18-01-2010, 11:13 PM
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Phase Angle Control in Triac-based Single-phase AC Regulators
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Instructional Objectives
Study of the following:
¢ The circuit used for the phase angle control in triac-based single-
phase ac regulators (ac to ac voltage converters)
¢ The operation of the various blocks used in the circuit, along with
the waveforms
¢ The harmonic analysis of the output voltage of a single-phase ac
regulator with resistive load
Introduction
In the last lesson - second one in the first half of this module,
various circuits of the three-phase ac regulators, also termed as ac to
ac voltage converters, are described. Two basic circuits - star-
connected and delta-connected, are first taken up. The operation of the
two circuits with three-phase balanced resistive ® load, along with
the waveforms, is then discussed. Lastly, the important points of
comparison of the performance with different types of circuits,
including the above two, are presented. In this case, the load is
balanced inductive (R-L) one.
In this lesson - the third and final one in the first half, firstly,
the circuit used for the phase angle control in triac-based single-
phase ac regulator, also termed as ac to ac voltage converter, is
presented. Then, the operation of the various blocks used in the above
circuit, along with the waveforms, is described. Finally, the harmonic
analysis of the output voltage of a single-phase ac regulator with
resistive load is, briefly discussed.
Keywords: Phase angle controller circuit, Triac-based single-phase ac
regulator, or ac to ac voltage converter, harmonic analysis of the
output voltage waveform.
Phase Angle Controller Circuit for Triac-based Single-phase AC
Regulator
The phase angle controller circuit for a triac-based single-phase ac
regulator (ac to ac voltage converter), is shown in Fig. 28.1. The
power circuit (also shown in Fig. 26.1c (lesson #26)) consists of a
Triac in series with inductive (R-L) load, fed from a single phase
supply, with rated voltage of, say 220 V(rms), having rated frequency
(=f50 Hz). Before going into the operation of the phase angle
controller circuit, some important points of the bidirectional
controlled device (TRIAC), used in the ac circuit, having already been
introduced in lesson #4 (module 1), is briefly presented, as it is not
frequently used. Similarly, for the same reasons, DIAC (may have been
introduced earlier), being used here as an uncontrolled bidirectional
device, is also briefly described.
TRIAC
A Triac is equivalent to two thyristors connected back to back as shown
in Fig. 26.1a. Thus, it is a bidirectional switching device, in
contrast to the thyristor, which is a unidirectional device, having
reverse blocking characteristic, preventing the flow of current from
Cathode to Anode. So, when it (triac) is in conduction mode, current
flows in both directions (forward and reverse). This switching device
is called as TRIAC (TRIode AC switch), with the circuit symbol shown in
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Fig. 28.1. The three terminals of the triac are designated as , and
gate, , shown in the same figure. These are similar to the terminals “
A (Anode), K (Cathode) and G (Gate), of the thyristor The terminal, is
taken as the reference point for the measurement of the voltages and
currents at other two terminals, G (gate) and . The gate (G) is near to
the terminal, . The thyristor conducts with the current direction from
Anode to Cathode (positive), when a positive pulse is fed at the Gate
terminal with respect to Cathode, and at that time, with positive
voltage applied between Anode and Cathode terminals, being connected in
series with the load. The triac conducts in the
1MT2MTG1MT2MT1MTpositive direction from to , when a 2MT1MTpositive
pulse is applied at the gate (G) terminal with respect to and at the
same time, the positive voltage is applied between two terminals, (+)
and (-). Similarly, the triac conducts in 1MT2MT1MTnegative direction
from to , when a 1MT2MTnegative pulse is applied at the gate (G)
terminal with respect to and at the same time, the positive voltage is
applied between two terminals, (+) and (-). Please note that the
voltage between two terminals, and , is 1MT1MT2MT2MT1MTnegative, in
this case. So, the triac can conduct in both directions (positive and
negative) as given here, whereas the thyristor conducts in one
(positive) direction only. Only one triac is needed, whereas it is to
be replaced by two thyristors, with consequent change in the control
circuit. The V-I characteristics of both thyristor and triac, have been
discussed in lesson #4 (module 1). A thyristor turns off (non-
conducting mode), if the current through it, falls below holding
current. Similarly, a triac turns off (non-conducting mode), if the
magnitude of the current, irrespective of its direction, falls below
holding current. As a triac is connected in an ac circuit, and if the
load in the circuit is resistive, the triac turns off at the zero
crossing points of the voltage in each half (the supply (input) voltage
reaches zero at the end of each half cycle). This will be nearly valid,
if the load inductance is small, though the triac in that case turns
off, as the current though it goes to zero, after the zero crossing
point is reached in each half. The case of higher inductance in the
load has been discussed in detail in lesson #26 (module 3).
