CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 1 Modified reference voltages and triangular carriers for a five-level SPWM scheme

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 1

Modified reference voltages and triangular carriers for a five-level SPWM scheme


The inverter switching vectors and their switching time durations during sampling interval TS (Reference voltages are within the inner carrier region, M <

0.433)


Determination of the Ta_cross , Tb_cross and Tc_cross during switching interval TS

(When reference voltages are spanning the inner carrier region, M < 0.433)


* *_

* *_

* *_

4

( 4)4

( 4)4

sa cross AN as

dc

sb cross BN dc bs s

dc

sc cross CN dc cs s

dc

TT V T

V

TT V V T T

V

TT V V T T

V

* *

* *

* *

1 1

( 4) / /

( 4) / /

( 4) / /

( 4) / /

dc s AN as

dc s BN bs

dc s CN cs

dc s offset offset

V T V T

V T V T

V T V T

V T V T

Determination of the Ta_cross , Tb_cross and Tc_cross during switching interval TS

(When reference voltages are spanning the inner carrier region, M < 0.433)


Determination of the Ta_cross , Tb_cross and Tc_cross during switching interval TS (When

reference voltages are spanning the entire carrier region, 0.433<M < 0.866)


Determination of the Ta_cross , Tb_cross and Tc_cross during switching interval TS (When

reference voltages are spanning the entire carrier region, 0.433<M < 0.866)


SUMMARY: Ta_cross , Tb_cross and Tc_cross for various carrier regions


Space Vector PWM signal generation for multi-level inverters using only the sampled amplitudes of reference phase voltages

Equivalence to Conventional SVPWM

• The reference signals in carrier based SVPWM are shifted to one carrier region • The outer sub-hexagon in the conventional SVPWM are shifted to central sub-hexagon in conventional SVPWM• The reference signal shifting in carrier based SVPWM is equivalent to sub-hexagonal shifting in the conventional SVPWM

180090000

*asT

180090000

_a crossT


_ _min ( )first cross x crossT T

sec _ _( )ond cross x crossT mid T)(max __ crossxcrossthird TT , x= a, b, c

_ _middle third cross first crossT T T

0 s middleT T T

0 _ 2

2 0 _

/ 2

/ 2

first cross offset

offset first cross

T T T

T T T

_ 2

_ 2

_ 2

ga a cross offset

gb b cross offset

gc c cross offset

T T T

T T T

T T T

Algorithm for inverter leg switching time calculation


The traces of Tfirst_cross , Tsecond_cross and Tthird_cross showing non-centered time duration for middle vectors


The traces of Tg_first_cross , Tg_second_cross and Tg third_cross showing centered time duration for middle vectors


Toffset1 + Toffset2 waveforms for various modulation indices


Tas +Toffset2 +Toffset2 waveforms


Generalization for ‘n’ level PWM (‘n’ even)


Generalization for ‘n’ level PWM (‘n’ odd)


*_

*_

*_

( / 2) (( ( / 2))* )

( / 2) (( ( / 2))* )

( / 2) (( ( / 2))* )

a cross s as a s

b cross s bs b s

c cross s cs c s

T T T I n T

T T T I n T

T T T I n T

Generalization for ‘n’ level PWM

‘n’ even

‘n’ odd

*_

*_

*_

(( ( 1) / 2)* )

(( ( 1) / 2)* )

(( ( 1) / 2)* )

a cross as a s

b cross bs b s

c cross cs c s

T T I n T

T T I n T

T T I n T


Proposed SVPWM signal generation in over-modulation









2 _offset s third crossT T T

sec _ sec _ 2g ond cross ond cross offsetT T T



2 _offset first crossT Tsec _ sec _ 2g ond cross ond cross offsetT T T


Summary: linear range of modulation


Summary: over-modulation condition


Inverter configuration


Phase-A voltage and phase-A current waveforms for modulation index 0.15 (Layer 1 operation).


Plot of Tga and offset time Toffset1 + Toffset2 for modulation index 0.15 (Layer 1 operation). [DAC output]




Plot of Tga and offset time Toffset1 + Toffset2 for modulation index 0.3 (Layer 2 operation) [DAC output]




Plot of Tga and offset time Toffset1 + Toffset2 for modulation index 0.6 (Layer 3 operation)[DAC output]


The phase-A voltage and phase-A current waveforms for modulation index 0.85 (Layer 4 operation).


Plot of Tga and offset time Toffset1 + Toffset2 for modulation index 0.85 (Layer 4 operation) [DAC output]


The phase-A voltage and phase-A current waveforms for modulation index 1.15 (over-modulation).


Phase-A current waveform for speed reversal from 40Hz to -40 Hz [modulation index 0.70]


Space Phasor Based Self Adaptive Current Hysteresis Controller

37

A Space Phasor Based Self Adaptive Current Hysteresis Controller Using Adjacent Inverter Voltage Vectors

with Smooth Transition to Six Step Operation for a Three Phase Voltage Source Inverter


• A self adaptive space phasor based current hysteresis controller is proposed for a voltage source inverter

• Current error space phasor is held within a hexagonal boundary

• Current errors are monitored along jA, jB , jC axes

• Ensures optimum switching

• Does not require computations, uses simple look up table

• Uses a self adaptive sector change logic

Introduction


iiΔi

The combine effect of the three current errors can be represented as a space phasor

34j

c3

2jba eΔieΔi Δi

Δi

The current error space phasor is kept within a boundary by switching an appropriate voltage vector

The nearest vector is selected

Current error space phasor


m]k[dt

dL V

Δi v

i i , Δi Δi ii

bsRdt

dL]k[ Vv i

i

bsRdt

dL V

ii

This equation defines the direction in whichcurrent error space phasor moves

= mV


Aj

Directions of current error space phasor in sector -1

m]k[dt

dL V

Δi v

1V

2V

ZV

42

V1

V2

VZ

R1 R2

R3

Vectors to be switched in sector-1 to bring back the error


Directions of current error space phasor in sector -2

m]k[dt

dL V

Δi v

2V3V

ZV

44

V2 V3 VZ

V3

VZ

V2

1R 2R

3R

1R

3R

2R

Vectors to be switched in sector-2 to bring back the error

V3


Vectors to be switched in different sectors


The combined error boundary

47

1R

Modified regions for odd sectors

Modified regions for even sectors

Region identification


Region identification contd.


