research article computer aided modeling and analysis of

Research ArticleComputer Aided Modeling and Analysis of Five-Phase PMBLDCMotor Drive for Low Power High Torque Application

M. A. Inayathullaah1 and R. Anita2

1 Department of Electrical and Electronics Engineering, Periyar Maniammai University, Thanjavur District, Tamil Nadu 614201, India2Department of Electrical and Electronics Engineering, Institute of Road and Transport Technology, Erode District,Tamil Nadu 638316, India

Correspondence should be addressed to M. A. Inayathullaah; [email protected]

Received 24 April 2014; Accepted 25 June 2014; Published 23 July 2014

Academic Editor: Neil Y. Yen

Copyright © 2014 M. A. Inayathullaah and R. Anita. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

In order to achieve high torque at low power with high efficiency, a new five-phase permanent magnet brushless DC (PMBLDC)motor design was analyzed and optimized. A similar three-phase motor having the same D/L ratio (inner diameter (𝐷) and lengthof the stator (𝐿)) is compared for maximum torque and torque ripple of the designed five-phase PMBLDCmotor. Maxwell softwarewas used to build finite element simulation model of the motor. The internal complicated magnetic field distribution and dynamicperformance simulation were obtained in different positions. No load and load characteristics of the five-phase PMBLDC motorwere simulated, and the power consumption of materials was computed. The conformity of the final simulation results indicatesthat this method can be used to provide a theoretical basis for further optimal design of this new type of motor with its drive so asto improve the starting torque and reduce torque ripple of the motor.

1. Introduction

Brushless DC (BLDC) motor drives are stabbing the marketin various consumer and industrial systems, such as homeappliances, computer peripherals, automotive applications,and aerospace motor drives in recent years because of theirhigh efficiency, silent operation, high reliability, and lowmaintenance requirement [1–3]. Power electronic convertersare being utilized for variable speed drives. The power ratingof the converter should meet the required level for themachine and driven load. However, the converter ratingscannot be increased over a certain range due to the limitationon the power rating of semiconductor devices.

The advent of inverter fed motor drives also removedthe limits of the number of motor phases. This fact made itpossible to design machine with more than three phases andbrought about the increasing investigation and applicationsof five-phase motor drives. Five-phase motor drives havemany advantages over the traditional three-phase motordrives such as reducing the amplitude and increasing the

frequency of torque pulsation, reducing the stator currentper phase without increasing the voltage per phase, andincreasing the reliability and power density. The purpose ofusing such systems ismainly for achieving higher power level,reducing torque pulsation, increasing the torque density, andimproving the reliability.

There are many performance analysis methods for thefive-phase PMBLD motor such as direct circuit motor anal-ysis, state equation simulation, analytic method of electro-magnetic field, and electromagnetic finite element numericalmethod. In particular, finite element numerical analysismethod is widely used in the analysis and calculation ofvarious electrical equipment, and it can consider the cir-cumstance of nonlinear ferromagnetic materials, as well asthe changes of parameters in motor [4]. The electromagneticanalysis software of Maxwell was adopted to emulate thebasic characteristics and the starting process of the five-phasePMBLDmotor.The results show that thismethod is lucid andfeasible.

Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2014, Article ID 686373, 8 pageshttp://dx.doi.org/10.1155/2014/686373

2 Modelling and Simulation in Engineering

BLDCmotor0

Commutation logic

Gate drive Hal

l sig

nals

Vd

−

+ Is1 Is3 Is5 Is7 Is9

S1 S3 S5 S7 S9

S6 S8 S10 S2 S4

Iline

(a)

A

B

C

D

E

ia

ib

ic

id

ie

Ra

Rb

Rc

Rd

Re

Mea

La

Mab

Lb

Mbc

Mcd

Lc

Ld

Mde

Le

Ea

Eb

Ec

Ed

Ee

(b)

Figure 1: (a) Five-phase MOSFET inverter based BLDC motor drive; (b) equivalent electrical motor model.

