CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 1 Combined voltage space vector locations of a dual five-level inverter fed open-end winding IM drive

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 1

Combined voltage space vector locations of a dual five-level inverter fed open-end winding IM drive (a nine-level inverter)

217 Combined Voltage Vectors

384 Triangular Sectors

15,625 Switching State Combinations

• Shaded voltage vectors generate zero common-mode voltage


Common-mode voltage of the dual five-level inverter fed open-end winding IM drive

CMA AO BO COV = V +V +V 3

CMA' A'O' B'O' C'O'V = V +V +V 3

CM CMA CMA'V = V -V

• Common-mode voltage generated by individual five-level inverters (Inverter-A or Inverter-A’)

• Common-mode voltage in the phase voltage of induction motor with the proposed dual five-level inverter fed drive

Inverter-A

Inverter-A’


Groups of common-mode voltage generated by individual five-level inverter

Group Switching state of the five-level inverter (Inv.-A or Inv.-A’)

VCM

1 222 Vdc/4

2 122, 212, 221 5Vdc/24

3 022, 112, 121, 202, 211, 220 Vdc/6

4 012, 021, 102, 111, 120, 201, 210, 22-1, 2-12, -122 Vdc/8

5 002, 011, 020, 101, 110, 12-1, 1-12, 200, 21-1, 22-2, 2-11, 2-22, -112, -121, -222

Vdc/12

6 001, 010, 02-1, 0-12, 100, 11-1, 12-2, 1-11, 1-22, 20-1, 21-2, 2-10, 2-21, -102, -111, -120, -212, -221

Vdc/24

7 000, 01-1, 02-2, 0-11, 0-22, 10-1, 11-2, 1-10, 1-21, 20-2, 2-1-1, 2-20, -101, -110, -12-1, -1-12, -202, -211, -

220

0

8 00-1, 01-2, 0-10, 0-21, 10-2, 1-1-1, 1-20, 2-1-2, 2-2-1, -100, -11-1, -12-2, -1-11, -1-22, -201, -210, -22-1, -

2-12

-Vdc/24

9 00-2, 0-1-1, 0-20, 1-1-2, 1-2-1, 2-2-2, -10-1, -11-2, -1-10, -1-21, -200, -21-1, -22-2, -2-11, -2-22,

-Vdc/12

10 0-1-2, 0-2-1, 1-2-2, -10-2, -1-1-1, -1-20, -20-1, -21-2, -2-10, -2-21

-Vdc/8

11 0-2-2, -1-1-2, -1-2-1, -20-2, -2-1-1, -2-20 -Vdc/6

12 -1-2-2, -2-1-2, -2-2-1 -5Vdc/24

13 -2-2-2 -Vdc/4

Voltage vectors and corresponding switching states resulting into zero common-mode voltage in individual five-level inverter (Inv.-A or Inv.-A’)

19 Voltage Vectors24 Triangular Sectors19 Switching States

• All the shaded switching states belong to the Group-7,which generate zero common-mode voltage at the inverter poles

Combined voltage space phasor locations resulting into zero common-mode voltage (a five-level inverter voltage space phasor structure)

• Achieved when individual five-level inverters (Inv.-A and Inv.-A’) are switched using the switching states belonging to the Group-7 only.



361 Switching State Combinations

Number of redundant switching states available for each voltage vectors of the five-level inverter with zero common-mode voltage



361 Switching Stats Combinations

• Achieved when individual five-level inverters (Inv.-A and Inv.-A’) are switched using the switching states belonging to the Group-7 only.


Some of the voltage vectors and their redundant switching states for five-level inverter with zero common-mode voltage

Voltage

Vector

Redundant switching state combinations(switching state of Inverter-A, switching state of Inverter-A’)

1 (000,000), (0-22,0-22), (1-21,1-21), (0-11,0-11), (1-10,1-10),(2-20,2-20), (11-2,11-2), (2-1-1,2-1-1), (-12-1,-12-1), (20-2,20-2),

(-110,-110), (-211,-211), (-101,-101), (-202,-202), (-220,-220),(-1-12,-1-12), (02-2,02-2), (01-1,01-1), (10-1,10-1)

9 (000,-101), (0-11,-1-12), (02-2,-12-1), (11-2,01-1), (10-1,000),(1-21,0-22), (1-10,0-11), (2-1-1,1-10), (20-2,10-1), (2-20,1-21),

(-110,-211), (-101,-202), (01-1,-110), (-12-1,-220)

11 (000,-202), (1-10,-1-12), (01-1,-211), (2-1-1,0-11), (02-2,-220),(11-2,-110), (20-2,000), (2-20,0-22), (10-1,-101)

28 (000,-1-12), (1-10,0-22), (01-1,-101), (2-1-1,1-21), (02-2,-110),(-12-1,-211), (11-2,000), (20-2,1-10), (-110,-202), (10-1,0-11)

95 (10-1,-202), (11-2,-211), (2-1-1,-1-12), (20-2,-101)

66 (01-1,-202), (02-2,-211), (10-1,-1-12), (11-2,-101), (20-2,0-11), (2-1-1,0-22)

174 (20-2,-202)

133 (11-2,-202), (20-2,-1-12)

98 (02-2,-202), (11-2,-1-12), (20-2,0-22)


Amplitude of maximum reference space vector possible in linear range of modulation without boost in the DC-link of the proposed inverter

SR dcmax

dc

3 3V = × V

2 2

3 = V

4

1, peak SR maxmax

dc

dc

2V = × V

32 3

= × V3 4V

=2


Generation of same maximum peak fundamental amplitude of the phase voltage equivalent to that of a conventional SVPWM

based five-level inverter

• A boost of 15% in the dc-link of the proposed drive is required to generate the maximum peak fundamental amplitude of the phase voltage equivalent to that of a conventional SVPWM based five-level inverter.


