2013 International Conference on Electrical Machines and Systems, Oct. 26-29, 2013, Busan, Korea
Investigation of LSPMSM with Unevenly Distributed Squirrel Cage Bars P. Li, J. X. Shen*, W. Sun, and Y. Zhang Department of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China E-mail:
[email protected],
[email protected],
[email protected],
[email protected] Abstract — In this paper, a squirrel cage with unevenly distributed bars is proposed for line start permanent magnet synchronous motors (LSPMSM) in order to improve the motor performance. Taking a 3-phase 15kW LSPMSM for example, from finite element analysis (FEA) results, it is proved that both the back EMF and the phase currents are optimized with lower harmonics, and the torque ripple during steady state operation is reduced. Keywords — line start permanent magnet synchronous motor, uneven squirrel cage, irreversible partial demagnetization, harmonics, torque ripple I.
INTRODUCTION
The first line start permanent magnet synchronous motor (LSPMSM) was designed in early 1980s [1-2]. Since then, the LSPMSM is considered as a better choice than the conventional induction motor in various industial applications [3-4], due to its high efficiency, high power factor and good line-start capability. However, for this kind of motor, the rotor squirrel cage slots greatly affect the performance, such as cogging torque, back EMF and armature current haromics, and steady sate operation [5]. Owing to the bar slots on the rotor, harmonic components of both air gap field and back EMF become rather abundant, which increase the iron losses and copper losses of the LSPMSM [5-7]. The waveform of the back EMF can be optimized by different ways, such as using lapwindings, short pitch windings, and uneven air gap [8-16]. However, these methods have some disadvantages, e.g., increased stator wingding resistance and equivalent air gap. In this paper, a squirrel cage with unevenly distributed bars is proposed. The stator slots and the rotor slots can both lead to harmonic components in the air gap field and the back EMF. With finite element analysis (FEA), it is found that by optimizing the distribution of the cage bars, the phase angles of the components with the same harmonic order caused by the stator slots and the rotor slots can differ by nearly 180 degree. It means that the harmonic components can be greatly reduced. Moreover, the squirrel cage is optimized in two ways to improve the motor operation performance, the one is to use closed slots, the other is to use unevenly distributed slots. FEA proves that the motor with the unevenly distributed colsed squirrel cage slots has the highest operation performance, and also, the lowest harmonic components in air gap field and back EMF. In this paper, a 3-phase 15kW LSPMSM motor is studied, by optimizing the distribution of the squirrel cage slots, so that the total harminic distortion (THD) of both the air gap flux
density and the back EMF is greatly reduced. Also, the steady state operation performance of the optimized motor is comparatively studied with that of the original motor. II. STUDIED MOTOR The 3-phase 15kW LSPMSM was originally designed and studied with FEA software. The cross section of the motor is shown in Fig. 1. In this motor, each magnetic pole consists of two separate magnet bars inserted in a V-shaped slot. The rotor squirrel cage has totally 32 aluminum bars. Main parameters of the studied LSPMSM are listed in Table I. Based on this original design, the rotor squirrel cage will be optimized, mainly by changing the opening and distribution of the cage slots, whilst the related performance will be investigated with FEA.
Fig. 1. Cross section of original LSPMSM. TABLE I MAIN PARAMETERS OF ORIGINAL LSPMSM Rated voltage (rms)
380 V
Rated output power
15 kW
Rated output torque
95.5 Nm
Outer diameter of stator core
260 mm
Inner diameter of stator core
170 mm
Air gap length
0.65 mm
Inner diameter of rotor core
60 mm
Length of stator and rotor cores
180 mm
Grade of NdFeB magnets
N35SH
Width of magnets
86 mm
Thickness of magnets
6.5 mm
Number of stator slots
36
Number of rotor slots Grade of core laminations Number of poles
32 DR510-50 4
Number of phases
3
Number of turns per coil
13
Number of coils per phase
6
978-1-4799-1447-0/13/$31.00 ©2013 IEEE
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III. OPTIMIZATION A. Uneven distribution of rotor cage slots The harmonic components of the air gap field are caused by many factors, such as the stator slots, rotor slots, stator windings, excitation method of the motor, size of the air gap and so on. This paper mainly focuses on how the stator slots and the rotr slots affect the waveform of the air gap field. In order to separate the influences of the stator slots and rotor slots on the air gap field waveform, three analytical motor models are studied. The first has stator slots only, but no rotor slots (except the flux barrier slots); the second has evenly distributed rotor slots only, but no stator slots; and the third has no slots (except the flux barrier slots). The cross sections of these three models are shown in Fig. 2. After the static magnetic field simulation, we get the waveforms of the air gap field of these three motors, of which the spectra are shown in Fig. 3. The THD are 42.23%, 27.35% and 33.34%, respectively. The following can then be concluded: (i) The stator slots make the fundamental of air gap field smaller. This is because the slot openings of the stator core enlarge the equivalent air gap length. (ii) The stator slots bring more harmonic components, especially high-order harmonic components, than the rotor slots. When the rotor is stalled at the position shown in Fig. 2, the phase angle of each harmonic component of the air gap field is listed in Table II. I it can be seen that at this fixed position the 19th, 21st and 29th harmonic components caused by the stator slots and the rotor slots have nearly opposite phase angles, thus, they cancel each other and eventually enhance the air gap field waveform. When the rotor spins, the harmonic components caused by the stator and rotor slots can also cancel each other from time to time.