2. Mathematical Model of Five-PhasePMBLDC Motor

The mathematical model of five-phase PMBLDC motor isgiven in [5]. Figures 1(a) and 1(b) show the overall systemconfiguration of the five-phase BLDC motor drive andits equivalent electrical motor model. The PWM invertertopology is a ten-switch voltage source configuration withconstant DC-link voltage (𝑉𝑑). The following assumption ismade for simplification of the analysis to come.

(1) The motor is not saturated.(2) Stator resistances of all the windings are equal, and

self- and mutual inductances are constant.(3) Power semiconductor devices in the inverter are ideal.(4) Iron losses are negligible.

Among the above-mentioned assumptions, the iron losscan be approximated using empirical equations, and thedynamic characteristics of the switching devices need to beconsidered for the investigation of transient state behavior.Under the above assumptions, the five-phase PMBLDCmotor can be represented as

[[[[[

[

𝑉𝑎𝑏

𝑉𝑏𝑐

𝑉𝑐𝑑

𝑉𝑑𝑒

𝑉𝑒𝑎

]]]]]

]

= 𝑅𝑆

[[[[[

[

𝑖𝑎 − 𝑖𝑏

𝑖𝑏 − 𝑖𝑐

𝑖𝑐 − 𝑖𝑑

𝑖𝑑 − 𝑖𝑒

𝑖𝑒 − 𝑖𝑎

]]]]]

]

+ 𝐿𝑆

𝑑

𝑑𝑡

[[[[[

[

𝑖𝑎 − 𝑖𝑏

𝑖𝑏 − 𝑖𝑐

𝑖𝑐 − 𝑖𝑑

𝑖𝑑 − 𝑖𝑒

𝑖𝑒 − 𝑖𝑎

]]]]]

]

+

[[[[[

[

𝐸𝑎 − 𝐸𝑏

𝐸𝑏 − 𝐸𝑐

𝐸𝑐 − 𝐸𝑑

𝐸𝑑 − 𝐸𝑒

𝐸𝑒 − 𝐸𝑎

]]]]]

]

,

(1)

where 𝐿𝑎, 𝐿𝑏, 𝐿𝑐, 𝐿𝑑, 𝐿𝑒 = 𝐿 are the self-inductance of eachphase inHenry,𝑀𝑎𝑏,𝑀𝑏𝑐,𝑀𝑐𝑑,𝑀𝑑𝑒,𝑀𝑒𝑎 =𝑀 are themutualinductances between the five phases in Henry, 𝐿𝑆 = 𝐿 −𝑀 isthe equivalent inductances per phase inHenry,𝑅𝑎,𝑅𝑏,𝑅𝑐,𝑅𝑑,𝑅𝑒 = 𝑅 are the per phase resistance of the five phases in Ohm,

𝑅𝑆 = 2𝑅 is the effective line to line resistance in ohm,𝑉𝑎𝑏,𝑉𝑏𝑐,𝑉𝑐𝑑, 𝑉𝑑𝑒, and 𝑉𝑒𝑎 are the line to line voltages in volt, 𝑖𝑎, 𝑖𝑏, 𝑖𝑐,𝑖𝑑, and 𝑖𝑒 are the phase currents of each coil in ampere, and𝐸𝑎, 𝐸𝑏, 𝐸𝑐, 𝐸𝑑, and 𝐸𝑒 are trapezoidal back EMF in volt. Theperformance analysis of five-phase PMBLD motor is basedon time domain mathematical model. Under these voltages,currents and total power loss of input power and outputpower are shown in (3)-(4). The output mechanical torque isshown as (6), and motor efficiency is shown as (7):

𝑃in =1

𝑇∫

𝑇

0

(𝑉𝑎𝑖𝑎 + 𝑉𝑏𝑖𝑏 + 𝑉𝑐𝑖𝑐 + 𝑉𝑑𝑖𝑑 + 𝑉𝑒𝑖𝑒) 𝑑𝑡,(2)

𝑉𝑎𝑏 = 𝑉𝑎; 𝑉𝑏𝑐 = 𝑉𝑏; 𝑉𝑐𝑑 = 𝑉𝑐;

𝑉𝑑𝑒 = 𝑉𝑑; 𝑉𝑒𝑎 = 𝑉𝑒,

(3)