Voltage space vector locations for proposed five-level inverter with common-mode voltage elimination (with dc-link boost)





Switching state combination selected to generate the voltage space phasors of five-level inverter with zero CMV





Power scheme of the proposed five-level inverter with CME


Experimental results

Two-level operationY-axis: 1 div. = 50 V

X-axis: 1 div. = 10 ms

Pole voltage (VAO)

Pole voltage (VA’O)

Phase voltage (VA’A)

Pole voltage FFT(two-level operation)

Y-axis: Normalized amplitudeX-axis: Order of harmonic

Phase voltage FFT(two-level operation)



Experimental results (contd…)

Three-level operationY-axis: 1 div. = 40 V

X-axis: 1 div. = 10 ms

Pole voltage (VAO)



Pole voltage FFT(three-level operation)


Phase voltage FFT(three-level operation)




Pole voltage (VAO)



Four-level operationY-axis: 1 div. = 70 VX-axis: 1 div. = 5 ms

Pole voltage FFT(four-level operation)


Phase voltage FFT(four-level operation)




Pole voltage (VAO)



Five-level operationY-axis: 1 div. = 75 VX-axis: 1 div. = 5 ms

Pole voltage FFT(five-level operation)


Phase voltage FFT(five-level operation)




Pole voltage (VAO)



Over-modulation operation

Y-axis: 1 div. = 80 VX-axis: 1 div. = 5 ms

Pole voltage FFT(over-modulation operation)Y-axis: Normalized amplitude

X-axis: Order of harmonic

Phase voltage FFT(over-modulation operation)Y-axis: Normalized amplitude

X-axis: Order of harmonic



Four-level operationX-axis: 1 div. = 5 ms

Five-level operationX-axis: 1 div. = 5 ms

Phase voltage (VA’A)Y-axis: 1 div. = 50 V

Phase current Y-axis: 1 div. = 1 A

Phase voltage (VA’A)Y-axis: 1 div. = 50 V

Phase current Y-axis: 1 div. = 1 A

CEDT, Indian Institute of Science CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 19

Salient features of the proposed common-mode elimination scheme for multilevel inverter fed drive

• A dual five-level inverter fed open-end winding induction motor drive with elimination of common-mode voltage in the entire operating range.

• Each five-level inverter of the proposed drive is formed by cascading two conventional two-level inverters and a conventional three-level NPC inverter. Hence, the proposed drive offers simple power-bus structure compared to the five-level NPC inverter fed drive.

• There is no alternating common-mode voltage in the inverter poles as well as at the phase windings of the induction machine.


Salient features of proposed common-mode elimination scheme for multilevel inverter fed drive (contd…)

• A common DC-link is used at both the ends of the open-end winding induction machine, for both the five-level inverters.

• The DC-link voltage requirement of proposed open-end winding IM drive is nearly half as compared to that of a single five-level inverter fed conventional IM drive.

• Hence, the voltage stress on the devices is reduced and devices with lower voltage blocking capability can be used, which makes the proposed drive scheme suitable for high power applications.


CONCLUSION

In the implemented scheme, the rotor flux position is estimated from the motor phase current ripples

During the low speed region of operation, the current ripple during the zero vector periods are used for rotor flux position estimation

During the high speed region of operation, the current ripple during the active vector periods are used for rotor flux position estimation

The scheme is implemented for a three phase motor, but the scheme can be extended to any multi phase motor and also with open-end winding structure


Linearization of the Multi-level SVPWM in Over-modulation Region

By

R. S. Kanchan, P. N. Tekwani, and K. GopakumarCentre for Electronic Design and Technology,

Indian Institute of ScienceBangalore, INDIA


Ref

eren

ce s

ign

als

and

car

rier

(wt)

vAN vBN vCN0.5

-0.5

Va0

Vb

0V

c0

Vdc

/2

Vdc

/2

Vdc/2

-Vdc

/2

-Vdc

/2

-Vdc/2

Vt

π/2 π 3 π/2 2 π

Conventional two-level Sine-Triangle PWM

( )1 *

*

AN pkdc

t

dc

vV V

V

k V

k = (peak amplitude of the sinusoidal reference) / (height of the triangular carrier signal)

Linearization of the Multi-level SVPWM in the Over-Modulation Region

• Three sinusoidal (1200 phase shifted) reference signals are compared with triangular carrier• The PWM signals are generated for three phases • The pole voltage is clamped to +ve DC link bus if Vref >Vt else to –ve DC link bus

The fundamental component in the output PWM waveform is equal to


π/2 π 3 π/2 2 π(wt)

V a0

V b0

V c0

-Vdc/2

-Vdc/2

-Vdc/2

Vdc/2

Vdc/2

Vdc/2

-Vdc/2

Vdc/2

VCNVBNVAN

Conventional Sine-Triangle PWM: Over-Modulation Range

• When ref signal is greater than carrier, the pole voltages are clamped to the DC link bus voltage• The fundamental component in output PWM waveform is not given by

• But there is reduction in the fundamental component in the output voltage


1 * dcV k V


0.5

0 wt00

1 sin( )f k t

π/2 π


• Reduction in the output fundamental is proportional to the shaded area

Conventional Sine-Triangle PWM: Over-Modulation Range



MI

k

Linear range Over-modulation

0.50

0.637

0.7854

Non-linear characteristic

• The voltage transfer characteristics i.e the ratio between the output fundamental and the reference signal amplitude is non-linear in the over-modulation region

Conventional Sine-Triangle PWM


200 400 600 800 1000 1200 1400 1600 1800

Ref

ere

nc

e s

ign

als

an

d c

arr

ier

200 400 600 800 1000 1200 1400 1600 1800

V a0

V b0

V c0

200 400 600 800 1000 1200 1400 1600 18001

(wt)

v*ANv*BN v*CN

Vdc

/2

Vdc

/2

Vdc

/2

-Vdc

/2

-Vdc

/2

-Vdc

/2

π/2 π 3 π/2 2 π

0.5

-0.5

Carrier based Space-Vector PWM (SVPWM)


