1

Advanced Topics in PWM for Voltage Source Converters

Assoc. Prof. Laszlo Mathe

Aalborg University, Dept. of Energy Technology

lam@et.aau.dk

www.et.aau.dk

2

Outline

• Introduction

• Basic inverter topologies

• Basic Modulation techniques

• Zero vector placement modulation techniques

• Performance of different PWM methods

3

Electrical energy conversion

• The residential and industrial electric grid supplies AC voltage with fixed amplitude and frequency

• Most of the low power devices like TV, PC etc. are using DC voltages typically 3-5-12V, - AC to DC conversion is needed

• Devices like washing machine, vacuum cleaner uses electrical motor drives, where the rotor speed is controlled through the amplitude and the frequency of the supplied voltage, - AC to AC conversion is needed

4

Electrical energy conversion

• The AC to AC conversion can be done by using a transformer. However, only the amplitude of the voltage can be changed to a fixed value

• DC to AC conversion can be done with transistors operating in linear range, typical application is the audio amplifier, the conversion efficiency is very low

• In order to achieve high efficiency in energy conversion, modulation based on on-off switching converters should be used

5

Modulation

• Modulation is a method to transmit a low frequency signal by varying a high frequency signal’s amplitude, frequency or phase

• It is the basic element for telecommunication and power electronics

• In power converters Pulse Width Modulation (PWM) technique is used, which is a method to create the on-off switching pattern for the power switches

6

Power semiconductor switches

• The converters are built from semiconductors based power switches which are: – Uncontrolled (Diode) – conducts the current when the

voltage across the anode and cathode is positive

– Half Controlled (Thyristor) – conduct current when the gate signal is applied and the anode and cathode is positive (it turns off uncontrolled when anode-cathode voltage is negative)

– Full Controlled (Transistor) – When a pulse is applied on the gate signal the transistor conducts (it can be turned on-off any time)

7

Power semiconductor switches

• Ideal switches do not exist (only in simulation), parasitic resistance, inductance and capacitance is always present

• The losses in a switch are caused by:

– On-resistance - when the switch is in conduction mode it acts like a resistor

– Switching loss – energy is need in order to turn on and off the device

8

Outline

• Introduction

• Basic inverter topologies

• Basic Modulation techniques

• Zero vector placement modulation techniques

• Performance of different PWM methods

9

Half Bridge (HB) Voltage Source Inverter (VSI)

– It has to be avoided to turn on both Sw1 and Sw2 at the same time (Vdc shoot through is created)

– The antiparallel diodes are needed to give free path for the current in case of inductive load

qa State Vl

0 Sw1 – off & Sw2 – on -Vdc/2

1 Sw1 – on & Sw2 – off Vdc/2

+

-dcV

2

dcV

2

dcV

aq

aq

lV

Loadn

li

1Sw

2Sw

Modulator

10

Hardware limitation – Dead time

• Due to the parasitic inductance and capacitance the voltage/current is maintained for a short time after the gate signal goes to zero (highlighted region in the fig.)

Turn off transient of a MOSFET

• The other switch should be turned on always after this transient period is over, otherwise, shoot-through appears which destroys the semiconductor device

11

Hardware limitation – Minimum Pulse Width

• The MPW filters duty is to block the pulses which duration is less than the double of the dead-time

• The short pulses creates only losses because the switch is not able to turn on-off properly

• MPW filter and dead-time causes nonlinearities which has to be considered in some application, compensation techniques have to be applied

12

Full Bridge (H-bridge) VSI

• Positive and negative Vdc can be applied on the load

• Three voltage levels can be applied on the load (± Vdc and 0)

qa qb Vl

0 0 0

0 1 Vdc

1 0 -Vdc

1 1 0

+

-dcV

2

dcV

2

dcV

aq

aq

lV

Load

nai

1Sw

2Sw

bq

bq

3Sw

4Sw

li

Modulator

13

1

2dcV

1

2dcV

Aq

Aq

dcV

nA

Bq

B

Cq

Cq

C

ANv BNv CNv

Bq

ABv

BCv

ACv

Modulator

Three phase bridge-type VSI

• Phase (VAN, VBN ,VBN) and line-to-line (VAB, VAC ,VBC) Voltages are created

• Relationship between them:

• Half-bridge arrangement can be extended to ‘n’ phases

3AB AN BN ANV V V V

14

Applications

• Electrical motor drives:

• Single phase grid connected PV systems:

Grid

N

L

FilterFilterBoost without trafo FB inverterFilterPV Array

S5

S1 S3

S2 S4

D1 D3

D2 D4

D5

15

Outline

• Introduction

• Basic inverter topologies

• Basic Modulation techniques

• Zero vector placement modulation techniques

• Performance of different PWM methods

16

Modulation techniques for half bridge

• Spectrum of rectangular signal contains low frequency harmonics

• Amplitude of the signal is fixed

• Modulation allows amplitude control

+

-dcV

2

dcV

2

dcV

aq

aq

lV

Loadn

li

1Sw

2Sw

Modulator

17

Pulse generation techniques

• In order to generate the train of pulses several methods exist:

