POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
PAGE 6 - 1
BASIC SWITCHING CIRCUITS
1 OUTLINE OF UNIT
2
2 RECTIFIER CIRCUITS
3
2.1
DIODE BRIDGE
3
2.2
P HASE DELAY, COMMUTATION & OVERLAP
4
CONTROLLING VDC
5
2.4
INCREASING BRIDGE RATINGS
7
2.5
HARMONIC CANCELLATION
8
2.6
P HASE SEQUENCE OF HARMONICS
10
2.7
SWITCHED MODE RECTIFIER
10
2.7.1 BASIC CIRCUIT AND OPERATION
2.7.2 BUCK & BOOST CONVERTERS
2.8
AC SWITCH
10
11
12
2.8.1
BURST MODE CONTROLLED BACK-TO-BACK THYRISTOR SWITCH.
Prepared by Dr K A Walshe
13
POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
1
PAGE 6 - 2
Outline of Unit
3. Basic
2 units
Diode bride , Gratez
Introduce concept of overlap
switching
bridge, buck and boost
to demonstrate how voltage
circuits
converters, need for
regulation occurs, impact of
snubbers
source impedance.
Preliminary Information:
Diodes : semi-conducting junction that permits conduction in one direction
(forward) only and a small current (leakage current) in the reverse direction.
Thyristor : two semi-conducting junctions with a third input terminal that enables
the ability to conduct in the forward direction to be controlled. Leakage current only
in the reverse direction. Forward conduction only occurs if thyristor is forward
biased and the gate is pulsed. Once current falls below the “holding current”
conduction will cease until next occasion when forward bias and gate pulse occur.
Ratings to >6kV and 4kA per device
GTO – Gate turn Off Thyristor : Similar to thyristor but also has ability to be turned
off by absence of Gate current. Lower ratings than thyristors
IGBT – Insulated Gate Bipolar Transistor : Switched State transistor; ON or OFF,
very high speed. Needs multiplicity of devices to real ratings; good for medium level
power circuits
Prepared by Dr. K A Walshe
PAGE 6 - 3
POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
2
Rectifier Circuits
2.1
Diode Bridge
Single phase diode bridge; waveforms.
Single Phase
f := 50
frequency & periodic time
T := f
−1
v ( t) := 2⋅ sin( 2⋅ f ⋅ π⋅ t)
vrect ( t) := v ( t)
2
1 ⌠
Vdc := ⋅ 
T ⌡
T
vrect ( t) dt
vrect( t )
0
1
Vdc = 0.9
0
DC voltage is 0.9Vrms
0
0.01
t
Three Phase


va ( t ) := 2⋅ sin(2⋅ f ⋅ π⋅ t )
vb (t ) := 2⋅ sin 2⋅ f ⋅ π⋅ t +
vrecta ( t) := va ( t)
vrectb ( t) := vb ( t )
2⋅ π 

3 


vc ( t ) := 2⋅ sin 2⋅ f ⋅ π⋅ t +
vrectc ( t) := vc ( t)
A1 ( t) := if( vrecta ( t ) > vrectb ( t) , vrecta ( t) , vrectb ( t) )
A2 (t ) := if(vrecta ( t) > vrectc ( t) , vrecta (t ) , vrectc ( t ))
A( t) := if( A1 ( t) > A2 ( t) , A1 (t ) , A2 ( t) )
1.5
T
1 ⌠
Vdc := ⋅  A ( t) dt
T ⌡
0
Vdc = 1.351
vrecta( t )
vrectb ( t )
1
vrectc( t )
A( t )
0.5
0
0
0.005
0.01
t
Prepared by Dr. K A Walshe
0.015
−2⋅ π 
3


POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
PAGE 6 - 4
NB once it is understood that a waveform is periodic within less than a cycle of the
50 Hz a shorter time period can be considered
The waveforms shown apply in the case of zero source impedance. This effect will
be considered next
2.2
Phase delay, Commutation & Overlap
Process of controlling voltage; commutation; effect on voltage output; Power factor.
Overlap; process of transference of current from one leg to another.; effect on
voltage
Actually, LHS is
initially on
On the assumption that the DC circuit possesses significant inductance, the DC side
current will remain constant for periods of many cycles. Initially consider the RHS
diode to be carrying the full load current and the LHS diode carries none. Once the
phase to neutral voltage of the LHS circuit exceeds that of the RHS a circulating
current will flow. This current is the integral of the voltage difference divided by
the sum of the inductance. As this current increases the RHS diode current falls
until reduced to zero at which point conduction ceases in the RHS leg and the LHS
leg carries the full DC load current.
Prepared by Dr. K A Walshe
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POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
2.3
Controlling Vdc
If the bridge uses thyristors or some other controlled turn-on device as opposed to
diodes, we can delay the point of turn on with respect to the “narurel” point of turn
on. In the example below, turn-on is delayed by approximately 60 degrees (there is
a small rounding error in the number (0.003306) used).


