88307a.ppt

8/10/2019 88307a.ppt

1/48

Topic 7: Pulse Width Modulation

Techniques for Voltage-Fed

Inverters

Spring 2004

ECE 8830 - Electric Dr

ives

8/10/2019 88307a.ppt

2/48

Introduction

While the 36-step inverter offers simplecontrol and low switching loss, lower order

harmonics are relatively high leading tohigh distortion of the current wave (unlesssignificant filtering is performed).

PWM inverter offers better harmonic controlof the output than 6-step inverter.

8/10/2019 88307a.ppt

3/48

PWM Principle

The dc input to the inverter is choppedby switching devices in the inverter. Theamplitude and harmonic content of the acwaveform is controlled by the duty cycleof the switches. The fundamental voltagev1has max. amplitude = 4Vd/for a

square wave output but by creatingnotches, the amplitude of v1is reduced(see next slide).

8/10/2019 88307a.ppt

4/48

PWM Principle (contd)

8/10/2019 88307a.ppt

5/48

PWM Techniques

Various PWM techniques, include:

Sinusoidal PWM (most common)

Selected Harmonic Elimination (SHE)PWM

Space-Vector PWM

Instantaneous current control PWM

Hysteresis band current control PWM

Sigma-delta modulation

8/10/2019 88307a.ppt

6/48

Sinusoidal PWM

The most common PWM approach issinusoidal PWM. In this method a

triangular wave is compared to asinusoidal wave of the desiredfrequency and the relative levels of thetwo waves is used to control the

switching of devices in each phase legof the inverter.

8/10/2019 88307a.ppt

7/48

Sinusoidal PWM (contd)

Single-Phase (Half-Bridge) Inverter

Implementation

8/10/2019 88307a.ppt

8/48


when va0> vTT+on; T-off; va0= Vd

va0< vTT-on; T+off; va0= -Vd

8/10/2019 88307a.ppt

9/48


8/10/2019 88307a.ppt

10/48


Definition of terms:

Triangle waveform switching freq. = fc(alsocalled carrier freq.)

Control signal freq. = f (also called modulationfreq.)

Amplitude modulation ratio, m = Vp

VT

Frequency modulation ratio,

mf(P)= fc/ f

Peak amplitude

of control signal

Peak amplitude

of triangle wave

8/10/2019 88307a.ppt

11/48


Harmonics

Note: Nearly independent of mf (P)for mf9.

8/10/2019 88307a.ppt

12/48


Harmonics (contd)

8/10/2019 88307a.ppt

13/48


At high fcthe nominal leakage inductanceof the machine will effectively filter outthe inverter line current harmonics at

high switching frequencies. High fcleadsto higher switch lossesbut lower machineharmonic loss.

Choose mf (P) = odd integer it eliminateseven harmonics.

8/10/2019 88307a.ppt

14/48


At m=1, the max. value of fundamentalpeak voltage =0.5Vd= 0.7855 . Vpk

sq.wave

(=4Vd/2). This max. value can be

increased to 0.907Vpksq.waveby injecting3rd order harmonics- this is a commonmode voltage and does not affect torqueproduction.

8/10/2019 88307a.ppt

15/48


Overmodulation (m > 1.0)

Gives non-linear control and increases

harmonics but results in greater output.

Vd < ( VA0)1< 4 Vd for m >1.

2 2

(see text)

8/10/2019 88307a.ppt

16/48


Two regions of operation - constant torqueand constant power.

For constant power, max. voltage obtainedby operating inverter in square wave mode.

For constant torque, voltage can be

controlled by PWM principle.

8/10/2019 88307a.ppt

17/48

8/10/2019 88307a.ppt

18/48

Single Phase Half-Bridge Inverter

C+, C- large and equal => voltage dividesexactly between capacitors at all times.

The current i0must flow through parallelcombination of C+and C-=> i0has no dc

component in steady state.

8/10/2019 88307a.ppt

19/48

Single Phase Full-Bridge Inverter

Essentially two one-leg inverters with the

same dc input voltage.Max. output voltage = 2 x max. output

voltage of -bridge. => output current is half

(useful at high powers since it means lessparalleling of devices.)