𝑖𝑎𝑏 =√1.38𝑖𝑎; 𝑖𝑏𝑐 =

√1.38𝑖𝑏; 𝑖𝑐𝑑 =√1.38𝑖𝑐;

𝑖𝑑𝑒 =√1.38𝑖𝑑; 𝑖𝑒𝑎 =

√1.38𝑖𝑒,

(4)

𝑃out = 𝑃in − 𝑃loss, (5)

𝑇out =𝑃out𝜔𝑟

, (6)

𝜂𝑡 =𝑃out𝑃in∗ 100%. (7)

3. Two-Dimensional Finite Element Model ofFive-Phase PMBLDC Motor

The model of five-phase PMBLDC motor was establishedand analyzed by Maxwell software. Initially, according tothe requirement of the control system, the main technicalparameters of the five-phase PMBLDC motor could beoptimized, as given in Table 1. Then, two-dimensional finite

Modelling and Simulation in Engineering 3

Table 1: Geometric motor parameters.

Parameter ValueRated voltage in volts 24Rated speed in rpm 3000Number of pole 4Stator outer diameter in mm 55.2Rotor outer diameter in mm 45.6Rated power in watt 210Number of phases 5Slot number 10Stator inner diameter in mm 46.6Air gap in mm 0.5

Y

XZ

Figure 2: Two-dimensional finite element model (time: 0.02 s).

element model was established by Maxwell 2D software, asshown in Figure 2. Finally, the no load and load of five-phase PMBLDC motor were computed and analyzed in thetransient state module of Maxwell 2D.

3.1. Control Circuit System. To make an accurate simulationanalysis, Maxwell circuit editor module in Ansoft softwarewas adopted to establish the external circuit model andcomplete finite element model along with the geometricmodel that was established [6]. Control circuit system fordriving the five-phase PMBLDC motor is mainly made upof the model of drive circuit and power converter. Controlcircuit system is shown in Figure 3. Here, V138 and V139 arevoltage sources; D140 toD151, D169 toD172, andD175 toD178are diodes; S 52 to S 57, S 67, S 68, S 73, and S 74 are voltagecontrolled switches; V120 to V125 and V218 to V221 arepulse voltage sources; IVC1 to IVC10 are ammeters; MOSFETpower controllable switches and diodes were applied tosimulate controllable switch silicon devices in the actual five-phase PMBLDC motor circuit. Diodes which are in serieswith the controllable switch are used to set the actual voltage

drop. Besides, ten diodes are required as freewheeling diodes.Pulse voltage sources, ground voltagemeters, and resistors areapplied to the drive circuit model.

3.2. Finite Element Grid System. To ensure the accuracyof magnetic circuit calculation and magnetic field analysis,finite element grid was subdivided by manual mode. Themagnetic field was divided into 22146 units by themethods ofinside selection and surface approximation [7–9].The overallsubdivision model and the partial enlargement model areshown in Figures 4(a) and 4(b), respectively. The subdivisionof finite element grid is relatively uniformly distributed on thewhole, and the grid subdivision has a higher density in thefield where the magnetic field is relatively strong and changesgreatly, such as the air gap part. Therefore, the subdivision offinite element grid can reach the desired effect and satisfy theaccuracy of finite element calculation.

4. Results and Discussions

A two-dimensional transient simulation model of five-phasePMBLDC motor and a three-phase PMBLDC motor fromCrouzet were modeled in the Maxwell 2D module software,namely, Ansoft Maxwell. Both motors’ rating is tabulated inTable 2.

4.1. Analysis of Electromagnetic Field. The distributions ofmagnetic line are made at the transient simulation time of23ms five-phase motor and three-phase motor. Similarly, themagnetic flux density for five-phase and three-phase motorsis done at 21ms and 25ms. The results are shown in Figures5 and 6, respectively. From the figure, the red magnetic lineof force is positive extreme, the blue magnetic line of forceis negative extreme, and there are flux leakages in statorslots too. Figure 5 gives the distribution of magnetic lines inthree- and five-phase PMBDLDC motor. It is seen that ina three phase motor the area occupied by the flux lines fora given angular position are more creating more strandedlosses, but in case of five phase motor the area occupied bythe flux lines for a given angular position is less, therebygenerating low stranded losses. Moreover, the distributionof flux around the air gap periphery is nonuniform in athree-phase motor compared to five-phase PMBLDC motor.Figure 6 shows that the magnetic flux density is higherin the yoke part of the stator and exhibits deeper colorwhich results from permanent magnets. Through analyzingthe distribution of magnetic line, the specific distributionof internal complicated magnetic field in the motor andmagnetic saturate situation of each part can be ascertained inthis work so as to provide a better theoretical basis to optimizethe structure of the motor.