1 max min / 2offsetv v v

max , ,is maximum of AN BN CNv v v v

min , ,is minimum of AN BN CNv v v v

1*

for X=A,B,C

XN XN offsetv v v

• The reference signals are added with an offset voffset1

• The resultant PWM is a Space Vector PWM


1

3sin( )

2f k t

1

3sin( / 6)

2f k t

0.5

0 wt00 π/6 π/3 π/2 2π/3 π


•Again when ref signal is greater than carrier, the pole voltages are clamped to the DC link bus voltage•There is reduction in the fundamental component in the output voltage•Reduction in the output fundamental is proportional to the shaded area

Carrier based Space-Vector PWM (SVPWM)



MI

Ou

tpu

t vo

ltag

e (p

er u

nit

w.r

.t V

dc )

Linear range Over-modulation

0.5

0.637

0.785

0.577

0.866

SPWM

SVPWM

Non-linear characteristic

• The extended linear region in SVPWM as compared to SPWM • The voltage transfer characteristics is again non-linear in the over-modulation region similar to SPWM

Ideal requirement for the PWM modulator : Linear voltage transfer characteristics


In the Proposed Work

An over-modulation scheme with the linear voltage transfer characteristics for a general n-level SVPWM signal generation

Reference signal to the PWM modulator is pre-scaled in over-modulation region such that

The fundamental component of the original and the modified reference signal is same

The modified reference signal is always within carrier region Thus voltage transfer characteristic is a linear function of the modulation index

both in the linear-modulation as well as in the over-modulation region The inverter leg switching times are directly obtained with a simple algorithm

using only the sampled amplitudes of the reference phase voltages



0 100 200 300 400 500 600 700-1

-0.5

0

0.5

1

f 1

0 100 200 300 400 500 600 700-1

-0.5

0

0.5

1

f 2 f2 fundamental

wt

k=0.637


2

1sin ( ) sin (3 )

2 3( )1

sin (5 ) ....5

wt wtf wt

wt

2

2(1) 0.637F

Principle of linearization: when k=0.637 i.e. six step mode

F1, the original reference signal in six step mode ( f1 (pk)=0.637) goes above the carrier (0.5)

The output voltage will be less, if f1 is used for PWM generation

f2 is a rectangular signal such that fundamental component of f2 is equal to f1, the original

reference signal in six step mode i.e. F2 (1)=0.637

Therefore, f2 can be used for PWM generation instead of f1


θ π-θ 2π-θπ +θπ/2 π 3 π/2 2 π

-1

0

1

f 2

-0.5

0

0.5

-1

0

1

f 1

-0.5

0

0.5

mo

dif

ied

ref

.s

ign

al

Ref

eren

ces

ign

al

Linearization of the Multi-level SVPWM in the Over-Modulation

Region

Principle of linearization: when 0.5 < k < 0.637

• A part of original reference signal is clamped• The fundamental component of the modified reference signal is same as original reference signal

• This requires that the fundamental component of rectangular pulse f2 is equal to fundamental component of part of the original reference signal f1


θ π-θ 2π-θπ +θπ/2 π 3 π/2 2 π

-1

0

1

f 2

-0.5

0

0.5

-1

0

1

f 1

-0.5

0

0.5

mo

dif

ied

re

f.si

gn

al

R

efe

ren

ce

sig

na

l

Linearization of the Multi-level SVPWM in the Over-Modulation

Region

1 1

2( )sin( ) ( )

2 11 ( ) sin (2 )

F f t t d wt

k

2

2 1sin( ) ( )

2

2cos ( )

F t d wt

1 2As

2 1 21 ( ) sin (2 ) cos ( )

F F

k

• Fundamental component of rectangular pulse f2 =

• Fundamental component of part of the original reference signal f1 =


0 10 20 30 40 50 60 70 80 900.7854

0.8168

0.8482

0.8796

0.9111

0.9524

0.9739

1

MI


2 1 21 ( ) sin (2 ) cos ( )k

/ 0.637MI k

• The relationship between modulation index MI and clamping angle

• Thus if MI is known, the clamping angle can be determined• The modified reference signal is clamped for the angle to π-θ and π+θ to 2π-θ


0.5

0

wt00

1

3sin( )

2f k t

1

3sin( / 6)

2f k t k

π/6 π/3 π/2 2π/3π

Principle of the proposed SVPWM in the over-modulation region


1

3( ) sin( ); 0

2 6

3sin( );

2 6 6 2

f t k t t

k t t

Reference signal goes out of the carrier two times in the positive half cycle

Modified reference signal


0.5

0 wt

θ0

00

1

3sin( )

2f k t

1

3sin( / 6)

2f k t

k

π/6 π/3 π/2

(2π/3- θ)0

2π/3 π


Principle of the proposed SVPWM in the over-modulation region

The reference signal is clamped to 0.5 twice in +ve half cycle

Again the fundamental component of the modified reference signal is same as original reference signal


0.5

0 wt

θ0

00 π/6 π/3 π/2

(2π/3- θ)0

2

3

1

4 3sin( ) in( ) ( )

2 6

3 2 11 sin 2

2 6 6

F k wt wt d wt

k

2

3

2

4 1 2sin( ) ( ) cos

2 6F t d wt

3 2 1 21 sin 2 cos

2 6 6 6k

Principle of the proposed SVPWM in the over-modulation


The fundamental component of the original reference signal f1 between to 2π/3-θ0.5

0

θ0

1

3sin( )

2f k t

1

3sin( / 6)

2f k t

(2π/3- θ)0

The fundamental component of rectangular pulse f2 between to 2π/3-θ

For the fundamental component of the modified reference signal to be same as original signal,

1 2F F


0.5

0 wt

θ0

00

1

3sin( )

2f k t

1

3sin( / 6)