8/10/2019 88307a.ppt

20/48

Square Wave Inverter

V01 = 4 Vd

No pulse width control . Frequencycontrol is possible. Amplitude control is

possible if Vdis varied.

v0Vd

-Vd

full

bridge

V01

8/10/2019 88307a.ppt

21/48

Bipolar PWM Switching

8/10/2019 88307a.ppt

22/48

Bipolar PWM Switching (contd)

Switch pairs: (TA+,TB- ) and (TB+, TA-)

Output of leg B is negativeof leg A

output => vB0(t) = -vA0(t)=>v0(t)=2vA0(t)

Peak of fundamentalfrequency

component, V01= maVd (ma< 1.0)

Vd< V01< 4 Vd (ma> 1.0)

8/10/2019 88307a.ppt

23/48

Dead Time Effect

Because of finite turn-on time and turn-off time of switches, you wait a blankingtime, tdafter switching one switch off in

a leg before switching on the otherswitch in the same leg. The blankingtime will increaseor decreasethe outputslightly depending on the directionof the

load current.

Also, additional high frequencies appearin the output waveform.

8/10/2019 88307a.ppt

24/48

Dead Time Effect (contd)

8/10/2019 88307a.ppt

25/48

8/10/2019 88307a.ppt

26/48

Selective Harmonic Elimination

By placing notchesin the output waveformat proper locations, certain harmonics canbe eliminated. This allows lower switchingfrequencies to be used -> lower losses,higher efficiency.

8/10/2019 88307a.ppt

27/48


(contd)

General Fourier series of wave is given by:

where

and

1

( ) ( cos sin )n nn

v t a n t b n t

2

0

1( ) cos( ) ( )na v t n t d t

2

0

1( ) sin( ) ( )nb v t n t d t

8/10/2019 88307a.ppt

28/48


(contd)

For a waveform with quarter-cyclesymmetry, only the odd harmonics withsine components will appear, i.e. an=0

and

where

1

( ) sinnn

v t b n t

2

0

4 ( ) sin( ) ( )nb v t n t d t

8/10/2019 88307a.ppt

29/48


(contd)

It can be shown (see text forderivation) that

Thus we have K variables (i.e. 1, 2,3, ... K) and we need K simultaneous

equations to solve for their values.WithK angles, K-1 harmonics can beeliminated.

1

41 2 ( 1) cos

KK

n KK

b nn

8/10/2019 88307a.ppt

30/48


(contd)

Consider the 5th and 7th harmonics (the3rd order harmonics can be ignored if themachine has an isolated neutral). ThusK=3 and the equations can be written as:

Fundamental:

5th Harmonic:

7th Harmonic:

1 1 2 3

4(1 2 cos 2 cos 2 cos )b

5 1 2 3

4(1 2 cos 5 2 cos 5 2 cos 5 ) 0

5b

7 1 2 3

4(1 2 cos 7 2 cos 7 2 cos 7 ) 07b

8/10/2019 88307a.ppt

31/48


(contd)

These transcendental equations can besolved numerically for the notch angles1, 2, and3for a specified fundamental

amplitude. For example, if thefundamental voltage is 50% (i.e. b1=0.5)the values are:

1=20.9,

2=35.8, and

3=51.2

This approach can easily be implementedin a microcomputer using a lookup tablefor notch angles (see text).

8/10/2019 88307a.ppt

32/48


(contd)

8/10/2019 88307a.ppt

33/48

Space-Vector PWM

Space vector PWMis an advanced,computationally intensive technique thatoffers superior performance in variable-

speed drives. This technique has theadvantage of taking account of interactionamong the phases when the load neutralis isolated from the center tap of the dc

supply. Space vector PWM can be used tominimize harmonic content of the three-phase isolated neutral load.

This approach is discussed in detail in the

textbook.

8/10/2019 88307a.ppt

34/48

Current Regulated PWM

The flux and torque output of an ac motoris directly controlled by the current inputto the motor. Thus having current control

on the output of a voltage-fed converterwith voltage control PWM is important. Afeedback current loop is used to controlthe machine current.