va( t) := 2⋅ sin (2⋅ f ⋅ π⋅ t )
vb ( t ) := 2⋅ sin  2⋅ f ⋅ π⋅t +
vrecta ( t ) := va( t)
vrectb ( t ) := vb ( t )
vcomca( t) :=
2⋅ π 

3 


vc ( t ) := 2⋅ sin 2⋅f ⋅π⋅ t +
−2⋅ π 
3


vrectc ( t ) := vc ( t )
vrecta ( t) + vrectc ( t )
2
A1( t) := if ( vrecta ( t ) > vrectb ( t) , vrecta ( t ) , vrectb ( t ) )
A2( t) := if ( vrecta ( t ) > vrectc ( t ) , vrecta ( t ) , vrectc ( t ) )
α := 30⋅
π
α0 := 0.003306⋅
180
A( t) :=  ift <
 
π
t2 := ( α0 + α )⋅
0.01
0.01
π
t1 := t2 − 0.003306
(α0 + α )⋅ 0.01 , vrectc (t ) , vrecta (t ) 



π 


1.5
6 ⌠
Vdc := ⋅ 
T ⌡
vrecta( t )
t2
A ( t ) dt
t1
Vdc = 1.164
vrectc( t )
1
vcomca( t )
A( t )
0.5
0
0
0.002
0.004
t
Thus by delaying the point on wave of the transfer from one arm to the next, the
output voltage can be reduced.
Prepared by Dr. K A Walshe
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POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
Note that the DC output voltage is given by
Vdc ( α ) := Vdc0 ⋅ cos
(α )
From this follows a most important fact – the current pulse in the AC line is also
delayed by the angle “alpha” thus the power factor of a phase controlled DC bridge
is “cos(alpha)”.
As shown in the earlier diagram, the presence of inductance in the AC lines delays
the rise of the commutating current resulting in the process of transfer of current
takes a finite time. During that period the output DC voltage is reduced
During commutation the circulating current that causes commutation is driven by the
two phase voltages involved in the current loop ie
vcomca (t ) := vrecta (t ) + vrectc ( t)
and the loop inductance (the source is assumed to be pure inductance "for simplicity")
is 2*Xphase/100/pi
However traditional texts talk of the average voltage applied to the phase inducatnce thus
vcomca ( t) :=
vrecta ( t) + vrectc ( t)
2
⋅V
icom( t) :=
t
1 ⌠
⋅  vcomca ( t) dt
L ⌡
t2
For the case of 300 amps DC load and 1 mH commutation inductance the current
and voltage waveforms are :
Prepared by Dr. K A Walshe
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POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
500
400
200
Vdc( t )
ia( t ) − 500
0
ic( t ) − 500
200
400
− 500
0.003
0.004
0.005
0.003
0.006
t
0.007
.008
NB the spike just after overlap starts is a minor error in Mathcad formulation of the
switching logic.
The effect of overlap is to cause a further reduction in the DC output voltage of the
bridge. The student should calculate the formula for the output DC voltage with
firing angle delay “?” and overlap angle “µ”
These two effects mean that we should consider the controlled bridge as a variable
voltage (the phase angle control feature) behind a non-linear resistance (AC source
regulation + overlap + device voltage drop + any significant resitance in the
bridge). With feedback control applied the non-linear resistance effect can be
removed.
2.4
Increasing Bridge Ratings
Three phase Greatez bridge is one of
many connections used to
•
Reduce DC voltage and hence
current ripple
•
Reduce input current ripple
•
Increase ratings above that of
single devices
Prepared by Dr. K A Walshe
POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
PAGE 6 - 8
When two off 6pluse bridges are connected in series the Dc voltage is doubled and
the current is still limited by the capacity of each bridge (NB devices might can be
connected in parallel within a bridge). If the bridges are connected in parallel the
DC load current is doubled but consideration must be given to current sharing
between bridges – this is achieved by the use of a special transformer (also known as
an interphase reactor) – see below.
“Diagram missing”
The interphase reactor forces current sharing by developing a voltage that opposes
the direction in which current is trying to build up. This results in a triple
frequency (i.e. 150 Hz) voltage across the reactor.
2.5
Harmonic Cancellation
With a 6 pulse bridge, conduction occurs for a period extending from the natural
voltage cross over points (see earlier diagram) i.e. for a period of 120 degrees per
half cycle.
Harmonic cancellation is achieved by phase displacing the 50Hz components far