O

mVP

Q

1

2

3

4

5

6

P’1V

2V3V

4V

5V6VF

A

BC

D

ECj

Detecting The Sector Change

Current error space phasor moves out through a uniqueaxis during sector change


Aj

Bj Cj

Aj

BjCj

AjiAji

S3toS2

S4toS3

S5toS4

S6toS5

S1toS6

S2toS1

Sector Change Detected using an outer hysteresis

Aji

AjAj Aji


AjOver modulation

Switching between the active vectors , V1 and V2

Sector 1


Over modulation

Sector change logic for over modulation region


Simulation Results

The error boundary

Sectors & Vectors

Nearest vectors are selected in every

sector

54

Simulation Results …. Over modulation

Transition to six step

Error space phasor Current space phasor


The error boundary1 div = 0.3 Amp

Phase voltage and current

Experimental Results


The machine current space phasor( no load ) 1 div = 1 amp

The machine current space phasor when loaded ( 1 div = 2 A mp )






Over modulation Six step operation

Transition to six step mode


The error boundary1 div = 1 amp

The machine current space phasor ( 1 div = 3 A mp )

Experimental Results : Over modulation


Salient Features

Space phasor based hysteresis controller with optimum switching is proposed

Self adaptive sector change logic

Smooth transition to over modulation and to six step mode

No computation of machine back emf is required

Uses simple look up tables

Ensures that only one inverter leg is switched during transition of inverter state


Current Error Space Phasor Based Hysteresis PWM Controller with Self Adaptive Logic and Adjacent Voltage Vector Selection

for The Entire Modulation Range for Three-level Voltage Source Inverter Fed Drive


Power Schematic of a Dual Two-level Voltage Source InverterFed IM Drive


Combined Voltage Space Phasor Locations and Inverter SwitchingVector Combinations for Three-level Inverter

j 2 3 j 4 3AA BB CCv v e v e

sV

24 Sectors19 Vectors64 Switching States


Directions of Current Error Space Phasor for Tip of Vm in Sector -7

d

dt L

k mΔi V V


Directions of Current Error Space Phasor for Tip of Vm in Sector -8

d

dt L

k mΔi V V


Directions of Current Error Space Phasor for Tip of Vm in Sector –1 and Sector-2

d

dt L

k mΔi V V


Vectors to be Switched in Sector-7 to Keep the Current Error Space Phasor Inside the Boundary


Vectors to be Switched in Sector-8 to Keep the Current Error Space Phasor inside the Boundary


Vectors to be Switched in Different Sectors for Different Regions


Vectors to be Selected in Different Sectors for Different Regions

Sector Region

R1 R2 R3 R1 R2 R3

1 V0 V1 V2 - - -

2 - - - V2 V3 V0

3 V4 V0 V3 - - -

4 - - - V0 V4 V5

5 V5 V6 V0 - - -

6 - - - V1 V0 V6

7 V1 V8 V9 - - -

: : : : : : :

24 - - - V8 V1 V7


Clamping of Inverters for Adjacent Sectors

Sector Region

R1 R2 R3 R1 R2 R3

1 87’ 17’ 27’ - - -

2 - - - 85’ 86’ 88’

3 48’ 88’ 38’ - - -

4 - - - 88’ 81’ 82’

5 57’ 67’ 77’ - - -

6 - - - 74’ 77’ 73’

7 84’ 14’ 24’ - - -

: : : : : : :

24 - - - 14’ 17’ 13’


Comparators Used for Region Detection

Aj B C

3i i i

2

A A Aj j ji i i


Region Formation from the Segments of the Hexagonal Boundary

When comparator along jA is ON and

else

B Cj jΔi Δ i [ a1R

a2R[


Region Formation from the Segments of the Hexagonal Boundary

a2 b1 b2 c1 1R or R or R or R RFor an odd sector [


Detecting The Sector Change Using an Outer Hysteresis


Sector Change Detection for Two-level Operation (Trajectory ‘a’)

Current error space phasor moves out through a uniqueaxis during a sector change


Mapping of Outer Sectors to Inner Sectors


Sets of Sector Changes Detected Along jA Axis and –jA Axis


Sector Change Along Corner to Corner Sectors (Trajectory ‘c’)

Sector Change from 23 to 8 is Detected Along –jA Direction


Prevention of Jitter Prevention of False Sector Change


Sector Change During Over Modulation (Trajectory ‘f’)


Sector Change During Over Modulation (Sector-7 to Sector-9)

Trajectory of Current Error Space Phasor


Sector Change During Over Modulation (Sector-9 to Sector-10)

Trajectory of Current Error Space Phasor


Sector Detection Including Over Modulation (Forward Rotation)

Sector Change DetectionFrom To

Direction along which the outer comparator is in ON state

jA jB jC -jA -jB -jC

1 * 8 2 * * *

2 * * * 11 3 *

3 4 * 14 * * *

4 * * * * 17 5

5 20 6 * * * *

6 * * * 1 * 23

7 * 9 8 9 * *

8 * * 11 9 1 *

: : : : : : :

24 * * * 7 * *


Simulation Results

Two-leveloperation

1 div. = 0.6 A


Simulation Results

Transition from two-level

to three-level

Transition from three-level

to over modulation


Simulation Results

Three-leveloperation

1 div. = 0.6 A


Simulation Results

Overmodulation

1 div.=0.6 A

Starting of the machine


Block Schematic of Experimental Set-up


1 div = 0.3 Amp

Two-leveloperation


1 div = 0.75Amp


Transition form two-level to

three-level and vice versa


CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 921 div = 0.3 Amp

Three-leveloperation


1 div = 0.75Amp

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 931 div = 0.75 Amp

Overmodulation



Starting of the

machine



Speed reversal of

the machine



Speed reversals of the machine



Normalized harmonic spectrum

of current waveforms

Two-level operation


Three-level operation


Normalized harmonic spectrum

of voltage waveforms

Two-level operation


Three-level operation

A HARMONIC ELIMINATION SCHEME FOR AN OPEN – END WINDING INDUCTION MOTOR DRIVE FED FROM

TWO INVERTERS WITH ASYMMETRICAL DC LINK VOLTAGES


A low order harmonic elimination technique for an open–end winding induction motor drive is proposed.

For the present open–end winding drive, the induction motor is fed from two 2-level inverters with different isolated DC-link voltages of ratio equal to 1:0.366.

With such a scheme it is found that all the 5th and 7th order (6n 1, where n = 1,3,5,7 etc.) harmonics are absent in the motor phase voltage.

The third harmonic order currents are eliminated from the motor by using isolated DC-link supply for the two inverters.

A smooth transition to the over-modulation region is also achievable from the present open– end winding IM drive.

