modeling and simulation of five-phase induction motor fed

6 Page 6-22 © MAT Journals 2019. All Rights Reserved

Journal of Advances in Electrical Devices

Volume 4 Issue 2

Modeling and Simulation of Five-Phase Induction Motor Fed With Pulse Width Modulated Five-Phase Multilevel Voltage

Source Inverter Topologies

Gerald .C. Diyoke1, Candidus.U. Eya2

1Department of Electrical and Electronic Engineering, Michael Okpara University of Agriculture Road 10, Federal Low Cost Umuahia,Umudike, Abia State Nigeria.

2Department of Electrical and Electronic Engineering, University of Nigeria Nsukka No 4 Umudikwu Village, Off-Orba Road, Nsukka, Enugu State, Nigeria

Email: [email protected]

Abstract

This paper presents modelling and simulation of five-phase induction motor fed with pulse width modulated five-phase multilevel voltage source inverter. The conventional and diode clamped multilevel five-phase inverter configurations are reviewed with pulse width modulation (PWM) techniques. A hybrid three-level inverter topology with less number of components count is proposed for five-phase induction motor drive. The dynamic analysis of five-phase voltage equations in d-q axis of the induction motor are stated and modelled using Matlab/Simulink/Simscape blocks. The simulation results based on conventional and three-level five-phase inverters are displayed while the hybrid inverter topology showed some better performance based on the following: : at 0.0127secs maximum torque of 34.54Nm occurred, maximum stator current occurred for 0.18secs with a value of 10A, 9.99% total harmonic distortion was obtained and 15KW power rating was obtained. Keywords: Five-phase induction motor, multilevel, sinusoidal pulse width modulation, voltage source inverter

INTRODUCTION Multiphase (more than three phase) machines are alternating current (AC) machines that are known for a stator winding [1-6]. They consist of generic number of phases. Recently, electric machines driven by multiphase inverter technology have many advantages over the conventional three phase machine and inverters. For instance, in decreasing the amplitude and increasing the frequency of torque pulsation, higher torque density, reducing the rotor harmonic current distortion per phase without increasing the voltage per phase, lowering the dc-link current harmonics, better noise characteristics, higher reliability and high fault tolerance [7-9]. Three phase induction motors have wide range of applications, thus, they are invariably used in many residential, commercial, industrial and utility applications due to their low cost, reliable operation, robust operation and low maintenance. Multiphase motor

drives with increased phase number lead to an improvement in medium to high power drives application. The multiphase induction motor finds application in a particular and vital area where high reliability is needed, for instance; Electric vehicle/Hybrid Electric vehicles, aerospace application, ship propulsion and locomotive traction, battery powered electric vehicles and high power application [10 – 12]. The performance analysis of five-phase and three phase induction motor was proposed [13]. The performance analyses are carried out using conventional five and three phase inverter topologies. The author observed that the five-phase induction motor has a good performance over the three-phase induction motor. A comparative study between three phase and five phase induction motor by using a converter topology are described in [14]. The author worked on the challenges of fault occurring on both phases. It is noticed that

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Volume 4 Issue 2

the five phase converter tolerates fault to a greater extent than the conventional three phase. A step by step approach of a dynamic modeling of five phase induction motor was carried out by authors in [15]. Also, an output total harmonic distortion (THD) of the five phase inverter configurations and agreeing dynamic performance of five phase induction motor are researched by [16]. The author successfully implemented the proposed inverter topology with induction motor load. The modeling and simulation of five phase inverter fed induction motor drive and three phase inverter fed induction motor drive was presented in [17]. The output of the five-leg inverter and three leg inverters is controlled by SPWM control technique method using Matlab/Simulink software. The author concluded that the ripple content of various parameters (current, torque and speed) can be smoothened by supplying the motor with five phase supply than three phase supply. Also Sequential Five Leg Inverter for Five Phase Supply is presented in [18]. The authors used space vector modulation strategy though time consuming and complex calculation involvement for the analysis and performance evaluation. THD with less harmonic content was obtained.This paper presents the Modeling and Simulation of Five Phase Induction Motor Fed with Five Phase Hybrid Multilevel Voltage Source Inverter Topologies. The structure of this paper is

