Comparative study of voltage distortion in fractional-slot ... - IEEE Xplore

2016 Eleventh International Conference on Ecological Vehicles and Renewable Energies (EVER)

Comparative Study ofVoltage Distortion in Fractional-Slot PM Machines Having Different Winding and Stator Configurations Y. X. Li, Z. Q. Zhu, and Guangjin Li Department of Electronic and Electrical Engineering University of Sheffield Sheffield, UK Email: [email protected]

Abstract-Three 12-slot/l0-pole closed slot permanent magnet machines having either all or alternate teeth wound winding and equal or unequal tooth width stator are analyzed and compared in terms of spike type voltage distortion. The difference between three machines, such as the rotor positions determining voltage distortion and the influence of current, is emphasized. Referring to the distorted voltage, the influence of such distortion on fluxweakening capabilities of three machines is compared as weIl. It is found that there is a larger voltage distortion for the machine with alternate teeth wo und winding compared with the all teeth wo und machine if they share the same machine dimensions. Besides, the unequal tooth width stator adopted for torque improvement purpose will further aggravate the voltage distortion. Keywords-Closed slot; Tooth width; Tooth-tip leakage; Voltage distortion; Winding topology. 1.

INTRODUCTION

Fractional-slot permanent magnet (PM) machines with non-overlapping windings have gained wide attention for decades due to their merits, such as high torque density, high efficiency, low torque ripple, etc. [1]. Among these machines, either all or alternate teeth wound windings can be used for some slot and pole number combinations [2]. In addition to winding configurations, the unequal tooth width (UETW) stator can also be adopted for further performance improvement in machines with alternate teeth wound winding [3]. The fractional-slot PM machines with c10sed slots can minimize torque ripple and this has been verified under open circuit condition [4]-[5]. However, adopting closed slots will lead to some evident drawbacks. Due to the tooth-tip leakage, the average torque will have some reduction [6] and the stator tooth-tip iron loss will increase because of the heavier local saturation caused by these leakages [7]. Furthermore, these machines will have obvious distorted phase voltage under on-load

978-1-5090-2464-3/16/$3l.00 «:12016 Crown

condition. The local saturation will cause higher torque ripple and decrease the flux-weakening capability, which is against the purpose of adopting closed slots [8]. The voltage distortion of surface-mounted PM machines with all teeth wound windings has been detailed analyzed in [9]-[ 10]. However, the machines with alternate teeth wound winding have also been widely applied [11]. Besides, the unequal tooth width stator can be used for machine with alternate teeth wound winding for torque improvement as weIl [12]. The voltage distortion ofthese machines should be analyzed for more in-depth understanding and better applications. In this paper, three 12-slot/1 O-pole PM machines are analyzed. One of them has equal tooth width (ETW) stator and all teeth wound winding. Another one adopts the same structure dimensions but the winding is alternate teeth wound type. The third one with alternate teeth wound winding uses unequal tooth width stator. For simplification, they are named as All ETW, Alternate ETW and Alternate UETW machine, respectively. The phenomenon of voltage distortion is described firstly. Then, the major difference of on-load phase voltages among three machines is analyzed, viz. the rotor positions determining voltage distortion and the influence of current. Finally, the influence of voltage distortion on f1ux-weakening capability IS compared for these machines as weIl. TI.

MACHINE TOPOLOGY

The cross-sections of prototype machines analyzed in the paper are shown in Fig. 1. In order to show the influence of tooth-tips on phase voltage, the machines with open slots are used as the reference and one of examples is shown in Fig. 1(b) for All ETW machine. The major parameters are listed in TABLE 1.

B

B

40 _ 20 ~ CI)

"f.

l>

;p-

"f.

Cl

S

~

0 - - AIIETW

-20

----- Alternate ETW Alternate UETW

0000

-40 90 180 270 Rotor position (electrical degree)

0

8-

8-

(a) All ETW with closed slot

(b) All ETW with open slot

(,

360

(a) Waveforms (closed slot) 25

»

"f.