Salient features


Open end winding circuit schematic Inverter – 1 DC-link voltage is VDC

Inverter – 2 DC-link voltage is Vdc

VDC = 0.366 Vdc

INVERTER - 2

O

INVERTER - 1

A

B

C C’

B’

A’

O’

Vdc/2

Vdc/2

VDC/2

VDC/2

Open-end winding IM drive


Vector diagram inverter – 1Vector magnitude = VDC

VDC4 (-++)

4’(-++)

1’(+--)

6’(+-+)5’(--+)

2’(++-)3’(-+-)

5 (--+) 6 (+-+)

1 (+--)

2 (++-)3 (-+-)

Vector diagram inverter – 2Vector magnitude = Vdc

Voltage space phasor diagrams of individual inverters

0.366 VDC


30

30

6’ 1,1’ (+--) 2,2’ (++-) 3,3’ (-+-) 4,4’ (-++) 5,5’ (--+) 6,6’ (+-+) 7,7’ (+++) 8,8’ (---)

1

23

4

5`

6

3’5’

4’1’

6’

2’

1’ 3’ 2’ 4’

5’

450

1.223 VDC

VDC

VDC sin150 = k VDC sin450 So k = sin150 / sin450 = 0.366

150

1200 k VDC

Selected combinations of the vector positions from inverter – 1 and inverter – 2 and calculation of DC – link voltage ratio (k) for both the inverters.


(a) - Fundamental

II21II1

1

-II21 -II1

1

I11 I2

1

Ref. point

(b) – 5th Harmonics

-II15 -II2

5

II15II2

5

I15 I2

5

Ref. point (c) – 7th Harmonics

-II17 -II2

7

I27I1

7

II17II2

7

Ref. point

(d) – 11th Harmonics

-II211 -II1

11

I111 I2

11

II211II1

11

Ref. point

(e) – 13th Harmonics

-II113 -II2

13

I113I2

13

II213 II1

13

Relative position of different harmonics (1st to 13th ) of the motor phase from both inverter – 1 and inverter – 2


Relative position of different harmonics (17th to 25th ) of the motor phase from both inverter – 1 and inverter – 2

(f) – 17th Harmonics (g) – 19th Harmonics

II223 II1

23

-II123

I223 I1

23

-II223

(h) – 23rd Harmonics (i) – 25th Harmonics

II117 II2

17

I217 I1

17

-II217 -II1

17

Ref. point

-II219 -II1

19

II219II1

19 I119I2

19

Ref. point

Ref. point

II125 II2

25

-II125-II2

25

I125 I2

25

Ref. point


60

VCO t

VAO

VBO

Switching vectors and pole voltage (VAO , VBO , VCO ) of inverter-1

16655433221 4I 1

360300240180120600

VA’O

VB’O

VC’O t

3423153 4 6 15 6 2II

3603002401801200

Switching vectors and pole voltage (VA’O , VB’O , VC’O ) of inverter - 2


EXPERIMENTAL RESULTS

OVER MODULATION

Phase voltage

Harmonic spectrum

Phase current

Phase current and Fourier spectrum

show absence of all 6n±1 (n = 1,3,5 .. etc) harmonics

Y- axis : 75v/div

Y- axis : 1 amp/div



MODULATING WAVE,TRIANGLE CARRIER WAVE AND CORRESPONDING GATE SIGNAL

a – Modulating wave and triangle carrier wave (inverter-1). b – Inverter-1 pole voltage. c – Modulating wave and triangle carrier wave (inverter-2). d – Inverter-2 pole voltage (fc = 6f)

Phase-A and A’

Phase-B and B’

Phase-C and C’

a

b

c

d

a

b

c

d

a

b

c

d



MODULATION INDEX LESS THAN ONE (fc = 6f)

PHASE VOLTAGE

FOURIER SPECTRUM

PHASE CURRENTThe Fourier spectrum shows increase in harmonic contents compared to that of over-modulation case.

Y axis : 100v/div

Y-axis : 1 amp/div



MODULATION INDEX = 0.45 (fc = 12f)

PHASE VOLTAGE

FOURIER SPECTRUM

PHASE CURRENT

The Fourier spectrum shows increase in 23rd and 25th harmonic contents.

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

Y-axis : 100v/div

Y-axis : 1 amp/div


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.4

-0.2

0

0.2

0.4

0.6

0.8

1fc/f = 6

Modulation index

Rela

tive

harm

onic

ratio Fundamental

11th

25th 23rd

13th

THE RELATIVE RATIO OF DIFFERENT HARMONICS GENERATED BY TRIANGULAR CARRIER AT DIFFERENT MODULATION INDICES fc = 6f



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.4

-0.2

0

0.2

0.4

0.6

0.8

1fc/f = 12

Modulation index

Rela

tive

harm

onic

ratio Fundamental

23rd

11th , 13th

25th



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9fc/f = 24

Modulation index

Rela

tive

harm

onic

ratio

fundamental

***: 11th , +++ : 13th

ooo: 23rd , xxx : 25th


THE RELATIVE RATIO OF DIFFERENT HARMONICS GENERATED BY TRIANGULAR CARRIER AT DIFFERENT MODULATION INDEX fc = 24f

fundamental

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.4

-0.2

0

0.2

0.4

0.6

0.8

1fc/f = 24

Modulation index

Rela

tive

harm

onic

ratio

fundamental

47th

***: 37th , +++ : 39th

49th


All the 6n 1, n = 1, 3, 5 etc,. order harmonics are eliminated from the motor phase voltage in the entire speed range.

A linear transition to the maximum modulation is possible.

By properly choosing the frequency modulation ratio (6, 12, 24, 48) at different speed ranges, the switching frequency of both inverters can be controlled within 500hz.

In the extreme speed range the lower voltage inverter is

switched more frequently than the higher voltage inverter. The 11th and 13th order harmonic voltage amplitudes in the

motor phase voltage can be suppressed by introducing notches in the modulating wave.

The resultant fundamental is reduced to 99.57%. The resultant 11th order harmonic is reduced to 50%.

And the 13th order harmonic is reduced to 31.86%.

CONCLUSION & SALIENT FEATURES


a – Modulating wave (11th and 13th harmonics suppressed) and triangle carrier wave (inverter-1)

b – Inverter-1 pole voltage

c – Modulating wave (11th and 13th harmonics suppressed) and triangle carrier wave (inverter-2)

d – Inverter-2 pole voltage

EXPERIMENTAL RESULTS: 11th and 13th suppression

Pole voltage of inverter-2 ( Over modulation)

Pole voltage of inverter-1 ( Over modulation)

Modulating wave and triangular carrier wave (over modulation ) fc/f = 12


EXPERIMENTAL RESULTSPHASE VOLTAGE,FOURIER SPECTRUM,PHASE CURRENTS(m > 1)

Modulation index = 1.0 Over-modulation. Phase voltage with 11th and 13th suppressed. Y-axis : 75v/div; X-axis : 5ms/div

Modulation index = 1.0 Over-modulation Fourier spectrum With 11th and 13th suppressed.

