Chapter 4 AC Voltage Regulators

1. Introduction

A power electronic ac/ac converter, in generic form, accepts electric power

from one system and converts it for delivery to another ac system with waveforms

of different amplitude frequency, and phase. They may be single- or three - phase

types depending on their power ratings. The ac/ac converters employed to vary

the rms voltage across the load at constant frequency are known as AC voltage

controllers, AC regulators or AC chopper.

The voltage control is accomplished either by:

(i) Phase control under natural commutation using pairs of silicon-controlled rectifiers (SCRs) or Triacs.

(ii) On-off control under forced commutation using fully controlled self-commutated switches such as Gate Turn-off Thyristors (GTOs), power transistors, Insulated Gate Bipolar Transistors (IGBTs), MOS-controlled Thyristors (MCTs), etc.

The most common applications of AC voltage controllers are: industrial

heating, on-load transformer tap changer, light control, induction heating of

metals, speed control of polyphase induction motors, electric welding, and

primary transformer control for electro-chemical processes and AC magnet

controls. Figure 1 shows the configurations of AC voltage controller.

The basic power circuit of a single-phase ac-ac voltage controller, as shown in

Fig. 1a, is composed of a pair of SCRs connected back-to-back (also known as

inverse-parallel or anti-parallel) between the ac supply and the load. This

connection provides a bidirectional full-wave symmetrical control and the SCR

pair can be replaced by Triac (Fig. 1b) for low-power applications. Alternate

arrangements are as shown in Fig. 1c with two diodes and two SCRs to provide a

common cathode connection for simplifying the gating circuit without needing

isolation, and in Fig. 1d with one SCR and four diodes to reduce the device cost

but with increased device conduction loss. An SCR and diode combination,

known as a thyrode controller, as shown in Fig. 1e, provides a unidirectional half-

wave asymmetrical voltage control with device economy but introduces a dc

component and more harmonics and thus is not very practical to use except for a

very low power heating load.

This chapter shows the operation of AC Chopper, for single phase R load, R-L

load, L-Vb load and the parallel operation of two single phase AC Choppers.

Methods of control:

For power transfer, two methods of control are used:

a. On-off control (Integral-Cycle Control):

The bidirectional AC switch is employed to connect the load circuit to

source for a few cycles (or half cycle) of the source voltage and disconnect it for a

comparable period as shown in Fig. 2

The thyristor switch connects the AC supply to load for a time tn; the switch

is turned off by a gate pulse inhibiting for time to. The on-time, tn, usually consists

of an integral number of cycles. The thyristors are turned on at the zero voltage

crossing of AC input voltage for resistive loads.

This type of control is applied in application, which have a high mechanical

inertia and high time constant such as temperature control, industrial heating and

speed control of motors,

Due to zero voltage switching of the thyristors, the harmonics generated by

switching actions are reduced, with low electrical noise.

Figure 1 Single-phase ac voltage controllers: (a) full-wave, two SCRs in inverse parallel; (b) full-wave with Triac; (c) full wave with two SCRs and two diodes; (d) full wave with

four diodes and one SCR

Figure 1 half-controlled with one SCR and diode in antiparallel.

Figure 2 On-off control (Integral-Cycle Control).

For a sinusoidal input voltage:

)sin()sin(2 tVtVv ms

If the input voltage is connected to load (pure resistance) for n cycles and is disconnected for m cycles, the rms output voltage is given by:

mn

ncycledutyk

kVmn

nV

tdtVmn

nV

ss

s

21

2

0

20 )sin(2(

)(2

Poav= average load power=Vs2K/R

kfactorpower

Example 4.1

A single phase AC voltage regulator has a resistive load of R=10 and the rms input voltage is 120V, 60Hz. The thyristors is On for n=25 Cycles and is Off for m=75 Cycles. Determine: a. rms output voltage. b. input power factor. c. average and rms current of thyristors. Solution: R=10, Vs=120V, n=25, m=75.

25.02575

25

nm

ncycledutyk

a. VkVV s 6025.01200 = rms load voltage.