– Carrier Based PWM (ST, SVM, RPWM, DPWM)

– Hysteresis Based PWM

– Programmed PWM (MP-PWM, Optimum PWM, HE-PWM)

Remark: During one modulation period unity gain has to be ensured

PWM Vref Vout

Filter

18

Sine Triangular PWM

• Oldest and simplest method to generate PWM pulses

• High frequency triangular or saw-tooth carrier signal is compared with the reference signal

19

Triangular vs. Saw tooth Carrier

• Different spectral properties can be achieved

Over-modulation

1

0

1

t

1

0

1

t

• In case the amplitude of the reference signal is larger than the amplitude of the carrier wave, low frequency harmonics are introduced

• A little increase in the amplitude of the fundamental component can be achieved

• In over-modulation the modulator is not linear

21

Modulation index

• Normalized output voltage amplitude

00

2,

dc

VMi whereV is the RMS reference voltage

V

Output Mi

1

0

0.785

Refrernce Mi0.785 1,57

Linear

region

22

Modulation for H-bridge

Unipolar PWM

+

-dcV

2

dcV

2

dcV

aq

aq

lV

Load

nai

1Sw

2Sw

bq

bq

3Sw

4Sw

li

Modulator

+

- Sw1

Sw2

Sw3

Sw4

+

-

+

-

Sw1

Sw2

Sw3

Sw4

-1

Bipolar PWM Hybrid PWM +

- Sw1

Sw2

+

-Sw3

Sw4

+

-

• More possibilities with different advantage / disadvantage

23

1

2dcV

1

2dcV

Aq

Aq

dcV

nA

Bq

B

Cq

Cq

C

ANv BNv CNv

Bq

ABv

BCv

ACv

Modulation for Three phase inverter

• Three 1200 shifted reference signals are compared with triangular carrier

t

T

t

1

0

Reference Signals PWM Signals

t

t

t

aq

bq

cq

Reference voltage for Phase A

Reference voltage for Phase BReference voltage for Phase C

1

24

Outline

• Introduction

• Basic inverter topologies

• Basic Modulation techniques

• Zero vector placement modulation techniques

• Performance of different PWM methods

Magnetic force between a coil and PM • Passing a current through a coil alines the magnet; reversing the current the

magnet will rotate the magnet by 1800 (direction of the rotation is not defined)

• With second pair of coils the direction of the rotation can be defined

• Better space usage can be achieved by placing three pair coils, 1200 shifted in space

• The three or multi phase system can always be reduced to a d-q system

i

i

s

n

n

n

s

s

q

s

n

n

n

s

i

n

i

n

s

s

s

d

q

s

nd

q

a

b

c

nn

ss

Rotating field generation

- During one fundamental period one revolution of the voltage vector is obtained through 6 fixed vectors

110v010v

011v

001v 101v

100vd

q

Vmax

Six Step mode operation

• Highest amplitude for the fundamental (end of over-modulation range)

• The RMS of the phase-neutral voltage is:

• Low frequency components appears in the output voltage spectrum

Van

Vbn

Vcn

2Vdc /3

-2Vdc /3

Vdc /3

-Vdc /30

2Vdc /3

-2Vdc /3

Vdc /3

-Vdc /30

-2Vdc /3

Vdc /3

-Vdc /30

t

t

t

2Vdc /3

2 DCV

t

t

t

t

aq

bq

cq

T

0zvt 1zvt 0zvtavt avt

XcXaXb

+Vdc

Xc

Xa

Xb

-Vdc

+Vdc

Xc

Xa Xb

+Vdc

-Vdc

XcXaXb

-Vdc

Xc

Xa Xb

+Vdc

-Vdc

Xc

Xa

Xb

-Vdc

+Vdc

XcXaXb

-Vdc

Space vector representation

- With the two level VSI 6 active and 2 zero sequence voltage vectors can be generated

- The ratio between the time while two active vectors are generated gives the position of the resultant voltage vector (Vs) in d-q plain

- The ratio between the time when active and zero vectors are applied sets the amplitude of the same vector

1

2dcV

1

2dcV

Aq

Aq

dcV

N

A

Bq

B

Cq

Cq

C

ANv BNv CNv

Loadcmvv

Bq

ABv

BCv

ACv

sV

110v010v

011v

001v 101v

100vd

q

211

0

dv

1 100d v

Xc

Xb

Xa

-Vdc

+Vdc

Xa

Xc Xb

+Vdc

-Vdc

Xc

Xa

Xb

-Vdc

+Vdc

Xa

Xc

Xb

-Vdc

+Vdc

Xb

Xa Xc

+Vdc

-Vdc

XcXa Xb

-Vdc

XcXa Xb

+Vdc

zero sequence voltage vectorsXc

Xa Xb

+Vdc

-Vdc

t

T

1

0

zoom

Calculation of timing for the vectors

- where d is the duty cycle (number between 0-1) multiplied with Tmod gives the timing