organized as follows. Section-II deals with the five-phase conventional inverter topology with sinusoidal pulse width modulation (SPWM) techniques. Also, switching sequence of five phase inverter presented. Section-III gives the five-phase diode clamped and hybrid inverter configurations with their mode of operations. Section-IV depicts the mathematical modeling of five phase induction motor which includes the q-d-0 axis equivalent circuit of five phase induction motor in arbitrary reference frame. Section-V presented mathematical model implementation using MATLAB/Simulink. In section VI, MATLAB/Simulink simulation results are presented and discussed. Finally, Section-VII presents the conclusion part. CONVENTIONAL FIVE PHASE INVERTER TOPOLOGY The basic power circuit topology of conventional five phase voltage source inverter is shown in Fig. 1. Insulated gate bipolar transistor (IGBT) is used as the power switches. The anti-parallel diodes provide reverse current path such that when a particular IGBT is ON, one output terminal and one input terminal will be connected. In multiphase inverter n number of phases can be generated, as each leg of the inverter represents a phase, thus by increasing the number of legs in the inverter, the number of phases can equally be increased.

n

g

aZbZ

avbv cv

dv ev

cZdZ

eZ

dcV

1S3S 5S

7S 9S

6S8S

10S 2S 4S

1D

6D

3D

8D

5D

10D

7D9D

2D4D

Figure 1: Five phase conventional inverter topology.

Ten-Step Inverter In five phases conventional ten step

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Volume 4 Issue 2

inverter topology, the upper three switches

and lower two switches are turned on at

same time and vice versa. So, ten modes of

operation are obtained, thereby making

each switch to conduct 36 degrees per

cycle. Two switches form one leg of the

inverter and they are complimentary to

each other during the mode of operation.

Harmonics of order five and multiples of

five are absent from both the line to line

and line to neutral voltages and

consequently absent from the current [16].

Appendix B denotes the switching vectors,

phase voltages, and output line-to-line

voltages of the conventional five-phase

inverter topology.

Table1: Switching sequence of five leg conventional inverter Mode Switches ON Switches OFF

1 7,8,9,10,1 2,3,4,5,6

2 8,9,10,1,2 3,4,5,6,7

3 9,10,1,2,3 4,5,6,7,8

4 10,1,2,3,4 5,6,7,8,9

5 1,2,3,4,5 6,7,8,9,10

6 2,3,4,5,6 7,8,9,10,1

7 3,4,5,6,7 8,9,10,1,2

8 4,5,6,7,8 9,10,1,2,3

9 5,6,7,8,9 10,1,2,3,4

10 6,7,8,9,10 1,2,3,4,5

Mode 1Switch Mode 2

1S

Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9 Mode 10

2S

tt

t3S

4S

5S

6S

7S

8S

9S

10S

ttttttt

Figure 2: switching sequence of ten step inverter operation.

−−−−

−−−−

−−−−

−−−−

−−−−

=

en

dn

cn

bn

an

eg

dg

cg

bg

ag

V

V

V

V

V

V

V

V

V

V

41111

14111

11411

11141

11114

5

1 (1)

Five Phase Sinusoidal Pulse-width

Modulated Inverter

In ten step inverters under sinusoidal pulse

width modulation control technique, the

output voltage waveforms are similar to

fundamental output voltage form of

multilevel inverter topologies, thus total

harmonic distortion will be high and will

equally degrade the performance of the

induction motor. The modulated pulses as

shown in Fig. 3 are obtained by comparing a

sinusoidal reference wave with triangular

carrier wave. The inverter output frequency

can be varied by varying the frequency of

the reference wave.



Volume 4 Issue 2

Figure 3: switching signals for SPWM inverter

MULTILEVEL FIVE PHASE

INVERTER TOPOLOGIES

Three-phase multilevel inverter topologies

of diode clamped and hybrid are extended

to five phase. Fig. 4 shows the inverter

power circuit for three-level five-phase

diode clamped configuration. While Fig. 6

shows the hybrid inverter power circuit

with less number of circuit components for

three-level five-phase topology.

Three Level Diode Clamped Inverter

Configuration

This circuit topology consists of two

battery sources connected in series whose

junction serves as a neutral point. The

three-level output voltage is generated as

dcV ,2

dcV,0. Each leg or pole voltage

consists of four power switches. In order

to improve on output voltage performance,

the number of power switches and series

battery have to be increased.