AR

VI 6

10

6000 =rms load current.

b. wattRIP 360)10(62200 =output power

wattIVP si 7206*1200 =input voltage ampere

laggingmn

nk

P

PPf

i

5.0

5.0720

3600

c. AR

VII s

tppeakthy

97.1610

)120(22

Ak

Imn

nItdtI

mn

nI tptptp

avthy35.1

25.0)97.16(

)().sin(

)(20

Amn

nItdtI

mn

nI

tp

tprmsthy

24.425.02

97.16

)(2].)]sin([

)(2[

0

2/12

b. Phase control method:

The bidirectional AC switch is employed to connect the load circuit to the

source for a chosen portion of each half cycle of the source voltage.

The power flow to the load is controlled by delaying the firing angle of

thyristors T1 and T2 as shown in Fig. 3. This method of control is the must

common used method.

1. Phase control AC Chopper connected to R load:

Figure 4 shows the typical voltage and current waveforms for the single-phase

bidirectional phase-controlled ac voltage controller of Figure 1.a with resistive

load. The output voltage and current waveforms have half-wave symmetry and

thus no dc component.

Figure 3 Phase control method.

If suitable gating pulses are applied to the thyristors T1, T2 while their

respective anode voltages are positive conduction is initiated, the conduction

angle depends on the firing angle (also known as triggering angle) measured from

anode- voltage zero. The effective load voltage vo can be varied from zero,

corresponding to extinction of both thyristors, to almost full supply voltage,

corresponding to full of both thyristors. A set of theoretical wave forms for

sinusoidal supply voltage with an arbitrary triggering angle is given in the

Figure 5.

)sin(2,1 tVvvvv sTo

12 TT vv

,

,01

2,

,

)sin*2

)sin(2

tVvv

tVvRiv

sT

soo

From the viewpoint of power transfer, the electrical parameters of interest are the

rms load voltage Vo and rms current Io.

R

Vtd

R

vI oo

o

2/122

02

1

i.e. for 2 tandt

where varies form 0 to

. then Io varies from Vs/R to 0

and Vo varies from Vs to 0

The rms value the thyristor voltage is

2

2sin

2

12/12

0

211

sTT VtdvV

It is assumed that the supply voltage remain sinusoidal in the presence of

the nonsinusoidal current drawn through the supply impedance.

The Fourier spectrum of the load voltage ant of the load current contains

only odd harmonics.

The time-average value of the load voltage is zero over any complete

2

2sin1

2

12/12

0

2

s

oo

V

tdvV

number of cycles. Half cycle average values of the load voltage Vav and thyristor

voltage VTav are given by

0

cos121 s

oavo

VtdvV

0

cos121 s

TTav

VtdvV

Power is correctly defined as the time rate of energy transfer. The instantaneous

power at the load terminals Pi.

tR

VivP s

ooi 22

sin2

For t ; + t 2

The double supply frequency pulsation is positive for all time regardless of

triggering angle. Average lower P into the circuit with resistive load is given by

the time-average of voio product.

2

2sin1sin

21

2

1 22

0

22

R

Vttd

R

VtdivP s

oo

RIR

Vo

o 22

An alternative viewpoint is to consider that average power is dissipated

only by combination of in phase voltage and current components of the same

frequencies. Since the terminal voltage is sinusoidal and of supply

frequency, average power is related to the supply voltage in combination

with in-phase component of fundamental current Io1.

11 cosos IVP

Where 1 is the phase angle of fundamental component of load current Io1.

Irrespective of waveform, the power factor of a circuit is the factor by which

the apparent power must be multiplied in order to give the average power.

Power factor (pf)=Average Power/Apparent Volt-Ampers= P/Vs/Io.

The factor cos 1 is given the special name "Displacement factor"

The power factor of a nonsinusoidal system is often significantly different

from the displacement factor and this has led to the use of the term distortion

factor.

Distortion factor = Power factor/displacement factor

Power factor 1111 cos

cos

o

o

os

os

os I

I

IV

IV

IV

P

Power factor =

2

2sin1

so

oo

VI

VI

The fundamental component Io1 lags the supply voltage by angle 1. It is

known that a fundamental lagging component of current usually associated

with energy storage in a magnetic field. But in the circuit with resistive load,

shown in this section no storage of energy is possible. For this reason the

pulsations of instantaneous power is always positive. Since the load is not

capable of storing energy, no return of energy can occur from the load to the

supply and the instantaneous power cannot go negative.

Figure 5 Waveforms for single-phase ac full-wave voltage controller with R-load.

2. AC Chopper connected to R-L load

Figure 6 shows the voltage and current waveforms for the controller in

Figure 1.a with R-L load. This type of AC depends on the load impedance

angle, therefore,

a. Let’s take the first α≥ where is the load impedance angle.