2f k t

π/6 π/3 π/2

(2π/3- θ)0

3 2 1 21 sin 2 cos

2 6 6 6k


The relationship between modulation index MI and clamping angle

Principle of the proposed SVPWM in the over-modulation

• Thus if MI is known, the clamping angle θ can be determined

; / 0.637MI k

• Clamping of the modulating signal starts when3

0.52

k and clamping angle θ is equal to π/3

• When clamping angle = π/6, k =0.60337• Thus the clamping scheme can be used only in the range 0.577<k <0.60337 as the clamping starts at an angle less than π/6, where modulating wave is (3/2)ksin(wt) instead of

This is referred as over-modulation Mode-I (0.577<k <0.60337)

( 3 / 2) sin( / 6)k t


0.5

0 wt

θ0

(π -θ)0

00

1

3sin( )

2f k t

1

3sin( / 6)

2f k t

k

π/6 π/3 π/2 2π/3π

.

• The MI range greater than 0.60337, angle θ at which clamping starts is less than π/3


Principle of the proposed SVPWM in the over-modulation MODE-II The reference signal is clamped to 0.5 for θ < wt < π- θ Again the fundamental component of the modified reference signal is same

as original reference signal (dotted line)


• The relationship between θ and k can be derived similarly


Principle of the proposed SVPWM in the over-modulation MODE-II

3 31 ( ) sin (2 )

2

2cos ( )

k

0.5

0 wt

θ0

(π -θ)0

00

1

3sin( )

2f k t

1

3sin( / 6)

2f k t

k

π/6 π/3 π/2 2π/3 π

.

5π/6



• Over-modulation Mode-II (0.60337<k <0.637) & clamping angle 0<θ< π/3

• Over-modulation Mode-I (0.577<k <0.60337) & clamping angle π/3<θ< π/6

3 3 21 ( ) sin (2 ) cos ( )

2k

3 2 1 21 sin 2 cos

2 6 6 6k

Summary: The relationship between θ and k

Principle of the proposed SVPWM in the over-modulation MODE-II



0 10 20 30 40 50 60 70 80 900.7854

0.8168

0.8482

0.8796

0.9111

0.9524

0.9739

1

MI

0 10 20 30 40 50 60 70 80 900.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

k

SVPWM

SPWM

Mode-IMode-II

The relationship between θ and k (MI) for SPWM and SVPWM

Steps• Read Modulation Index MI• Determine clamping angle θ• Clamp the reference signal to 0.5 appropriately• The implementation needs instantaneous angle information


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

1 max min / 2offsetv v v

1*

for X=A,B,C

XN XN offsetv v v

• n-level SPWM scheme uses n-1 level shifted carrier waves• Sinusoidal reference signals are added with offset which centers them within carrier region

max , ,is maximum of AN BN CNv v v v

min , ,is minimum of AN BN CNv v v v

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


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

reference voltages are spanning the inner carrier region, MI < 0.433)

Ta_cross , Tb_cross and Tc_cross : the time duration from the start of switching interval when the reference phase - A, B and C cross the carrier


_

* 4a cross S

AN dc

T T

V V

*_ 4

sa cross AN

dc

TT V

V


*1

* *_

* *_

* *_

for X=A,B,C

4

( 4)4

( 4)4

XN XN offset

sa cross AN as

dc

sb cross BN dc bs s

dc

sc cross CN dc cs s

dc

V V V

TT V T

V

TT V V T T

V

TT V V T T

V


reference voltages are spanning the inner carrier region, MI < 0.433)

T*as , T*

bs and T*cs : Time equivalents of the modified reference signal amplitudes

Carrier- C1

Carrier- C2

Carrier- C2

* * * *

* * * *1 1

,4 4

,4 4

S Sas AN bs BN

dc dc

S Scs CN offset offset

dc dc

T TT V T V

V V

T TT V T V

V V




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

*_

*

*_

*

*_

*

( 4)4

( 2)4

2

( 4)4

Sa cross AN dc

dc

as S

Sb cross BN dc

dc

bs S

Sc cross CN dc

dc

cs S

TT V V

V

T T

TT V V

V

T T

TT V V

V

T T



SUMMARY: Ta_cross , Tb_cross and Tc_cross for various carrier regions to bring the reference within a carrier region

* *

4S

xs XNdc

TT V

V

*

* 4xs S

XN dc

T T

V V

: 4S dcT V



*

* 4as S

AN dc

T T

V V

3600

1800900 270000 wt

ST

2* ST

2* ST

ST

*asT

: 4S dcT VDetermination of the Ta_cross:

Represent the carriers and ref. signals in terms of time equivalents using relationship



*

* 4as S

AN dc

T T

V V

: 4S dcT V

36001800900 270000 wt

ST

2* ST

2* ST

ST

*_a cross as ST T T


Determination of the Ta_cross:

Shift the ref. signal into one carrier region (first +ve carrier) by adding proper offset


*

* 4as S

AN dc

T T

V V

: 4S dcT V

36001800900 270000 wt

ST

2* ST

2* ST

ST

*_a cross as ST T T


Determination of the Ta_cross


_a crossT

*

* 4as S

AN dc

T T

V V

: 4S dcT V

36001800900 270000 wt

ST

2* ST

2* ST

ST

*_ 2a cross as ST T T


Determination of the Ta_cross



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 ( )third cross x crossT T

_ _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 for x=a,b,cgx x cross offsetT T T Inverter leg

switching times

Algorithm for inverter leg switching time calculation: Tfirst_cross , Tsecond_cross and Tthird_cross : the time duration from the start of switching interval when the reference phases cross the carrier for first, second and third time respectively.

, x= a, b, c



The traces of Tgfirst_cross , Tgsecond_cross and Tgthird_cross showing centered time duration for middle vectors

Tgfirst_cross , Tgsecond_cross and Tgthird_cross : the inverter leg switching time for the reference phases which cross the carrier for first, second and third time respectively.

