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Abstract –

As poly-phase motor drive system is become more

popular and practical leads to its advantages. This paper

proposes a five-phase induction motor (IM) drive system fed

from five-phase matrix converter (MC) with three-phase

grid input. The modulation strategy of this converter is

based on indirect space vector modulation (ISVM). The

analysis of this strategy was carried out. Simulation model is

developed and used during the design process of the

converter prototype. The implemented converter was based

on discrete semiconductors. A five-phase induction motor

has been designed and implemented in the lab. A laboratory

system has been implemented based on digital signal

processor (DS1104). Experimental results are given, and

then the drive system performance is discussed.

Keywords - five-phase matrix converter, indirect space

vector modulation, five-phase induction motor

I. I NTRODUCTION

owadays, the interest in poly-phase motor drive

system has been increased due to several

advantages over than of a three-phase drive

system. These advantages are inherent to the

own structure of the machine, such as reducing the

amplitude and increasing the frequency of torque

pulsations, reducing the rotor harmonic current losses,

and lowering the dc link current harmonics [1-3]. As a

result, there is an urgent need for the AC-AC poly-phase power converters to transform a constant voltage constantfrequency three-phase supply into a variable voltage with

variable frequency (VVVF) output required for these

machines.

The MC is a direct m-phase to n-phase converter, was

firstly introduced in 1976 by [4] and it steadily growth,

pushed by the progress of the power electronics devicetechnology. In recent years the MC has received an

increased amount of interest and has been studied

intensely as an alternative to AC-DC-AC power

converters. After almost three decades of intensive

research, the development of MC has been involved in

industrial applications. In 2008, Yaskawa Company inJapan introduces the first product of three-phase MC.

Until the time of writing this paper, more than 1350

papers directly related to the MC technology are

published in IEEE journals and conferences. This data has

been collected from IEEE explore data base. It should be

mentioned here, the most common configuration of the

MC discussed in the literature is the three-phase to three-

phase, little attention has been aid on the development of

MC with output more than three, except in [5] – [11].

This paper proposes a three-phase to five-phase

matrix converter supplies a five-phase induction motor

S. M. Dabour, A. Hassan and E. M. Rashad are with the Department ofElectrical Power and Machines, Faculty of Engineering, Tanta

University, Tanta, 31521, Egypt. (e-mail: [email protected]).

drive system using V/f control. The converter modulationstrategy is based on ISVM technique. The model of

a five-phase induction motor has been introduced. The

overall drive system has been implemented using Matlab/

Simulink. Then, the MC control algorithm is compiled toreal time system based on DS1104 dSPACE card. The

generated signals from the card are applied to the

implemented MC through an interface circuit. Full details

of the design and implementation of the MC was

introduced in [8 and 12]. Finally the experimental results

are given and discussed.

II. DIRECT FIVE-PHASE MC TOPOLOGY

The five-phase MC is a direct three-phase to five-phase

through one stage; it utilizes 15th

switches, as shown in

Figure 1. Each of the 15th

switches depicted is a

bidirectional switch (BDS), which are connected so that,

any of the input phases (A, B, and C) can be connected to

any of the output phases; (a-e) for a given switching. Withthe 15

th BDS, the MC has 2

15 different switching states.

Some of the basic rules must be regarded when applying

different switching states to the MC at any switching

time. These rules are: (1) input phases must never be

shorted, and (2) output phases must not be left open, due

to the inductive nature of the load. Due to these rules, the

switching states reduce to 35

different switchingcombinations for connecting the output to the input. The

output voltages (va - ve) and the input currents (i A i BiC ) are therefore derived directly from the input voltages

(v A v B vC ), and the output currents (ia - ie) as follows:

= . (1)

where, S is the modulation matrix or the duty cycles of

the switches.

=

(2)

SaA SbA ScA SdA SeA

SaB SbB ScB SdB SeB

SaC SbC ScC SdC SeC

V A

V B

V C

a

b

cd

e

M

C f

L f Switching Matrix

Input Filter

Figure 1: Direct five-phase matrix converter topology.