4.2. Analysis of Dynamic Processes. The induced voltagesof the no load and load of five-phase PMBLDC motorare carried on simulation computation, and the simulationresults were compared, as shown in Figure 7 (with load) andFigure 9 (with no load). Figure 7 shows that the load voltagedistribution of stator winding induced EMF is nonsinusoidal


D146

S 152 D141

D148

D143S 154

S 153 S 155 S 157 S 167 S 173

S 156

S 168 S 174

12V

12V+−

+−

0

D150D145

D170 D176D177

D171

Model

Model

DModel1

SModel1

D147

D140 D142

D149

D144

D151

D172

D169D178

D175

LabelID = V138

LabelID = V139

LabelID = VIA

LabelID = VIB

LabelID = VIC

LabelID = VID

LabelID = VIE

LabelID = V120 LabelID = V123LabelID = V122 LabelID = V124

0LabelID = V125

LabelID = V221LabelID = V220

LabelID = V219LabelID =

V218

LabelID = IVc1 LabelID = IVc2 LabelID = IVc3 LabelID = IVc4

LabelID = IVc5 LabelID = IVc8

LabelID = IVc7LabelID =IVc6

LabelID =IVc9

LabelID =IVc10

AA

AA

A

V V V V V V V V V V

LA

LB

LC

LD

LE

RA

RB

RC

RD

RE

R126 R127 R128

0.000320H∗Kle

0.000320H∗Kle

0.000320H∗Kle

0.000320H∗Kle

0.000320H∗Kle

0.3056Ohm

0.3056Ohm

0.3056Ohm

0.3058Ohm

0.3058Ohm

LPhase A

LPhase B

LPhase C

LPhase D

LPhase E

100Ohm 100Ohm 100OhmR139

100OhmR130

100OhmR131

100OhmR217

100OhmR216

100OhmR215

100OhmR214

100Ohm

−11V

−11V

−11V

−11V

−11V

−11V

−11V

−11V

−11V −1

1V

Figure 3: Control circuit system.

0 20 40

(mm)

Time = 0.0419999999999999 sSpeed = 1500.000000 rpmPosition = 15.500000 deg

(a) (b)

Figure 4: Grid subdivision model (time = 41.9ms, 15.5 deg displacement). (a) Overall subdivision model. (b) Partial enlargement model.

and approximately less than no load voltage. It gives thedynamic behavior of induced voltage for a five-phase motorwhen loaded with 0.2Nm load torque at 1500 rpm. It is seenthat the speed of the motor drops from 1500 rpm to 628 rpmwithin 33ms.The induced EMF also drops from 8.2V to 6.1 Vpeak voltage for phase winding A.

4.3. Waveforms and Discussions. The waveforms for boththe three-phase and five-phase motors running at 1500 rpm

are shown for no load conditions. Figure 8 shows the phasecurrents of the motors indicating that the current drawn bythe five-phase motor is 1.2 times that of three-phase motor.Similarly, Figure 9 infers that the five-phase induced voltageis 1.4 times that of three-phase motor. Figure 10 shows thatthe five-phase flux linkage is 1.3 times that of the three-phasemotor. The motoring torque of the two motors is shownin Figure 11. It is seen that the torque of the three-phasemotor varies from 0.18 to 1.7Nm over one cycle producingan average torque of 0.94Nm. In case of five-phase motor,


Table 2: Three-phase and five-phase motors.