It is supposed that uneven distribution of the rotor cage slots presents more opportunities to adjust the phase angle of the harmonic components generated by the rotor slots, so that more harmonic components generated by the stator slots can be cancelled. It is then important to determine how to place the cage slots unevenly. Fig. 4 shows an example of the uneven squirrel cage which was designed by the authors. Here, more cage bars are placed above the end of each pole, whilst fewer above the pole center. In this case, the phase angles of the harmonic components of air gap field caused by the even cage slots and uneven cage slots are compared in Table III. It is found that, by using the uneven cage slots, the 5th, 7th, 25th and 27th harmonic components have the opposite phase angle, too. Therefore, all the 5th, 7th, 19th, 21st, 25th, 27th and 29th harmonic components caused by the stator slots and the unevenly distributed rotor slots have nearly opposite phase angles and can cancel each other. TABLE II PHASE ANGLE OF AIR GAP FIELD HARMONIC COMPONENTS IN THE THREE ANALYTICAL MODELS
Harmonic orders 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Model with stator slots only 90.2 90.5 90.9 91.3 271.9 272.0 272.5 272.7 273.0 93.3 92.9 271.8 97.9 95.9 274.2
Model with rotor slots only 90.2 90.6 90.9 91.4 270.9 272.2 272.5 272.6 273.1 273.5 273.4 274.1 95.1 95.1 95.2
Model without slots 90.2 90.5 90.9 91.3 271.7 272.0 272.2 272.6 272.9 273.5 274.4 274.3 94.8 94.3 276.2
(a) model with stator slots only
Amplitude of Air Gap Field Harmonics (T)
1 0.9 model with stator slots only
0.8
model with rotor slots only
0.7
model without slots
0.6 0.5 0.4 0.3 0.2 0.1 0 1
(b) model with rotor slots only
3
5
7
9
11 13 15 17 19 21 23 25 27 29 Harmonic Order
Fig. 3. Air gap field spectra of the three analytical models.
(c) model without slots Fig. 2. Cross sections of three theoretical motor models.
Fig. 4. Cross section of rotor with unevenly distributed cage slots.
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TABLE III PHASE ANGLE OF AIR GAP FIELD HARMONIC COMPONENTS IN THE MODELS WITH EVEN AND UNEVEN ROTOR CAGE SLOTS
Harmonic orders 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Model with even rotor slots only 90.2 90.6 90.9 91.4 270.9 272.2 272.5 272.6 273.1 273.5 273.4 274.1 95.1 95.1 95.2
Model with uneven rotor slots only 90.2 90.6 270.3 271.5 271.7 271.8 271.9 273.1 274.2 273.5 274.2 274.5 275.0 276.2 96.0
Amplitude of Air Gap Harmonics (T)
1 0.9 0.8 with even rotor slots with uneven rotor slots
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 Harmonic Order
Fig. 5. Comparison of air gap field spectra of the studied motors with even and uneven rotor cage slots, respectively.