»

I2I AIIETW

_20 ~ ~ 15

!!!! Alternate ETW IJAlternate UETW

... :::l

'eCl 10 CIS

:E 5 (c) Alternate ETW

(d) Alternate UETW

0 3

Fig. 1. Cross-sections of prototype PM machines. TABLE I MAJOR PARAMETERS OF THREE MACHINES All ETW

!tem Stator outer diameter (mm) Stator inner diameter (mm) Stator yoke thickness (mm) Stator tooth width (mm) Air-gap length (mm) PM thickness (mm) PM remanence (T) PM relative permeability Turns per phase Rated current in peak value (A)

4 8

Alternate ETW 100 57 4

8

Alternate UETW

7

9

1 3 1.2 1.05 184 10

23 25

(b) Harmonics (closed slot)

_

20

~ 5 10a and 6b

11 13 15 17 19 21 Orders

40 ,----------------------------------,

CI)

Cl

:ll!o >

o

0 0

-

-----------------~' ------------------ ~

0

- - AIIETW

-20

----- Alternate ETW 0 0 0 Alternate U ETW

o

-40

+--------.--------.--------.------~

o

90 180 270 Rotor position (electrical degree)

, the tooth with a coi! b the tooth without a coi1.

TTT.

5

360

(c) Waveforms (open slot) 25 ,------------------------------------,

VOLTAGE DISTORTION COMPARISON

I:Oi AIl ETW !!!! Alternate ETW IJAlternate UETW

A. Phenomenon olVoltage Distortion

The on-load phase voltages of three machines with c10sed slots are shown in Fig. 2 when the windings are supplied with rated currents. Since there is negligible difference between d- and q-axis inductances, IrQ contral strategy is adopted. In order to c1arify the reason for the spike type voltage distortion, the results of machines with open slots are also shown.

3

5

7

9

11 13 15 17 19 21 Orders

23 25

(d) Harmonics (open slot) Fig. 2. On-load phase A voltage comparison (400 rpm).

Fram Fig. 2, several phenomena can be observed: (1) The on-load voltages of three machines with closed slots are heavily deteriorated compared with those

of open slot machines. The spike type distortion in phase voltages of closed slot machines results in abundant higher order harmonics. (2) Although the machines with closed slots have more obvious voltage distortion, they still have larger fundamental component than the machines with open slots, which is due to the flux focusing effect of toothtips. The difference of values among three machines is mainly due to the different working harmonie winding factors. (3) There are six and two rotor positions with obvious spike type distortion for machines with all and alternate teeth wound windings, respectively. Besides, some minor distortion can be seen in Alternate ETW and All UETW machines. All of these rotor positions related to voltage distortion are determined by the variation rate of tooth-tip leakage, which will be shown in the following part. The phase voltage is predicted as follows: Vph

= Rphiph + ~ (lf/PM + If/arm)

(1)

where Vph, Rph and iph are the phase voltage, resistance and current, respectively; !fIPM and !fIarm are the f1uxlinkages due to PM and armature current, respectively. By frozen permeability technique [10], the PM and armature current components can be obtained and are shown in Fig. 3. 300 ~---------------r==~~====~ - - PM ~

~ CI)

Cl

.l!!

----- Armature

150 0

-p;.a"}-T-~ -i=; ~~ ~-:;-+:;:-O:;-~

"•

"0

::> -150

-300 + - - - - - , - - - - - , - - - - - - - , - - - - - - 1 180 270 o 90 360 Rotor position (electrical degree)

(a)AII ETW

300 ~--------------r===~~====" - - PM

~

~ CI)

Cl

.l!!

"0

150

,..

0

----

-:..---....--

I I

I

CI)

"0

::> -150

-300 +----.------.------,--------1 180 270 o 90 360 Rotor position (electrical degree)

(e) Alternate UETW Fig. 3. Components ofphase A voltage (400 rpm).