_ _ 2

sec _ sec _ 2

_ _ 2

gfirst cross first cross offset

g ond cross ond cross offset

gthird cross third cross offset

T T T

T T T

T T T





InverterGating SignalsTime

EquivalentsTxs

VAN

VBN

VCN

Toffset1

PWM Compa-rators

Gating Signals

Tgx

Ta_cross,

Tb_cross

Tc_cross

Toffset2

++

Schematic representation of the Multi-level SVPWM



InverterGating SignalsPre-

scaler

TimeEquivalents

Txs

VAN

VBN

VCN

MI

Toffset1

Vs

PWM Compa-rators

Gating Signals

Tgx

Ta_cross,

Tb_cross

Tc_cross

Toffset2

+

+

Implementation of the Multi-level SVPWM with Linear Transfer Characteristics in Over-Modulation

In overmodulation, clamps the reference signals appropriately


0.5

0 wt00 π/2 π

A

SVPWM MODE-I, (θ> π/6)

0.5

0 wt00 π/2 π

A

SVPWM MODE-II, (θ< π/6)

Implementation of the Multi-level SVPWM with Linear Transfer Characteristics in Over-Modulation

Pre-scaler: • Read Modulation Index MI• Determine clamping angle θ and then Clamping level ‘A’ • Clamp the reference signal if it is greater than ‘A’


0

10

20

30

40

50

60

0.9 0.92 0.94 0.96 0.98 10

0.1

0.2

0.3

0.4

0.5

Modulation Index 'MI'

Cla

mp

ing

le

ve

l 'A

'

θ

A


A for3S2

k sin / 6 * ( n 1)T / 2 / 6 / 3

A forS2

3 k sin * ( n 1)T / 2 0 / 6

The clamping angle information is converted into a level signal ‘A’

Prescaler: A simple look-up table of MI vs A


(wt)

Simulation Results: Linear-Modulation Region

Pre-scaler

TimeEquivalents

Txs

VAN

VBN

VCN

MI

Toffset1

Vs

PWM Compa-rators

Gating Signals

Tgx

Ta_cross,

Tb_cross

Tc_cross

Toffset2

++

No clamping of Tas in linear range of modulation

Pre-scaler is inactive in linear modulation range


0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

Tas

T*as

Ta_cross

Tga

(wt)

Simulation Results: Over-Modulation Region (MI: 0.92)

Clamping of Tas in over-modulation (Mode-I)

Pre-scaler is active in over-modulation range


0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

Tas

T*as

Ta_cross

Tga

(wt)



0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

Tas

T*as

Ta_cross

Tga

(wt)


Clamping of Tas in over-modulation (Mode-II)

Pre-scaler is active in over-modulation range


0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

Tas

T*as

Ta_cross

Tga

(wt)



0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

Tas

T*as

Ta_cross

Tga

(wt)

Simulation Results: Over-Modulation Region (MI: 0.98 )


0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 30

2

4x 10

-4

0 0.5 1 1.5 2 2.5 3

-0.8

-0.4

0

0.4

0.8

x 10-3

Tas

T*as

Ta_cross

Tga

(wt)


Square-wave switching mode


Experimental verification: Five-level inverter fed IM drive configuration


Ref: V. T. Somasekhar, K. Gopakumar, “Three - level inverter configuration cascading two 2-level inverters”, IEE Proc. – EPA, Vol. 150, No. 3, May 2003, pp.245-254

+

1C

2C

2dcV

2dcV

Inv1

Inv2

-

• Each three-level inverter configuration by cascading two two-level inverters

• The pole voltage can attain three levels:Vdc/2, 0 ,

-Vdc/2

Inverter-A

Five-level inverter fed IM drive configuration


• Five-level space phasor generation across induction motor windings : Vdc/2,Vdc/4, 0 , -Vdc/4, or -Vdc/2

+

1C

2C

4dcV

4dcV

Inv1

Inv2

-

1C

2C

4dcV

4dcV

+Inv3

Inv4

-Inductionmotor

+ +

- -

Ref: M. R. Baiju, K. K. Mohapatra, V. T. Somasekhar, K. Gopakumar and L. Umanand, “A five-level inverter voltage space phasor generation for an open-end winding induction motor drive”, IEE Proc. EPA, Vol. 150, No. 5, Sept 2003, pp: 531-538

Five-level inverter fed IM drive configuration


Linear-Modulation Region (MI: 0.906)

T*as

Tga

Experimental Results: The traces of pre-scaler output T*as and inverter leg switching time Tga


T*as

Tga

Over-Modulation Region (MI: 0.92)



T*as

Tga




T*as

Tga




T*as

Tga




T*as

Tga

Square wave switching mode (MI: 1.00)



Phase voltage

Tga

Linear modulation region (MI: 0.906)

Experimental Results: The traces machine phase voltage and inverter leg switching time Tga


Phase voltage

Tga




Phase voltage

Tga




Phase voltage

Tga




Phase voltage

Phase current


Experimental Results: The traces machine phase voltage and phase current


Phase voltage

Phase current




Phase voltage

Phase current




Phase voltage

Phase current




Phase voltage

Phase current




Experimental Results: Transition from Linear to square wave switching mode

Top Trace: time equivalent of modified reference signals T*as

Bottom Trace: Inverter gate switching time Tga


Experimental Results: Transition from Linear to six-step mode

Top Trace: Phase voltage, Bottom Trace: Phase current


Fundamental output voltage as a function of modulation index-MI

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MI (%)

Vfu

nd(P

.U.)


90 92 94 96 98 1000

0.05

0.1

0.15

0.2

0.25

MI (%)

nth H

arm

on

ic (

P.U

.)