Modulation index = 1.0 Phase current during overmodulation.(No load operation with 11th and 13th suppressed) Y-axis : 1A/div; X-axis : 5ms/div


EXPERIMENTAL RESULTSPHASE VOLTAGE,FOURIER SPECTRUM,PHASE CURRENTS(m > 0.9)

Y- axis : 1A/div

Y- axis : 75v/div

Modulation index = 0.9. Phase voltage. fc = 12f, With 11th and 13th suppressed. Y-axis : 75v/div; X-axis : 5ms/div

Modulation index = 0.9. fourier spectrum. fc = 12f.

With 11th and 13th suppressed

Modulation index = 0.9. Phase current waveform. fc = 12f ( no load operation with 11th and 13th suppressed). Y-axis : 1A/div; X-axis : 5ms/div


EXPERIMENTAL RESULTSPHASE VOLTAGE,FOURIER SPECTRUM,PHASE CURRENTS(m > 0.45)

Y- axis : 1A/div

Y- axis : 75v/div

Modulation index = 0.45. Phase voltage. fc = 12f. With 11th and 13th suppressed. Y-axis : 75v/div; X-axis : 5ms/div

Modulation index = 0.45. Phase current waveform. fc = 12f

( no load operation with 11th and 13th suppressed). Y-axis : 1A/div; X-axis : 10ms/div

Modulation index = 0.45. Fourier spectrum. fc = 12f.

With 11th and 13th suppressed


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.4

-0.2

0

0.2

0.4

0.6

0.8

1With notch and fc/f = 12

Modulation index

Rela

tive

harm

onic

ratio

Fundamental

25th

23rd

11th , 13th

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9With notch and fc/f = 24

Modulation index

Rela

tive

harm

onic

ratio fundamental

***: 11th , +++ : 13th


fc = 12f fc = 24f

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9With notch and fc/f = 48

Modulation index

Rela

tive

harm

onic

ratio fundamental

***: 11th , +++ : 13th


fc = 48f

HARMONIC ANALYSISRATIO OF DIFFERENT HARMONICS VERSES MODULATION INDEX

A Novel Modulation Scheme for a Six Phase Induction Motor with Open-End Windings


Six phase (split phase)motor configuration is achieved by splitting the phase belt of a conventional 3-phase induction motor into two halves namely abc and a’b’c’.

The phase separation between a and a’, b and b’ and c and c’ is 30°

Winding disposition of a six-phase machine


For a six phase induction motor drive harmonics of the order 6n 1( n=1,3,5 etc.,) will not contribute to the air gap flux.

All these 6n 1 ( n=1,3,5 etc.,) order harmonic currents are limited by the stator impedance only and hence contribute to large harmonic currents.

Inverter fed six-phase IM drive


The phase voltages and currents in a six phase motor can be represented by a six dimensional vector.

By proper transformation three different sub-spaces can be generated which correspond to three different set of harmonic orders.

The generalised vector used for the transformation matrix is Sk(a) = [cos k(a) cos k(a-θ) · · · · cos k(a-9θ)].

Winding disposition of a six-phase machine


By putting a = 0 and π/2, and θ equals to multiples of 30º in the generalised vector a transformation matrix is obtained.

θ = angular space separation between the two sets of 3-phase windings.


The harmonics of order 6n1 ( n = 0, 2,4 etc.,) span a 2-dimesional subspace ‘s1’.

The harmonics of order 6n1 ( n = 1, 3,5 etc.,) span a 2-dimesional subspace ‘s2’.

The triplen order harmonics span a 2-dimesional subspace ‘s3’.

They are orthogonal to each other.


All switching vectors projected on subspace‘S1’ generates 6n1 ( n = 0, 2,4 etc.,) harmonics.

Switching vectors in sub-space ‘S1’


• All switching vectors projected on subspace‘S2’ generates 6n1 ( n = 1, 3,5 etc.,) harmonics

Switching vectors in sub-space ‘S2’


In the proposed scheme a modulation technique is used to eliminate all the 6n1 ( n = 1,3,5 etc.,) harmonics from the stator phases .

An open-end winding drive configuration with DC-link voltages chosen in a ratio of 1:0.366 will eliminate 6n1 ( n = 1,3,5 etc.,) harmonics.

Power schematic to suppress the 6n1 ( n = 1,3,5 etc.,) harmonics


From one side of open-end winding (inverter-1 and inverter-4) 11’,21’, 22’,

32’,33’,43’,44’,54,,55’,65’,66’ and 16’ vectors are switched. From the opposite side (inverter-2 and inverter-3) vectors 53’,

45’, 64’, 56’, 15’, 61’, 26’, 12’, 31’, 23’, 42’, and 34’ are switched.

Inverter vector selection to suppress the 6n1 ( n = 1,3,5 etc.,) harmonics


Vectors 11’ and 53’ get added in ‘S1’ plane

With DC-link voltage ratio of |11’| / |53’| = 0.366 combined vectors on ‘S2’ plane are cancelled implying all 6n1 ( n = 1,3,5 etc.,) harmonic elimination .

Inverter vector selection to suppress the 6n1 ( n = 1,3,5 etc.,) harmonics contd.


With DC-link voltage ratio of 0.366 12-sided polygonal voltage space phasor combinations are achieved for each 3-phase groups independently.

A modulation scheme based on 12-sided polygonal voltage space phasors will cancel the 6n1 ( n = 1,3,5 etc.,) harmonics voltage from all the motor phases.


Phase voltage

Harmonic spectrum

Phase currents.

6n1 ( n = 1,3,5 etc.,) harmonics are absent.

Experimental results


To suppress the 11th and 13th order harmonics in motor phases additional notches of 3.75° are provided in the modulation voltage.

This results in a reduction of 11th harmonic to 50% ,13th harmonic to 31.86% and fundamental to 99.57% in magnitude.


Experimental results(with notch)

Phase voltage

Harmonic spectrum Reduction in 11th

and 13th order harmonic magnitude.

Phase currents.


Experimental results(with notch) Modulation ratio of 12.

Phase voltage

Phase currents


Experimental results(with notch) Modulation ratio of 24

Phase voltage

Phase currents

IA


Experimental results(with notch) Modulation ratio of 48

Phase voltage

Phase currents


Conclusion & salient features• A modulation technique to eliminate the 6n 1 ( n=1,3,5 etc.,)

harmonic currents, without the need for harmonic filters, from the stator phases of a six phase induction motor drive is explained.

• By appropriately choosing the frequency ratio between 12,24 and 48 for different speed ranges the inverter switching frequency can be limited to 600 hz .

• The proposed scheme used 4 inverters with a DC-link voltage of 0.41VDC and 0.15VDC , where VDC

is the DC-link voltage of a 2-level 3-phase inverter, if the six-phase machine is run as a conventional 3-phase machine.

INDEPENDENT SPEED CONTROL OF TWO SIX PHASE INDUCTION MOTORS USING A SINGLE SIX PHASE INVERTER


A method of independent speed control of two induction motors from a single six-phase inverter is proposed.