The triac is a low power device, used in voltage control circuits, used
as light dimmers, speed control for fan motors (single-phase), etc.
Some of the advantages and disadvantages of the triac vis-a-vis
thyristor are given.
Advantages
1. Triacs are triggered by positive or negative polarity voltages
applied at the gate terminal.
2. A triac needs a single heat sink of slightly larger size, whereas
anti-parallel thyristor pair needs two heat sinks of slightly smaller
sizes, but due to the clearance total space required is more for
thyristors.
Disadvantages
1. Triacs have low rating as compared to thyristors. dtdv/
2. Triacs are available in lower rating as compared to thyristors.
3. Since a triac can be triggered in either direction, a trigger
circuit for triac needs careful consideration.
4. The reliability of triacs is lower than that of thyristors.
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DIAC
A Diac is equivalent to two diodes connected back to back. Also, it is
a bidirectional device, in contrast to the diode, which is a
unidirectional device, having reverse blocking characteristic,
preventing the flow of current from Cathode to Anode. So, when it
(diac) is in conduction mode, current flows in both directions (forward
and reverse). This switching device is called as DIAC (DIode AC
switch), with the circuit symbol shown in Fig. 28.1. The two terminals
of the diac are designated as and , shown in the same figure. These are
similar to the terminals, A (Anode) and K (Cathode), of the diode. The
diac conducts, when the break-over voltage is reached in either
polarity across its two terminals. When is 1T2T1Tpositive with respect
to , and if at that time if the voltage, exceeds (break-over voltage),
the diac conducts in 2T12V1BOVpositive direction from to . Similarly,
when is 1T2T2Tpositive with respect to , and if at that time if the
voltage, exceeds (break-over voltage), the diac conducts in
1T21V2BOVnegative direction from to . So, a diac can conduct in both
directions (positive and negative), whereas a diode conducts only in
positive direction from Anode (A) to Cathode (K), if, at that time, the
voltage, exceeds (break-over voltage). A diode does not conduct in the
negative direction, if the voltage, is negative. A diode turns off
(non-conducting mode), if the current through it, falls below holding
current. Similarly, a diac turns off (non-conducting mode), if the
magnitude of the current, irrespective of its direction, falls below
holding current. If the V-I characteristic of diode is known, as given
in lesson #2 (module 1), the V-I characteristic of diac, on the lines
of the triac can be developed. The students are requested to study the
characteristic of diac from a text book, as it is not included here for
obvious reason. 2T1TAKVBOVAKV
Now, the operation of the phase angle controller circuit (Fig. 28.1) is
presented, with the waveforms at various points shown in Fig. 28.2. The
power circuit, the main component of which is the triac, has been
described earlier. The diac is symmetrical, unlike the triac, as
described earlier. So, the diac (Fig. 28.1) can be connected in
opposite direction, with in place of , and vice versa, i.e., , in place
of . But the operation here is described with the connection as in the
figure. The triac is not symmetrical, though it conducts in both
directions like diac. Two reasons are: the presence of third terminal,
Gate (G), and the gate signal to be fed between G & (reference) for
triggering. The snubber part ( & ), shown in the figure, is used for
the protection of the triac “ the power switching device. The remaining
part, including the diac used for triggering of the triac, is the
controller for the triac. 1T2T2T1T1T1MTsRsC
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~ RSCSvcC DIACR1Rpot.TRIACMT2MT1loadSnubber A B 1-phase ac supply + -
ControlCircuit GFig. 28.1: Phase angle controller circuit for a single
-phase ac regulator using TRIAC T1+-T2D
Vm-Vmvi0p/2p 3p/2 2p 5p/23p (t) (a) vc0a1a2pp+a1p+a22p 2p+a12p+a23p
DIAC breaks down(b) (Ver
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Vm-VmvL0a1p/2 p p+a13p/2 2p 2p+a15p/23p Vm-VmvL0a2p p+a22p 2p+a23p ©
(d) Fig. 28.2: Waveforms at various points of the controller circuit
(a) Input (source) voltage, vAB (b) Voltage across capacitor, c(vc) ©
Output (load) voltage, vDB with Rput = R2 (lower) (d) Output (load)
voltage, vDB with Rput = R3 (higher)
As soon the input (supply) voltage is given to the circuit, the
capacitor, C starts getting charged through the potentiometer
resistance, 2RRpot=, the value of which is low and the load resistance.
