139 Journal of International Conference on Electrical Machines and Systems Vol. 3, No. 2, pp. 139~147, 2014
Preliminary Design Analysis of Low Speed Interior Permanent Magnet Machine with Distributed and Concentrated Windings
Kazi Ahsanullah , Rukmi Dutta and M. F. Rahman
Abstract – The paper presents a systematic comparison of four topologies of the interior permanent magnet machine (IPMM) designed for low speed applications. This comparative study investigates the suitability of the concentrated winding and distributed winding in the stator and the flat-shaped or V- shaped magnets in the rotor poles. The paper also studies the inductance characteristics of the designs using finite element analysis. Various steps taken to minimize the cogging torque and torque ripple in the studied machines were also discussed in details.
Keywords: AC standstill saliency test, Cogging torque, Concentrated winding, Distributed winding, Direct-drive, Interior Permanent Magnet Machine, PM machine, Torque ripple
1. Introduction
In direct drive wind turbine systems, intermediate gear boxes are eliminated to increase the efficiency and reliability of the whole system, as well as reducing maintenances down-time. The generator used in such systems needs to have a low rated speed. This demand for an increase in the number of pole pairs of the generator. A review done in [1], [2] on direct-drive wind turbines suggests that permanent magnet (PM) machines are the most favorable for direct- drive wind turbine.
While the most common type of PM machines used in the wind industry is the radial flux surface mounted magnet (SPM) type, an interior PM synchronous machine (IPMSM) offers a number of advantages over the SPM type. The most commonly cited advantages are: the presence of reluctance torque ( ) as shown in (1) in an IPM machine is beneficial in achieving a higher torque with lower magnet volumes and IPMSM has a mechanically and magnetically robust rotor. It should be noted that the presence of saliency in the IPSM results in the reluctance torque and also contributes toward the constant power speed range. A recent study carried out in [3] found that the use of an IPM machine in a small scale direct drive wind turbine can provide quicker return of investment compared to a SPM machine, especially in sites where average wind speed is low.
According to [3] the return of investment can be achieved by taking advantage of provision for a constant power speed range available in IPMMs. But cogging torque in an IPMM is generally greater compared to a SPM machine due to the greater variation of reluctance between the stator and rotor [4]. This makes reduction of the cogging torque crucial in a low speed IPM machines [5]. The IPMSM with radially magnetized V-shaped (V-S) magnets has a better flux concentration and higher saliency ratio than its counter-part
flat-shaped (F-S) magnet designs which makes it more attractive for traction drives [6]. The torque components of an IPM machine is
(1)
where, = magnet alignment torque, = cogging torque, and reluctance torque. The majority of IPM machines are designed with distributed windings (DW).
Recently, the concentrated winding (CW) for the IPMSM is getting attention from the research community due to its high slot-fill factor, high tolerance to phase fault, simplified manufacturing process, non-overlapping coils resulting in shorter end-windings and reduced copper usage. In spite of having these advantages, the CW was not widely used in the past due to its characteristics in producing EMF and MMF waveforms with unacceptably high total harmonic distortion.
However, in recent years, it has been shown that through appropriate choice of slot and pole combinations [7], the CW stator has the ability to produce sinusoidal EMF waveform with high a winding factor, and smooth average torque.
In this paper, four design topologies of IPMSM were considered for investigation which includes (a) conventional distributed winding in the stator and flat-shaped IPM structure in the rotor( DW FS-IPMM), (b) distributed winding in the stator and V-shaped IPM structure in the rotor (DW VS-IPMM), (c) concentrated winding in the stator and flat-shaped IPM structure in the rotor (CW FS- IPMM), (d) concentrated winding in the stator and V-shaped IPM structure in the rotor(CW VS-IPMM). Fig. 1 shows the cross-section of the four topologies and no-load flux distribution. The objective of this paper is to present a detailed comparison of the major performance characteristics of all the four topologies illustrated in Fig.1.
The selection process of the major dimensions and winding structure of the proposed IPMM is described in Section 2.
Section 3 presents the cogging torque and torque ripple minimization of all the four investigated designs.