The positive sequence component consists of all the 12n 1 (n = 0,1,2, ….etc.) order harmonics.

One of the two zero sequence components consists of all the 6n 1 (n = 1,3,5 ….etc.) order harmonics .

Introduction


30˚

INVERTER – 2 INVERTER - 1

AVDC/2

NN’ C ’

CB’B

A’A

A’

B’o BCVDC/2

C’

• A six phase induction motor driven from six phase inverter• Vas,Vbs,Vcs are the phase voltages of the a,b,c three

phase group• Va’s,Vb’s,Vc’s are the phase voltages of the a’,b’,c’ three

phase group

Inverter fed six-phase IM drive


s'Vc

Vcs

s'Vb

Vbs

s'Va

Vas

101010

010101

9sin4sinsin8sin5sin0

9cos4coscos8cos5cos1

9sin8sin5sin4sinsin0

9cos8cos5cos4coscos1

)3/1(

2V

1V

2V

1V

V

V

• Vas, Vbs, Vcs for a,b,c group.• Va’s, Vb’s, Vc’s for a’,b’,c’ group.

• Vα, Vβ … Harmonics spanning subspace S1 [12n 1 (n = 0,1,2,3 ….etc.,)]

• V1, V2 … Harmonics spanning subspace S2

[6n 1 (n = 1,3,5 order ….etc.,)]

• Vo1, Vo2… Harmonics spanning subspace S3 [triplen harmonic ]


risrLsissLdt

dsisRVs

Stator Voltage equation

Vs is input voltage vectors, si is input stator current vectors,

is input stator current vectors, ri

sR is stator resistance matrix, ssL is stator self inductance matrix,

srL is stator to rotor mutual inductance matrix.


riC1CsrLCsiC1CssLC

dt

dsiC1CsRCVsC

101010

010101

9sin4sinsin8sin5sin0

9cos4coscos8cos5cos1

9sin8sin5sin4sinsin0

9cos8cos5cos4coscos1

)3/1(C

109sin9cos9sin9cos

014sin4cos8sin8cos

10sincos5sin5cos

018sin8cos4sin4cos

105sin5cossincos

010101

)3/1(1C

Applying the orthogonal transformation to the stator voltage equation


r2ir1iriri

.

0000

0000

00)rcos(M3)rsin(M3

00)rsin(M3)rcos(M3

dt

d

s2is1isisi

.

lsL000

0lsL00

00M3lsL0

000M3lsL

dt

d

s2is1isisi

44sR

2V1V

V

V

si,si are two orthogonal components of stator currents spanning subspace S1 ,

s2i,s1i are two orthogonal components of stator currents spanning subspace S2 ,

ri,ri are the two orthogonal components of rotor currents spanning subspace S1 ,

r2i,r1i are two orthogonal components of rotor currents spanning subspace S2 .


Rotor voltage equation

si.rsLri.rrLdt

dri.Rr0

rR is stator resistance matrix, rrL is stator self inductance matrix,

rsL is rotor to stator mutual inductance matrix.


si.C1C.rsL.Cri.C1C.rrL.C

dt

dri.C1C.rR.C0

• By applying the orthogonal transformation to the rotor voltage equation

s2is1isisi

.

0000

0000

00)rcos(M3)rsin(M3

00)rsin(M3)rcos(M3

dt

d

r2ir1iriri

.

lrL000

0lrL00

00M3lrL0

000M3lrL

dt

d

r2ir1iriri

44rR

0

0

0

0


• The corresponding voltage equations of stator and rotor spanning subspaces S1 and S2 can be separated out

ririsisi

.

M3lrL0)rcos(M3)rsin(M3

0M3lrL)rsin(M3)rcos(M3

)rcos(M3)rsin(M3M3lsL0

)rsin(M3)rcos(M30M3lsL

dt

d

ririsisi

rR000

0rR00

00sR0

000sR

0

0

V

V

r2ir1is2is1i

.

lrL000

0lrL00

00lsL0

000lsL

dt

d

r2ir1is2is1i

rR000

0rR00

00sR0

000sR

0

02V1V

Subspaces S1 ….

Subspaces S2 ….


•Only the positive sequence components traversing subspace S1 contribute for the air gap flux and electromagnetic torque production in machine.

•The zero sequence components do not contribute towards air gap flux production with the existing winding

disposition.


A scheme is proposed where the zero sequence components corresponding to the 6n 1 (n = 1,3,5 ….etc.) order harmonics are impressed across a second six phase motor in proper phase sequence.

The zero sequence components acts as positive sequence component for the second motor and hence develop air gap flux and electromagnetic torque in the second motor.


B’

180˚ +30˚

N

N’C ’

C

B

A’

A

Stator schematic of the reconfigured six phase induction machine ( voltage components in the S2 plane create air gap flux and torque)

Six-phase IM winding disposition:-S2 subspace components produce torque


ri1srLsi1ssLdt

dsisRsV

Stator Voltage equation

Vs is input voltage vectors, si is input stator current vectors,

is input stator current vectors, ri

sR is stator resistance matrix, 1ssL is stator self inductance matrix,

1srL is stator to rotor mutual inductance matrix.


riC1C1srLCsiC1C1ssLC

dt

dsiC1CRsCVsC

By applying the orthogonal transformation to the stator voltage equation

r2ir1iriri

.

)rcos(M3)rsin(M300

)rsin(M3)rcos(M300

0000

0000

dt

d

s2is1isisi

.

M3lsL000

0M3lsL00

00lsL0

000lsL

dt

d

s2is1isisi

44sR

2V1V

V

V


si.1rsLri.1rrLdt

dri.Rr0

Rotor Voltage equation

rR is stator resistance matrix, 1rrL is stator self inductance matrix,

1rsL is rotor to stator mutual inductance matrix.


siC1C1rsLCriC1C1rrLC

dt

driC1CrRC0

• By applying the orthogonal transformation to the rotor voltage equation

s2is1isisi

.

)rcos(M3)rsin(M300

)rsin(M3)rcos(M300

0000

0000

dt

d

r2ir1iriri

.

M3lrL000

0M3lrL00

00lrL0

000lrL

dt

d

r2ir1iriri

44rR

0

0

0

0


• The corresponding voltage equations of stator and rotor spanning subspaces S1 and S2 can be separated out

Subspaces S1 ….

Subspaces S2 ….

ririsisi

.

lrL000

0lrL00

00lsL0

000lsL

dt

d

ririsisi

rR000

0rR00

00sR0

000sR

0

0

V

V

r2ir1is2is1i

.