Five-Phase Induction Motor Drive System Fed from Five-

Phase Matrix-Converter

Sheriff M. Dabour, Abd El-Wahab Hassan and Essam M. Rashad, Senior Member, IEEE 1

Proceedings of the 15th International Middle East Power Systems Conference (MEPCON’12), Alexandria University, Egypt,December 23-25, 2012, Paper ID 302, pp 898-903

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III. I NDIRECT TOPOLOGY OF FIVE-PHASE MC

This topology to model the MC actually corresponds to

regard the MC as a double-PWM converter without any

DC-Link energy storage, where MC was described to an

equivalent model combining current source rectifier andvoltage source inverter connected through virtual dc link

and it was first proposed by [13] for three-phase to three-

phase MC, and by applying this algorithm on the directfive-phase MC, the resulting indirect five-phase MC is

shown in Figure 2. The rectifier stage has the same

topology of the three-phase rectifier with six switches, S1

~ S6, and the Inverter stage has a standard five-phase

voltage source inverter topology consisting of ten

switches, S7 ~ S16. Both power stages are directly

connected through virtual dc-link and inherently provide

bidirectional power flow capability because of its

symmetrical topology.

IV. ISVM OF THE PROPOSED CONVERTER

The ISVM technique constructs the desired sinusoidal

output five-phase voltage by selecting the valid switchingstates of a MC and calculating their corresponding on-

time durations. The basic idea of this technique is to

decouple the control of the input current and the control

of output voltage. This is done by splitting the modulation

matrix S for the converter into the product of a rectifier

transfer function R and an inverter transfer function I .

The modulation matrix for the MC is thus defined as

following [3], [4]:

= . (3)

Where =

7 8

9 10

1113

15

1214

16

& = 1

3

5

2 4 6 (4)

Based on ISVM the following sections describe two

independent space vector modulations for three-phase

current source rectifier, and five-phase voltage source

inverter stages and then the two modulation results are

combined to modulate the five-phase MC.

Space Vector Rectifier (SVR)

The rectifier converts the input three-phase voltage to

DC-voltage. At the same time the rectifier algorithm

assures the input currents to be sinusoidal. This section

introduces a SVM in the rectifier stage. The rectifier partof the equivalent model shown in Figure 2 can be

assumed to be a stand-alone current source rectifier.

Figure 2: Indirect Five-phase Matrix converter topology.

The rectifier switches, S 1 ~ S 6 can have only possible

nine allowed combinations to avoid an open circuit at the

dc link rails. The nine combinations can be divided intosix nonzero input currents which are active vector I 1 ~ I 6

and three zero input currents which are zero vector I 7 ~ I 9

Figure 3 shows current space vector hexagon. The

reference input current vector (Ii*) within a sector of the

current hexagon (Figure 3) is synthesized by impressing

the adjacent switching vectors Iγ and Iδ with the dutycycles dγ and dδ, respectively. If the input currents are

considered constant during a short switching interval (TS),

the reference vector can be expressed by the current-time

product sum of the adjacent active vectors as;

∗ = . + . + . (5)

Thus, the duty cycle of the active vectors are written as;

= .sin3−

= . sin() (6)

= 1

−(

− )

where, θC indicates the angle of the reference current

vector within the actual hexagon sector. The mC is thecurrent modulation index and defines the desired current

transfer ratio such as:

0 ≤ ≤ 1 & =∗

Space Vector Inverter (SVI)

This section introduces a SVM in the inverter stage.

Consider the inverter part of the equivalent model in

Figure 2 as a standalone VSI supplied by a dc voltage

source, as shown in Figure 4. The output voltage space

vector is expressed as a function of phase voltages asfollows:

=2

5 + . + 2 . + 3. + 4 .

= (7)

where, = 2/5 , V out is the output voltage, and is

the space vector angle. The inverter switches, S 7 – S 16

have only thirty two allowed combinations to avoid a

short circuit through five half bridges. The thirty two

combinations have thirty nonzero output voltages or

active vectors (V 1 to V 30) and two zero output voltages or

zero vector V 0. The discrete thirty two space vectors can

be represented as a decagon in a complex plane shown inFigure 5.

Figure 3: Rectifier current hexagon

S 1

S 2

S 3

S 4

S 5

S 6

S 7

S 8

S 9

S 10

S 11

S 12

Rectifier Stage Inverter Stage

V DC

A

B

C

abc

+

-

S 13

S 14

S 15

S 16

d e

I p

In

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Figure 4: Inverter stage from of indirect five-phase matrix converter

The space vector scheme reviewed here considers the

outer most and the intermediate decagons of space

vectors. Figure 6 shows the outermost decagon of theinput reference voltage vector (V o*) within a sector of the

voltage decagon. The V o* is synthesized by impressing

the adjacent voltage vectors and with the duty

cycles , and d ov respectively.