Fig.3 shows that both ofthe voltage components due to PM and armature current contribute to the voltage distortion. Although they are quite high around the rotor positions where the spike type voltage distortions ex ist, the resultant phase voltage does not have such a huge value. Comparing the voltage components of three machines, it can be seen that All ETW machine has the highest distortion of two components, while Alternate UETW machine has the lowest degree of distortion in this aspect. However, the distortion of resultant phase voltage shows opposite result, which has already been shown in Fig. 2.

B. Rotor Positions Determining Voltage Distortion Since voltage distortion is harmful, the rotor positions determining voltage distortion should be identified. Fig. 3 has clearly shown these rotor positions. Based on the results compared in Fig. 2, it can be seen that the spike type voltage distortion is caused by the tooth-tips; therefore the rotor positions where the tooth-tip leakage sharply changes determines the phase voltage distortion. Oue to the odd periodic symmetry property of these machines, half of the machine is considered. Choosing phase A as example, tooth-tips 1,2 and 3 for All ETW; I and 2 for Alternate ETW and UETW machine are monitored, respectively. The induced voltages due to tooth-tip leakage are shown in FigA. 4

:> ';2 Cl S

g o

:::I

'C

0 -2

c

Rotor position (electrical degree)

(b) Alternate ETW

-----

~~~~~~~ = ='::I._~ - -

'". __.. , ..

0 ,--:;.. i'rI'""-.w: - -~ --aiii --;;;-.. - ~'n· ~

CI)

-300 + - - - - - , - - - - - , - - - - - - - , - - - - - - 1 180 270 o 90 360

•••• PM+Armature

>.!\

E

'C

::> -150

I,

~

300 ~---------------r==~~====~ - - PM ----- Armature •••• PM+Armature

----- Armature

150

~

-4

•,

~ o

.. ......!-

I Tooth-ti P 1 I ----- Tooth-tip 2

)

•••• Tooth-tip 3

. "

• -"~'f"". ~.r

\,.

"• H


(a) AllETW

. . ..---"" .

...... -

:

,

. I I

.. ~

360

4

~ CI)

Cl

-

Tooth-tip 1

----- Tooth-tip 2

2

S

"0 0 >

--~

ji

\..

,/

)

'C CI)

0

:::I

'C

.:

-2

-4 0


360

~ CI)

Cl

Tooth-ti P 1 I I ----Tooth-tip 2

2

S

"0 0 > 'C

:::I

'C

.:

r.

I, 1\

I

I

~~~ -, --r'~ - _............:=. ---=-'l =-' -~ ,

CI)

0

j

I

, I

""•

-2

-4 0


(e) 8r==186°

Fig. 5. Variation oftooth-tip leakage direetion.

(b) Alternate ETW 4

(b) 8r==17T

(a) 8r==168°

360

Fig. 5 iIIustrates that when the rotor passes the specific positions, the flux path of tooth-tip leakage will sharply change. This results in phase voltage distortion. The rotor positions determining the voltage distortion have been summarized in [9] for fractional-slot machines with all teeth wound windings. However, some rotor positions related to voltage distortion cannot be fully covered by the method. According to [9], the voltage distortion pattern (VDP) is:

(e) Alternate UETW

(2)

Fig. 4. Comparison oftooth-tip indueed voltages (400 rpm).

Fig. 4 clearly shows that the rotor positions where there are huge tooth-tip induced voltage spike are the same as those having phase voltage distortion. Since the leakage reference directions of all tooth-tips are the same, some tooth-tips have positive induced voltage, while others show negative value during half period. However, all of them will aggravate the phase voltage distortion. The difference among three machines can be seen from Fig. 4 as weIl. Comparing Figs. 4(a) and (b), it can be found that All ETW machine has heavier distortion level than Alternate ETW machine, though it has less rotor positions where voltage distortion happens. Figs. 4(b) and (c) show that the machine adopts UETW stator will make the rotor positons determining voltage distortion close to each other in half operation period and this will further worsen the scenario. That is why Alternate UETW machine has larger voltage distortion than Alternate ETW machine. In order to more clearly show the mechanism of tooth-tip leakage induced voltage, the tooth-tip leakage paths ofthree typical rotor positions is shown in Fig. 5.

k=l

k is Type I slot

(3)

k is Type II slot . .