- Vs varies between 0-1 and it does not depend on the ratio between tzv1 and tzv2

1 2s x yV d v d v

1

2

1 2

3 sin( )

3 sin( )3

1

s

dc

s

dc

zv

Vd

V

Vd

V

d d d

t

t

t

t

aq

bq

cq

0zvt 1zvt 0zvtavt avt

modT

sV

110v010v

011v

001v 101v

100vd

q

211

0

dv

1 100d v

Third harmonic injection (TH-PWM)

:

AB AN BN AN T BN T

BC BN CN BN T CN T

AC AN CN AN T CN T

T

v v v v v v v

v v v v v v v

v v v v v v v

where v is the third harmonic

Again, relationship between the phase and line voltages:

Note: by adding the same voltage (VT) to the phase voltages it will not affect the line to line voltage!

Third harmonic injection waveform

- The peak of the phase voltages is reduced by around 15% - From modulation point of view 3rd harmonic injection

changes only the time ratio between the applied 2 zero vectors during a modulation period

- Same principles can work with 9th and 15th harmonics

t

rd3 Harmonic added to the reference signals

3rd harmonic

15%

Implementation TH-PWM

qa

qb

• The 3rd harmonic has to be in phase with one of the three reference signals

• Usually the amplitude of the 3rd is 1/4th or 1/6th of the reference signal

qc

33

Space Vector Modulation (SVM)

• Minimal current ripple can be achieved during one modulation period by applying for the two zero vectors the same duration

t

modT

1

1

Reference Signals SVM

0

cmvu

0 1 mod

1

2zv zv zvt t d T

34

1200 Discontinuous PWM

t

T1

0

DPWM MAX

1

t

PWM Signals

t

t

t

aq

bq

cq

T

0zvt 0zvtavt

cmvu

t

1

0

1

0 mod 1

1 mod 0

0

0

zv zv zv

zv zv zv

t d T and t or

t d T and t

DPWM MIN

• Number of switching are reduced by 25%

• Only one zero voltage vector is generated for 1200

• Increased stress for the switch which conducts 1200

35

300 Discontinuous PWM

DPWM0 DPWM1

DPWM2 DPWM3

• The increased stress, due to 1200 conduction of a switch, can be reduced by changing between DPWM-MAX and DPWM-MIN in each 300

36

0.902MI

1V

refV

Output MI

1

0

0.902

0.785

0.900.78 1.57

Ove

r-M

od

ula

tio

n

reg

ion

Linear

region

Reference MI

2V

23

DCV

Modulation index – Three Phase Inverter

• Normalized output voltage amplitude

• Note: The modulation index can be also defined to be 1 at the end of the linear range

1

1 ,6

*

1 ,6

2

m

m step dc

m step

V V

VMI

V

Other representation of the SVM • Time representation of 7th harmonic injected and SVM in Cartesian

coordinates

NOTE: In SVM representation the zero vector distribution is not visible

T

0tz0

tav1

tav2

tz1

tz0

tav1

tav2

tz1

Carrier wave Carrier wave

0.5*T

γ (deg)0 50 100 150 200 250 300 350

Position of reference voltage vectror γ (deg)

γ (deg)0 50 100 150 200 250 300 350

Position of reference voltage vectror γ (deg)

Polar coordinate representation

SVM representation

L. Mathe, et al., "Shaping the spectra of the line-to-line voltage using signal injection in the common mode voltage," IEEE conference proceedings, 2009.

38

Zero vector-less modulation: AZSPWM

• In order to reduce the CMV instead the zero sequence vectors two opposite active vectors can be applied

sV

110v010v

011v

001v 101v

100vd

q

211

0

dv

1 100d v

3 010d v

4 101d v

3 4

1

2zvd d d

Disadvantage: • Very high current ripple • Implementation difficulties

39

Outline

• Introduction

• Basic inverter topologies

• Basic Modulation techniques

• Zero vector placement modulation techniques

• Performance of different PWM methods

40

Output Voltage Linearity

A. M. Hava, et al., "Simple analytical and graphical methods for carrier-based PWM-VSI drives," Power Electronics, IEEE Transactions on, vol. 14, pp. 49-61, 1999.

41

Harmonic Distortion Function

A. M. Hava, et al., "Simple analytical and graphical methods for carrier-based PWM-VSI drives," Power Electronics, IEEE Transactions on, vol. 14, pp. 49-61, 1999.

42

Switching Loss Function for DPWM

A. M. Hava, et al., "Simple analytical and graphical methods for carrier-based PWM-VSI drives," Power Electronics, IEEE Transactions on, vol. 14, pp. 49-61, 1999.

43

Summary

• Half Bridge topology widely used in power electronics can be extend to poly-phase

• ST-PWM - has limited linear range • TH-PWM – extended linear range • SVM – has minimal current ripple • DPWM – Reduced switching losses • AZSPWM – Reduced CMV • Over-modulation – Fundamental amplitude increased, low

frequency harmonics are introduced Many more modulation strategies exit they offer no or very small benefit compared to the 5 basic method