The polarity of the input voltage is important. The start of the input
voltage is taken as the positive zero-crossing point (Fig. 28.2a), when
the voltage changes from negative to positive. The point, A is now
positive with respect to B (Fig. 28.1). The polarity of the voltage
across the capacitor, C is that the left hand side is positive, with
the right hand side as negative. The capacitor voltage () is shown in
Fig. 28.2b. As soon as the capacitor voltage, reaches the break-over
voltage () of the diac (about 30 V), the diac starts to conduct in the
positive direction from to . At this point, the triac gets a positive
pulse at its gate (G is now positive with respect to ) and also is at a
higher potential than . So, the triac is turned on at the angle,
CvCvBOV1T2T1MT2MT1MT1112tftpa===. The current through the triac is in
the positive direction from to . Please note that the time constant of
the charging circuit is related to the potentiometer resistance (),
which is low. So, the time needed for the capacitor voltage to reach
the break-over voltage () is 2MT1MT2RBOV11at. The triac is turned off
at p=, when the input
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voltage reaches the negative zero-crossing point. So, the conduction
period (angle in rad) is from 1a to p in the positive half. The output
(load) voltage (DBLvv=) waveform (Fig. 28.2c) is nearly same as the
input voltage (ABivv=), neglecting the voltage drop across the triac.
The capacitor voltage (Fig. 28.2b) starts decreasing at 1tt=, and
reaches zero after some time, the time being small. The discharge path
is through diac, the resistance , and the gate, G & terminals of the
triac, the total resistance is quite low. So, the time constant during
discharge is quite low, as compared to that during charging. The
resistance, is used to decrease the capacitor current during discharge.
1R1MT1R
The pattern is repeated in the negative half of the input voltage,
which is briefly described. The capacitor, C starts charging in the
opposite direction through the same path as given earlier. The charging
starts from the negative zero-crossing of the input voltage (Fig.
28.2a). The polarity of the input voltage is now opposite, with the
point, B being positive with respect to A. The polarity of the
capacitor voltage (Fig. 28.2b) is also opposite, with the right hand
side as positive, and the left hand side as negative. The charging time
constant remains same (low), as it was earlier. The capacitor voltage,
(in magnitude) reaches the break-over voltage () of the diac after time
Cv
BOV11at, measured from the negative zero-crossing of the input voltage
(p=). The diac now starts to conduct in the negative direction from to
. At this point, the triac gets a negative pulse at its gate (G is now
negative with respect to ) and also is at a higher potential than . So,
the triac is turned on at the angle, (2T1T1MT1MT2MT1ap+=). The current
through the triac is in the negative direction from to . The triac is
turned off at the next positive zero-crossing point (1MT2MTp2=). The
conduction period (Fig. 28.2c) is from (1ap+) to (p2) in the negative
half, the total conduction time (1ap-) being same in both half. The
output voltage waveform is identical, but it is opposite in this
(negative) half. As in the earlier case, the capacitor voltage (Fig.
29.2b) starts decreasing, and reaches zero after some time, the
discharge path remaining same. Thus, the diac helps in the turning on
of the triac in both directions, making the control circuit simple with
few components only (Fig. 28.1). Though the function of the diac could
have been performed by using two diodes connected back to back, the
control circuit would have to be modified.
To change the conduction period, or the start of conduction of the
triac, the potentiometer resistance is to be increased from to , which
is higher. The capacitor voltage waveform for this case is shown in
Fig. 28.2b as dotted line, as the time constant of the charging circuit
also increases. So, the time needed for the capacitor voltage (in
magnitude, as both halves are considered) to reach the break-over
voltage () of the diac is now (2R3RBOV22at). The conduction period in
the positive half (Fig. 28.2d) is from 12aa> to p, the total time in
both half is (2ap-). The conduction period decreases. The rms value of
the output voltage also decreases. Other conditions, say during
discharge of the capacitor voltage remaining same, is not described.
The range of phase angle delay, in the ideal case, is pa<<°0. But
normally, the lower limit is higher than , while the upper limit is
lower than °0)180(°p. The input voltage (Fig. 28.2a) is zero at the two
limits ( & ) in the ideal case. As the input voltage has to exceed at
least the voltage drop in the triac, and the capacitor voltage (Fig.