Two PWM techniques for current controlwill be considered:

1. Instantaneous Current Control

2. Hysteresis Band Current Control

8/10/2019 88307a.ppt

35/48

Instantaneous Current Control

The below figure shows an instantaneouscurrent control scheme with sinusoidal PWMin the inner control loop.

8/10/2019 88307a.ppt

36/48

Instantaneous Current Control

(contd)

Actual current i is compared to commandedcurrent i* and the error fed to a proportional-integral (P-I) controller. The rest of the

circuit is the standard PWM topology. For a3inverter, three such controllers are used.

Although the control approach is simple, thismethod produces significant phase lag athigh frequencies which are very harmful tohigh-performance drives.

8/10/2019 88307a.ppt

37/48

Hysteresis-Band Current Control

In hysteresis-band current control theactual current tracks the command currentwithin a hysteresis band.

In this approach a sine reference currentwave is compared to the actual phasecurrent wave. As the current exceeds aprescribed hysteresis band, the upperswitch in the half-bridge is turned off andthe lower switch is turned on. As thecurrent goes below the hysteresis band,

the opposite switching takes place.

8/10/2019 88307a.ppt

38/48

Hysteresis-Band Control (contd)

8/10/2019 88307a.ppt

39/48


With upper switch closed, the positivecurrent slope is given by:

where 0.5Vdis the applied dc voltage,

Vcmsinet is the opposing load counter EMF,and L = effective load inductance.

Similarly, with the lower switch closed, thenegative current slope is given by:

0.5 sind cm eV V tdi

dt L

(0.5 sin )d cm e

V V tdi

dt L

8/10/2019 88307a.ppt

40/48


Pk-to-pk current ripple and switching freq.are related to width of hysteresis band.Select width of hysteresis band to

optimally balance harmonic ripple andinverter switching loss.

Current control tracking is easy at low

speed but at high speeds, when counterEMF is high, current tracking can be moredifficult.

8/10/2019 88307a.ppt

41/48


A simple control block diagram forimplementing hysteresis band PWM isshown below:

8/10/2019 88307a.ppt

42/48


The error in the control loop is input to aSchmitt trigger ckt. The width of thehysteresis band HB is given by:

Upper switch on: (i*

-i) >HBLower switch on: (i*-i)

8/10/2019 88307a.ppt

43/48


This approach is very popular because ofsimple implementation, fast transientresponse, direct limiting of device pk.current, and practical insensitivity to dclink voltage ripple (=> small filtercapacitor).

However, PWM freq. is not const. which

leads to non-optimal harmonic ripple inmachine current. Can be overcome byadaptive hysteresis band. Also, significantphase lag at high freqs. is a drawback of

this method for high-performance drives.

8/10/2019 88307a.ppt

44/48

Sigma Delta Modulation

Sigma-delta modulation is a usefultechnique for high frequencylink converter

systems - uses integral half-cycle pulses togenerate variable freq., variable voltagesinusoidal waves.

8/10/2019 88307a.ppt

45/48

Sigma Delta Modulation (contd)

Principle is as follows:

Modulator receives command phasevoltage va0

*at variable freq./mag. And is

compared to actual discrete phase voltagepulses. The error (deltaoperation) isintegrated (sigmaoperation) to generatean integral error function e:

Polarity of e is used to select either a

positive pulse or negative pulse.

*

0 0a ae v dt v dt

8/10/2019 88307a.ppt

46/48

Sigma Delta Modulation (contd)

8/10/2019 88307a.ppt

47/48

Output Ripple

The output ripple may be defined as thedifference between the instantaneousvalue of the current/voltage compared tothe value of the fundamental frequencycomponent.

Consider the load to be an ac motor.

v0= v01+ vripple ; i0= i01+ iripple

Single -Phase

Inverter

+ -i0

+v0

-

L

vL= vL1+ vripple

+e0 = 2E0sint-

8/10/2019 88307a.ppt

48/48

Output Ripple (contd)

Using superposition:

vripple(t) = v0(t) - v01(t)

Note: The ripple is independentof the

power being transferred to the load.

kdvL

tit

rippleripple )(1

)(0

constant

Documents

88307a.ppt