Kazi Ahsanullah, R. Dutta and M. F. Rahman are with the School of Electrical Eng. and Telecommunications, University of New South Wales, New South Wales, Australia (E-mail: a.kazi@unsw.edu.au)
Received 20 April 2014; Accepted 09 May 2014
Fig. 1.Cross sections and no-load flux distributions of the our machine designs. (a) Flat shaped IPMM with DW( DW FS-IPMM), (b) V-shaped IPMM with DW (DW VS-IPMM), (c) Flat shaped IPMM with CW (CW FS-IPMM) and (d) V- shaped IPMM with CW (CW VS-IPMM).
Section 4 discusses the effect of MMF and winding factor on Back-EMF. The calculation of the Inductance and saliency ratio of each machine design, using an AC standstill test like condition in the 2D finite element analysis was presented in Section 5. Performance analysis and efficiency obtained from the finite element model were presented in Section 6 and Section 7, respectively. The concluding remarks of this study were provided in section 8.
2. Design Model
2.1 Design Specification
Careful considerations of the magnetic and electric loading through well-known analytical equations were conducted and the key dimensions of the prototype machine were determined analytically [8]. These dimensions were kept same for all the four designs mentioned in Section 1 for a fair comparison. Table 1 presents these key specification and dimensions of the proposed four designs.
2.2 V-angle selection for IPMM with V-shaped Magnets In machines with large number of pole pairs, the pole pitch is relatively small and hence, selecting the V-angle of the V-shaped magnets is paramount for an acceptable performance. A study was conducted in [9] to find the optimum V-angle that can give a similar performance as that of the flat-shaped IPMM. It was found that the optimum V-angle is 120°. Hence, V-angle of the V-shaped IPMMs with DW and CW stators were fixed to this value in this paper.
2.3 Winding structure
In a DW stator, number of slots per pole and arrangement of the phase windings are the decisive factors in the pitch of the winding. Usually, in a high pole number machine, a full pitch winding (i.e. 3 slots per pole) is commonly used. However, a full pitch winding also results in higher space harmonics in the magneto-motive force
Table 1. Key parameters of the proposed machine
Quantity Value
Stator outer diameter (mm) 680
Stack length (mm) 162
Stator bore diameter (mm) 622.2
Air-gap length (mm) 1.1
Remament flux density Br (@120°C) (T) 1.16
Rated Power (KW) 4
L-L Rated Voltage (V) 360
Rated Current (A) 6.5
Base Speed (rpm) 143
No. of Poles 42
(MMF). Such stator structures are also known to produce a higher cogging torque in a PM machine due to the position of the slots with respect to rotor magnet poles. For the selection of the appropriate pitch in the DW winding of the proposed design, the air gap flux density and cogging torque were compared between a full pitch (i.e. 3 slots per pole) and 1-slot short pitch winding (i.e. 6 slots per pole) in [9]. It was found that set goal of the cogging torque cannot be achieved in a full pitch winding. Thus, 6 slots per pole (short-pitch winding) were selected.
In a CW stator, the output torque can be increased while reducing cogging torque through proper selection of the number of slots per pole per phase (Spp) [10]. Moreover, in a double-layer CW stator , the torque ripples are smaller and magnet eddy current losses due to lower air-gap MMF harmonic components are lower than that of a single layer CW stator [11, 12]. The authors of [10] showed that with a Spp of 3/7, a CW machine can produce a sinusoidal EMF with a fundamental winding factor >0.9. Apart from this, a very low cogging torque and a wider flux-weakening range were also achieved in this CW machine [10]. Hence, for the proposed high pole number CW-IPMSM in this paper, a double layer CW with 3/7 Spp was selected. In the proposed designs the number of rotor poles was selected as 42 to achieve 143 rpm at grid frequency for the rated wind speed. Hence, in order to maintain Spp equal to 3/7, the total number of slots in the proposed machine with a CW winding was calculated as 54.
