By Suman Karmakar
Roll No: 20EE4204
Power Electronics and Machine Drives
Under the Guidance of
Jitesh Chandra Barman
Assistant Professor
NIT Durgapur
2
Outline

Objectives

Introduction

Literature Review

Three Phase Induction Machine Model

Simulation Result 3 Phase Induction Machine

Multiphase Induction Machine

Six Phase Induction Machine

Advantages of Six phase Induction Machine

Equivalent Circuit of 6 Phase Induction Machine

6 Phase Induction Machine Model

6 Phase Induction Machine Characteristics

Future Work

References

Acknowledgement
3
Objectives

To study the modeling of three phase induction machine and implement in the
MATLAB Simulink.

To study the advantages of multiphase Induction Machine over the
conventional three phase induction machine.

To study the modeling of six phase induction machine in d-q axis frame.

Implementation of six phase induction machine in MATLAB Simulink

To study the control scheme of Six Phase Induction Machine Drive and
hardware implementation.
4
Introduction

Induction machines are very popular in industrial applications because of their
simple construction, less maintenance, robust structure and self-starting
nature.

In general three phase induction machines are mostly used because of the
availability of three phase supply. But now a days using different power
electronics converter multiphase power supply can be easily generated.

Although multiphase induction machines are relatively costlier but it has
many advantages over three phase induction machines.

Due to their many advantages over conventional three phase induction
machine , research on multi phase induction machine has increased
significantly in the past decade.

Multiphase induction machines are used in high power applications and has
applications in electric ship propulsion, electric and hybrid electric vehicles,
railway traction, more-electric aircraft, wind power generation systems etc.
5
Literature Review

In 1969, E.E. Ward and H. Harer presented an inverter fed five phase induction
motor and suggested that the amplitude of torque pulsation can be reduced by
increasing the number of stator phase. [1]

The detailed modelling procedure is explained by D.C. White and H. H.
Woodson in [2]

R.H. Nelson and P.C. Krause done computer simulation on three types of sixphase induction motor and found that by using a motor with 30O phase belts,
sixth harmonic torque pulsation was eliminated. [3]

Machine with two set of three phase winding displaced with 30o and powered
by a current source inverter is described by T.A. Lipo in [4].

E. Levi et. al. described a physical variable model for multiphase induction
machine in [5] and a generalized simulation model of multiphase induction
motor is developed.
6
Literature Review

In [6] S. C. Wang et.al. described current source inverter fed six phase
induction machine with two groups of insulated coils that are 30o out of phase
which is used in high power drives.

Basset and Potter proposed that the induction machine can be operated as an
induction generator in isolated mode by using excitation capacitors [7]

In [8] Duran proposed a different approach for self-excited six phase induction
generator with the help of space vector theory.

Three phase Induction Motor Simulink model is discussed in [9] & [10].