M3lrL0)rcos(M3)rsin(M3

0M3lrL)rsin(M3)rcos(M3

)rcos(M3)rsin(M3M3lsL0

)rsin(M3)rcos(M30M3lsL

dt

d

r2ir1is2is1i

rR000

0rR00

00sR0

000sR

0

02V1V


•Only the harmonic components traversing subspace S2 contribute for the air gap flux and electromagnetic torque production in machine.

•The the harmonic components traversing subspace S1 do not contribute towards air gap flux production with the existing winding disposition.


)6/9wt5(cos)3/2wt5(cos)6/wt5(cos)3/4wt5(cos)6/5wt5(cos)wt5(cos5V

'cc'bb'aa

)6/9wt7(cos)3/2wt7(cos)6/wt7(cos)3/4wt7(cos)6/5wt7(cos)wt7(cos7V

'cc'bb'aa

• The 5th harmonic voltage, which spans the subspace S2 is represented by

• The 7th harmonic voltage, which spans the subspace S2 is represented by

• The phase relationship among the elements of the vector represented by 5th

harmonic and 7th harmonic are similar except that the frequencies are different.

• Hence if the frequency and in the equations are replaced by , then a vector corresponding to the fundamental frequency spanning the subspace can be obtained.

'5' wt 'wt7'

'wt'2S


•This orthogonal property is made use of for controlling two split-phase induction motors independently by connecting them in series and controlling with a single six-phase inverter.

•The reference modulating signals for the whole drive system are generated by superimposing the reference signals belonging to the subspace S1 and the reference signals belonging to the subspace S2.


30˚

N2

N2

N2

A2B2’

C2’

C2 B2

A2’

C1’

C1

B1’

B1

A1’A1

MACHINE-1( 2-pole 2kw)

MACHINE-2( 4-pole 1kw)

180˚ +30˚

N’

Schematic of the stator phase windings of the two series connected six phase induction motors


0

0

0

0

V

V

1C

1s'Vc

1Vcs

1s'Vb

1Vbs

1s'Va

1Vas

0

0

2V

1V

0

0

1C

2s'Vc

2Vcs

2s'Vb

2Vbs

2s'Va

2Vas

2s'Vc1s'Vc

2Vcs1Vcs

2s'Vb1s'Vb

2Vbs1Vbs

2s'Va1s'Va

2Vas1Vas

s'Vc

Vcs

s'Vb

Vbs

s'Va

Vas

Motor-1 phase voltage generation

Motor-1 and motor-2 combined phase voltage generation

Motor-2 phase voltage generation


MOTOR-1 CONTROL BLOCK

MOTOR-2 CONTROLBLOCK

Integrator

Vc2

Vc’2

Vb2

Va’2

SpeedRef2.

SpeedRef1.

Va2

Vc’

Vc

Vb’

Vb

Va’

Va

Vb’2

Vc’1

Vc1

Vb’1

Vb1

Va’1

Va1

Vβ

Vα

Vm1

V/f

Integrator

Vα , Vβ Generator C-1

V2

V1

Vm2

V1 , V2 Generator

C-1

PWM

IN

V

E

R

T

E

R

M1

M2

V/f

f1

f2

Control blocks for series connected six phase motor drive


Voltage waveform of phase-a and phase-a’ of motor-2 (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 250rpm(9hz) . The motors are running in opposite direction).No - load operation. X- axis 20ms/div. Y- axis 20v/div.

Voltage waveform of phase-a and phase-a’ of motor-1 (Motor-1is running at 1000rpm(18Hz) and motor-2 is running at 250rpm(9Hz) .The motors are running in opposite direction). No - load operation. X- axis 10ms/div. Y- axis 50v/div

Reference voltage of phase-a’ of motor-1 and motor-2 and the their combined voltage for PWM generation (Motor-1 is running at 1000rpm(18Hz) and motor-2 is running at 250rpm(9hz) . The motors are running in opposite direction). No - load operation. X- axis 50ms/div. Y- axis 200mv/div.

Reference voltage of phase-a of motor-1 and motor-2 and the their combined voltage for PWM generation (Motor-1 is running at 1000rpm(18 Hz) and motor-2 is running at 250rpm(9 Hz) . The motors are running in opposite direction). No - load operation. X- axis 50ms/div. Y- axis 200mv/div.



0 10 20 30 40 500

0.2

0.4

0.6

0.8

1

RELATIVE AMPLITUDES OF DIFFERENT FREQUENCY COMPONENTS IN PHASE CURRENT

NORMALISED FREQUENCY

RE

LA

TIV

E A

MP

LIT

UD

EHarmonic spectrum of current waveform in phase-a’ (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 250rpm(9hz) . The motors are running in opposite direction). Along normalised frequency axis 9hz = 1unit.

Current waveform of phase-a and phase-a’ (Motor-1 is running at 1000rpm(18hz ) and motor-2 is running at 250rpm(9hz) . The motors are running in opposite direction).No - load operation. X- axis 50ms/div. Y- axis 1A/div.

Combined phase-a’ voltage waveform (Motor-1is running at 1000rpm(18hz) and motor-2 is running at 250rpm(9hz) .The motors are running in opposite direction). X- axis 10ms/div. Y- axis 50v/div.

Combined phase-a voltage waveform (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 250rpm(9hz) .The motors are running in opposite direction). X- axis 10ms/div. Y- axis 50v/div.



Combined phase-a’ voltage waveform [VA1’N2’ of Fig.4b] (Motor-1is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz) .The motors are running in same direction). X- axis 10ms/div. Y- axis 50v/div.

Combined phase-a voltage waveform [VA1A2 of Fig.4b] (Motor-1is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz) .The motors are running in same direction). X- axis 10ms/div. Y- axis 50v/div.

Voltage waveform of phase-a and phase-a’ of motor-2 (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz) .The motors are running in same direction). X- axis 10ms/div. Y- axis 20v/div.

Voltage waveform of phase-a and phase-a’ of motor-1 (Motor-1is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz) .The motors are running in same direction). X- axis 10ms/div. Y- axis 50v/div.



Voltage waveform of phase-a and phase-a’ of motor1 (Motor-1 is running at 1000rpm(18hz) and motor-2 is stalled ). X- axis 10ms/div. Y- axis 50v/div.

Voltage waveform of phase-a and phase-a’ of motor2 (Motor-1is running at 1000rpm(18hz) and motor-2 is stalled ). X- axis 10ms/div. Y- axis 50v/div.

Current waveform of phase-a and phase-a’ (Motor-1 is running at 1000rpm(18hz) and motor-2 is running at 500rpm(18hz) .The motors are running in same direction). X- axis 50ms/div. Y- axis 1A/div. No-load operation.



Current waveform of phase-a and phase-a’ (Motor-1 is running at 1000rpm(18hz) and motor-2 is stalled ). X- axis 10ms/div. Y- axis 2mv/div. No-load operation.