enough to make a particular pair of harmonics cancel by becoming 180degrees out
of phase.
Note the inherent assumptions
1. 50Hz currents are exactly 120 deg apart
2. phase and magnitude of harmonics is same on each phase (i.e. all 5ths are the
same)
3. phase shifting device gives the exact phase and amplitude shift required.
Prepared by Dr. K A Walshe
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POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
Harmonic Cancellation by Star & Delta Secondary Windings
A := 1
amplitude of components
a5 :=
t := 0 , 0.00005.. 0.04
set the constants
Star winding (taken as ref winding)
2
a7 :=
5
ω := 100⋅ π
1
7
α := 30⋅
π
180
τ := 120⋅
π
180
ia( t ) := A sin(ω ⋅ t) + a5⋅ sin( 5⋅ ω⋅ t) + a7⋅ sin(7⋅ ω⋅ t )
Form the currents in the two delta windings on the same core of the transformer
ib1( t) :=  A ⋅ sin( ω⋅ t + α + τ) + a5⋅ sin5⋅ ( ω⋅ t + α + τ) + a7⋅ sin7⋅ ( ω⋅ t + α + τ)  ⋅
1
ib2( t) :=  A ⋅ sin( ω⋅ t + α + 0) + a5⋅ sin5⋅ ( ω⋅ t + α + 0) + a7⋅ sin7⋅ ( ω⋅ t + α + 0)  ⋅
1
3
3
ib( t ) := ib1( t) − ib2( t)
Calculate the primary (star) winding current
ic( t) := ia( t ) − ( ib1(t ) − ib2( t) )
5
ia ( t ) +6
ib1 ( t ) + 4
ib2 ( t ) + 2
ib ( t)
ic ( t ) ⋅− 2
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
t
By generalising the above it can be shown that the necessary phase shift for
harmonic ancellation is :12 pulse – 30 degrees – eliminates 5, 7, 17, 19, 29, 31 etc
18 pulse – 20 degrees – eliminates 5, 7, 11, 13, 23, 25, 29, 31
24 pulse – 15 degrees - eliminates 5, 7, 11, 13, 17, 19, 27, 29 etc.
Prepared by Dr. K A Walshe
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POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
2.6 Phase Sequence of Harmonics
In a three phase system with identical waveshape on each phase, it can be shown
that the odd order harmonics can be classified as positive, negative or zero phase
sequence. The solution is :“n”
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Seq
+ 0
-
+
0
-
+
0
-
+
0
-
+
0
-
In the process of rectification the odd/even pairs (i.e. 5th & 7th) result from the 6th
harmonic on the DC side note how the +ve seq of each of these +/- seq groups
advances whilst the –ve seq component retards.
2.7
2.7.1
Switched Mode Rectifier
Basic circuit and operation
See Mohan chapter 7
In this generic group of converters a DC voltage is established by varying the
charging rate of a capacitor using forced commutation. The switch can be a
GTO (for heavy current and higher voltages – but slower switching
frequencies), IGBT (lower currents but much higher switching frequencies),
MOSFET and the like (small currents such as for consumer electronics).
A common form has
series inductor for limiting the di/dt and Imax , and
freewheeling diode to allow continuous current conduction.
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POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
The series inductor has some resistance, but if it is overlooked a simple circuit
model can be obtained.
E = - L * di/dt thus if the input and output voltages are known then
Switch closed
di/dt = [Vin(t) – Vout(t)] / L
Switch open
di/dt = [0 – Vout(t)] / L
Suppose that the output voltage is 75% of the input then
di/dt (switch closed) = 0.25 per unit
di/dt (switch open) = -0.75 per unit
Thus the current waveform will be a saw-tooth.
Variations in the input and output voltages change the di/dt. In practice this
can be mistaken for R-C exponential. The practical implication is that any
control system built on the assumption of constant di/dt rates will suffer
some loss of precision or stability (see the H-1 for instance).
In very large power supplies several of these switch / diode / inductor circuits
will be connected in parallel feeding a common DC capacitor. By staggering
the switch-on instances, the effective switching frequency can be increased
(i.e. 4 circuits in parallel increases the apparent switching frequency by 4
times as far as the external circuit is concerned).
2.7.2 Buck & Boost Converters
The prior description shows that a voltage source switched mode converter
results in a reduced output voltage.