In [11] a generalized discussion on multi phase induction machine drive’s
development and future application is discussed by G.K.Singh.
7
3 Phase Induction Machine Model
𝑖𝑑𝑠 =
Ψ𝑑𝑠 𝐿𝑙𝑟 + 𝐿𝑚 − 𝐿𝑚 Ψ𝑑𝑟
(𝐿𝑙𝑠 𝐿𝑙𝑟 + 𝐿𝑙𝑠 𝐿𝑚 + 𝐿𝑙𝑟 𝐿𝑚 )
𝑖𝑑𝑟 =
Ψ𝑑𝑟 𝐿𝑙𝑠 + 𝐿𝑚 − 𝐿𝑚 Ψ𝑑𝑠
(𝐿𝑙𝑠 𝐿𝑙𝑟 + 𝐿𝑙𝑠 𝐿𝑚 + 𝐿𝑙𝑟 𝐿𝑚 )
Calculation of ids & idr
1 −1/2 −1/2 𝑉𝑎
𝑉𝑑𝑠
𝑉
𝑉𝑞𝑠 = 0 3/2 − 3/2 𝑏
𝑉𝑐
abc to d-q
transformation
Ψ𝑞𝑠 = 𝐿𝑙𝑠 × 𝑖𝑞𝑠 + 𝐿𝑚 𝑖𝑞𝑠 + 𝑖𝑞𝑟
Ψ𝑑𝑠 = 𝐿𝑙𝑠 × 𝑖𝑑𝑠 + 𝐿𝑚 𝑖𝑑𝑠 + 𝑖𝑑𝑟
Ψ𝑞𝑟 = 𝐿𝑙𝑠 × 𝑖𝑞𝑟 + 𝐿𝑚 𝑖𝑞𝑠 + 𝑖𝑞𝑟
Ψ𝑑𝑟 = 𝐿𝑙𝑠 × 𝑖𝑑𝑟 + 𝐿𝑚 𝑖𝑑𝑠 + 𝑖𝑑𝑟
Flux equation
𝑖𝑞𝑠 =
𝑖𝑞𝑟 =
Ψ𝑞𝑠 𝐿𝑙𝑟 + 𝐿𝑚 − 𝐿𝑚 Ψ𝑞𝑟
(𝐿𝑙𝑠 𝐿𝑙𝑟 + 𝐿𝑙𝑠 𝐿𝑚 + 𝐿𝑙𝑟 𝐿𝑚 )
Ψ𝑞𝑟 𝐿𝑙𝑠 + 𝐿𝑚 − 𝐿𝑚 Ψ𝑞𝑠
(𝐿𝑙𝑠 𝐿𝑙𝑟 + 𝐿𝑙𝑠 𝐿𝑚 + 𝐿𝑙𝑟 𝐿𝑚 )
Calculation of iqs & iqr
𝑇𝑒 =
𝜔𝑟 =
3 𝑃 𝐿𝑚
Ψ𝑑𝑟 𝑖𝑞𝑠 − Ψ𝑞𝑟 𝑖𝑑𝑠
2 2 𝐿𝑟
𝑃
𝑇 − 𝑇𝑙 𝑑𝑡
2𝐽 𝑒
Calculation of torque & rotor speed
Simulation Result of 3 Phase Induction Machine
8
Steady State Stator Current
Stator Current and Rotor Current
Steady State Rotor Current
(a) Load torque and Mechanical torque; Speed (b) Torque Speed Characteristics
9
Multiphase Induction Machine
 General Nomenclature

The number of phase for a machine is assumed to be the same as the number of stator
terminals.

But the number of phases is not the adequate information because two machine can have
different characteristics based on two possible values of the phase belt angle.

Three phase machines have 60o phase belts but sometimes these machines are wound with
120 o phase belts and have different characteristics.
 Winding Layout
 A six phase induction machine can be constructed by splitting the 60o phase belts into two
30o spanning.
 The winding distribution factor increases from 0.965 for three-phase to 1.0 for six-phase
for the split phase belt connection.
°
 Phase belt per pole is given by 180 ൗ𝛽 , where 𝛽 is phase belt angle in electrical degree.
 Space Harmonics in Multiphase machine

Air gap distribution in cylindrical rotor machines contains undesirable harmonics which
contains phase belt harmonics, slot harmonics.

These harmonics produce cusps and dips in the torque curve for slip near unity

The phase belt harmonics of order k will satisfy the equation 𝑘 = 2𝑞𝑖 ± 1; where q is no
of phase belt per pole and i is any in integer.

Thus for a 12 phase machine the lowest order harmonic will be 11th . Thus stator coil pitch
need not to be chosen to reduce 5th and 7th harmonics
 Winding distribution of higher phase order machines (Multiple of 3 phase)
10
11
Advantages of Multi Phase Induction Machine

The stator excitation in a multi phase induction machine produced field with lower
space harmonic therefore efficiency is higher than a three phase machine.

Multi phase induction machine have greater fault tolerance than three phase
machine. If one phase of multi phase Induction Machine is open circuited it will
continue to run with lower power rating and can be self-starting where as if one
phase of three phase machine is open circuited it may continue to run as single phase
induction machine but it requires some external means for starting..

Due to 30o displacement angle between two three phase sets of a six phase machine
the air gap flux harmonics of the order (6𝑚±1, 𝑚=1,2,3 …). Which will reduce the
rotor copper losses and eliminate torque harmonics of the order (6𝑚, 𝑚=1,2,3 …)

Other advantages include lower current per phase without an increase in voltage per
phase, lower dc link harmonics, higher reliability and increased power.
Six Phase Induction Machine

The stator of six phase induction machine has two set
of three phase winding. The two set of three phase
winding is displaced by an angle of 60o.