Consequently, increasing the circuit

performance increases its cost, switching

losses, weight and complexity of the

circuit configuration. The firing signals are

generated by comparing the carrier and

reference signals as shown in Fig. 5.

g

aZbZ cZ dZ

eZ

n

1aS1bS 1cS 1dS

1eS

2aS

1aS

2aS

2bS

1bS

2bS

2cS

1cS

2cS 2dS 2eS

1dS 1eS

2dS 2eS

2

dcV

2

dcV

av bv cv dvev

Figure 4: Three level five phase diode clamped inverter configuration.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

0

2

4

6

8

10

12

14

16

18

20

Time [s]

Am

pli

tud

e [

v]

S1

S3

S5

S7

S9

S6

S8

S10

S2

S4



Volume 4 Issue 2

Figure 5: switching signals for three-level five-phase diode clamped inverter configuration.

Three-Level Hybrid Inverter

Configuration

This circuit topology consists of two

battery sources connected in series whose

junction serves as a neutral point and a

bidirectional switch is connected at this

point. The three-level output voltage is

generated as: dcV ,2

dcV, 0. Each leg or pole

voltage consists of two power switches

and one bidirectional switch which

consists of four diodes and one power

switch as shown in Fig. 6. In order to

improve on output voltage performance,

the number of power switches and series

battery have to be increased.

Consequently, increasing the circuit

performance increases its cost, switching

losses, weight and complexity of the

circuit configuration. Fig. 7 shows all the

power switches control signals for the five

poles or legs.

1S

6S

aSav

1D

6D

1aD

1aD

2aD

2aD

3S

8S

bSbv

3D

8D

1bD

1bD

2bD

2bD

5S

10S

cScv

5D

10D

1cD

1cD

2cD

2cD

7S

2S

dSdv

7D

2D

1dD

1dD

2dD

2dD

9S

4S

eS ev

9D

4D

1eD

1eD

2eD

2eD

g

aZ bZ cZdZ eZ

n

2

dcV

2

dcV

Figure 6: Three level five phase hybrid inverter configuration.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-7

-6

-5

-4

-3

-2

-1

0

1

2

Time [s]

Am

pli

tud

e [

v]

Va

Vb

Vc

Vd

Ve

Vcr1

Vcr2

Vcr3

Vcr4

Sa1

Sa2

NotSa1

NotSa2

11 -22 © MAT Journals 2019. All Rights Reserved


Volume 4 Issue 2

Figure 7: switching signal for hybrid inverter topology

DYNAMIC MODELING OF FIVE

PHASE INDUCTION MOTOR

The mathematical model of five-phase

induction motor given in equations (2) to

(9) is used to simulate the five-phase

induction machine as reported in [19-20].

The machine’s voltage equations in the

common reference frame:

+=

+=

+=

++=

+−=

ssss

ysyssys

xsxssxs

qsdsaqssqs

dsqsadssds

piRV

piRV

piRV

piRV

piRV

000

(2)

+=

+=

+=

+−+=

+−−=

rrrr

yryrryr

xrxrrxr

qrdraqrrqr

drqradrrdr

piRV

piRV

piRV

piRV

piRV

000

)(

)(

(3)

Where

=

=

=

++=

++=

slss

yslsys

xslsxs

qrmqsmlsqs

drmdsmlsds

iL

iL

iL

iLiLL

iLiLL

00

)(

)(

(4)

=

=

=

++=

++=

rlrr

yrlryr

xrlrxr

qsmqrmlrqr

dsmdrmlrdr

iL

iL

iL

iLiLL

iLiLL

00

)(

)(

(5)

Torque equation can be expressed by

−=

−=

][

)(2

5

qrdsqsdrme

qrdsqsdre

iiiiPLT

iiiiMP

T (6)

dt

d

P

JTT r

Le

=− (7)

The line-to-neutral voltages can be transformed to the d-q planes using the following

transformation matrix as shown below

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

5

10

15

20

25

30

Time [s]

Am

pli

tud

e [

v]

S1

Sa

S6

S3

Sb

S8

S5

Sc

S10

S7

Sd

S2

S9

Se

S4



Volume 4 Issue 2

−

+

−

+

−

+

−

+

+

+

−

−

+

+

−

−

=

2

1

2

1

2

1

2

1

2

15

4sin

5

2sin

5

2sin

5

4sinsin

5

4cos

5

2cos

5

2cos

5

4coscos

5

4sin

5

2sin

5

4sin

5

2sinsin

5

4cos

5

2cos

5

4cos

5

2coscos

5

2

K

(8)