3. Cogging torque & Torque ripple Minimization
3.1 Cogging torque reduction
The cogging torque in a PM machine is the circumferential component of the attractive force that attempts to maintain the alignment between the stator teeth and the permanent magnets [13]. It is produced when the magnet flux of leading and trailing edge of a permanent magnet enters a slot. The cogging torque can be approximated as follows [4]:
(a) (b)
(c) (d)
(2) Where, = relative position of the PM with respect to iron core, and = Stored magnetic energy in the air gap of the motor. Since, the magnet pole arc and are directly related, the variation of the magnet pole arc length influences the resultant cogging torque. The cogging torques of the proposed DW FS-IPMM and the DW VS-IPMM for various pole arc lengths were calculated in [9]. Table 2 shows the change in the cogging torque with various magnet arc lengths for the DW FS-IPMM. It was found that although the overall magnet arc length of a DW VS- IPMM is smaller than that of the DW FS-IPMM, the cogging torque is nearly two times higher in the VS-IPMM. Thus, in terms of cogging torque, DW FS-IPMM performance is better. Although pole arc length of DW VS-IPMM is lower, the total magnet volume in this machine is found to be higher to obtain similar performance as a DW FS-IPMM.
Hence, it can be concluded that in a IPMM with large pole number flat-shaped magnet with the DW stator is a better choice.
The cogging torque calculated in the CW FS-IPM machine with the same optimized magnet arc length as the DW FS-IPMM was found to be 2.8 times higher. This indicated that further magnet arc optimization is necessary in the CW FS-IPM machine to minimize the cogging torque.
Thus, further magnet arc length optimization was carried out for the CW FS-IPMM. It should be noted here that the change of the magnet arc length results in a change in the overall magnet volume which in turn results in variation of the air-gap flux density. Table 3 summarizes the result of this investigation. Table 4 shows the change in the cogging torque with various magnet lengths for the CW VS-IPMM.
The cogging torques of both CW FS-IPMM and VS-IPMM very similar and magnet length of CW VS-IPMM is slightly higher.
Fig. 2 and Fig. 3 show the cogging torque waveforms of all four designs. The machines with a CW produce significantly less cogging torque compared with the DW machines. This is because of the fact that CW eliminates periodicity between slots and poles which aids in the reduction of the cogging torque.
Table 2. Change in the cogging torque with respect to the variations in magnet length of the DW FS-IPMM
DW FS-IPMM Magnet length(mm) Cogging
torque(Nm)
Air-gap flux density 𝐁𝐦 𝐓
38.92 10.46 0.785
39 11.1 0.79
40.84 2 0.8
42.2 5.83 0.837
Table 3. Change in the cogging torque with respect to the variations in magnet length for the CW FS-IPMM
Magnet length(mm)
% Reduction in magnet volume with respect to DW
FS-IPMM
Cogging
torque(Nm) 𝐁𝐦(T)
40.84 0 5.67 0.837
38.7 2.5 4.89 0.82
37.6 5 3.06 0.8
36.6 7.6 0.5 0.794
35.5 10 1.47 0.77
Table 4. Change in the cogging torque with respect to the magnet length for CW VS-IPMM
Fig. 2. Cogging torque of DW IPMM’s
.
Fig. 3. Cogging torque of CW IPMM’s.
3.2 Torque ripple minimization
Torque ripple is mainly caused by the harmonics in the air-gap flux density. These harmonics are introduced by the slot openings of the stator and the magnet flux-barrier of the rotor in an IPMM. Hence, the design of flux barriers influences the minimization of the torque ripple provided the slot opening is unchanged. The torque ripple of the DW FS-IPMM and the DW VS-IPMM were optimized in [9] by varying the flux barrier designs with respect to the slot opening in the stator. Fig. 4 shows three design variations of the flux barrier as investigated in [9]. The results of DW FS-IPMM and DW VS-IPMM are presented in Fig. 5 and Fig. 6 respectively.