The phases as, cs and es belongs to the first set while
the phases bs, ds and fs belongs to the another set of
three phase stator winding, and ar, br and cr represents
the rotor winding.

d-q model is used for analysis of six phase induction
machine.

Some assumptions are made for the development of the
d-q model like uniform air gap, sinusoidal winding
distribution, friction and winding loss are neglected etc.

In case of symmetrical six phase induction machine two
stator winding is separated by 𝜃 = 2𝜋Τ3 .

The stator and rotor variables have to be transformed to
a common d-q reference frame using Clarke’s
Transformation.
Winding arrangement of six
phase induction machine
12
Equivalent Circuit of 6 Phase Induction Machine
13
𝑅1 = Stator resistance per phase for set I
𝑋𝑙1 = Stator leakage reactance for set I
𝑅2 = Stator resistance per phase for set II
𝑋𝑙2 = Stator leakage reactance for set II
𝑋𝑙𝑚 = Mutual leakage reactance between two set of
stator winding
𝑋𝑚 = Mutual reactance between stator and rotor
𝑅𝑟 = Rotor per phase resistance referred to stator
𝑋𝑙𝑟 = Rotor leakage reactance referred to stator
Vqs1,Vqs2 = q-axis stator voltages
Vds1,Vds2 = d-axis stator voltages
𝑉𝑞𝑟′ = q-axis rotor voltage
𝑉𝑑𝑟’= d-axis rotor voltage
𝛹𝑞𝑠1, 𝛹𝑞𝑠2 = q-axis stator flux linkages
𝛹𝑑𝑠1, 𝛹𝑑𝑠2 = d-axis stator flux linkages
𝛹𝑞𝑟′ = q-axis rotor flux linkage
𝛹𝑑𝑟’= d-axis rotor flux linkage
𝑖𝑞𝑠1, 𝑖𝑞𝑠2 = q-axis stator currents
𝑖𝑑𝑠1, 𝑖𝑑𝑠2 = d-axis stator currents
𝑖𝑞𝑟′ = q-axis rotor current
𝑖𝑑𝑟’= rotor d-axis current
𝐿𝑙𝑠 = stator leakage inductance
𝐿′𝑙𝑟 =rotor leakage inductance
Llm =stator mutual leakage inductance
𝐿𝑚=mutual inductance between stator and rotor
𝜔𝑘, 𝜔𝑟 = speed of reference frame and rotor