= .sin/5 − = . sin() (8)

= 1 − ( − )

where

=∗

sin(4/5) & = 0.6472

Therefore maximum fundamental peak output voltage

Vmax is given by:

= 0.6472 cos 10

= 0.6155

Figure 5: The inverter stage decagon

Figure 6: Synthesis of reference voltage vector

Space vector modulation with large and medium

vectors is based on the proportional sub-division of the

time of application of each vector from outer andintermediate sectors. The times obtained are sub-divided

according to the ratio of medium and large vector lengths,

so that the duty ratios are given by: =

+ =

+

(9) =

+

= +

where = 0.4 and = 0.6472

The time of zero space vectors application can be

obtained so that its duty ratio is given by:

= 1

−(

+

+

+

) (10)

To minimize the number of the inverter-switching, the

sequence of the impressed voltage vectors is given by:

→ → → → → → → →

The current modulation index mc is often fixed to unity

and the voltage modulation index mv is variable according

to a required overall voltage transfer gain. To assure the

proper operation of the MC, the two modulations must be

to combine to generate the switching pattern for theconverter.

V. FIVE-PHASE I NDUCTION MOTOR

Compared with the traditional three-phase induction

motor, the five-phase induction motor provides some

salient features, such as the ability to start and run even

with some phases open circuited. This increases the

reliability of the drive system. High power density can bemore easily achieved than in the case of three-phase

machines by increasing the number of phases without

increasing the rated current. Torque ripple behavior is

also inherently superior to that of a three-phase drive

system [14].

To simplify the development of the five-phase

induction motor model, the stator windings of all phases

are assumed to be identical and coils are sinusoidallydistributed. Furthermore, a linear magnetic core is

considered. The inherent 72º stator winding structure

causes unsymmetrical line-to-line voltages (i.e. vab and

vac). In this analysis the iron saturation is neglected. The

line-to-neutral voltages can be transformed to the d-q

planes using the following transformation matrix K [15]:

2

1

2

1

2

1

2

1

2

1

5

4

5

2

5

2

5

4

5

4

5

2

5

2

5

4

5

2

5

4

5

4

5

2

5

2

5

4

5

4

5

2

5

2

) sin( ) sin( ) sin( ) sin( sin

)cos( )cos( )cos( )cos( cos

) sin( ) sin( ) sin( ) sin( sin

)cos( )cos( )cos( )cos( cos

K

o

0.5V DC S 7

S 8

S 9

S 10

S 11

S 120.5V DC

abc

+

-

S 13

S 14

S 15

S 16

d e

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The general equations of five-phase induction motor

can be introduced as follows:

The stator q-d axes voltages are given by:

ds

qs

qs sqsdt

d ir v

(11)

qs

ds

ds sds dt

d

ir v

(12)

For the stationary reference frame ω = 0, substitute intoEquations (11) and (12) yields:

dt

d ir v qs

qs sqs

(13)

dt

d ir v ds

ds sds

(14)

The stator q-d axes flux linkages are given by:

)(

)(

qr qsmqslsqs

qr mqsmlsqr mqs sqs

ii Li L

i Li L Li Li L

(15)

)(

)(

dr dsmdslsds

dr mdsmlsdr mds sds

ii Li L

i Li L Li Li L

(16)

The electromagnetic torque is given by:

dsqsqsdse ii p

T

22

5 (17)

Bdt

d J T T Le (18)

The d-q model of five-phase induction motor in arbitrary

reference frame is shown in the Figure 1.

(a) q-axis circuit

(b) d-axis circuit

Figure 7: q-d Equivalent circuit in arbitrary reference

VI. IMPLEMENTATION OF THE CONVERTER

The switching matrix is realized by 15-bidirectionalswitch, each is composed of a Power MOSFET and four

Fast Recovery Diodes. The interface circuit uses an ultra

speed optocoupler. Figure 8 shows the prototype of a five

phase matrix converter which fabricated in the laboratory

using semiconductor devices. Figure 9 shows main parts

of the proposed system implementation. The system is

composed of mainly three parts, namely; Power, Control,

and Interface circuits.

Figure 8: Photograph of the five-phase matrix converter prototype.

