Dynamic and steady state performance comparison of line-start permanent magnet synchronous motors with interior and surface rotor magnets

A comprehensive comparison of the dynamic and steady state performance characteristics of permanent magnet synchronous motors (PMSM) with interior and surface rotor magnets for line-start operation is presented. The dynamic model equations of the PMSM, with damper windings, are utilized for dynamic studies. Two typical loading scenarios are examined: step and ramp loading. The interior permanent magnet synchronous motor (IPMSM) showed superior asynchronous performance under no load, attaining faster synchronism compared to the surface permanent magnet synchronous motor (SPMSM). With step load of 10 Nm at 2 s the combined effect of the excitation and the reluctance torque forced the IPMSM to pull into synchronism faster than the SPMSM which lacks saliency. The ability of the motors to withstand gradual load increase, in the synchronous mode, was examined using ramp loading starting from zero at 2 s. SPMSM lost synchronism at 12 s under 11 Nm load while the IPMSM sustained synchronism until 41 seconds under 40 Nm load. This clearly suggests that the IPMSM has superior load-withstand capability. The superiority is further buttressed with the steady state torque analysis where airgap torque in IPMSM is enhanced by the reluctance torque within 90E to 180E torque angle.


Introduction
The recent concentration of research efforts in the design, analysis and control of the Permanent Magnet Synchronous Motors (PMSM) is justified because for the same output power, PMSM offer performance enhancement over the conventional induction and synchronous motors in terms of power factor, efficiency, power density and torque-to-inertia ratio [1][2][3][4][5][6][7].The performance superiority of the PMSM over the traditional induction and wound rotor synchronous motors have also been reported in [8][9][10][11].The PMSM has also been favoured, when compared to induction motor, for line start operation, variable speed operation and in the field of semi-hermetic drives as respectively reported in [12][13][14].
A key issue of interest in the design of PMSM is the nature of the permanent magnet material.The properties of the permanent magnet material will affect directly the performance of the PMSM.Neodymium Iron-Boron, ( B Fe Nd 14

2
) is presently the best choice due its superior B-H characteristics [15].The problem of high cost and limited supply makes supply unpredictable and researches are presently on to enhance on ferrites to achieve competitive power density and efficiency of the rare-earth PMSM [16][17][18].
Interior Permanent Magnet Synchronous Motor (IPMSM) and Surface Permanent Magnet Synchronous Motor (SPMSM) are the two major classes of PMSM based on the placement of the rotor permanent magnets.Surface-mounted PM motors have each of the permanent magnets mounted on the surface of the rotor, making it easy to build, and specially skewed poles are easily magnetized on this surface mounted type to minimize cogging torque.This configuration is used for low speed applications because of the limitation that the magnets will fly apart during high-speed operations.These motors are considered to have insignificant saliency, thus having practically equal inductances in both the q and d axes.The ratio between the quadrature and direct axis inductances is unity (i.e.q d L L = ).Figure 1 shows the placement of rotor magnets in SPMSM [19,20].Because of the internal positioning of the rotor magnets, it is good for high-speed operation.These motors have saliency with q-axis inductance greater than the d-axis inductance (L q > L d ).
The magnets are very well protected against centrifugal forces [21].Several other classifications of PMSM, based on the placement of rotor magnets, are discussed in [22].Special rotor designs have continued to evolve to satisfy specific operational requirements.
The difference in rotor magnet placement affords the two PMSM configurations different performance characteristics.In the present study, a comprehensive dynamic and steady state comparison is made between the IPMSM and the SPMSM, of the same 4 hp rating, for linestart operation.Specifically, the run-up characteristics will be observed from rest to synchronous speed affording the opportunity to study and compare the motors within the asynchronous speed range under no load.This will be followed by two loading scenarios; (1) Step loading and (2) ramp loading to establish the load withstand capabilities of the two motors.Finally, the steady state torque characteristics of the two motors would be examined to verify the effect of the reluctance torque component associated with IPMSM as the torque angle varies.MATLAB will be used as the software tool for this research.

Line-Start dynamic model of PMSM
Although the industrial use of inverters for variable speed drives is widespread, constant speed line-start operation of PMSM is still dominant in medium, low, and fractional horsepower applications.The PMSM being inheritably non self starting, damper windings are employed to run the machine up to speed on induction motor action with the motor pulling into synchronism by a combination of the reluctance and synchronous motor torques provided by the magnet.During the start-up, the magnet exerts a braking torque that opposes the inductionmotor-type torque provided by the damper windings.The torque provided by the damper windings must therefore overcome this magnet braking torque in addition to the load and friction, to run-up the motor successfully.
Figures 3, 4, and 5, respectively, show the q-axis equivalent circuit, d-axis equivalent circuit and the zero-sequence equivalent circuit of the Line-Start Permanent Magnet Synchronous Motor.
The following parameters are defined: The equivalent qd0 circuit of a line-start permanent magnet synchronous motor with the reference frame fixed in the rotor is shown below.The corresponding qd0 dynamic equations for the motor are summarised below.The developed electromagnetic torque is derived as where P is the number of poles and p = d/dt is the differential operator.