Combined phase-a voltage waveform [VA1A2 of Fig.4b] (Motor-1 is running at 1000rpm(18hz) and motor-2 is stalled). X- axis 10ms/div. Y- axis 50v/div.

Combined phase-a’ voltage waveform [VA1’N2’ of Fig.4b] (Motor-1 is running at 1000rpm(18hz) and motor-2 is stalled). X- axis 10ms/div. Y- axis 50v/div.



Current waveform of phase-a’ and speed of motor-2 (Motor-1 is making speed reversal from -1000rpm to 1000rpm and motor-2 is running at constant speed at 250rpm ). X- axis 5s/div. Y- axis 1A/div (current), 125rpm/div (speed)

Current waveform of phase-a’ and speed of motor-1 (Motor-1 is making speed reversal from -1000rpm to 1000rpm and motor-2 is running at constant speed at 250rpm ). X- axis 5s/div. Y- axis 1A/div (current), 500rpm/div (speed)

Current waveform of phase-a’ and speed of motor-2 (Motor-1 is making speed reversal from 1000rpm to –1000rpm and motor-2 making speed reversal from -250rpm to 250rpm ). X- axis 5s/div. Y- axis 4A/div (current), 125rpm/div (speed)

Current waveform of phase-a’ and speed of motor-1 (Motor-1 is making speed reversal from 1000rpm to –1000rpm and motor-2 making speed reversal from -250rpm to 250rpm ). X- axis 5s/div. Y- axis 4A/div (current), 500rpm/div (speed)



Current waveform of phase-a’ and speed of motor-2 (Motor-1 is running at constant speed of 1000rpm and motor-2 is making speed reversal from -250rpm to 250rpm ). X- axis 5s/div. Y- axis 1A/div (current), 250rpm/div (speed)

Current waveform of phase-a’ and speed of motor-2 (Motor-1 is running at constant speed of 1000rpm and motor-2 is making speed reversal from -250rpm to 250rpm ). X- axis 5s/div. Y- axis 1A/div (current), 125rpm/div (speed)

Current waveform of phase-a and phase-a’ (Motor-1 running at six step mode and motor-2 is stalled ). X- axis 20ms/div. Y- axis 1A/div

Voltage waveform of phase-a’ of motor-1 and motor-2 (Motor-1 running at six step mode and motor-2 is stalled ). X- axis 10ms/div. Y- axis 100v/div.



0 10 20 30 40 500

0.5

1

1.5

2

2.5

3x 10

5


RE

LA

TIV

E A

MP

LIT

UD

E

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5x 10

4


RE

LA

TIV

E A

MP

LIT

UD

E

Harmonic spectrum of voltage waveform in phase-a’ of motor-1 (Motor-1 is running in over modulation (12 step) and motor-2 is stalled).

Harmonic spectrum of voltage waveform in phase-a’ of motor-2 (Motor-1 is running in over modulation (12 step) and motor-2 is stalled).

Current waveform of phase-a and phase-a’ (Motor-1 is stalled and motor-2 is running at six step mode). X- axis 20ms/div. Y- axis 1A/div

Voltage waveform of phase-a’ of motor-1 and motor-2 (Motor-1 is stalled and motor-2 is running at six step mode). X- axis 10ms/div. Y- axis 100v/div.



Conclusion & salient features• A de-coupled speed control of two split phase (six phase) induction motor, from a single six phase inverter system is presented.

• In normal six phase motor the phase voltages corresponding to the 6n 1 (n = 1,3,5 ….etc.,) harmonic orders do not create torque and air gap flux.

• But the phase voltages corresponding to the 6n 1(n = 1,3,5 ….etc.,) harmonic orders when applied to another six phase motor in proper phase sequence , torque and air gap flux are created.

• Thus by the proper series connections of phases of the two six phase motors, the two motors can be run independently from a single six phase inverter.

• Independent speed control of the two motors are possible without the need for costly and bulky harmonic filters to suppress the high amplitude 6n 1 (n = 1,3,5 ….etc.,) order zero sequence harmonic current components.


Independent Field Oriented Control Of Two Split-phase Induction Motors From A Single Six-phase Inverter


Terminal connection of the two series connected split-phase (six-phase) induction motors.


Speed reversal of motor-1( Bottom Trace) and motor-2 at different instants (Motor-1 500rpm to –500rpm and motor-2 between-300rpm to

300rpm).


Torque currents of motors


simultaneous speed reversal of motors [( motor-1( Bottom trace) 500rpm to –500rpm and motor-2 ( Top Trace) -300rpm to 300rpm]


Torque currents of motor-1 ( Bottom Trace) and motor-2 (Top Trace)


Motor-1 is accelerating and motor-2is running at constant speed


Motor-1 is doing speed reversal and Motor-2 is at constant speed operation



• Independent speed control of the two motors are possible without the need for costly and bulky harmonic filters to suppress the high amplitude 6n 1 (n = 1,3,5 ….etc.,) order zero sequence harmonic current components.

A SENSORLESS SPEED CONTROL FOR INDUCTION MOTORS USING RIPPLE CURRENTS IN SPACE PHASOR BASED PWM CONTROL


A new method to estimate speed of induction motor without shaft transducer is proposed.

The motor phase current ripple is used for estimation of rotor flux position.

Two different schemes are used for flux position estimation in two different regions, one in low speed region and the other in high speed region.

The proposed method uses space vector modulation with constant switching frequency.

Introduction


Steady state equivalent circuit of induction motor in rotor reference frame.

The back emf vector lags the rotor flux vector by 90˚

rR L

sR rrjW

kV L)1(

dt

d s

dt

dV r

m

Wsynchronous

dt

id s

mV

axis

axis r

m-V


The stator equation is

ms

ssk Vdt

idlriV

kV Applied voltage vectors

(out of eight inverter states) mV Machine back emf vector

si = Stator current space phasor

l = Stator leakage inductance sr = Stator resistance


During the effective period Teff (T1& T2) both back emf vector and active vectors cause the ripple current to flow.

During the zero vector period T0

only the back emf vector causes the ripple current to flow.

20T

2T 2T

ski

20T

20T

1T

1V

20T

0V 0V 0V 0V

)1( ksi

effT

2V

1T

1V 2V

2

T

si

T T

effT


Two samples of current vectors are taken in T/2 time period difference during the zero vector period.

When the modulating frequency is less than 50% of the base frequency the zero vector period T0 is more than the the effective period Teff i.e. T0 is more than half of the switching period T/2 and hence there is sufficient deviation in current vector during zero period T0 .

Flux position estimation in low speed region


Flux position estimation in high speed region

Three samples of current are taken at t = 0, t = T/2 and t = T. Effective period Teff is more than T/2(half of the

switching period).

Ripple current dependent on the two consecutive active vectors and the back emf vector.