The stator currents can be expressed as

=

s

ys

xs

qs

ds

es

ds

cs

bs

as

i

i

i

i

i

i

i

i

i

i

0

15

16sin

5

16cos

5

8sin

5

8cos

15

12sin

5

12cos

5

6sin

5

6cos

15

8sin

5

8cos

5

4sin

5

4cos

15

4sin

5

4cos

5

2sin

5

2cos

10101

5

2

(9)

MATLAB/SIMULINK

IMPLEMENTATION

The inverter voltage, flux, torque

equations and transformation matrices

are used to implement the model of five

phase multilevel inverter fed induction

motor in MATLAB/Simulink as shown

in appendix and general block diagram

depicted Fig. 8. The input to the motor

is generated from five phase multilevel

SPWM inverter supply. The five phases

to two phase conversion blockstransfers

the five phase stator voltages to d-q axis

voltages.

DC Input

Voltage

Five-phase

Multilevel

Inverter

Figs. (1 or 4 or 6)

Eqns. (2, 3,

4 and 5)Eqns. (6 and 7) Display

Load

TL

Figs. (3 or 5 or 7)Reference signal

Carrier signalComparator

Figure 8: The general block diagram of the five-phase inverter fed induction motor.

SIMULATION RESULTS AND

DISCUSSIONS

The mathematical model given in the

paper is implemented in

MATLAB/Simulink/Simpower system

block sets. The inbuilt IGBT/Diode blocks

are used to simulate the inverter power

circuit. The three different inverter



Volume 4 Issue 2

topologies are analyzed through their

output voltages, stator currents, motor

speed, electro-magnetic torque, speed-

electromagnetic and total harmonic

distortions. The input voltage for the

inverter is 440 volts dc supply. The

simulations are carried out under

modulation index of 1 and frequency index

of 40 at 50Hz operating frequency. The

five-phase induction motor is loaded with

10N-m and the performance of each

topology is as discussed as follow.

Five Phase Conventional Inverter

Topology

Figures (9 – 10) show the inverter output

voltage and stator current respectively.

Fig. 11 shows motor speed and

electromagnetic torque. Figures (12–

13) depict speed-electromagnetic and

FFT analysis respectively. Total

harmonic distortion is 8.48% with rms

voltage of 250.9V at 50Hz. The

maximum stator transient current is

recorded as 8.8A which lasted for

0.2secs. 34N-m maximum torque

occurred at 0.0124secs and maximum

speed of 1445rpm occurred at 0.18secs.

This model has a power rating of

14KW. The signal generator contains

two carrier signals and five reference

signals. Furthermore, the power circuit

configuration contains ten power

switches as shown in Fig. 1.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

-500

0

500

500

Time [secs]

Am

plitu

de

Output Voltage Plots

V ea [V]

V de [V]

Vcd

[V]

V bc [V]

V ab [V]

0

-500

500

0

0

0

-500

Figure 9: Inverter Output Voltages

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-10

-10

0

-5

5

0

10

Stator Currents

Cur

rent

s [A

]

Time [Secs]

ies

ids

i cs

ibs

ias

0

0

10

0

Figure 10: Stator Current



Volume 4 Issue 2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

500

1000

1500

Speed Plot

Wr

[RP

M]

(A) Time [secs]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

10

20

30

Electromagnetic Torque Plot

Te

[N-m

]

(B) Time [secs] Figure 11: (A) Speed curve, (B) Torque curve

0 200 400 600 800 1000 1200 1400 1600

-5

0

5

10

15

20

25

30

35

Electromagnetic Torque Versus Speed Plot

Te [

N-m

]

Speed [RPM] Figure 12: Electromagnetic curve.

0 5 10 15 200

50

100

150

200

250

Harmonic order

Fundamental (50Hz) = 250.9 , THD= 8.48%

Mag

2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

Figure 13: FFT analysis of conventional Inverter.