Steady state torque analysis
Steady state torque characteristics of the PMSM highlights the relationship between the torque components and the torque angle *.Assume the following set of balanced polyphase current as the input to the PMSM: where * is the angle between the rotor flux 8 af and stator current phasor and known as the torque angle since it determines the steady state torque.
Using the inverse transformation ratio , ] [ The steady state stator current components in the rotor reference frame as shown in Figure 6 are: which is due to the interaction of the rotor magnetic field and the q axis stator current and the reluctance torque

Results and analysis
The parameters of the interior and surface PMSM are shown in the Appendix 1.The two motors are rated 4 Hp and operated at the rated voltage of 220 V and 50 Hz frequency.The results of the dynamic and steady state studies are presented in the plots below.The dynamic characteristics of the two motors are investigated under two scenarios.The first scenario allows the motor to run-up to synchronous speed before a step load of 10 Nm is applied at 2 s.The load is then removed suddenly at 3 s.It is seen from Figure 7 that the IPMSM synchronises faster than the SPMSM.This faster synchronisation of IPMSM is also observed during speed recovery from sudden gain or loss of load as shown in Figure 8.

Steady state torque comparison
From Figures 9 and 10, the airgap (electromagnetic) torque for the IPMSM is greater than that of the SPMSM below synchronous speed.This region is the asynchronous region.Upon initial attainment of synchronous speed, a combination of the excitation and the reluctance torque enables the IPMSM to quickly synchronise as shown in Figure 10.The direct proportionality between stator current and airgap (electromagnetic) torque explains the behaviour of the stator current in response to electromagnetic torque as shown in Figures 11 and 12.
The second loading scenario compares the load-withstand capabilities of the two motors as shown in Figures 13 and 14.Ramp loading is applied at 2 s (after synchronisation).Unlike the SPMSM that lost synchronism at 12 s under 11 Nm load, the IPMSM sustained synchronism until 41 s absorbing as much as 40 Nm load torque before lose of synchronism.
For the steady state torque comparison, the airgap torque and its components are plotted with a stator current magnitude of 4 A for the IPMSM as shown in Figure 15.It is noted that the peak of the airgap torque is at angle greater than 90E.The reluctance torque enhances the airgap torque only in the torque angle range from 90E to 180E; thus the preferred torque angle range of operation is between 90E to 180E. Figure 16 compares the airgap torque for the IPMSM and the SPMSM.The enhancement offered by the reluctance torque at torque range between 90° to 180° is clearly evident and this makes the peak of the torque curve to occur at angle above 90° for the IPMSM.The SPMSM has airgap torque equal to the synchronous (excitation) torque.Being a pure sinusoid, the peak of the steady state torque occurs at torque angle of 90°.

Conclusions
This paper has, objectively, compared the dynamic and the steady state performance of the IPMSM and the SPMSM for line-start operation under two dominant loading scenarios.Emphasis was on the run-up characteristics under no load and the response of the motors to loading upon attainment of synchronism as well as the steady state torque characteristics.
The IPMSM showed superior asynchronous performance under no load leading to a faster attainment of synchronism compared to the SPMSM.In event of sudden load change, a faster speed synchronisation is achieved in the IPMSM due to the combined effect of the excitation and the reluctance torque which forces the motor to pull into synchronism.
The ability of the motors to withstand gradual load increase was examined using ramp loading.Once again, while the SPMSM lost synchronism at 12 s under 11 Nm load, the IPMSM sustained synchronism until 41 s absorbing as much as 40 Nm load torque before lose of synchronism.The clearly suggests that the IPMSM has superior load-withstand capability compared to the SPMSM.
Finally, due to the reluctance variation in the IPMSM, the steady state torque of the IPMSM is superior to the SPMSM.Reluctance torque aids the airgap torque in the torque angle range from 90E to 180E thereby making 90E to 180E the preferred torque angle range of operation.
The outcome of this research will serve as a guide to operation engineers in taking logical decisions in the selection of machines to execute specific assignment.The design engineers also will find the work useful in the appropriate selection of design parameters in designing PMSM to satisfy specific application area.
It is pertinent to mention that constant frequency line-start operation of PMSM is still dominant in medium, low, and fractional horsepower applications.The development of the PMSM: the design, analysis and control to provide accurate line-start capabilities will continue to occupy research attention for years to come.

L
sequence voltage, r qs i = stator q-axis current, r ds i = stator d-axis current, 0 i = zero sequence current, s R = stator resistance, r ω = rotor speed, r ds λ = stator d-axis flux linkage, r qs λ = stator q-axis flux linkage, mq L = q-axis magnetizing inductance, md L = d-axis magnetizing inductance, ls L = stator leakage inductance, = q-axis damper winding inductance, r lkd L = d-axis damper winding inductance, r kq R = q-axis damper winding resistance, r kd R = d-axis damper winding resistance, r kq i = q-axis damper winding current, r kd i = d-axis damper winding current, linkage, J = moment of inertia, B = frictional coefficient. ,

Fig. 3 .
Fig.3.q-axis equivalent circuit first, second and third components of T e are the excitation torque, reluctance torque and induction torque respectively.The damper windings are practically disengaged as soon as the rotor reaches synchronous speed.Equations 12 reduces to .