The flux position is estimated by creation of a virtual short circuit i.e. by eliminating the effect of active vectors from the ripple current.


When the reference vector position θ is within 30˚ from the first active vector in any sector, i.e. 0 < θ <= 30˚, the time period T1 for the first active vector, is greater than the time period T2 for the second active vector

Three samples of current are taken at t = 0, t = T/2 and t = T

20T

20T

effT

1T 2T

0V 1V 2V 0V

1errI 2errI

ski )1( ksi )2( ksi

2

T

2

T


2

T

2

T

20T

20T

effT

1T 2T

0V 1V 2V 0V

1errI 2errI

ski )1( ksi )2( ksi

When the reference vector position θ is more than 30˚ from the first active vector in a sector i.e. 30˚ < θ <= 60˚,the time period T1 for the first active vector is less than the time period T2 for the second active vector

Three samples of current are taken at t = 0, t = T/2 and t = T


Considering one case when reference vector is in sector-1

When < 30° in sector-1 i.e. when 1T period is more than 2T period

)2/2/(1

11 TVTVl

i mefferr

}2/)2/({1

22212 TVTVTTVl

i mefferr

When > 30° in sector-1 i.e. when 2T period is more than 1T period

}2/)2/({1

12111 TVTTVTVl

i mefferr

)2/2/(1

22 TVTVl

i mefferr


By plotting the current deviation vector due to active vectors in the first half of sampling period

for all the sectors we get a hexagon distorted clockwise.

By plotting the current deviation vector due to active vectors in the second half of sampling period

for all the sectors we get a hexagon distorted anticlockwise.

00

030

0120 090

b -c

-a a

c -b

0150

0180

0210

0240 0270

0300 0330

axis

060

axis

00

030

0120

090

b -c

-a a

c -b

0150

0180

0210 0240

0270

0300

axis

060

1_ actveerI

2_ actveerI

axis

0330

0106.15

073.85

1_ actveeri

2_ actveeri


By extracting the fundamental components we get that , the fundamental component of lags by Φ from

, the fundamental component of reference vector and , the fundamental component of leads by Φ from

.

Φ = 16.15˚.

fV

1_ actveerfI

2_ actveerfI

t

t

t

1_ actveerfi

1_ actveeri

fV

2_ actveerfi

2_ actveeri

fV


Hence 1_actveerfi =

03.322_

jactveerf ei

ferri 1 t he fundamental components of 1erri can be written as

mfactveerfferr Vii 1_1

mfV = The fundamental components of the current deviation

phasor contributed by back emf . Similarly ferri 2 the fundamental components of 2erri can be

written as mfactveerfferr Vii 2_2

A high resolution band pass filter whose center frequency is dynamically tuned to the fundamental frequency, is used for extraction of these fundamental components from the sampled ripple currents .


From the three equations the back emf position is found as

The rotor flux position leads by 90˚ from the back emf position, hence it can be obtained by adding 90˚ to the position of back emf vector.

A speed control scheme is implemented based on the estimated rotor flux position.

)1(0

0

3.32

3.3221

j

jferrferr

mfe

eiiV


Block diagram of sensorless speed control scheme

V/F actual

slipW

*slipW

*Vsd

*Vsq

Isd

*

*

*

c

b

a

V

V

V

2 – phase to 3 – phase Tra nsfn

I N V E R T E R

***cba VVV

Low Pass Filter

K

Threshold

sW V/F estimator

V/F ref

mfbW

Isq

*Isd

*Isq PI

PI

PI

setW *mrefW

Soft Start

ba ii

ba ii

Current change calculation

Flux Position estimator

est

est

Isd

Isq 3- phase

to dq Slip calculation

sW 3- phase to dq

Slip calculation


Flux position at frequency equal to 10 hertz.





Reference speed and estimated speed for speed reversal application. Speed scaling = 800rpm/div


Phase current and estimated speed for speed reversal application. Current scaling = 5A/div, Speed scaling = 800rpm/div.

Speed reversal (zoomed).


Torque current and estimated speed during acceleration. Current scaling = 5A/div, Speed scaling = 600rpm/div

Phase current and estimated speed during acceleration. Current scaling = 5A/div, Speed scaling = 600rpm/div


A Five-level Inverter Topology With Common-mode Voltage Elimination for Induction Motor Drives


• A five-level inverter topology and the switching state selection strategy for the PWM control, is proposed.

• The proposed scheme completely eliminates the common-mode voltages in the entire modulation range of the induction motor drive.

• The proposed scheme is based on a dual five-level inverter fed open-end winding induction motor configuration.

• With the absence of common-mode voltage, associated problems, such as, shaft voltages, bearing currents, etc., are also eliminated in the proposed drive.

Introduction

• A five-level inverter topology is proposed.

• It is formed by cascading two conventional two-level inverters and a conventional three-level NPC inverter. • It offers simple power-bus structure compared to the five-level NPC inverter. • It needs only two power diodes per leg (pole).

One leg of the proposed five-level inverter topology

CEDT, Indian Institute of Science CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 205

*[“1” ON, “0” OFF]**S11-S14, S21-S34, S24-S31, and S41-S44 are

complementary pairs of switches

Realization of the five different voltage levels

Voltage

Level

PoleVolta

ge

State of the switch**

S11 S21 S24 S41

2 Vdc/4 1 1 0 1

1 Vdc/8 0 1 0 1

0 0 0 0 0 1

-1 -Vdc/8 0 0 1 1

-2 -Vdc/4 0 0 1 0

IGBT Gating Logic*

Requirement of blocking voltage capability of devices

• The requirement of blocking voltage capability of individual device goes to as low as

Vdc/8 for S11, S14, S41, and S44 while, it is Vdc/5.33 (3xVdc/2x8) for S21, S34, S24, and S31 in the proposed open-end winding IM drive.


Power schematic of the dual-five level inverter fed IM drive


The nine-level voltage space phasor generation using the dual five-level inverter fed open-end winding IM

• Voltage space phasor of individual five-level inverters

• Machine phase voltage in terms of inverter pole voltages

j 2π 3 j 4π 3SR1 AO BO COV = v + v e + v e

j 2π 3 j 4π 3SR2 A'O' B'O' C'O'V = v + v e + v e

AA AO A O

BB BO B O

CC CO C O

v = v - v

v = v - v

v = v - v

j 2π 3 j 4π 3SR AA' BB' CC'V = v + v e + v e

Inverter-A

Inverter-A’

• Combined voltage space phasor


Switching states and voltage space vector locations of the individual five-level inverter (Inv.-A or Inv.-A’)

61 Voltage Vectors96 Triangular Sectors125 Switching States

• Shaded vectors and states generate zero common-mode voltage

Documents

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 1 Modified reference voltages and triangular carriers for a five-level SPWM scheme