This is known as the “Buck” converter.
If however the switched mode converter is fed by a constant current source,
then the output voltage can be regulated to be larger than the input voltage.
This is known as a boost converter. There are many variants to these two
circuits – see the course text “Mohan”.
The quality of the output voltage is dependant on the size of the output
capacitor and the quality of the control system being used. It is folly to
believe that ripple can be reduced by simply using a bigger output capacitor
(particularly true when the converter is large relative to the available fault
level). A situation can be reached where non-linear oscillations occur
Prepared by Dr. K A Walshe
POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
PAGE 6 - 12
2.8 AC Switch
Some applications are not waveshape sensitive and can then use phase controlled
thyristors. This allows a very rugged and low cost electronic switch to be created.
Heaters are a good example of this.
Sometimes known as “Solid State Relays”1, simple back-to-back thyristor switches
are marketed through a number of outlets where the technical expertise of the
retailer is minimal. When using these devices it is essential to recognise the strict
limitations of peak voltage and junction temperature otherwise there will be
repeated failures and possibly fires. The real problem with these Solid State Relays
is that the dictates of mass marketing result in all design limits being stretched to
the n-th degree; the devices are fine as long as you are very careful in their selection
and use.
The phase controlled reactor (TCR) is used in parallel with detuned capacitor
banks or harmonic filters in large voltage stabilisers.
1
Solid state relays; see Appendix 1 for a typical data sheet
Prepared by Dr. K A Walshe
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POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
2.8.1 Burst mode controlled back-to-back thyristor switch.
Harmonic currents can be quite pronounced with phase controlled resistors. It
used to be held that conducting for an integer number of cycles then holding off for
a different number would generate a variable, if somewhat grainy, controller. In
heating applications the time constant of the load to be heated is usually
sufficiently long that the oscillation of temperature are very small. However whilst
burst mode firing does not produce integer harmonics, it does produce subharmonics (also known as inter-harmonics) and voltage flicker.
This can be readily understood because
Voltage dip is :dV is approx = -(dP * R + dQ * X) pu (all quantities in per unit)
Imagine that the load is switched On for 0.5 sec and then Off for 0.5 sec. The
mains would experience a voltage dip of “dV” (as calculated above) with a periodic
time of 1.0 seconds and thus if a Fourier analysis of the mains waveform was made
with a total data capture time being an integer mutliple of 1.0 sec , a fundamental of
1.0Hz would be seen. In the plot below, such a load has been modelled using
EMTP-ATP; the source impedance and the load choosen such as to emphasise the
point being made.
1000
500
0
vn
500
1000
0
2000
4000
6000
8000
1 .10
4
n
1 .10
3
100
vfftn
10
1
0.1
0
20
40
60
n
Prepared by Dr. K A Walshe
80
100
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POWER ELECTRONICS
CHAPTER 6 – BASIC SWITCHING CIRCUITS ; REV B2002
Resolution of the Fourier spectrum shows that the 50Hz has been modulated at 1
Hz. This shows up most significantly in the “Voltage squared”, ie the output of an
ideal incandecant lamp. When a 50 Hz sinewave is squared and then analysed by
FFT a spectrum comprising a DC and 100 Hz compenent arrise.
FFT of lamp spectrum
100 100
lfftn
lfft0
10
⋅100
1
.1
0.1
0
0
2
4
6
n
Frequency Hz
8
10
10
In the spectrum above the DC compoenet can be seen as well as sidebands at 1, 3, 5
etc Hz. These “sidebands” are associated with the 1Hz switched load. Because the
V(t)^2 waveform corresponds approximately to the lumminous output of the lamp,
it follows that the 1Hz switched load creates a 1, 3, 5 etc Hz fluctuation in output
level of the lamp.
Prepared by Dr. K A Walshe