.

·k·

.

·k 1

1

posItIve zero-crossmg negative zero-crossmg

(4)

others where er is the rotor position; N, is the stator slot number; Type I slot means the coil sides in this slot belonging to one phase and Type II slot means there are two different phase coil sides in the slot. The normalized VDPs of three machines are shown in Fig. 6, together with the corresponding phase voltage. 2

40

- - Normalised VDP ----- Voltage

a.

:~,'

>

"t:I CI)

.!!1

0

...E0

-1

cu

z

-,

,\' .... _------

'I

----"

~ II

ii : , ... ------.......

C

, ," ,

I

rr

...... , ...

20

~

" \ \ I I I I

0

-20>

-2 +----.------.-----.------+ -40 180 270 o 90 360 Rotor position (electrical degree)

(a) AllETW

CI)

Cl

.l!! '0

2

c..

----- Voltage

1

40

I~

- - Normalised VDP

,""' ......... - ... ...

, ""·, I

C

11

> "C Q)

0

~ ca

.

E

,"

1-

-1

0

z

\ ......... , .... --'

,- ... ,

,"

"

"

,

I

"

~4 Tr==~====~--------------~40

.- ...

.0

_ ,,

3:

20

....

",

'.l

1

"-,

E.2

~

-

Q) /. 0 Cl ca " \1 '0

,"

-20 ::>

Q)

ca .;,:: 0 ca


0

360

- - Normalised VDP ----- Voltage

c..

I, f " " _...., , ......

r" . , ,I

C

>

"C Q)

0

.!!1 ca

..

E

,,

-1

0

Z

-2

...

,

..........'-,'

",

... ,

",

,"

,

"

''

Q.

:;;; -2

' ...

...... _'"

..\. . .

tII

- ,, I "

,,

1 1 1


~

Q)

0

Cl

ca

'0

-20 ::> -40

360

tooth-tip leakage +----r----,---~---4

0


4 r-;::==:::::;::::====:::;------------r 40

•

•

Q)

Cl

ca ~ 0 ~ Q.

-

I

------------------~~"'~.:

o ~ -4

""'-_~-""--~------~.-.J.~-------., I ,

..........

:;;; -2 ..c:

20 ~ Q)

0

Cl

I . "

00

o

I

,

,.

fiel

I '"

'-

0

'

\/~------------ 7, 7

-20

tooth-tip leakage

90 180 270 Rotor position (electrical degree) (a) Alternate ETW

360

.l!!

'0 >

Q)

~----_.------._----_.----__+-40

o

-40

360

Fig. 7 demonstrates that when the tooth-tip leakage almost reaches the peak and has the huge variation rate under open-circuit condition, the corresponding ideal armature field is constant and in opposite direction. Therefore, there will be voltage distortion happening in these rotor positions which cannot be found out by VDP. In order to cover all of the rotor positions have spike type voltage distortion, the modified VOP (MVOP) lS put forward. It is defined based on former VDP:

I

N

It is obvious that the VOP is effective for all three machines. However, some rotor positions determining voltage distortion for machines with alternate teeth wound windings are missing. For example, the rotor positions have huge induced voltage of slot 2 in Figs. 5(b) and (c). Due to the feature of alternate wound winding, these rotor positions can be identified by the variation rate of tooth-tip leakage under open-circuit condition. Taking Alternate ETW machine as example, the tooth-tip leakages of slot 2 for different conditions (open-circuit and ideal armature field) and on-load phase voltage are shown in Fig. 7.

E.2

-20 ~ c..

0

..c:

20

",

3:

>

Q)

0

Fig. 6. Rotor positions determining voltage distortion by VDP.

