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ECE 8830 - Electric Drives
Topic 6: Voltage-Fed Converters
Spring 2004
Introduction
Voltage-fed converters convert dc input
to ac output. These converters can
operate 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 term
Voltage Stiff Inverters (VSI) is used to
describe these types of converters.
Introduction (cont’d)
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.
Single-Phase Inverters
Half-Bridge Inverter
One of the simplest types of inverter.
Produces a square wave output.
Single-Phase Inverters (cont’d)
Full Bridge (H-bridge) Inverter
Two half-bridge inverters combined.
Allows for four quadrant operation.
Single-Phase Inverters (cont’d)
Quadrant 1: Positive step-down converter
(forward motoring)
Q1-On; Q2 - Chopping; D3,Q1 freewheeling
Single-Phase Inverters (cont’d)
Quadrant 2: Positive step-up converter
(forward regeneration)
Q4 - Chopping; D2,D1 freewheeling
Single-Phase Inverters (cont’d)
Quadrant 3: Negative step-down converter
(reverse motoring)
Q3-On; Q4 - Chopping; D1,Q3 freewheeling
Single-Phase Inverters (cont’d)
Quadrant 4: Negative step-up converter
(reverse regeneration)
Q2 - Chopping; D3,D4 freewheeling
Single-Phase Inverters (cont’d)
Phase-Shift Voltage Control - the output
of the H-bridge inverter can be controlled
by phase shifting the control of the
component half-bridges. See waveforms
on next slide.
Single-Phase Inverters (cont’d)
Single-Phase Inverters (cont’d)
The waveform of the output voltage vab is
a quasi-square wave of pulse width . The
Fourier series of vab is given by:
4Vd
vab  
n 1,3,5... n
  n  
sin  2   cos  n t 
  
The value of the fundamental, a1=
4Vd

sin  / 2 
The harmonic components as a function of
phase angle are shown in the next slide.
Single-Phase Inverters (cont’d)
Three-Phase Bridge Inverters
Three-phase bridge inverters are widely
used for ac motor drives. Two modes of
operation - square wave and six-step.
The topology is basically three halfbridge inverters, each phase-shifted by
2/3, driving each of the phase windings.
Three-Phase Bridge Inverters (cont’d)
Three-Phase Bridge Inverters (cont’d)
Three-Phase Bridge Inverters (cont’d)
The three square-wave phase voltages
can be expressed in terms of the dc
supply voltage, Vd, by Fourier series as:
va 0 
2Vd
vb 0 
2Vd
vc 0 
2Vd




(1) n 1 cos(nt )
n 1,3,5...

(1)
n 1
n 1,3,5...

n 1,3,5...
(1)
2
cos(nt  )
3
n 1
2
cos(nt  )
3
Three-Phase Bridge Inverters (cont’d)
The line voltages can then be expressed as:
vab  va 0  vb 0 
2 3Vd
vbc  vb 0  vc 0 
2 3Vd
vca  vc 0  va 0 
2 3Vd




cos( t   / 6)  cos(nt   6)

cos( t   / 2)  cos(nt   2)