2.22° 4.44° 6.66° 8.88° 11.1°
-3%
-2%
-1%
0 1%
2%
3%
Mechanical angle (deg.) Cogging torque ( % of rated torque) DW VS-IPMM
DW FS-IPMM
2.22° 4.44° 6.66° 8.88° 11.1°
-.05%
-.025%
0 .025%
.05%
Mechanical angle (deg.) Cogging torque (% of rated torque)
CW FS-IPMM CW VS-IPMM
Magnet length (mm)
Cogging Torque (Nm)
37.7 0.66
38.7 0.63
39.7 3
40.7 5.4
41.7 6.5
Fig. 4. Flux barrier shape
Fig. 5. Variations in torque ripple with the change in flux barrier design and slot opening for the DW FS- IPMM
Fig. 6. Variations in torque ripple with the change in flux barrier design and slot opening for the DW VS- IPMM
In CW IPMM, the positioning of the slots with respect to flux barrier is not the same as the DW IPMM. Initially, for the CW FS-IPMM, the magnet length is kept similar as that of the DW FS-IPMM for a fair comparison. The variation in the dimensions of x and y of the flux barriers (as shown in Fig. 7) were required to minimize torque ripple in the CW FS-IPMM. Table 5 summarizes the effect of the changes in the flux barrier dimension on the torque ripple for the CW FS-IPMM with a constant slot opening length. It can be seen from Table 5 that Design B generates more torque as compared to Design ‘A’ and ‘C’. Although Design ‘C’
generates the least amount of torque ripple, but it has not been taken into account because it produces less overall torque compared to the other two designs. Thus, design ‘B’
was chosen for the CW FS-IPMM for further analysis.
A further torque ripple analysis of CW IPMM was carried out by using the flux barrier design ‘B’ while varying the slot openings. The analysis has been conducted using two different magnet lengths in the rotor; (a) magnet length of 39.788mm which is the same as in the DW FS- IPMM and (b) optimized magnet length of 36.57 mm in which the cogging torque is the minimum. The variations in torque ripple for the CW FS-IPMM under these conditions are compared in Fig. 8. The minimum torque ripple for CW FS-IPMM was found to be 1.48% of the total rated torque with a flux barrier design of “B” and with a slot opening of
2.05 mm having a magnet length of 36.57 mm. Similar analysis has been conducted for the CW VS-IPMM, which shows that Design ‘A’ generates the least amount of torque ripple for the CW VS-IPMM. This is because Design ‘A’
reduces the flux leakage significantly compared to the other two designs which in turns reduces the harmonics in the air- gap that causes torque ripple for the CW VS-IPMM.
Fig. 7. Cross sectional view of a flat shaped IPMM with different flux barrier shapes
Table 5. Change in torque ripple with the change in flux barrier shape and size for CW FS-IPMM
Design A
x y Area of the flux barrier Total torque Torque ripple
2.469 1.882 2.34 274.2 5.67%
2.588 2.056 2.62 274.5 5.7%
2.8 2.4 3.2 274.8 5.84%
Design B
3.7 1.2 1.6 279 6.98%
3.8 1.5 2.2 280.5 6.09%
3.8 1.7 2.5 281 5.7%
Design C
1.4 3.3 2.1 272.31 4.9%
1.59 3.49 2.4 272.49 4.97%
Fig. 8. Variation in torque ripple with the change in slot openings inthe stator slots for the CW FS-IPMM
A
B
C
a
b c
120?
1.2 1.3 1.4
0 10 20 30
Slot opening (mm) Torque ripple (% of rated torque)
A B C
1.2 1.3 1.4
0 5 10 15 20 25
Slot opening (mm)
Torque ripple ( % of rated torque)
a b c
Magnet Width Magnet pole Arc
Flux barrier
A
B
x y x y
C
0 1 2 3 4 5 6 7
1.2 1.5 1.8 2.05 2.2 2.3 2.5
Torque ripple ( % of rated torque )
Slot opening (mm) Magnet length : 39.788 mm
Magnet length : 37.64 mm
Fig. 9. Variation in torque ripple with the change in slot openings in the stator slots for the CW VS-IPMM Table 6. Magnet area, Flux barrier design, Slot opening,
Cogging torque, torque ripple (TR) and air-gap flux density for all of the designed machines Machine
type Mag
net Area 𝐦𝐦
Flux barrier
design SO
Cog.
torque Nm
TR
% of rated torque
𝐁𝐦 (T) DW FS-
IPMM
119 B 1.2 2 6% 0.8
DW VS- IPMM
114 B 1.3 4.53 14.4% 0.76
CW FS- IPMM
110 B 2 0.5 1.48% 0.77
CW VS- IPMM
116 A 1.4 0.63 1.47% 0.71
The effect of slot opening on CW VS-IPMM with a flux barrier of design ‘A’ is shown in Fig. 9. Table 6 compares the cogging torque and torque ripple of all four designs investigated in this paper. It can be seen from Table 6 that the CW FS-IPMM and the CW VS-IPMM are the best choices as they have the lowest torque ripple and cogging torque. The torque ripple for DW VS-IPMM is too high and may not be able to satisfy design specifications of low speed applications. Hence, no further analysis was conducted with this design. Other three designs – DW FS- IPMM, CW FS-IPMM and CW VS-IPMM are considered for further studies. Some of the results of the further studies of these three designs were presented in the following sections.