~

'0

Fig. 7. lndueed voltage of tooth-tip leakage far different eonditions (400 rpm).

(e) Alternate UETW

.0

.l!!

(b) Alternate UETW

40

+----....-------.------r------1-

o

Q)

Cl

o

(b) Alternate ETW

2

20 ?: -

~

~ -4

-40

I'

Cl

0

-2

......

tII

~

c..

MVOP(8r )=

[Jk(8Jn;+o-k(8r )sJ

(5)

k=1.2,3 ...

I, { o-k (8r ) = -1, 0,

interpole positive maximum interpole negative maximum

(6)

others

= {I, special conditions

s I

0, others

(7)

where cf(()r) is the unit pulse function which indicates the rotor interpole positions that are in the range around the center of tooth-tips. Si is the filter function which selects the rotor positions where ideal armature flux is constant and the direction of open-circuit PM and ideal armature flux is opposite . When the MVOP is applied for three machines, the corresponding results are shown in Fig. 8.

2 ----- Voltage

e..

c

> ::E "t:I CI)

:.~

,,'

,."-------

,/

40

0

~

.,

' ...

I I

.!!1 cu

...0E

vpeak -Vfund Vfund

20

............

J ,...

VDR =

-1

0

I I I I

CI)

Cl

J!! '0 -20 ::>

0


360

-40

-,

--1- -- --I

__ 1___ -1 __ -- - -- -

e..

~

,,.".,," ,I

c

> ::E "t:I CI)

cu

...0E

,

0

.!::!

-1

,\

'. ...--' '"

z

-2

0

, .... - ... , "

I

__ 1-

,r, - ... - ...... _ ,

" ,

-1---

_ --: - -- -- - -

0::

o

>1

40

,

- - Normalised MVDP ----- Voltage

j-- -

__ I __ _

(a)AII ETW

2

(5)

where Vpeak and Vtund are fundamental and peak values of phase voltage, respeetively. The VDR of three maehines having different eurrent amplitude and angle are shown in Fig. 9.

z

-2

xl00%

....

20

,

".

0

I \1" \

,.",

90

~

",,

\./

I

CI)

Cl

J!! '0 -20 ::>

Current amplitude (A)

Current angle (degree)

(a) All ETW --


360

-T

--

-

--

-40

(b) Alternate ETW

2 - - Normalised MVDP ----- Voltage

e..

c

> ::E "t:I CI)

0

~

cu

...0E

-1

"

:~

... _ .....' ............

,.1 ,-,'

, :

... ' ....... ""..., '.

20 ' ....\ ",

,,'

.,

, ....... , I'"

"''''--'''v''''''''

z

-2

40

I

0


I

I I

",

I

•I

360

~

0

CI)

Current angle (degree)


(b) Alternate ETW

Cl

cu

'0 -20::>

-j

-40

I

__ 4 -- - -~ -

- -- -

- -- -

(e) Alternate UETW Fig. 8. Rotor positions determining voltage distortion by MYDP.

In Fig. 8, the MVDP is the same as VDP for All ETW maehine. However, the MVOP of Alternate ETW and Alternate UETW maehines ean aeeount for all of the rotor positions having voltage distortion due to loeal saturation. This verifies the effeetiveness ofthe MVOP. C. Influence ofCurrent on Voltage Distortion

As has been stated before, voltage distortion is eaused by loeal saturation of tooth-tips and they are affeeted by armature field. Thus, both the eurrent amplitude and phase will lead to different level of voltage distortion. The influenee of eurrent on voltage distortion is shown with the help of voltage distortion ratio (VOR) whieh is expressed as folIows:

90 Current angle (degree)


(e) Alternate UETW Fig. 9. Intluenee of eurrent on voltage distortion (400 rpm).

