6 and 12 Step Inverter

7/29/2019 6 and 12 Step Inverter

1/42

Topic 6: Voltage-Fed Converters

Spring 2004

ECE 8830 - Electric Dr

ives


2/42

Introduction

Voltage-fed converters convert dc inputto ac output. These converters canoperate bidirectionally as either an

inverter or as a rectifier.

The input voltage should be stiff-indicating that the Thevenin impedance

should be close to zero. Often the termVoltage Stiff Inverters (VSI) is used todescribe these types of converters.


3/42

Introduction (contd)

Input Sources:

Utility line or ac generator through

rectifier/filter. Battery, fuel cell, PV array

Output Format:

Single phase/Polyphase Square wave, sine wave, PWM wave,

stepped wave, or quasi-square wave.


4/42

Single-Phase Inverters

Half-Bridge Inverter

One of the simplest types of inverter.Produces a square wave output.


5/42

Single-Phase Inverters (contd)

Full Bridge (H-bridge) Inverter

Two half-bridge inverters combined.

Allows for four quadrant operation.


6/42


Quadrant 1: Positive step-down converter

(forward motoring)

Q1-On; Q2 - Chopping; D3,Q1 freewheeling


7/42


Quadrant 2: Positive step-up converter

(forward regeneration)

Q4 - Chopping; D2,D1 freewheeling


8/42


Quadrant 3: Negative step-down converter

(reverse motoring)

Q3-On; Q4 - Chopping; D1,Q3 freewheeling


9/42


Quadrant 4: Negative step-up converter

(reverse regeneration)

Q2 - Chopping; D3,D4 freewheeling


10/42


Phase-Shift Voltage Control - the outputof the H-bridge inverter can be controlledby phase shifting the control of the

component half-bridges. See waveformson next slide.


11/42



12/42


The waveform of the output voltage vab isa quasi-square wave of pulse width . TheFourier series of vab is given by:

The value of the fundamental, a1=

The harmonic components as a function ofphase angle are shown in the next slide.

1,3,5...

4sin cos

2

dab

n

V nv n t

n

4

sin / 2dV


13/42



14/42

Three-Phase Bridge Inverters

Three-phase bridge inverters are widelyused for ac motor drives. Two modes of

operation - square wave and six-step.The topology is basically three half-bridge inverters, each phase-shifted by2/3, driving each of the phase windings.


15/42

Three-Phase Bridge Inverters (contd)


16/42



17/42


The three square-wave phase voltagescan be expressed in terms of the dcsupply voltage, Vd, by Fourier series as:

1

0

1,3,5...

2( 1) cos( )nda

n

Vv n t

1

01,3,5...

2 2

( 1) cos( )3

nd

bn

V

v n t

1

0

1,3,5...

2 2( 1) cos( )

3

ndc

n

Vv n t


18/42


The line voltages can then be expressed as:

0 0

1,3,5...

2 3cos( / 2) cos( 2)dbc b c

n

Vv v v t n t

0 0

1,3,5...

2 3cos( 5 / 6) cos( 5 6)d

ca c a

n

Vv v v t n t

0 01,3,5...

2 3

cos( / 6) cos( 6)d

ab a bn

V

v v v t n t


19/42


The line voltages are six-step waveformsand have characteristic harmonics of 6n1,where n is an integer. This type of inverter

is referred to as a six-step inverter.

The three-phase fundamental andharmonics are balanced with a mutual

phase shift of 2/3.


20/42


If the three-phase load neutral n isisolated from the the center tap of the dcvoltage supply (as is normally the case in

an ac machine) the equivalent circuit isshown below.


21/42


In this case the isolated neutral-phasevoltages are also six-step waveforms with

the fundamental component phase-shiftedby /6 from that of the respective linevoltage. Also, in this case, the triplenharmonics are suppressed.


22/42


For a linear and balanced 3 load, theline currents are also balanced. Theindividual line current components can be

obtained from the Fourier series of theline voltage. The total current can beobtained by addition of the individualcurrents. A typical line current wave with

inductive load is shown below.