4. Winding Factor, MMF and Back EMF As previously discussed, a CW machine produces higher harmonic contents in the armature MMF distribution compared with a DW machine. These harmonics cause flux variations in the air-gap and as a result increases rotor losses. The number of slots (Q) and pole pairs (p) in a CW machine have an effect on MMF distribution [14].
Periodicity is given as
t=GCD{Q,p} (3) Q/t = EVEN; Only odd order harmonics present in
MMF distribution
The prototype CW machine for this paper has a periodicity of 1 which makes Q/t=54 an even number. The MMF produced by stator coils can be expressed as
Ƒ BsA ℜai (4) Where, Bs= Flux density produced by stator, A = Air-gap surface area and ℜai = Air-gap reluctance. In all the machines, the air-gap length and overall slot opening widths are kept constant which makes the MMF of all 3 machines proportional to the air-gap flux density produced by the stator coils. Fig. 10 and Fig. 11 show the harmonic spectrum of the flux density produced by stator coils for the DW FS-IPMM and the CW FS-IPMM, respectively. The main harmonic order is equal to the number of pole pairs which is 21 for both the prototype machines. No notable sub harmonics are present for the DW machines as seen in Fig. 10 whereas for the CW machine, significant odd order harmonics are present in the MMF distribution. Due to the imperfections in the machine i.e. slot openings and reluctance of the flux path, some even order harmonics are also present in the spectrum which are negligible.
EMF is induced in the phase coils when the flux varies across the air-gap. Its magnitude depends on three main variables- rotor speed (ωm), flux-density (Bmax), winding factor (kw) and number of series turns per phase (Nph).
e pωmkwNphBmax (5) This equation shows that the winding factor directly affects the generated EMF and hence the output torque of the machine. Generator designs with higher winding factor and flux density produce higher Back-EMF as shown in Table 7. CW design’s results in smaller EMF total harmonic distortion compared to DW flat shaped IPMM. This justifies the fact that by an appropriate selection of slot and pole combination, CW has the ability to produce sinusoidal EMF with a very small THD.
Fig. 10. MMF harmonic spectrum for DW FS-IPMM
Fig. 11. MMF harmonic spectrum for CW FS-IPMM
1.3 1.5 1.7 1.9
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Torque ripple ( % of rated torque)
Slot opening (mm)
0 25 50
0 0.005 0.01 0.015
Harmonic No.
Flux density produced by stator ( Tesla)
Fundamental term
0 25 50
0 0.005 0.01 0.015 0.02
Harmonic No.
Flux density produced by stator ( Tesla)
Sub-harmonic components Fundamental term
Table 7. Effect of flux density , Spp and winding factor on the EMF of all 3 machine design’s
Machine type Spp
Flux density
T
Winding factor
Fundamental EMF Component
EMF THD DW FS-
IPMM
2 0.8 0.933 508 4.18%
CW FS- IPMM
3/7 0.79 0.902 505 0.76%
CW VS- IPMM
3/7 0.73 0.902 480 0.67%
5. Inductance and Saliency Ratio
Saliency ratio (ξ ) given by (3) contributes to the additional reluctance torque as shown in (1) which is additive to the total machine torque. In an IPMM, ξ>1.
𝜉= Lq/Ld (6) where, Lq= q-axis inductance; Ld= d-axis inductance. The measurement of Ld and Lq are usually carried out by the AC standstill test method. AC standstill test like condition can be simulated in the finite element model to calculate Lq and Ld. Although this method takes longer computational time, it is found to be more accurate than various magneto-static methods available in the literature, especially for the CW-IPMM. This method is conducted by exciting one of the phase coils with an AC current source at a specified frequency. Voltage drop across the excited winding and the neighboring phase winding are measured for various rotor positions (θ). For accuracy of the results the simulations are conducted every 0.1° (mechanical) and the self-inductance (La) and mutual inductance (Mab) at each rotor position are calculated by (7) and (8), respectively.