28.2b) also has to reach the break-over voltage of the diac as given
earlier, the normal range of phase angle delay is to be used, not the
ideal ones. Also, if the load is inductive, the current in the triac
has to exceed a threshold value, before the gate pulse can be
withdrawn. Otherwise, the triac may not be °0°180
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triggered, returning to off state again. This point may have been
described in the case of phase-controlled single-phase (bridge)
converters (ac-dc), with inductive load in series with battery or back
emf, in lessons #10-11 (module 2).
Harmonic Analysis of the Output Voltage Waveform
Before the harmonic analysis of the output voltage waveform is taken
up, the following points may be noted. The output (load) voltage in ac
regulators (both single-phase and three-phase) decreases, as the delay
angle is increased. This can be observed from the voltage waveforms
given in the previous lessons (#26-27) in the first half of this module
(#4), for both types of ac regulators. These are mainly used to
decrease the speed of the induction motor with fan type load (), not
for constant load torque operation. The application is in the low power
range. The major disadvantage of these regulators is that the power
factor and also displacement factor decrease, with the increase in
delay angle. 2LTN
The harmonics are also present in the output (load) voltage waveforms,
being phase-controlled ones, of ac regulators. The harmonic analysis of
the output voltage waveform (Fig. 28.3) of a single-phase ac regulator
with resistive ® load (please see the waveforms given in figures
28.2c-d, which are nearly same as Fig. 28.3) is briefly presented. The
symbols, including some described earlier, are given.
0v = Instantaneous value of the output (load) voltage VVm2= = Peak
value of the input voltage 2/mVV= = RMS value of the input voltage
Tf/1= = Frequency (Hz) of the supply (input)
fp2= = Angular frequency (rad/s)
t= = Angle (rad)
fT/1= = Time period (s)
na& are the maximum values of the sine and cosine components of the
harmonics of order n, present in the output voltage waveform
respectively. nb
nc& n are the maximum value (amplitude), and phase angle, of nth
harmonic component respectively.
The relationships are 22nnnbac+=, and , )/(tan1nnnab-=
and the other relationships are nnncacos=and nnncbsin=.
The rms value of nth harmonic component 2/nc=
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Vm-Vmvoa pp + a2p(t) Fig. 28.3: Input and output voltage waveforms of a
single-phase ac regulator with resistive load.
The output (load) voltage waveform (Fig. 28.3) consists of two parts,
the first one is positive in the positive half cycle, while the second
part is negative in the next (negative) half cycle. The waveform has
half-wave asymmetry, with only odd (12+=mn) harmonics being present.
The even () harmonics are not present in this case, as the second part
is cancelled by the first part. Also to be noted that the average value
is zero. This can also be computed by the formulas for the harmonic
analysis of the output (load) voltage waveform of the buck converter
(dc-dc) circuit, given in lesson #18 in module 3. It can be observed
for the single-phase ac regulator circuit shown in lesson #26 in this
module (#4) that the switching device (triac or two thyristors
connected back to back) is turned on at the delay angle, mn2=a=, and
then turns off at p=, when the input voltage and also the output
current goes to zero, in the first (positive) half, as the load is
resistive ®. This is repeated in the second (negative) half.
The output (load) voltage waveform for one cycle is,
00=v for 0<<a; sin2sin0VVvm== for ap<<;
00=v for pap<<+)(; sin2sin0VVvm== for )()2(app+<<
In terms of the Fourier components, the expression is,
)(sin)cossin(,7,5,3,1,7,5,3,10nnnnnnncnbnav+=+=SS8=8=
where, =pp00)(sin2dnvan; =pp00)(cos2dnvbn
Please note that two formulas given here, differ from two formulas
given in lesson #18 (module 3). The expressions for the components of
the fundamental and third harmonic, of the output voltage are derived.
