in this paper based on the National Natural Science Foundation Project "Research on the self-starting permanent Magnet synchronous motor system with high voltage and Middle Power Composite Solid Rotor"(51777118),the author carries out a systematic study on the composite solid rotor LSPMSM in terms of electromagnetic parameters and motor performance analysis.The main research work is summarized as follows:1.Calculation of electromagnetic parametersAimed at fast calculation of starting process and accurate evaluation of starting performance,the calculation system of electromagnetic parameters of composite solid-rotor LSPMSM is established in this paper.First,the d-q-axis coupling inductance and q-axis permanent magnet flux are introduced to modify the state equations to take into account the coupling effect.Afterwards,according to the basic law that the electromagnetic state changes much faster than the speed at the starting stage,the calculation of transient-varying electromagnetic parameters at starting stage is changed into calculation of a series of steady-state electromagnetic parameters at different slips.Steady-state electromagnetic parameters at certain slips are calculated through combing the modified state equations and the finite element method.When the solution of parameters is accomplished,the electromagnetic parameters obtained are substituted into the state equations to establish the dynamic model of the composite solid-rotor LSPMSM.Speed-and torque-time response curves obtained from the dynamic model agree well with those obtained from the finite element method whereas the time consumption of the dynamic model is much smaller than that of finite element method.After the calculation of electromagnetic parameters and establishment of dynamic model,this paper deduces the electromagnetic torque expression at the starting stage of the motor based on the state equations considering the coupling effect and selects the starting-capability evaluation indicator.Based on the electromagnetic torque expression,the mathematical relation between starting-capability evaluation indicator and electromagnetic parameters is determined.The starting-ability evaluation indexes corresponding to different electromagnetic parameters are solved and the specific influences of electromagnetic parameter variation on the starting capability of the motor are obtained.2.Calculation of magnetic-field distribution2.1 Calculation of magnetic field at synchronous speedIn priot to the synchronous magnetic-field calculation,this paper transforms the shapes of critical regions(such as the stator-winding coils and permanent magnets)into radial sectors of which the centers are totally located at the origin point.After the transformation,the shapes of each region meet the shape requirements of the subdomain method for magnetic field calculation.The subdomain method is used to calculate the synchronous magnetic field of the motor after the region transformation.The comparison of the results with the finite element method verifies the rationality of the shape transformation and the accuracy of the magnetic field calculation results.2.2 Calculation of magnetic field at asynchronous speedIn this paper,a hybrid magnetic field calculation method is presented to calculate the magnetic field distribution of the composite solid rotor LSPMSM running at stable asynchronous state.The method combines the subdomain method with the finite difference method,in which the former is used to calculate the magnetic field distribution in the stator and air gap region,and the latter is used to solve the magnetic field distribution in the rotor region.The combination of the subdomain method with the finite difference method can not only avoid the problem that the subdomain method is unable to deal with the radial boundary conditions of the rotor region,but also have a faster calculations speed compared with the numerical method.3.Analysis and depression of electromagnetic vibrationIn this paper,terms including permanent magnet magnetomotive force and effect coefficient of air gap conductance due to stator and rotor slotting are obtained in terms of their cosine series expressions using the synchronous magnetic-field calculation.Then,the airgap magnetic density is obtained using the magnetomotive force-permeance method.Afterwards,the analytical expression of the radial electromagnetic force density is obtained using the Maxwell tensor method.The calculation accuracy of the expression is verified by comparing with the finite element simulation results.Based on this expression,number features of the spatial order and alternating frequency of the harmonic components of the radial electromagnetic force density are obtained.After the analytical derivation of the radial electromagnetic force density and the analysis of the harmonic characteristics,the radial electromagnetic force densities corresponding to two electromagnetic-vibration depression measures as non-uniform air gap and step-skewed permanent magnets are obtained.The effectiveness of the two methods is verified by comparing the amplitude of each harmonic component in the expression of the radial electromagnetic force density in the case of non-uniform air gap or step-skewed permanent magnets permanent magnet with that in the case of uniform air gap and permanent magnet without skewing.4.Rotor eddy-current loss depression and cooling system improvement4.1 Rotor eddy-current loss depressionA qualitative analysis of the air-gap flux-density harmonics causing rotor eddy current is performed first.Based on the calculation results,it is known that stator slotting is the main reason for the generation of air-gap flux-density harmonics as well as the rotor eddy currents.In this paper,the rotor eddy-current loss is effectively reduced by increasing the length of air gap,adopting non-uniform air gap and magnetic stator-slot wedges to suppress the asynchronous harmonics of air gap flux density.The variation tendencies of electromagnetic losses,power factor and starting-capability evaluation index corresponding to the change of air-gap length,level of air-gap non-uniformity and relative permeability of magnetic stator-slot wedges are calculated.Based on the calculation results,effects of the rotor-loss reduction methods on the motor general performance are clarified.Afterwards,the non-dominated sorting genetic algorithm-?(NSGA-II)embedded with a neural network is utilized to conduct motor optimization.The multi-objective optimization permits a balance among various performance indexes.4.2 Cooling system improvementWhen the ordinary air cooling system is applied to the composite solid-rotor LSPMSM with large capacity,the stator contains radial ventilations whereas the rotor does not have any ventilations.The heat generated inside rotor can not be exhausted effectively,due to which the possibility of PM demagnetization due to high temperature and motor performance deterioration turns higher.Aimed at reducing the rotor temperature raise and improving the heat dissipation efficiency,this paper makes some developments on the air-cooling system:With reservation of stator radial ventilations,both axial and radial ventilations are applied to the rotor core.Locations of radial rotor ventilations are in coincidence with the radial stator ventilations.Along with the utilization of axial and radial rotor ventilations,a large amount of cooling air is forced by fans located at two sides of motor to flow successively through the axial rotor ventilations,radial rotor ventilations,air gap and stator radial ventilations.These ventilations lead to larger contacting area between cooling air and rotor cores,by which the depression of rotor temperature rise can be realized.Temperature fields of a 355 kW,10 kV composite solid-rotor LSPMSM using ordinary/developed air-cooling system are calculated through coupling the electromagnetic simulation software Maxwell with the fluid dynamics simulation software Fluent.According to the calculation results,it can be found that the highest average temperature of rotor cage,rotor cores and rotor permanent magnets decreases by 10.19?,by which the rotor temperature depression using the developed cooling system can be verified.5.Prototype testA 355 kW prototype and a 5.5 kW prototype are manufactured respectively.The no-load voltage,on-load performance indexes(including stator winding current,power factor,efficiency),blocking torque and blocking currents of the 355 kW prototype are measured.The speed-time responses during starting stage,no-load voltage and blocking torque of the 5.5 kW prototype are measured.Experimental results derived from tests on the two prototypes are used to verify the theoretical analysis and calculation results of this paper.