Fig. 12 and Fig. 13 show the harmonics of self- and mutual inductances of all 3 machine designs. The self- inductance for the DW FS-IPMM is low due to its lower harmonic contents [15] in the MMF waveform as seen in Fig. 12 but mutual inductance is much higher as seen in Fig 13 due to presence of mutual coupling between phases. Fig.
14 and Fig. 15 show the harmonic spectrum of self- and mutual inductances, respectively.
La
√ Va
Is
2 Ra2
2πf
(7)
Mab Vb 2πfIs
(8) where,
Is= Input current
Va= Voltage drop across the excited phase Ra= A phase resistance
Vb= Voltage drop across another phase f= Supply frequency
From the harmonic components of La and Mab values, Ld and Lq can be determined by (9) and (10), respectively. As higher order harmonics in the mutual
inductance contributes toward the difference between d- and q-axis inductances, so the calculation has been conducted by using harmonics till 20th order.
Conventionally with DW, Ld and Lq are calculated from self-inductance using equations (11) and (12).
Ld L0 M0 L1
2 M1 L2
2 M2 ⋯ … … (9) Lq L0 M0 L1
2 M1 L2
2 M2 ⋯ … … (10) Ld 32 L0 L1 (11) Lq 32 L0 L1 (12) Table 8 compares theLd and Lq values that were calculated using the above equations from the measured self- and mutual inductances. It should be noted here that the saliency ratio is very different in a DW FS IPMM when Ld and Lq are calculated using (11) and (12) which neglects mutual inductance. Since, mutual inductance is much larger in DW FS-IPMM, it should be included in calculation of d- and q-axis inductances. However, effect of mutual inductance on the d- and q-axis inductances of CW IPMM is much less as can be seen from Table 8.
The comparison in Table 8 also shows that CW machine has much lower saliency ratio compared to the DW machine. This is due to a large increase in d-axis inductance which becomes comparable to q-axis inductance resulting in a lower saliency ratio. A comparison of inductances between the two CW designs reveals that saliency ratio is the lowest in the CW VS-IPMM. This indicates reluctance torque component of such a machine will be lower compared to that of the CW FS-IPMM. However, the wider constant power speed range is still possible in a PM machine with low or nil saliency, if its characteristic current as defined in (13) is equal or close to rated current I . As for the DW FS-IPMM, the saliency ratio is higher than the other two but with smaller d-axis inductance values.
Therefore, its characteristic current will be larger compared to two CW designs.
I ΨPM
Ld
(13)
where, ΨPM PM flux linkage.
Table 8. Inductance and saliency of DW FS-IPMM and CW VS-IPMM
Machine type
𝐋𝐝 (mH)
𝐋𝐪 (mH)
𝛏 𝛏
(excl.𝐌𝐚𝐛) DW FS-
IPMM
1.7 9.5 5.6 2.07
CW FS- IPMM
5.2 13.9 2.7 2.46
CW VS- IPMM
10.2 15.7 1.55 1.54
Fig. 12. Self-inductance of all three machine designs
Fig. 13. Mutual inductance of all three machine designs
Fig. 14. Harmonics of self-inductance
Fig. 15. Harmonics of mutual inductance
The unsaturated characteristic current was calculated in the FE model to investigate possibility of the constant power speed range in the three designs. It was found that the unsaturated characteristic currents of all three designs were much larger than the rated current. Thus, the expected constant power speed range for all three designs will be lower. Future work will investigate how to increase the saliency ratio or reduce the characteristic current by design variations in CW machine.
6. Some Key Results
This section presents some of the key performance characteristics of the proposed designs. The air-gap flux density of the base design DW FS-IPMM was found to be 0.8 T. As shown in Table 7, air-gap flux density of the CW FS and VS IPMM are slightly lower because of the reduction of the overall magnet volume in these machines.