VII. EXPERIMENTAL R ESULTS

Using the previously presented setup, experimental

results have been obtained to confirm the analysis given

in previous sections. Preliminary tests with R-L load has

been carried out to confirm the proper operation of the

designed MC based on SVM control method. The output phases (a-e) of the MC are connected to the five-phase

star connected resistors in series with the three phase

inductors. The per phase load parameters are R = 144 Ωand L = 0.25 H. To test the steady state behavior of the

matrix converter, a small input voltage supply of 100

Volts/line at 50 Hz via an autotransformer is applied. The

voltage transfer ratio set to 0.5 and the reference input

current displacement angle adjusted to zero. The

switching frequency is 1.25 kHz and the sample time is200µsec as a result of the DS1104 capabilities.

Figure 9 shows the measured supply phase voltage

(CH-1) and current (CH-2) waveforms at 10 Hz output

frequency, also the spectrum analysis of the input currentis shown. Because there was no input current filter, the

input current waveform is pulse width modulated. It is

clear that the fundamental component of the input current

is approximately in phase with the input phase voltage

(Figure 9). This is owed to adjusting displacement angle

to zero, which achieves maximum available voltage

transfer ratio using SVM method.

(a)Waveforms

(b)Spectrum Analysis

Figure 9: Input phase voltage (CH1) and input phase current (CH2)waveforms at f o = 10 Hz and spectrum analysis of input current

qsv

sr

qsi

ds

ls L

m L

lr L

dr r )( r r

qr i

dsv

dsi

qs

ls L

m L

lr L

qr r )(

r r dr i

sr

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Figure 10 shows the output line voltage of the matrix

converter and its spectrum analysis when the output

frequency is 10 Hz. The spectrum shows fundamentalvoltage amplitude of 43.3V (at 10 Hz). The difference

between the measured value (43.3V) and the reference

value of the line voltage (50V) is due to a voltage drops

on the semiconductor elements. Moreover, the employed

DSP capabilities limit sampling time to 200µsec, which

may cause losing some voltage intervals. The amplitudespectrum also shows dominant harmonics components

around switching frequency 1.25 kHz.

(a)Waveforms


Figure 10: Output line voltages waveforms at f o = 10Hz

Figure 11 shows the output phase current at 10 Hz output

frequency and its spectrum analysis. The output current

has a near sinusoidal waveform with significant 3rd

, 7th

,

9th

, 11th

, 13th

and 17th

harmonic components.

(a)Waveforms


Figure 11: Output phase-voltages waveforms at f o = 10 Hz

Induction Motor Drive

Experimental results of the five-phase MC fed five-phase

induction motor with scalar control were obtained forvarious operating conditions. The motor parameters are

given in the appendix. The sampling time is kept at

200µsec. Figure 12 shows the motor speed and current

variations for a start up period. The reference frequency is

set at 30 Hz (i.e. 1800 r/min). In this case, the motor is

accelerated from standstill to 1775 r/min.

Figure 12: Motor speed (CH1) and phase current (CH2) of during

start-up period

Figure 13 shows experimental results for a step change infrequency from 30 to 20 Hz after attaining steady-state

condition.

Figure 13: Motor speed (CH1) and phase current (CH2) of during

Step change from 30 to 20 Hz

Finally, Figure 14 shows the experimental results for a

motor speed reversal. Initially the reference frequency is

set at 30 Hz. Then, the speed is reversed to the same

value.

Figure 14: Motor speed (CH1) and phase current (CH2) of speed

reversal

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VIII. APPENDIX

The Per-phase equivalent circuit parameters of the 380V,

1.1 kW, 2-pole, 50-Hz five- phase induction motor (J =

0.007 kgm2): R s = 14Ω, R r = 4.6Ω, Lls = L lr = 0.8714 H,

Lm = 0.85-H.

IX. CONCLUSION

In this paper a five-phase induction motor drive systemfed by three-phase to five-phase MC has been introduced.

The analysis and implementation of the converter is

carried out. The MC model has been performed in

Matlab/Simulink and then converted to real time codes

for dS1104 card. A preliminary test with R-L load has

been presented to confirm the proper operation of thedesigned converter. Experimental results were introduced

for a five-phase induction motor with V/f control at

various operating conditions. The feasibility of the

proposed system has been verified through experiments

with a good performance and the drive performance can

be improved by reducing sampling time, according to the

controller capabilities.

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