The students are requested to derive, say the expressions for the
other, say fifth harmonic components. -===papappppdVdVdva)2cos1(2)
(sin22sin)(2 2001 10
()()aappaappppa2sin5.0)(22sin)(2)2sin(22121+-=+-=-=VVV ()aaappcossin)
(2+-=V ===papappppdVdVdvb2sin2cossin22cos)(2001()()2sin22cos12)2
(cos2apappap-=--==VVV -===papappppdVdVdva)4cos2(cos23sinsin223sin)(2
003 ()aapppa2sin24sin42)4sin2sin(24121-=-=VV -===papappppdVdVdvb)2sin4
(sin23cossin223cos)(2003()12cos24cos42)2cos4cos(22141+-=-=aappapVV
Using two sets of two expressions given earlier, the rms value (2/nc)
and phase angle (n), of the harmonic components of the output (load)
voltage, are obtained. As there is no inductance in the load circuit,
the rms values of the harmonic components of the output current are
proportional to those (the rms values of the harmonic components) of
the output voltage. It may be stated that the rms values of the
harmonic components of both output voltage and current decrease, though
not in inverse proportion to (n) as given in lesson #18 (module 3), as
the order of harmonic () increases. n
The expression for the rms value of the output voltage, as a function
of phase angle delay a, is given in lesson #26 of this module (4), and
not repeated here. The relation between the rms value, and the rms
values of all rV0odd harmonic components is, )2/(,7,5,3,120S==nnrcV
It may be noted that this expression is different from that given in
the section on the harmonic analysis of the output voltage waveform of
a buck converter (dc-dc) in lesson #18 (module 3). This is, because the
average value, is zero, and the rms values of all 0Veven harmonic
components are also zero, with only odd harmonic components being
present, as this waveform has half-wave asymmetry (given earlier). The
rms values of all odd harmonic components, including that of
fundamental one, can, first, be computed as per the formula given
earlier. It may be noted that, the rms values of only a few odd
harmonic components need be computed, because the rms values decrease,
as the order of harmonic increases, as given earlier. Then, using the
expression for the rms value, it (rms value) can be computed. Finally,
it can be checked from the expression for the rms value (given in
lesson #26).
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The rms value of the fundamental (1=n) component of the output voltage,
(2/1c) is maximum (highest) for °Ë0a with °>0a, in normal case, though
it reaches maximum at °=0a (ideal case). Also the rms value of the
output voltage, is maximum (nearly same as the rms value of input
voltage) for rV0°Ë0a, and is slightly higher than the rms value of its
fundamental component. If the expression under the square root for the
rms value is divided into two parts “ the rms value of fundamental
component and the rms values of other odd harmonic components, starting
from third one, the new form is, )2/()2/(,7,5,32210S=+=nnrccV
This expression can also be written as, 2120,7,5,32)2/()( )2/(cVcrnn-
=S=
From this expression, and also from the expressions given earlier, it
can be observed that the rms values of all odd harmonic components,
except fundamental one, starting from third, are very low.
The rms value of the fundamental component of the output voltage,
(2/1c) is minimum (lowest) for )180(°Ëpa with pa<, in normal case,
though it is minimum (zero) at pa= (ideal case). Also the rms value of
the output voltage, is minimum (not zero, but nearly zero) for rV0paË,
and is slightly higher than the rms value of its fundamental component.
From the expression, using the rms value, and the rms value of
fundamental component only, and other expressions given earlier, it can
be observed that the rms values of all odd harmonic components, which
also includes fundamental one in this case, are very low.
This type of harmonic analysis can be performed for the output voltage
of controlled (half/full) single/three-phase converters (ac-dc) with
resistive load, as discussed in lessons #10-11 & 13-14 in module 2. In
the case of three-phase ones, the resistive load is balanced one.
Taking the case of a single-phase controlled bridge converter with
resistive load, the output voltage waveform obtained is of the same
type, except that it is a dc one, with the second half of the periodic
waveform being also positive, unlike the case shown in Fig. 28.1. The
voltage waveform in that case, has half-wave symmetry (having dc and
only even () harmonic components, but no odd harmonic components),
unlike the case here, of the voltage waveform having half-wave
asymmetry (with only odd (mn2=12+=mn) harmonic components, but no even
harmonic and also dc components, as given earlier).
In this lesson - the third and final one in the first half of this
module, the circuit used for the phase angle control in triac-based
single-phase ac regulator or ac to ac voltage converter is, first,
presented. Then, the operation of the various blocks used in the above
circuit, along with the waveforms, is described. Finally, the harmonic
analysis of the output voltage of a single-phase ac regulator with
resistive load is, briefly discussed. Starting with the next (fourth)
lesson - first one in the second half, the various types of cyclo-
converters, used as ac to ac voltage converters, are presented. The
power circuit using mostly thyristors, the output voltage waveforms for
both single-phase and three-phase ones, and the various blocks of
control circuit required (in brief), are mostly described in detail.