Due to the inductance, the current carried by the T1 may not fall to zero

at ωt = π when the input voltage goes negative and may continue until

ωt= β (the extinction angle) as shown.

The conduction angle is:

The conduction angle of the SCR depends on the firing delay angle (α) and the load impedance angle ( ),

There some cases can take in considerations that depend on the firing angle and the power impedance and such as:

Figure 6 Typical wave forms of single-phase ac voltage controller with an RL-load.

1. Where [ ], that produces discontinuous AC output (AC

Chopper) as shown in figure 6.

2. For [α= ] that produces continuous output (Vorms = Vs).

3. Finally for [ ] that represent single phase half wave rectifier

and the output is a discontinuous DC. That is discussed in the single-phase half wave controlled rectifier.

4. State what happing if the gate pulse is sustain?

For The expression for the load current io (ωt) when conducting from

α to β can be derived in the same way as that used for a phase-controlled

rectifier in a discontinuous mode.

By solving the relevant Kirchhoff voltage equation:

)sin(2 tV

dt

diLRi

vv so

This equation of the first order has the solution of:

t

Aez

tVti

)sin(2

)(

Where R

LandLRz

R

L

221 )(,tan

From initial condition at t=α, the load current (io) equal to zero

e

z

VAAe

z

V )0sin(2)0sin(20

The load current equation is given by:

])sin()[sin(2

)( tan/)( tetZ

Vti

This equation valid from t

The angle β, when the current io falls to zero, can be determined from the

following transcendental equation obtained by putting io (ωt = β) = 0 in the

above equation.

tan/)()sin()sin( e

From the above Equation. One can obtain a relationship between γ and α for

given value of Φ, it is obtained that as α is increased the conduction angle γ

decreases and the rms value of the current decreases. The rms output voltage

2/12/122]

2

2sin

2

2sin[])(sin2

1[

VsttdVV so

Vo can be evaluated for two possible extreme values of Φ=0 when β= π and

Φ= π/2 when β=2π- α.

The rms SCR current:

])(2

1[ 2

)(

tdiI rmsSCR

The rms load current

)(2 rmsSCRo II

The average value of SCR current

)(

2

1)( tdiI oavSCR

3. For pure inductance load L: The power circuit is shown in figure 1.(a). As in the case of inductive load

(resistance connected in series with inductance), the pure inductive load

depends also the power angle of the load. In this case the power angle equal

to 90o, therefore,

1. When α90o that produces discontinuous AC output (AC Chopper) as shown in figure 7.

2. For α=90o, that produces continuous output (Vorms = Vs),

3. Finally for α 90o, that represent single phase half wave rectifier and the output is a discontinuous DC. That is discussed in the single-phase half wave controlled rectifier fed pure inductive load.

4. State what happing if the gate pulse is sustain?

Let’s discuss the first case (α90o), the waveform is shown in figure 7. The

thyristor T1 conducts at > /2 and it remain in conduction until (t = 2 -

), due to the flow of current even that the supply voltage is negative. The

thyristor T2 conducts at (t= +). The current io exists for (< t< 2- ).

When T1 conducts and for ( + <t < 3- ) when T2 conducts.

io= 0 for (2-<t<+)

It is noticed that there is asymmetrical operation for the circuit shown.

If the firing pulse are of short time and /2; the current io cease to

conduct later than the firing pulse received by T2; and no current can start in

the opposite direction.

Figure 7. waveforms of pure inductive load when α90o.

4. Parallel operation of phase angle controlled load: For resistive load: Figure 8 shows the parallel operation with phase angle controlled load and

its waveform. The supply voltage and current are given by:

bcss iiitVv sin2

c = firing angle for T1, b = firing angle of T3 with two phase angle

tL

Vi

ttdVL

i

dt

diLv

tVv

so

t

so

o

s

coscos2

sin21

sin2

controllers connected in parallel, a power is delivered into

independently adjustable resistance loads.

For c < b

tfortIi

tfortIi

tfortIi

tfortIi

bcbs

bccs

bbb

ccc

sin2

sin2

sin2

sin2

tdt

IItd

II

b

c b

bccs

22

22

2 sin)(2

sin)2(

Figure 8. The circuit and the wave form

of the parallel operation of AC Chopper