cos( t  5 / 6)  cos(nt  5 6)
n 1,3,5...
n 1,3,5...
n 1,3,5...
Three-Phase Bridge Inverters (cont’d)
The line voltages are six-step waveforms
and have characteristic harmonics of 6n1,
where n is an integer. This type of inverter
is referred to as a six-step inverter.
The three-phase fundamental and
harmonics are balanced with a mutual
phase shift of 2/3.
Three-Phase Bridge Inverters (cont’d)
If the three-phase load neutral n is
isolated from the the center tap of the dc
voltage supply (as is normally the case in
an ac machine) the equivalent circuit is
shown below.
Three-Phase Bridge Inverters (cont’d)
In this case the isolated neutral-phase
voltages are also six-step waveforms with
the fundamental component phase-shifted
by /6 from that of the respective line
voltage. Also, in this case, the triplen
harmonics are suppressed.
Three-Phase Bridge Inverters (cont’d)
For a linear and balanced 3 load, the
line currents are also balanced. The
individual line current components can be
obtained from the Fourier series of the
line voltage. The total current can be
obtained by addition of the individual
currents. A typical line current wave with
inductive load is shown below.
Three-Phase Bridge Inverters (cont’d)
The inverter can operate in the usual
inverting or motoring mode. If the phase
current wave, ia, is assumed to be perfectly
filtered and lags the phase voltage by /3
the voltage and current waveforms are as
shown below:
Three-Phase Bridge Inverters (cont’d)
The inverter can also operate in rectification
or regeneration mode in which power is
pushed back to the dc side from the ac side.
The waveforms corresponding to this mode
of operation with phase angle = 2/3 are
shown below:
Three-Phase Bridge Inverters (cont’d)
See Bose text for Input Ripple and
Device Ratings.
Three-Phase Bridge Inverters (cont’d)
The phase-shift voltage control principle
described earlier for the single-phase
inverter can be extended to control the
output voltage of a three-phase inverter.
Three-Phase Bridge Inverters (cont’d)
The circuit shows three H-bridge inverters
(one for each phase winding) where each
H-bridge is connected to the primary
winding of a transformer. The output
voltages are derived from the
transformer’s secondary windings
connected in a wye configuration.
Three-Phase Bridge Inverters (cont’d)
Three-Phase Bridge Inverters (cont’d)
The three waveforms va0,vb0, and vc0 are
of 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 .
Three-Phase Bridge Inverters (cont’d)
The transformer’s secondary phase voltages,
vA0, vB0, and vc0 may be expressed as
follows:
vA0  mvad  m(va 0  vd 0 )
vB 0  mvbe  m(vb 0  ve0 )
vC 0  mvcf  m(vc 0  v f 0 )
where m is the transformer turns ratio
(= Ns/Np). Note that each of these waves is
a function of  angle.
Three-Phase Bridge Inverters (cont’d)
The output line voltages are given by:
vAB  vA0  vB 0
vBC  vB 0  vC 0
vCA  vC 0  vA0
While the component voltage waves va0, vd0,
vA0 … etc. all contain triplen harmonics, they
are eliminated from the line voltages
because they are co-phasal. Thus the line
voltages are six-step waveforms with order
of harmonics = 6n1 at a phase angle .
Three-Phase Bridge Inverters (cont’d)
The Fourier series for vA0 and vB0 are
given by:
vA0
4mVd
 
n 1,3,5... n
  n  
sin  2   cos  n t 
  
vB 0
4mVd
 
n 1,3,5... n
  n  
sin  2   cos  n t  2 / 3
  
Three-Phase Bridge Inverters (cont’d)
The Fourier series for vAB is given by:
vAB  vA0  vB 0
4mVd
 
n 1,5,7,11... n
  n   
2

sin  2   cos  n t   cos n   t  3

   
Note that the triplen harmonics are
removed in vAB although they are present
in vA0 and vB0.



Three-Phase Bridge Inverters (cont’d)
See text for a description of Voltage
and Frequency Control for the
three-phase H-bridge inverter.
Three-Phase Bridge Inverters (cont’d)
A twelve-step inverter can be created
by combining two six-step inverters.
Three-Phase Bridge Inverters (cont’d)
Features of the 12-step inverter:




The lower bridge is phase shifted by /6
with respect to the upper bridge.
Each inverter is connected to the primary
delta winding of each transformer.
Upper bridge transformer only has one
secondary winding per phase whereas
lower bridge transformer has two
secondary windings per phase.
Note the difference in turns ratio for the
two transformers.
Three-Phase Bridge Inverters (cont’d)
Phasor diagram for voltage synthesis
and output voltage waveform are shown
below:
Three-Phase Bridge Inverters (cont’d)
The output phase voltages are obtained
by the interconnection of three
secondary windings to satisfy the
phasor diagram on the previous slide,
e.g. vNA = vab+vde-vef
Three-Phase Bridge Inverters (cont’d)
Since the lower bridge lags by /6, considering
vab as the reference, the Fourier series of the
component voltages are given by:
vab 
2 3nVd 
1
1

cos

t

cos
5

t

cos
7

t

...



5
7
vab
 2nVd
vde 
 
6

3
 
 1
 1
 


cos   t  6   5 cos  5 t  6   7 cos  7 t  6   ...





 

vab
5 2nVd
vef 


6

3
 
5
cos   t  6
 
5
 1

  cos  5 t 
6
 5

5
 1

  cos  7 t 
6
 7



  ...


where n is the turns ratio of the upper transformer.
Three-Phase Bridge Inverters (cont’d)
The fundamental component of vNA is
given by:
4 3nVd
vNA( f )  vab ( f )  vde ( f )  vef ( f ) 
cos  t

The output phase voltage Fourier series
can be expressed as:
vNA 
4 3nVd 
1
1

cos

t

cos11

t

cos13

t

...



11
13
Note the lower harmonic content
compared to the six-step inverter.
Three-Phase Bridge Inverters (cont’d)
See Bose text for 18-step inverter.
Simulating Three-Phase Bridge
Inverters
The below figure shows a SIMULINK block
diagram for a 3-phase voltage-fed inverter.