Parameters Symbol Type of motor3-phase Crouzet PMBLDC motor 5-phase developed PMBLDC motor

Rated power 𝑃 160W 210WRated input voltage 𝑉in 24V 24VRated armature current 𝐼𝑎 8.8 Amps 10.8Rated speed 𝑁 3500 rpm 1400Resistance (per phase) 𝑅𝑎 0.12Ω 0.305ΩArmature inductance 𝐿𝑎 0.6mH 0.32mHMagnetic flux linkage Φ 0.02Wb 0.02WbNumber of poles 𝑃 4 4Rated torque 𝑇 0.4365Nm 1.5NmWinding configuration Delta Delta

0 20 40

(mm)


6.2416e − 003

5.0995e − 003

3.9574e − 003

2.8153e − 003

1.6732e − 003

5.3113e − 004

−6.1096e − 004

−1.7531e − 003

−2.8952e − 003

−4.0373e − 003

−5.1794e − 003

−6.3215e − 003

−7.4635e − 003

A(W

b/m

)

(a)


6.6141e − 0035.7856e − 0034.9572e − 0034.1287e − 0033.3002e − 0032.4718e − 0031.6433e − 0038.1483e − 004

−1.3642e − 005−8.4211e − 004−1.6706e − 003−2.4990e − 003−3.3275e − 003−4.1560e − 003−4.9845e − 003−5.8129e − 003−6.6414e − 003−7.4699e − 003

0 20 40

(mm)

A(W

b/m

)

(b)

Figure 5: Distribution of magnetic lines in three- and five-phase motors.

0 20 40

(mm)

2.6157e + 0002.4522e + 0002.2888e + 0002.1253e + 0001.9618e + 0001.7983e + 0001.6348e + 0001.4714e + 0001.3079e + 0001.1444e + 0009.8091e − 0018.1743e − 0016.5395e − 0014.9047e − 0013.2699e − 0011.6351e − 0012.5904e − 005

B(te

sla)


(a)

2.1381e + 0002.0123e + 0001.8866e + 0001.7608e + 0001.6350e + 0001.5093e + 0001.3835e + 0001.2577e + 0001.1319e + 0001.0062e + 0008.8040e − 0017.5463e − 0016.2886e − 0015.0309e − 0013.7732e − 0012.5155e − 0011.2578e − 0018.3103e − 006

B(te

sla)


0 20 40

(mm)

(b)

Figure 6: Magnetic flux density in three- and five-phase motors.


Ina fivephase8.00

6.00

4.00

2.00

0.00

−2.00

−4.00

−6.00

−8.00Y1

(V)

Induced voltage with 0.2nm load

Time (ms)

1500.00

1375.00

1250.00

1125.00

1000.00

875.00

750.00

625.00

Mov

ing1

spee

d (r

pm)

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Moving1 speed Moving1speedSetup1: transient

Setup1: transientInduced voltage (phase A)

Curve info y-axis

Setup1: transientInduced voltage (phase B)

Setup1: transientInduced voltage (phase C)

Setup1: transientInduced voltage (phase D)

Setup1: transientInduced voltage (phase E)

Y1

Y1

Y1

Y1

Y1

Figure 7: Five-phase induced voltage and speed (with a load torque of 0.2Nm).

Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

5.00

2.50

0.00

−2.50

−5.00

Y1

(A)

Current (phase A)Setup1: transient

Setup1: transient

Setup1: transient

Current (phase B)

Current (phase C)

Ina threephase

Curve info

Phase currents

(a)

5.00

3.00

1.00

−1.00

−3.00

−5.00

Y1

(A)

Phase currents

0.04 5.00 10.00 15.00 20.00 25.00 30.00 34.60

Time (ms)

Current (phase A)Setup1: transient

Setup1: transient

Setup1: transient

Current (phase B)

Current (phase C)

Current (phase D)Setup1: transient

Setup1: transientCurrent (phase E)

Ina fivephase

Curve info

(b)

Figure 8: Three-phase and five-phase currents.

Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Curve info




Y1

(V)

Induced EMF Ina threephase10.00

7.50

5.00

2.50

0.00

−2.50

−5.00

−7.50

−10.00

(a)

Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Curve info




Setup1: transientInduced voltage (phase D)

Setup1: transientInduced voltage (phase E)

10.00

8.00

6.00

4.00

2.00

0.00

−2.00

−4.00

−6.00

−8.00

Y1

(V)

Induced EMF Ina fivephase

(b)

Figure 9: Three-phase and five-phase induced voltages.


Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Curve info

Setup1: transientFlux linkage (phase A)

Setup1: transientFlux linkage (phase B)

Setup1: transientFlux linkage (phase C)

Flux linkage Ina threephase0.015

0.10

0.005

0.000

−0.005

−0.010

−0.015

Y1

(Wb)

(a)

Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Curve info

Setup1: transientFlux linkage (phase A)

Setup1: transientFlux linkage (phase B)

Setup1: transientFlux linkage (phase D)

Setup1: transientFlux linkage (phase E)

Setup1: transientFlux linkage (phase C)

0.020

0.015

0.010

0.005

0.000

−0.005

−0.010

−0.015

−0.020

Y1

(Wb)

Flux linkage Ina fivephase

(b)

Figure 10: Three-phase and five-phase flux linkages.

Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Curve infoMoving1. torque

Setup1: transient

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

−0.25

Mov

ing1

. tor

que (

Nm

)

Motoring torque Ina threephase

(a)

Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Curve info Avg.Moving1. torque 1.5554

Setup1: transient

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

Mov

ing1

. tor

que (

Nm

) 2.002.25

Motoring torque Ina fivephase

(b)

Figure 11: Three-phase and five-phase motoring torques.

the torque varies from 0.92Nm to 2.2Nm over one cycleproducing an average torque of 1.56Nm. These results showthat the torque produced in a five-phase motor running at1500 rpm is 1.6 times the torque of a three-phasemotor havingthe same 𝐷/𝐿. From the above torque values, it is concludedthat the torque ripple of the five-phase motor is 50.29%less than that of the three-phase motor as seen in Figure 13.Figure 12 indicates that the five-phase stranded loss is 2.19times that of three-phase motor.

5. Conclusion

The software Maxwell 2D was adopted to establish the sim-ulation model of five-phase brushless direct current motor

by finite element analysis. The transient and dynamic perfor-mance of the motor are accurately accomplished. Simulationresults show that the internal magnetic field distributionis reflected accurately and also provides a theoretical basisto make further optimal design. The main properties ofthe motors include electromagnetic torque, speed, windinginduced voltage, and power loss, which can provide a refer-ence to reduce torque ripple, improve the starting torque, andmake further optimal design of the motor. It is also shownthat the torque ripple in five-phase PMBLDC motor is lowcompared to its three-phase counterparts. It is concluded thatthe average torque produced in a five-phasemotor running at1500 rpm is 1.6 times the torque of a three-phasemotor havingthe same 𝐷/𝐿, and the torque ripple of the five-phase motoris 50.29% less than that of the three-phase motor. Though


Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Curve infoStranded loss

Setup1: transient

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

0.00

Stra

nded

loss

(W)

Losses Ina threephase

(a)

Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

Curve infoStranded loss

Setup1: transient

Losses Ina fivephase16.00

14.00

12.00

10.00

8.00

6.00

4.00

2.00

0.00

Stra

nded

loss

(W)

(b)

Figure 12: Three-phase and five-phase stranded losses.

Time (ms)0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

2.50

2.00

1.50

1.00

0.50

0.00

−0.50

Y1

(Nm

)

Curve info Avg.

Torque comparison

Moving1. torque imported

Moving1. torque 1.5648

0.9407

Setup1: transient

Imported moving1. torque

Ina fivephase

Figure 13: Three-phase and five-phase torque comparison.

the amount of torque ripple present in this analysis for three-phase and five-phase motors is not desirable, this method ofanalysis will enhance the theoretical understanding onmotordesign and its impact on motor performance.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

References

[1] A. Kusko and S. M. Peeran, “Definition of the brushless DCmotor,” in Proceedings of the IEEE Industry Application SocietyAnnual Meeting (IAS ’88), pp. 20–22, 1988.

[2] J. R. Hendershot and T. J. E. Miller, Design of BrushlessPermanent-Magnet Motor, Oxford Science, 1994.

[3] T. Kenjo and S. Nagamori, PermanentMagnet and Brushless DCMotors, Tokyo Sogo Electronics, 1984.

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