23/42


The inverter can operate in the usualinverting or motoring mode. If the phasecurrent wave, ia, is assumed to be perfectly

filtered and lags the phase voltage by /3the voltage and current waveforms are asshown below:


24/42


The inverter can also operate in rectificationor regeneration mode in which power ispushed back to the dc side from the ac side.

The waveforms corresponding to this modeof operation with phase angle = 2/3 areshown below:


25/42


26/42


The phase-shift voltage control principledescribed earlier for the single-phaseinverter can be extended to control the

output voltage of a three-phase inverter.


27/42


The circuit shows three H-bridge inverters(one for each phase winding) where eachH-bridge is connected to the primary

winding of a transformer. The outputvoltages are derived from thetransformers secondary windingsconnected in a wye configuration.


28/42



29/42


The three waveforms va0,vb0, and vc0 areof amplitude 0.5Vd and are mutually

phase-shifted by 2/3.

The three waveforms ve0,vf0, and vg0 are

of similar but phase shifted by .


30/42


The transformers secondary phase voltages,vA0, vB0, and vc0 may be expressed asfollows:

where m is the transformer turns ratio

(= Ns/Np). Note that each of these waves is

a function of angle.

0 0 0( )A ad a dv mv m v v

0 0 0( )B be b ev mv m v v

0 0 0( )C cf c f v mv m v v


31/42


The output line voltages are given by:

While the component voltage waves va0, vd0,

vA0 etc. all contain triplen harmonics, theyare eliminated from the line voltagesbecause they are co-phasal. Thus the linevoltages are six-step waveforms with order

of harmonics = 6n1 at a phase angle .

0 0AB A Bv v v

0 0BC B Cv v v 0 0CA C Av v v


32/42


The Fourier series for vA0 and vB0 aregiven by:

0 1,3,5...

4

sin cos2

d

An

mV n

v n tn

0 1,3,5...

4sin cos 2 / 3

2

d

Bn

mV nv n t

n


33/42


The Fourier series for vAB is given by:

Note that the triplen harmonics areremoved in vAB although they are presentin vA0 and vB0.

1,5,7,11...

4 2sin cos cos

2 3

d

n

mV nn t n t

n

0 0AB A Bv v v


34/42


See text for a description of Voltageand Frequency Control for the

three-phase H-bridge inverter.


35/42


A twelve-step inverter can be createdby combining two six-step inverters.


36/42


Features of the 12-step inverter:

The lower bridge is phase shifted by /6with respect to the upper bridge.

Each inverter is connected to the primarydelta winding of each transformer.

Upper bridge transformer only has one

secondary winding per phase whereaslower bridge transformer has twosecondary windings per phase.

Note the difference in turns ratio for the

two transformers.


37/42


Phasor diagram for voltage synthesisand output voltage waveform are shownbelow:


38/42


The output phase voltages are obtainedby the interconnection of threesecondary windings to satisfy the

phasor diagram on the previous slide,e.g. vNA = vab+vde-vef


39/42


Since the lower bridge lags by /6, consideringvab as the reference, the Fourier series of thecomponent voltages are given by:

where n is the turns ratio of the upper transformer

2 3 1 1cos cos 5 cos 7 ...5 7

dab

nVv t t t

2 1 1cos cos 5 cos 7 ...

6 6 5 6 7 63

ab dde

v nVv t t t

25 5 1 5 1 5cos cos 5 cos 7 ...

6 6 5 6 7 63

ab def

v nVv t t t


40/42


The fundamental component of vNA isgiven by:

The output phase voltage Fourier seriescan be expressed as:

Note the lower harmonic content

compared to the six-step inverter.

( ) ( ) ( ) ( )

4 3cosdNA f ab f de f ef f

nVv v v v t

4 3 1 1cos cos11 cos13 ...

11 13

dNA

nVv t t t


41/42


See Bose text for 18-step inverter.

S


42/42

Simulating Three-Phase Bridge

Inverters

The below figure shows a SIMULINK blockdiagram for a 3-phase voltage-fed inverter.

Documents

6 and 12 Step Inverter