respectively
14
6 Phase Induction Machine Model
Six phase to d-q
axis
transformation
Calculation of flux
linkage Ψ𝑞𝑠 , Ψ𝑑𝑠 ,
Ψ𝑞𝑟 , Ψ𝑑𝑟
Calculation of stator
and rotor current in dq axis
Torque and rotor
speed calculation
15
6 Phase Induction Machine Model
𝐶=
1 cos 2𝜋ൗ3 cos 2𝜋ൗ3 cos 2𝜋ൗ3 cos 2𝜋ൗ3 cos 2𝜋ൗ3
0 sin 2𝜋ൗ3 sin 2𝜋ൗ3 sin 2𝜋ൗ3 sin 2𝜋ൗ3 sin 2𝜋ൗ3
2
1 cos 2𝜋ൗ3 cos 2𝜋ൗ3 cos 2𝜋ൗ3 cos 2𝜋ൗ3 cos 2𝜋ൗ3
6
0 sin 2𝜋ൗ3 sin 2𝜋ൗ3 sin 2𝜋ൗ3 sin 2𝜋ൗ3 sin 2𝜋ൗ3
1
1
1
0
0
0
0
0
0
1
1
1
Clark’s Transformation
Ψ𝑞𝑠1 = −𝐿𝑙𝑠 × 𝑖𝑞𝑠1 − 𝐿𝑙𝑚 𝑖𝑞𝑠1 + 𝑖𝑞𝑠2 + 𝐿𝑚𝑞 −𝑖𝑞𝑠1 − 𝑖𝑞𝑠2 + 𝑖𝑞𝑟
Ψ𝑑𝑠1 = −𝐿𝑙𝑠 × 𝑖𝑑𝑠1 − 𝐿𝑙𝑚 𝑖𝑑𝑠1 + 𝑖𝑑𝑠2 + 𝐿𝑚𝑑 −𝑖𝑑𝑠1 − 𝑖𝑑𝑠2 + 𝑖𝑑𝑟
Ψ𝑞𝑠2 = −𝐿𝑙𝑠 × 𝑖𝑞𝑠2 − 𝐿𝑙𝑚 𝑖𝑞𝑠1 + 𝑖𝑞𝑠2 + 𝐿𝑚𝑞 −𝑖𝑞𝑠1 − 𝑖𝑞𝑠2 + 𝑖𝑞𝑟
Ψ𝑑𝑠2 = −𝐿𝑙𝑠 × 𝑖𝑑𝑠2 − 𝐿𝑙𝑚 𝑖𝑑𝑠1 + 𝑖𝑑𝑠2 + 𝐿𝑚𝑑 −𝑖𝑑𝑠1 − 𝑖𝑑𝑠2 + 𝑖𝑑𝑟
𝑑
Ψ
+ 𝜔𝑘 × Ψ𝑑𝑠1
𝑑𝑡 𝑞𝑠 1
𝑑
𝑉𝑑𝑠1 = 𝑅𝑠 × 𝑖𝑑𝑠1 +
Ψ
− 𝜔𝑘 × Ψ𝑞𝑠1
𝑑𝑡 𝑑𝑠1
𝑑
𝑉𝑞𝑠 2 = 𝑅𝑠 × 𝑖𝑞𝑠 2 +
Ψ
+ 𝜔𝑘 × Ψ𝑑𝑠2
𝑑𝑡 𝑞𝑠 2
𝑑
𝑉𝑑𝑠2 = 𝑅𝑠 × 𝑖𝑑𝑠2 +
Ψ
− 𝜔𝑘 × Ψ𝑞𝑠2
𝑑𝑡 𝑑𝑠2
𝑑
𝑉𝑞𝑟 ′ = 𝑅𝑟 ′ × 𝑖𝑞𝑟 ′ +
Ψ ′ + 𝜔𝑘 − 𝜔𝑟 × Ψ𝑑𝑟 ′
𝑑𝑡 𝑞𝑟
𝑑
𝑉𝑑𝑟 ′ = 𝑅𝑟 ′ × 𝑖𝑑𝑟 ′ +
Ψ ′ − 𝜔𝑘 − 𝜔𝑟 × Ψ𝑞𝑟 ′
𝑑𝑡 𝑑𝑟
𝑉𝑞𝑠 1 = 𝑅𝑠 × 𝑖𝑞𝑠 1 +
Voltage Equation
𝑖𝑞𝑠 =
𝑖𝑞𝑟 =
Ψ𝑞𝑠 𝐿𝑙𝑟 + 𝐿𝑚 − 𝐿𝑚 Ψ𝑞𝑟
(𝐿𝑙𝑠 𝐿𝑙𝑟 + 𝐿𝑙𝑠 𝐿𝑚 + 𝐿𝑙𝑟 𝐿𝑚 )
Ψ𝑞𝑟 𝐿𝑙𝑠 + 𝐿𝑚 − 𝐿𝑚 Ψ𝑞𝑠
(𝐿𝑙𝑠 𝐿𝑙𝑟 + 𝐿𝑙𝑠 𝐿𝑚 + 𝐿𝑙𝑟 𝐿𝑚 )
Calculation of iqs & iqr
Ψ𝑞𝑟 = 𝐿𝑙𝑟 × 𝑖𝑞𝑟 + 𝐿𝑚 −𝑖𝑞𝑠1 − 𝑖𝑞𝑠2 + 𝑖𝑞𝑟
Ψ𝑑𝑟 = 𝐿𝑙𝑟 × 𝑖𝑑𝑟 + 𝐿𝑚 −𝑖𝑑𝑠1 − 𝑖𝑑𝑠2 + 𝑖𝑑𝑟
Flux-linkage Equation
𝑖𝑑𝑠 =
Ψ𝑑𝑠 𝐿𝑙𝑟 + 𝐿𝑚 − 𝐿𝑚 Ψ𝑑𝑟
(𝐿𝑙𝑠 𝐿𝑙𝑟 + 𝐿𝑙𝑠 𝐿𝑚 + 𝐿𝑙𝑟 𝐿𝑚 )
𝑖𝑑𝑟 =
Ψ𝑑𝑟 𝐿𝑙𝑠 + 𝐿𝑚 − 𝐿𝑚 Ψ𝑑𝑠
(𝐿𝑙𝑠 𝐿𝑙𝑟 + 𝐿𝑙𝑠 𝐿𝑚 + 𝐿𝑙𝑟 𝐿𝑚 )
Calculation of ids & idr
16
6 Phase Induction Machine Simulation Result
Steady State Stator Current
Stator Current and Rotor Current
Steady State rotor Current
17
6 Phase Induction Machine Simulation Result
(a) Load torque and Electrical torque ; Speed
(b) Torque Speed Characteristics
18
Future Work