Volume 4 Issue 2

Five Phase Three Level Diode Clamped

Inverter




electromagnetic torque. Figures (17 – 18)

depict speed-electromagnetic and FFT

analysis respectively. Total harmonic

distortion is 9.09% with rms voltage of

248.9V at 50Hz. The maximum stator

transient current is recorded as 10A which

lasted for 0.2secs. 34.65N-m maximum

torque occurred at 0.0127secs and

maximum speed of 1434.3rpm occurred at

0.18secs. This model has a power rating of

14.5KW. The signal generator contains

four carrier signals and five reference

signals. Furthermore, the power circuit

configuration contains twenty power

switches as shown in Fig. 4.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-500

500

-500

0

500

500

500

Time [secs]

Am

plitu

de


V ea [V]

Vde [V]

V cd [V]

Vbc

[V]

Vab

[V]

0

0

0

0

Figure 14: Inverter Output Voltages

0 0.1 0.2 0.3 0.4 0.5 0.6-10

0

10

0

-10

0

10

0

-10

0

10 Stator Currents

Cu

rren

ts [

A]

Time [Secs]

ies

ids

ics

ibs

ias

Figure 15: Stator Currents



Volume 4 Issue 2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

500

1000

1500

Speed Plot

Wr [

RPM

]

(A) Time [secs]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

10

20

30


Te

[N-m

]


0 200 400 600 800 1000 1200 1400 1600

-5

0

5

10

15

20

25

30

35


Te

[N-m

]

Speed [RPM] Figure 17: Electromagnetic Curve

0 5 10 15 200

20

40

60

80

100

Harmonic order


Ma

g (

% o

f F

un

da

men

tal)

2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

Figure 18: FFT analysis

Five Phase Three Level Hybrid Inverter

Configuration




electromagnetic torque. Figures (22 – 23)

depict speed-electromagnetic and FFT

analysis respectively. Total harmonic

distortion is 9.99% with rms voltage of

249.7V at 50Hz. The maximum stator



Volume 4 Issue 2

transient current is recorded as 10A which

lasted for 0.2secs. 34.54N-m maximum

torque occurred at 0.0127secs and

maximum speed of 1440rpm occurred at

0.18secs. This model has a power rating of

15kW. The signal generator contains four

carrier signals and five reference signals.

Furthermore, the power circuit

configuration contains fifteen power

switches as shown in Figure 6.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05-500

0

500

0

-500

0

500

0

500

0

500

Time [secs]


Vea

[V]

Vde

[V]

Vcd [V]

V bc [V]

Vab

[V]

Figure 19: Inverter Output Voltage

0 0.1 0.2 0.3 0.4 0.5 0.6-10

0

10

0

-10

0

10

0

-10

0

10 Stator Currents

Cur

rent

s [A

]

Time [Secs]

ies

ids

ics

ibs

ias

Figure 20: Stator Currents

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

500

1000

1500

Speed Plot

Wr

[RPM

]

(A) Time [secs]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

10

20

30


Te

[N-m

]




Volume 4 Issue 2

0 200 400 600 800 1000 1200 1400 1600

-5

0

5

10

15

20

25

30

35


Te

[N-m

]

Speed [RPM] Figure 22: Electromagnetic Curve

0 5 10 15 200

20

40

60

80

100

Harmonic order

Ma

g (

% o

f F

un

da

men

tal)


2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

7

8

Figure 23: FFT analysis

CONCLUSION

The investigation in the area of multi-

phase inverter and induction machine

indicates that it is technically viable to use

phase number higher than three in

multilevel inverters and induction

machines. The successful accomplishment

of the proposed inverter configurations

connection scheme is elaborated by using

simulation results. Then, from the above

conventional and three-level five-phase

inverters, the hybrid inverter topology

showed some better performance based on

the following: at 0.0127secs maximum

torque of 34.54Nm occurred, maximum

stator current occurred for 0.18secs with a

value of 10A, 9.99% total harmonic

distortion was obtained and 15KW power

rating was obtained. Therefore, this hybrid

inverter circuit configuration can be used

instead of three-level five-phase diode

clamped inverter topology for better

performance and economical operation.

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Volume 4 Issue 2

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5. A. Tani, M. Mengoni, L. Zarri, G. Serra, D. Casadei.(2011), “Control of Multi–Phase Induction Motors with an Odd Number of Phases Under Open–Circuit Phase Faults,” IEEE Transactions on Power Electronics, DOI: 10.1109/TPEL.2011.2140334.