571113

Harmonic components in the output waveform in the over-modulation region



• A simple n-level PWM signal generation with linear voltage transfer characteristics throughout the modulation range, up to six-step mode of operation

• Linear voltage transfer characteristics in the over-modulation region is achieved by modifying the reference signal such that• the modified reference signal has the same fundamental component as

the original reference signal • modified reference signals are always within the carrier region

• Inverter leg switching times are directly obtained from the sampled amplitudes of reference phase voltages signals

• Does not require any sector identification, sine look-up tables for switching vector identification

• Does not use sector mapping or complex timing calculations

SUMMARY:

Twelve-sided polygonal voltage space vector based multilevel inverter for induction motors.


Topology of a multilevel inverter for generation of 12-side polygonal voltage space vectors for induction motor drives.


Generation of voltage space vectors


0 0 0 01 2. (( 1).30 15 ) . ( .30 15 ) .( )ST V m T V m T V jV

0 0 0 01 2. ( 1).30 . .30 .( ).( 15 15 )ST V m T V m T V jV Cos jSin

0 0 0 01

2. . ( .30 15 ) . ( .30 15 )ST

T V Sin m V Cos mV

0 0 0 02

2. . (( 1).30 15 ) . (( 1).30 15 )ST

T V Sin m V Cos mV

0 0 0 01

2 3.. . ( .30 15 ) . ( .30 45 )S

B C

TT v Sin m v Cos m

V

0 0 0 02

2 3.. . (( 1).30 15 ) . (( 1).30 45 )S

B C

TT v Sin m v Cos m

V


‘Va’ positive ‘Vb-Vc’ positive: 1st quadrant

‘Va’ negative ‘Vb-Vc’ positive: 2nd quadrant

‘Va’ negative ‘Vb-Vc’ negative: 3rd quadrant

‘Va’ positive ‘Vb-Vc’ negative: 4th quadrant


If in quadrant 1:

If |Vb-Vc|<=|Va|.√3.tan150 then sector 1 else

If |Vb-Vc|<=|Va|.√3.tan450 then sector 2 else

If |Vb-Vc|<=|Va|.√3.tan750 then sector 3

else sector 4

If in quadrant 2:If |Vb-Vc|<=|Va|.√3.tan150 then sector 7 elseIf |Vb-Vc|<=|Va|.√3.tan450 then sector 6 elseIf |Vb-Vc|<=|Va|.√3.tan750 then sector 5 else sector 4





V/f scheme for the drive


Comparison to obtain time durations


Pole voltage at 30Hz.

• Voltage levels at 0.366Vdc, 1.0Vdc and 1.366Vdc are observed.


Phase voltage at 30Hz.


Pole voltage at 50Hz.


Phase voltage at 50Hz.


Fig. 14a: Phase voltage and motor current at 15Hz. (X-axis: 1div=20ms, Y-axis: 1div=100V)

Fig. 14b: Pole voltage at 15Hz. (X-axis: 1div=20ms, Y-axis:1div=50V)


Fig. 15a: Phase voltage and motor current at 30Hz. (X-axis: 1div=10ms, Y-axis: 1div=50V)

Fig. 15b: Pole voltage and motor current at 30Hz.(X-axis: 1div=5ms, Y-axis: 1div=50V)


Fig. 16a: Phase voltage and motor current at 45Hz.(X-axis: 1div=10ms, Y-axis: 1div=100V)

Fig. 16b: Pole voltage at 45Hz. (X-axis: 1div=10ms, Y-axis: 1div=50V)


Fig. 17a: Phase voltage and motor current at 50Hz.(X-axis: 1div=5ms, Y-axis: 1div=100V)

Fig. 17b: Pole voltage at 50Hz.(X-axis: 1div=5ms, Y-axis:1div=50V)


Fig. 18: Harmonics at 15Hz operation. (X-axis: nth harmonic, Y-axis: Relative amplitude)


Fig. 19: Harmonics in 30Hz operation. . (X-axis: nth harmonic, Y-axis: Relative amplitude)


Fig. 20: Harmonics in 45Hz operation. (X-axis: nth harmonic, Y-axis: Relative amplitude)


Fig. 21: Harmonics in 50Hz operation. . (X-axis: nth harmonic, Y-axis: Relative amplitude)


Control of Switching Frequency Variation inHysteresis Controller for IM Drives Using

Variable Parabolic Bands for CurrentError Space Phasor


• Common problems associated with the conventional, as well as current error space phasor based hysteresis controllers with fixed bands (boundaries), are the wide variation of switching frequency in a fundamental output cycle and variation of switching frequency with the variation in the speed of the load motor.

• These problems cause increased switching looses in the inverter, non-optimum current ripple, and excess harmonics in the load current, which leads to additional heating in the motor.

Problem of Switching Frequency Variation


Two-Level VSI fed IM Drive

Power Schematic

Voltage Space Phasor Structure

Start of the Sector Middle of the Sector

End of the Sector

k mΔi V Vd

dt L

Directions of Current Error Space Phasor When Different Voltage Vectors are Switched for Different Positions of Vm in Sector-1


• Leakage inductance of the machine (L)• Machine voltage vector (Vm) (dominated by the back

emf vector Vb)• DC-link voltage (as amplitude of Vk is decided by dc-

link voltage) • Current error space phasor ripple ((i))

Factors Influencing the Switching Frequency Variation

( )

k m

Δi

V V

Lt


• Over a fundamental period, the position of Vm varies with respect to the inverter voltage vectors of space phasor structure.

• Also, the selected inverter voltage vector Vk (V1, …, V8) keeps on changing in a fundamental cycle during hysteresis PWM current control.

• Therefore, either the inverter switching frequency or/and the current error space phasor ripple will vary over a fundamental inverter period.

Variation of Switching Frequency inHysteresis Current Controller


• For the given operating speed, if the shape of the fixed boundary of the current error space phasor is not properly selected, the switching frequency of inverter will vary over a fundamental cycle.

• Further to this, if the same boundary of current error space phasor is maintained at different operating speeds of the machine (for different fundamental values of the machine back emf) then also the inverter switching frequency will vary.