Study of different control schemes of six phase induction machine drives and
MATLAB Simulink Implementation.

Study of fault toleration of six phase induction machine.

Hardware Implementation of six phase induction machine drive system.
Conclusion

In order to derive the six phase induction machine model first three phase
induction machine is analyzed and simulated in MATLAB Simulink

The generalized dq model of six phase induction machine is explained and
simulated in MATLAB Simulink.

The steady state and dynamic behavior as well as speed torque characteristics
are shown.
References
19

[1] E.E. Ward, H. Harer, Preliminary investigation of an inverter- fed 5-phase induction motor, Proc. IEE 116 (6) (1969) 980–
984.

[2] D.C. White and H.H. Woodson. Electromechanical Energy Conversion, New York, Wiley, pp. 545-593

[3] R.H. Nelson, P.C. Krause, Induction machine analysis for arbitrary displacement between multiple winding sets, IEEE
Trans. 93 (1974) 841–848

[4] Lipo, T. A., A d-q model for six-phase induction machine‘, Proc. International conference, Electric Machines, Athens,
Greece, pp. 860-867, Sept 15-17, 1980.

[5] E. Levi, R. Bojoi, F. Profumo, H. A. Toliyat and S. Williamson, "Multiphase Induction Motor Drives-A Techology Status
Review, "IET Elect. Power Appl., vol. 1, no. 4, pp. 489-516, 2007.

[6] Wang, S. C. Foroosh, J. Jatskevich, and A. Davoudi, ―Physical variable modelling of multi-phase induction machines,‖
Canadian Conference on Electrical and Computer Engineering CCECE, pp. 999-1004, Niagara Falls, Canada, 2008.

[7] E.D. Basset F.M. potter, ―capacitive excitation of induction generators‖, Transactions of the Amer. Inst. Electr. Eng., Vol.
54, May 1935, pp540-545.

[8] M.J. Duran, F. Barrero, S. Toral, M. Arahal, R. Gregor, R. Marfil, ―Multi-phase generators viability for offshore wind
farms with HVDC transmission‖ in Proc. Of International Conference On Renewable Energies and Power Quality (ICREPQ'14)
Santander, Spain, 12-14, 2008.

[9] K. L. Shi, T. F. Chan, and Y. K. Wong, “Modelling of the three-phase Induction Motor using SIMULINK,” pp. 6–8, 1997.

[10] L. J. Phukon and N. Baruah, “A Generalized Matlab Simulink Model of a Three Phase Induction Motor,” pp. 2926–2934,
2015, doi: 10.15680/IJIRSET.2015.0405036.

[11]G. K. Singh, “Multi-phase induction machine drive research — a survey,” vol. 61, pp. 139–147, 2002.

www.researchgate.net/publication/224262277_Modelling_of_the_three-phase_induction_motor_using_SIMULINK

en.wikipedia.org/wiki/Induction_motor

www.researchgate.net/publication/229008024_Model_of_Multiphase_Induction_Motor
20
Acknowledgement

I express my deep and sincere regard towards my guide Jitesh Chandra
Barman Sir , assistant Professor, Department of Electrical Engineering for his
valuable guidance, constant help, encouragement and inspiration throughout
the project work, which also help me doing a lot of research and I came to
know about so many things.

I would like to thank other faculty members of the Department of Electrical
Engineering at NIT Durgapur for their valuable suggestion and helpful
discussion.

Last but not the least I want to thank my parents and my friends who were also
a backbone to the research work.
21