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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
3
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
5
~ 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
6
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
8
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=
9
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).
11
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.

how to make triac- based ac regulator using microcontroller so that the the unconsistence voltage can be regulate.