Two motors are then studied. One has evenly distributed rotor cage slots and it has been shown in Fig. 1. The other has unevenly distributed rotor cage slots, its rotor is shown in Fig. 4 and its stator is the same as that in Fig. 1. The air gap field spectra of both motors are compared in Fig. 5. Clearly, by optimizing the distribution of the rotor cage slots, the fundamental air gap field increases slightly, while the field THD decreases from 37.7% to 30.1%, which will be further beneficial to reduce the THD in the back EMF. It should also be pointed out that the fundamental air gap field in the motor with even rotor slots (see the left bar in Fig. 5) is lower than that in the model with even rotor slots only (refer to the middle bar in Fig. 4). This is because the motor has stator slots which also enlarge the equivalent air gap length and reduce the field, but that model has no slots on the stator. B. Rotor cage slot openings From FEA, it is found that the rotor cage slot openings slightly affect the harmonic components of the air gap field. By way of example, for the motor with evenly distributed rotor cage slots, the air gap field THD with open slots is
37.7%, while that with closed slots is 37.4%. For the motor with unevenly distributed rotor cage slots, the air gap field THD with open slots is 30.1%, and becomes 29.6% while using closed slots. Nevertheless, from the point of view of manufacturing, open slots are preferred if the squirrel cage is made with casting aluminium, while closed slots (especially, round slots) are applicable if copper bars are directly inserted in the slots and then connected with copper end rings so as to form a cage. IV. OPERATION PERFORMANCE A. Rotor topologies According to the optimization here-above, five different rotor topologies are designed for the same LSPMSM, each being combined with the same stator. The rotors are shown in Fig. 6. Rotor-A and Rotor-B have evenly distributed cage slots, while Rotor-A has open slots and Rotor-B has closed slots. Rotor-C and Rotor-D have unevenly distributed cage slots, and their difference is that open slots are used on Rotor-C but closed slots on Rotor-D. In these four rotors, each cage slot is filled with a cage bar. However, some cage slots are actually empty (see the 6 white slots) on Rotor-E, although the cage slots of Rotor-E are identical to those of Rotor-D. By comparing these five rotors, the influence of cage slot openings, distribution of cage slots and distribution of cage bars can all be examined. B. Performance comparison In the preceding section, it has been shown that the waveform of the air gap field can be improved by optimizing the distribution and shape of the rotor cage slots. What is more, the motor operation performance should be further studied. It is supposed that Rotor-D should exhibit better steady state operation performance than Rotors -A, -B and -C, since it brings lower THD in the air gap field and thus fewer harmonics in the back EMF and phase current. This is verified by 2-dimensional FEA, as given in Table IV.
(a)
(b)
(c)
(d) (e) Fig. 6. Five rotor topologies for comparative study. (a) Rotor-A with even open slots, (b) Rotor-B with even closed slots, (c) Rotor-C with uneven open slots, (d) Rotor-D with uneven closed slots, (e) Rotor-E with uneven closed slots but fewer squirrel cage bars.
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TABLE IV OPERATION AND STARTING PERFORMANCE WITH THE FIVE ROTORS Rotor-A Rotor-B Rotor-C Rotor-D Rotor-E Number of cage slots 32 32 48 48 48 Number of cage bars 32 32 48 48 24 Cogging torque (Nm) 10.7 10.5 20.9 12.2 12.2 Back EMF THD 23.8% 20.2% 17.2% 13.1% 13.7% Rated operation at 1500rpm Electromagnetic torque (Nm) 95.6 95.5 95.5 95.5 95.5 Torque ripple (pk-pk) (Nm) 84.1 73.1 71.4 57.0 50.6 Phase current (rms) (A) 25.0 24.7 25.6 24.9 24.4 Phase current THD 14.9% 9.9% 11.0% 9.2% 8.3% Stator copper loss (W) 380 371 398 377 362 Stator core loss (W) 353 329 331 293 295 Rotor core loss (W) 57 57 50 52 54 Squirrel cage ohmic loss (W) 165 64 500 254 70 Output power (W) 15016 15001 15001 15001 15001 Efficiency (while neglecting 94.0% 94.8% 92.1% 93.9% 95.1% mechanical losses) Power factor 0.966 0.972 0.965 0.972 0.979 Starting Starting current (A) 237 234 237 234 218 Starting torque (Nm) 347.6 337.9 350.6 345.1 354
Moreover, Rotor-E which has fewer cage bars performs even better than Rotor-D, as shown in Table-IV. The back EMF is calculated under open-circuit condition. Although the magnetic circuits of Rotor-D and Rotor-E are the same when assuming the permeability of cage bars is the same as that of air, there is current in the squirrel cage which will further smoothen the back EMF in the armature windings. Therefore, Rotor-E which has fewer cage bars than Rotor-D exhibits a little higher THD in the back EMF. However, Rotor-E brings fewer harmonics in the phase current than Rotor-D, and lower ohmic losses in both armature windings and squirrel cage. In general, Rotor-E performs the best in the aspects of torque ripple, armature current harmonics, efficiency and even power factor. On the other hand, the starting performance associated with these five rotors is also investigated. Again, Rotor-E is the best solution regarding both starting current and starting torque.
steady-state operation performance and starting performance can be both boosted. ACKNOWLEDGMENT This work was supported by the Natural Science Foundation of China (NSFC 51077116) and the National Basic Research Program of China (2013CB035604 and 2011CB707204).
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V. CONCLUSIONS An LSPMSM has been optimally designed with FEA, particularly by changing the distribution and shape of rotor cage slots. It has been verified that the closed slots bring a little fewer harmonics than the open slots in both air gap field and armature winding back EMF. More importantly, uneven distribution of the rotor cage slots, e.g., having fewer slots above the pole center and more slots above the pole ends, is beneficial to reduce the back EMF and current harmonics as well as the torque ripple, however, harms the motor efficiency slightly. Complementally, some rotor slots can be empty (i.e., there is no cage bar in those rotor slots), so that the motor
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