Variation of Switching Frequency in HysteresisCurrent Controller (Contd…)


Investigation of Current Error Space Phasor inVC-SVPWM based VSI fed IM Drives

Typical SVPWMswitching pattern

of the invertervoltage vectors

for two consecutivePWM

switching intervals

Investigation of Current Error Space Phasor in VC-SVPWM based VSI fed IM Drives (Contd…)

* *m m

1 S 2 S 0 S 1 2dc dc

V Vsin(60° -θ) sinθT = T , T = T , and T = T - (T + T )

V sin60° V sin60°

Switching times for inverter voltage vectors in a switching interval

Investigation of Current Error Space Phasor in VC-SVPWM based VSI fed IM Drives (Contd…)

Current error space phasor during switching of various voltage vectors

hence k k

k k

kk

*(V ) (V )k m

(V ) (V )

(V )(V )

Δi ΔVV VΔi

Δi ΔV

ΔVΔi

σ

σ

σ

dd,

dt L dt L

ddt dt

dt L

tL

Specific form for Sector-1

1 2 0T T and T01 21 2 0

(V )(V ) (V )(V ) (V ) (V )

ΔVΔV ΔVΔi Δi Δi

σ σ σ

= , = , =L L L

Movement of current error space phasor (on - plane) in a few sampling intervals of VC-SVPWM based two-level VSI fed IM drive

[Y-axisAnd

X-axis:Current

InAmperes]

Vm at start of the sector( varies from 0 to 7)

Vm at middle of the sector( varies from 27 to 33)

Vm at end of the sector( varies from 54 to 60)

Approximate theoretical boundary of i for VC-SVPWM based two-level VSI fed IM drive for position of Vm in Sector-1

[Y-axisAnd

X-axis:Current

InAmperes]

10 Hz 20 Hz

30 Hz 40 Hz

Simulation results for VC-SVPWM based two-level VSI fed IM drive

10 Hz Operation


20 Hz Operation


30 Hz Operation


35 Hz Operation


41 Hz Operation

Comparison of boundary obtained by theoretical calculations and simulation studies for VC-SVPWM based two-level VSI fed IM drive

10 Hz 20 Hz 30 Hz 40 Hz0.1 A/div. 0.2 A/div. 0.2 A/div. 0.5 A/div.

Theoretical

Simulation

Establishing variable boundary for proposed hysteresis controller

The parabola is defined as the locus of a point which moves so that it is always at the same distance from a fixed point (called the focus) and a given line (called the directrix).

•Formula for a vertical parabola (having Y-axis as axis of symmetry) with the vertex on (h, k), is: (x-h)2=4p(y-k).

•Formula for a horizontal parabola (having X-axis as axis of symmetry) with the vertex on (h, k), is: (y-k)2=4p(x-h).

Here, p is the distance betweenvertex and focus of the parabola.

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

Equivalent new X-axis and Y-axis for the parabolas of current error space phasor boundary in different sectors

Sectors X-axis Y-axis

1, 4 B-axis jB-axis

2, 5 A-axis jA-axis

3, 6 C-axis jC-axis


Generalized technique to find the parameters of the boundary defining parabolas for given induction motor

Generalized Technique(Matlab Program)

Developed in Proposed Work

input output

(x, y),(h, k),

pFor boundary

defining parabolasfor operating

frequencyfrom 1 Hz to 45 Hzwith the resolution

of 1 Hz

Vdc,Base_freq,

L,TS,

Boundary for proposed hysteresis controller with new reference axis

1

2

0

22(V ) m dc m dc

22(V ) m dc m dc

(V ) m

ΔV = V + V - 2 V V cosθ

ΔV = V + V - 2 V V cos(60° - θ)

ΔV = V

0

0

(V )0

(V ) σ

=0

=0

ΔVTΔi L

x1_new = sin30 = sin302 2

0

0

(V )0

(V ) σ

=0

=0

ΔVTΔi L

y1_new = cos30 = cos302 2

0

0

(V )0

(V ) σ

=30

=30

ΔVTΔi L

k2_new = =2 2

0

2

0

1

22 (V )

(V ) θ=30°θ=30°

22 (V )

(V ) θ=30°θ=30°

Δih1_new = Δi -

2

Δih3_new = Δi -

2

dcm

(ope_freq)

ope_freq in Hz x 0.955VV =

50 Hz


Parameters of boundary defining parabolasfor proposed hysteresis controller

2

2

2

2

p1 = (y1_new - k1_new) 4(x1_new - h1_new)

p2 = (x2_new - h2_new) 4(y2_new - k2_new)

p3 = (y3_new - k3_new) 4(x3_new - h3_new)

p4 = (x4_new - h4_new) 4(y4_new - k4_new)

x1_new, y1_new h1_new,k1_new




Output of the generalized technique in terms of parameters of boundary defining parabolas

Output of the generalized technique in terms of the current error space phasor boundary for different operating frequencies

[conventional Y-axis and X-axis: 1div.=0.5 A]


Voltage vector selection in Sector-1 for forward as well as reversedirection of rotation of machine

Present vector“ON”

Conditions to be satisfied and next vector to be switched “ON”

(y2-4p1 (x-h1)) 0

up to 24 Hz operation (x2-4(p2 (y-k2))) 0

25 Hz onwards operation (x2-4(p2 (y-k2))) 0

(y2-4(p3 (x-h3))) 0 up to 24 Hz operation

(x2-4(p4(y-k4))) 0

25 Hz onwards operation

(x2-4(p4(y-k4))) 0

ijC 0 &

ijA 0

ijA 0

&ijB 0

ijC0 & ijA0 ijC 0

&ijA 0

ijC 0

&ijB 0

ijC 0 & ijA 0

V1 - - - V2 - V7

V2 V1 - - - - V8

V7 - V1 V1 - V2 -

V8 - V1 V2 - V2 -

Sector changed detection using outer parabolic boundary

[Y-axis: 1div.=0.2 A and X-axis: 1div.=0.5 A]