Comparing the VDR of three maehines in Fig. 9, it ean be found that all of them will have a higher voltage distortion with the inerease of eurrent amplitude if the eurrent angle is fixed. Besides, if the maehine has the given eurrent amplitude, the VDR will vary with eurrent angle and the higher VDRs will be obtained if the eurrent angle is near to 0 and 90 degree. Overall, the voltage distortion of all teeth wound maehine is the lowest eompared with the maehines with alternate teeth wound windings under eonstant torque and deep fluxweakening operations, viz. 0 and 90 eurrent angles. The

Alternate UETW machine can worsen phase voltage under the two situations, although most of other current amplitude and angle combinations have lower voltage distortion than Alternate ETW machine.

40 ~35

~

GI

~30

IV.

"0

INFLUENCE OF VOLTAGE DISTORTION ON FLUX-

::> 25

WEAKENING CAPABILITIES

As has been seen in the previous section, the on-load voltage is evidently deteriorated, which will affect the machine f1ux-weakening capability. When the hysteresis control strategy is adopted, the torque-speed and powerspeed characteristics can be predicted by considering the following constraints: 1 = "1-=-2-+-1-:-2 -::;. 1 (6) '\J d Cf rat

v =~V} + ~2 -::;.3..~)C

(7)

Jr

where I, Id, I q and l ral are the resultant, d-axis, q-axis and rated current, respectively; V, Vd, ~l and Vf)C are the resultant, d-axis, q-axis and DC bus voltage, respectively. There are two kinds of resultant voltage values being considered here. One is the fundamental component and the other is the peak value over one electrical period. When the machines are fed with rate current, these different voltage definitions are shown in Fig.l0. 40

20

•••• Maximum ----- Limit

0

(e) Alternate UETW

From Fig. 10, it shows that the peak voltage is always larger than fundamental value and the machines with alternate wound windings suffer higher difference. The UETW stator further contributes to such difference. Therefore, the flux-weakening characteristics predicted by the two different values will be different, as shown in Fig. 11.

E ~

GI

8~-------------r==~~~~==~ - - Peak (All ETW)

----- Peak (Alternate ETW)

6

••••

~ ---- 25

- - Peak (All ETW) ----- Peak (Alternate • • •• Peak (Alternate ~ Fund (All ETW) - - Fund (Alternate --- 25 20

180

Fig. 10. Definition of different voltages (400 rpm).

~35

20


0

45 135 90 Rotor position (electrical degree) (b) Alternate ETW

180

2500

torque ripple-speed curve considering voltage distortion will shift to the left referring to the one acquired from the fundamental value. The torque ripple reaches maximum when the current is close to 90 degrees, since the average value oftorque will be almost zero.

400

~

300

; 200 3: 0 c.. 100 0

0

500

1000

1500

2000

2500

Speed (rpm)

(c) Power-speed characteristics

15 10

...

~ 5 c:

...~

:::l

()

. -__________________-I~==~P~ea~k~(A ..I~IE~T~~~---. ----- Peak (Alternate ET~ •••• Peak (Alternate UET~ \_' ----6-- Fund (All ET~ _ Fund Alternate E

0

\

-5

Id

0

Overall, the flux-weakening characteristics of machines with alternate teeth wound winding will be much worse than the ideal ones in flux-weakening region. V.

'. '-'

-10 -15

(5) The power-speed characteristics show the similar variation as the torque-speed curves. It can be seen that the machines with alternate teeth wound windings are affected more evidently.

500

1000

1500

2000

2500

Speed (rpm)

(d) Current-speed characteristics Fig. 11. Influence performances.

of voltage

distortion

on

flux-weakening

Fig. 11 shows the following phenomena: (1) When the peak val ue is adopted to predict torquespeed characteristics, both the turning speed and the maximum speed will be lower than the results predicted by the fundamental voltage. This is due to the voltage limit of inverter DC bus. (2) The machine with alternate teeth wound winding will enter the flux-weakening region earlier than the machine with all teeth wound winding, since the d- and q-axis inductances of the latter is larger than the former. However, larger inductance will benefit the enhancement of flux-weakening capability, which is one major advantage for this kind ofwinding.