The optimum magnet arc length to achieve the minimum cogging torque was about 7.6% lower than that of the DW IPMM. As a result, the output power and torque in these machines will be slightly smaller than that of the DW- IPMM. In order to achieve the design specification of the
rated power, the stator outer diameter of the CW IPMM were increased by 2.9%. It should be noted that increase of the stator outer radius also increase the cogging torque and torque ripple marginally. Table 9 compares the key results of the three designs. It can be seen from the Table 9 that the overall volume of the CW IPMM is larger by 2.9% and cogging torque is smaller by 68.5% than those of the DW IPMM. Thus, it can be concluded that the selection of the DW versus CW stator for the high pole number IPMM will be influenced by the reduction of the cogging torque rather than by the increase in overall volume.
The Line-Line EMF voltage waveforms of all three designs are shown in Fig. 16. Fig.17 plots the L-L EMF harmonics of all the machines. It can be seen that the THD of the CW VS-IPMM is at a much lower level compared to the other ones. Fig. 18 and Fig. 19 show the total power and the FFT of the developed torque for these three machine designs. From Fig. 19 it can be seen that 6th and 12 harmonic of torque in a DW FS IPMM is much higher than the CW IPMM.
Table 9. Output parameters for all 3 machines designed Machine
type
SOR mm
L-L EMF
V
Total torque
Nm
Total power W
Cogging torque
Nm
TR
% of rated torque DW FS-
IPMM
340 363 276 4137 2 6%
CW FS- IPMM
350 360 270 4038 0.5 1.48%
CW VS- IPMM
350 340 260 3890 0.63 1.47%
Fig. 16. L-L Back EMF of all 3 machines designed
Fig. 17. Spectrum analysis of the L-L EMF of all 3 machines designed
0° 10° 20° 30° 40° 50° 60° 70° 80° 90°
10 15 20
Rotor positions (Mech. Deg) Self Inductance La (mH)
CW FS-IPMM CW VS-IPMM DW FS-IPMM
0° 10° 20° 30° 40° 50° 60° 70° 80° 90°
1 2 3 4
Rotor positions ( Mech. Deg.) Mutual Inductance Mab (mH) CW FS-IPMM CW VS-IPMM DW FS-IPMM
0 1 2 3 4
0 5 10 15
Harmonic order La (mH)
CW VS-IPMM CW FS-IPMM DW FS-IPMM
2 3 4
0 0.1 0.2 0.3
Harmonic order La (mH)
Lo
0 1 2 3 4
0 1 2
Harmonic order Mab (mH)
DW FS-IPMM CW FS-IPMM CW VS-IPMM M0
0 0.01 0.02 0.03 0.04
-600 -200 200 600
Time
L-L Back EMF (V)
DW FS-IPMM CW VS-IPMM CW FS-IPMM
0 1 2 3 5 7 9 11 13 15
0 200 400 600
Harmonic No.
L-L EMF Harmonics (V)
2 3 5 7 9 11 13 15
0 5 10 15 20
Harmonic No.
L-L EMF Harmonics (V)
DW FS-IPMM CW FS-IPMM CW VS-IPMM DW FS-IPMM CW FS-IPMM CW VS-IPMM
L
0
Lo
Fig. 18. Total power of all 3 machines designed
Fig. 19. Variation in torque ripple with the change in slot opening in the stator slots for CW VS-IPMM
Fig.20. Cu. loss and Iron losses versus percentage of loading for DW FS-IPMM
Fig.21. Cu. loss & Iron losses versus percentage of loading for CW FS-IPMM
Fig.22. Cu. loss & Iron losses versus percentage of loading for CW VS-IPMM
7. Efficiency
In this paper, only electromagnetic losses of all three machine designs have been calculated. Fig. 20 shows the copper losses and iron losses for the DW FS-IPMM for different load settings at the rated speed. Fig. 21 and Fig. 22 show the losses for the CW FS-IPMM and CW VS-IPMM, respectively. It can be seen that for all three machines, the maximum efficiency is achieved at full load. All three machines achieve efficiency over 90%.