Sector change detection logic (based on outer parabolic bands)for forward rotation of machine

From sector

Presentvector “ON”

Condition to be satisfied for the sector change and next sector to be considered as new sector

(y2-4(p3_outer(x-h3_outer))) 0

(y2-4(p1_outer(y-h1_outer))) 0

ijA < 0 &

ijB < 0

ijB < 0 &

ijC < 0

ijC < 0 &

ijA < 0

ijC 0 &

ijA 0

ijA 0 &

ijB 0

ijB 0 &

ijC 0

1 V2 or V7 or V8 2 * * * * *

2 V3 or V7 or V8 * * * 3 * *

3 V4 or V7 or V8 * 4 * * * *

4 V5 or V7 or V8 * * * * 5 *

5 V6 or V7 or V8 * * 6 * * *

6 V1 or V7 or V8 * * * * * 1(‘*’ means continue with the same sector)

Simulation results of proposed hysteresis controller

10 Hz Operation


10 Hz Operation


20 Hz Operation


20 Hz Operation


30 Hz Operation



30 Hz Operation


35 Hz Operation



35 Hz Operation


40 Hz Operation

Comparison of boundary obtained by theoretical calculations and simulation studies for VC-SVPWM based two-level VSI fed IM drive

10 Hz 30 Hz 35 Hz 40 Hz

SVPWM Simulation

Proposed Hysteresis Controller Simulation



47 Hz Operation


Six-Step Mode of Operation


Block schematic of experimental set-up used for proposedhysteresis controller

Experimental results of proposed hysteresis controller

10 Hz Operation

vAN, 130 V/div.

iA, 1.3 A/div.

i, Sector-1 i, Sector-2 i, Sector-3

i, 0.2 A/div.



10 Hz Operation

iA, 1.3 A/div.

iA*, 1.3 A/div.

i, 1 A/div.


20 Hz Operation

vAN, 130 V/div.

iA, 1.3 A/div.


i, 0.35 A/div.


20 Hz Operation

iA, 1.3 A/div.

iA, 1.3 A/div.

iA*, 1.3 A/div.

iA*, 1.3 A/div.

i, 1 A/div.


30 Hz Operation

vAN, 135 V/div.

iA, 1.3 A/div.


i, 0.45 A/div.


30 Hz Operation

iA*, 1.3 A/div.

iA, 1.3 A/div.

iA, 1.3 A/div.

iA*, 1.3 A/div.

i, Sector-3, 0.45 A/div.

i, 1 A/div.


35 Hz Operation

vAN, 130 V/div.

iA, 1.3 A/div. i, 0.55 A/div.

i, Sector-2, 0.55 A/div. i, Sector-3, 0.55 A/div. i, Sector-3-4, 0.55 A/div.



35 Hz Operation

iA*, 1.3 A/div.

iA, 1.3 A/div.

iA, 1.3 A/div.

iA*, 1.3 A/div.


40 Hz Operation

vAN, 130 V/div.

iA, 1.3 A/div.

i, Sector-1, 0.6 A/div. i, Sector-2, 0.6 A/div. i, Sector-3, 0.6 A/div.

i, 0.6 A/div.


40 Hz Operation

iA, 1.3 A/div.

iA*, 1.3 A/div.

iA, 1.3 A/div.

iA*, 1.3 A/div.

i, Sector-4-5, 0.6 A/div.



45 Hz Operation

vAN, 130 V/div.

iA, 1.3 A/div. i, 0.6 A/div.



47 Hz Operation

vAN, 130 V/div.

iA, 1.3 A/div. i, 0.5 A/div.


50 Hz Operation(Six-Step Mode)

vAN, 130 V/div.

iA, 1.3 A/div.

i, 0.65 A/div. i, 1.4 A/div.


Acceleration Transients

vAN, 130 V/div.

iA, 1.3 A/div.


Starting Operation

vAN, 160 V/div.

iA, 1.3 A/div.

iA, 1.5 A/div.

iA*, 1.5 A/div.

iA, 1.7 A/div.

speed, 910 rpm//div.


Starting Operation

vAN, 160 V/div.

iA, 1.3 A/div.

iA*, 1.5 A/div.

iA, 1.5 A/div.

iA, 1.7 A/div.



Speed Reversal

vAN, 130 V/div.

iA, 1.1 A/div.

iA, 1.5 A/div.

iA, 1.35 A/div.

iA*, 1.35 A/div.



Speed Reversal

vAN, 130 V/div.

iA, 1.1 A/div.

iA, 1.5 A/div.

iA*, 1.5 A/div.

iA, 1.65 A/div.



• Current error space phasor based simple hysteresis controller

• Controls the switching frequency variation in a two-level VSI fed IM drive

• Based on the novel concept of on-line variation of hysteresis band, depending upon the speed of the machine

• Uses parabolic boundary for the current error space phasor

• Obtains switching frequency spectrum in the output voltage similar to that of the constant switching frequency VC-SVPWM based VSI fed IM drive.

Salient features of the proposed hysteresis controller


• Performance of the proposed controller is independent of the load machine parameters

• The unique parabolic boundary for different operating speeds for any given induction motor is determined using generalized technique (Matlab program) developed in proposed work

• Calculation of machine back emf vector is not needed

• Sector change logic is self-adaptive and is capable of taking the drive up to six-step mode of operation, if needed

• Controller always selects the adjacent inverter voltage vectors, forming a sector, in which the tip of the machine voltage vector lies

Salient features of the proposed hysteresis controller(Contd…)


Multimotor drive setup


Multimotor drive setup



Inverter setup for multilevel structure


Inverter setup for multilevel structure





Documents

CEDT, INDIAN INSTITUTE OF SCIENCE, BANGALORE, INDIA 1 Combined voltage space vector locations of a dual five-level inverter fed open-end winding IM drive