CONCLUSION

By comparing the voltage distortion of three machines, it is found that the machines with alternate teeth wound windings will suffer more deterioration than those with all teeth wound windings. Lf the unequal tooth width stator is adopted for improving the torque performance of alternate teeth wound machine, the voltage will be further distorted. Due to such influence, the flux-weakening characteristics of these machines are worse than the desired ones. Therefore, the careful design consideration for the tooth-tips of these machines should be taken. REFERENCES

[1]

[2]

[3]

[4]

(3) With the increase of rotor speed, the torque-speed characteristics considering voltage distortion are always lower than the results obtained by the fundamental voltage. The torque-speed curves considering voltage distortion will be closer to the ideal one in the beginning of current angle increase. However, the difference between two curves will be enlarged again when the current angle is near to 90 degree, viz. the maximum speed operation point.

[5]

(4) The torque ripple will vary under flux-weakening operation as weIl. From Fig. ll(b), it is clear that the

[8]

[6]

[7]

A. M. EI-Refaie and T. M. lahns, Optimal flu:x weakening in surface PM machines using fractional-slot concentrated windings, IEEE Trans. Ind. Appl., vol. 41, no. 3 , pp. 790-800, May/lun. 2005. N. Bianchi, M. D. Pre, G. Grezzani and S. Bolognani, Design considerations on fractional-slot fault-tolerant synchronous motors, IEEE Trans. Ind. Appl., vol. 42, no. 4, pp. 997-1006, Jul./Aug. 2006. A. M. EI-Refaie. Fractional-slot concentrated-windings synchronous permanent magnet machines: opportunities and challenges, IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 107121, lan. 2010. M. F. Momen and S. Datta, Analysis of flux leakage in a segmented core brushless permanent magnet motor, IEEE Trans. Energy Convers., vol. 24, no. I, pp. 77-81, Mar. 2009. .T. H. Choi et al., Design ofhigh power permanent magnet motor with segment rectangular copper wire and closed slot opening on electric vehicles, IEEE Trans. Magn., vol. 46, no. 6, pp. 2070-2073,lun.2010. H. V. Xuan, D. Lahaye, H. Polinder and J. A. Ferreira, Influence of stator slotting on the performance of permanent-magnet machines with concentrated windings, IEEE Trans. Magn., vol. 49,no.2,pp. 929-938,Feb. 2013. P. B. Reddy and T. M. lahns, Modeling of stator teeth-tip iron losses in Jractional-slot concentrated winding surface PM machines, in IEEE Energy Conversion Congress and Exposition (ECCE 2009), Sep. 20-24, 2009, pp. 1903-1910. D. Wu and Z. Q. Zhu, On-load voltage distortion in fractional slot surface-mounted permanent magnet machines considering

local magnetic saturation, IEEE Trans. Magn., vol. 51, no. 8, pp. 1-10, Aug. 2015. [9] D. Wu and Z. Q. Zhu, lnfluence of slot and pole number combinations on voltage distortion in surface-mounted permanent magnet machines with local magnetic saturation, IEEE Trans. Energy Convers., vol. 40, no. 4, pp. 1460-1471, Dec.2015. [10] J. A. Walker, D. G. Dorrell and C. Cossar, Flu:x-linkage calculation in permanent-magnet motors using the frozen

permeabilities method, IEEE Trans. Magn., vol. 41, no. 10, pp. 3946-3948, Oct. 2005. [11] N. Bianchi, S. Bolognani, Pre, x and M. D., Magnetic loading of fractional-slot three-phase pm motors with nonoverlapped coUs, IEEE Trans. lnd. Appl., vol. 44, no. 5, pp. 1513-1521, Sep./Oct. 2008. [12] J. Cros and P. Viarouge, Synthesis of high performance PM motors with concentrated windings, IEEE Trans. Energy Convers., vol. 17, no. 2, pp. 248-253, Jun. 2002.