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9. H. Guzmán, J.A. Riveros, M.J. Durán, F. O.Barrero.(2012), “Modeling of a Five-Phase Induction Motor Drive with a Faulty Phase,”15th International Power Electronics and Motion Control Conference, EPE-PEMC ECCE Europe, Novi Sad, Serbia.

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Volume 4 Issue 2

About Authors

Gerald .C. Diyoke (Engr.) was

born in Aku Nigeria on 9th October, 1980.

He received his B.Eng. (Second Class

Upper Honors), and M. Eng. (Distinction)

from the Department of Electrical

Engineering, University of Nigeria Nsukka

(UNN) in 2005 and 2013 respectively. He

is currently a Ph. D. student in the

Department of Electrical Engineering

UNN and a Lecturer at the Department of

Electrical and Electronic Engineering,

Michael Okpara University of Agriculture,

Umudike, Abia, Nigeria. His research

interests are Power electronics,

conventional and multilevel inverter,

Induction motor drives.

Candidus .U. Eya (Engr. Dr.)

was born in Urukpa, Ezimo- Agu Udenu

local government area, Enugu state,

Nigeria on 8th August, 1980. He received

his Ph. D and M. Eng from the Department

of Electrical Engineering, University

Nigeria, Nsukka in 2017 and 2013

respectively. In 2006, he received his

B.Eng. from the Department of Electronics

Engineering University Nigeria, Nsukka.

He is a Coren Registered Engineer in

Nigeria. He is also a member of Nigerian

Societies of Engineers and International

association Engineers (IAENG). He

specializes in power electronics and new

energy systems. He is a reviewer in

Nigerian Journal of technology. He is

presently a Lecturer in the Department of

Electrical Engineering, University of

Nigeria, Nsukka. His research interests

are: Power electronics, Conventional

Inverters, Multilevel inverters, Modular

inverters, grid-connected inverters, motor

drives and Hybrid power systems.

Appendix A

Matlab/Simulink Simulation model for the system



Volume 4 Issue 2

Appendix B

Switching vectors, phase voltages, and output line-to-line voltages Voltage

Vector Switching Vector ( dcV ) Line to neutral Voltage ( dcV ) Line to Line Voltage ( dcV )

anv

bnv

cnv

dnv

env

agv bgv cgv dgv egv abv

bcv

cdv

dev

eav

0V 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1V 1 0 0 1 1

5

2

5

3−

5

3−

5

2

5

2

1 0 -1 0 0

2V 1 0 0 0 1

5

3

5

2−

5

2−

5

2−

5

3

1 0 0 -1 0

3V 1 1 0 0 1

5

2

5

2

5

3−

5

3−

5

2

0 1 0 -1 0

4V 1 1 0 0 0

5

3

5

3

5

2−

5

2−

5

2−

0 1 0 0 -1

5V 1 1 1 0 0

5

2

5

2

5

2

5

3−

5

3−

0 0 1 0 -1

6V 0 1 1 0 0

5

2−

5

3

5

3

5

2−

5

2−

-1 0 1 0 0

7V 0 1 1 1 0

5

3−

5

2

5

2

5

2

5

3−

-1 0 0 1 0

8V 0 0 1 1 0

5

2−

5

2−

5

3

5

3

5

2−

0 -1 0 1 0

9V 0 0 1 1 1

5

3−

5

3−

5

2

5

2

5

2

0 -1 0 0 1

10V 0 0 0 1 1

5

2−

5

2−

5

2−

5

3

5

3

0 0 -1 0 1

11V 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0

APPENDIX C

MACHINE PARAMETERS Stator resistance 0.78Ω

Rotor resistance 0.66Ω

Stator inductance 0.00345H

Rotor inductance 0.00345H

Mutual inductance 0.0297H

Moment of inertia 0.0435kg/m2

Viscous friction coefficient 0.0435N.m.s

Number of poles 4

APPENDIX D

NOMENCLATURE

f = Frequency (Hz)

I = current (A)



Volume 4 Issue 2

V = voltage (V)

P = number of poles

L = inductance (H)

M = Mutual inductance (H)

R = Resistance (Ω)

Te = Electromagnetic Torque (N-m)

= ngle between successive phases in electrical degrees

= Flux (wb)

= Angular frequency (rad/secs)

Subscript

d,q – direct and quadrature axes

m- Magnetizing

s – Stator

r – Rotor

modeling and simulation of five-phase induction motor fed

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