8. Conclusion
This paper presents a design comparison between a flat
shaped IPMM and a V-shaped IPMM with distributed and concentrated windings for low speed applications. In the studied 42 pole structure, distributed winding stator with V- shaped magnet in the rotor was found to be least favorable for low speed application. The minimization of the cogging torque without severely compromising output power in such a machine was not possible. The distributed winding IPMM with flat-shaped magnet in the rotor can achieve relatively low cogging torque while providing rated output power. Following remarks can be made from the comparative study of the distributed winding flat-shaped IPMM, concentrated winding flat-shaped and V-shaped IPMM presented in the paper:
Both the concentrated winding designs have much lower cogging torque and torque ripple compared to the distributed winding IPMM with flat-shaped magnet.
The concentrated winding IPMM designs have sinusoidal back EMF waveform with low THD than the distributed winding design. However, winding factor of the concentrated winding IPMM is slightly lower than the distributed winding design.
Greater than 94% efficiency can be achieved in both CW and DW IPMM.
Saliency ratio is much lower in the CW IPMM compared to DW IPMM. Thus, a larger reluctance torque component is possible in the DW IPMM. However, the characteristic current in all three designs were found to be much larger than the rated current. Therefore, the constant power speed range will be limited.
Although the cogging torque and torque ripple were lower, the overall volume of the CW IPMM machine is higher than the DW IPMM.
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0 0.004 0.008 0.012 0.016 0.02
3800 3900 4000 4100 4200 4300
Time(s)
Total Power (W) DW FS-IPMM CW FS-IPMM CW VS-IPMM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 1 2 3 4 5
Harmonic No.
Torque Ripple (Nm)
DW FS-IPMM CW FS-IPMM CW VS-IPMM
25 50 75 100
0 40 80 120
% Loading
Cu loss & Iron loss (W)
Iron loss Cu loss
P: 3996W Eff: 95.56%
P: 3079W Eff: 95.5%
P: 3504W Eff: 94.85%
P: 2744W Eff: 94.02%
25 50 75 100
0 50 100 150
% Loading
Cu loss & Iron loss (W)
Iron loss Cu. loss
P:1935W
Eff:94.5% P:2904W Eff:95.5%
P:3870W Eff:95.8%
P:966W Eff:90.77%
0 50 100 150 200
% Loading
Cu loss & iron loss (W)
Cu loss Iron loss
100 75
50 25
P:3099W Eff:93.96%
P:2062W Eff:93.08%
P:1029W Eff:89.17%
Eff:Efficiency P:Power
P:4137W Eff:94.03%
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Kazi Ahsanullah has received the B.E ng. degree in electrical engineering fr om Ahsanullah University of Science
& Technology, Bangladesh, 2008 an d is currently doing his Ph.D. de gree from the University of New S outh Wales, Australia. He has worked as a lecturer at Ahsanullah Univers ity of Science & Technology, Bangladesh and is curre ntly on leave for higher studies. His research interest s are PM machine, electromagnetics, drives and renewa ble energy.
Rukmi Dutta has received the PhD degre e in electrical engineering from the Univ ersity of New South Wales, Australia, 2 007 and the Bachelors of Engineering de gree in electrical engineering from Assa m Engineering College of Guwahati Uni versity, India, 1996. She is currently working as a lectu rer at University of New South Wales, Australia. Befor e this, she worked as an Electrical Engineer at CMG Pty Ltd, and as an associate lecturer at University of New South Wales. She also worked at Institute of Indu strial Science, Tokyo University and Reliance Industry Ltd, India. Her research interests are PM machine desi gn and control, electromagnetic analysis of electric dev ices, renewable energy, distributed generation.
M. F. Rahman received the B.Sc.Eng. de gree in electrical engineering from Bangl adesh University of Engineering and tech nology, Dhaka,Bangladesh, and the Maste r’s and Ph.D. degrees in electrical engin eering from the University of Mancheste r Institute of Science and Technology, Manchester,U.K., in 1975 and 1978, respectively. He was a System Desi gn Engineer at the General Electric Company, U.K., fo r two years. In 1980, he joined the National Universit y of Singapore. In 1988, he joined the University of New South Wales, Sydney, N.S.W.,Australia, as a Se nior Lecturer, where he is currently a Professor and h ead of the energy systems research group. His current research interests include power electronics, motor driv e, electrical machines and motion control system, and electromagnetics.
