APROJECT REPORT ON

STUDY OF AC TO DC CONVERTER USING MATLAB SIMULINKSUBMITTED IN THE PARTIAL FULFILLMENT OF THE AWARD OF DEGREE OF

BACHELOR OF TECHNOLOGYIN

ELECTRICAL AND ELECTRONICS ENGINEERING

UNDER THE GUIDANCE OF:-

MR. ASIF JAMIL ANSARISENIOR PROFESSOR

EEED, INTEGRAL UNIVERSITYLUCKNOW

SUBMITTED BY:-1. PRANAV TRIPATHI2. ZAINAB 3. TEJASVINI 4. PREETI SINGH5. ABHISHEK NIGAM

INTEGRAL UNIVERSITY, LUCKNOWKursi Road, Lucknow-226026, Uttar Pradesh (INDIA)

Phone: 022 2890812, 2890730, 3296117, 6451039

Fax No.: 0522-2890809

Web: www.integraluniversity.ac.in

CERTIFICATE

This is to certify that the project work entitled ‘Study of AC to

DC Converters using MATLAB’, which is being submitted by

Pranav Tripathi, Zainab, Abhishek Nigam, Preeti Singh and

Tejasvini Gupta in partial fulfillment of award of degree of

Bachelor of Technology in Electrical and Electronics Engineering

from integral university, is carried out under my supervision and

guidance.

Under the guidance of: - Head of Department Mr. Asif Jamil Ansari Mr. M.A. Mallick Senior Professor EEED, Integral University Lucknow

Department of Electrical and Electronics Integral University, Lucknow

2

ACKNOWLEDGEMENT

I would first of all thanks Mr.Asif Jamil Ansari who helped me

to select such an important topic for my project work in which I

received nice exposure of my field and a innovation to do something

in this field. It was very exciting along with interesting and amazing

facts.

I wish to express our sincere thanks to Mr. M A Mallick, Head

of Department. I also express sincere thanks to the Integral

University, Lucknow for providing us with all the necessary

facilities for completing the project work.

I would also like to thank all the faculty and staff members of

CAD lab who extended their full cooperation for completion of this

work. Lastly and most importantly, we wish to thank all our friends

for being the surrogate family during the years we stayed here and

for their moral support.

3

INDEX

Chapter

No.

NAME OF CHAPTER Pg. No.

1. Introduction 5-7

2.Half Wave Controlled Rectifiers

8-

2.(i)Single Phase Half Wave Thyristor Circuit with

R-load

2.(ii)1-Φ Half Wave Thyristor Circuit with RL load

2.(iii)1-Φ Half Wave Thyristor Circuit with RL-load

& Freewheeling Diode

2.(iv) Single Phase Half Wave Circuit with RLE-

load

3.Full Wave Controlled Converters

3.(i)Single Phase Full Wave Mid Point Converters

(M-2 Connection)

3.(ii) Single phase full wave bridge converter

(B-2 Connection)

3.(iv)Line-Commutated Inverter

4

3.(iv) Single-phase semiconverter

3.(v) Single-phase Full Converter Drives

4.Three Phase Converters

5.Simulation Design and Analysis

CHAPTER 1

INTRODUCTION

5

INTRODUCTION

Many Industrial applications need controllable DC power.

Examples of such applications are:-

1. Steel rolling mills, paper mills, printing presses and textile

mills employing DC motor drives.

2. Traction systems working on DC.

3. Electromechanical and Electrometallurgical processes.

4. Magnet Power supplies

5. Portable hand tool drives

6. High Voltage DC transmission

Earlier, dc power was obtained from motor-generator (MG)

sets or ac power was converted to dc by means of mercury-arc

rectifiers or thyratrons. The advent of thyristors has changed the

6

art of ac to dc conversion. Presently, phase controlled ac to dc

converters employing thyristors are extensively used for changing

constant ac input to controlled dc output voltage. In an industry

where there is a provision for modernization, mercury arc

rectifiers and thyratrons are being replaced by thyristors.

In phase controlled rectifiers, a thyristor is turned off as ac

supply reverse biases it, provided anide current has fallen to a

level below the holding current. The turning-off, or commutation,

of a thyristor by supply voltage itself is called as natural or line

commutation. In industrial applications, rectifier circuits make

user of more than one SCR. In such circuits, when an incoming

SCR is turned on by triggering, it immediately reverse biases the

outgoing SCR and turns it off. As phase controlled rectifiers need

no commutation circuitry, these are simple, less expensive and

are therefore widely used in industries where controlled dc power

is required.

In the study of thyristor systems, SCRs and Diodes are assumed

to be ideal switches which means that

(i) there is no voltage drop across them.

(ii) no reverse current exists under reverse voltage

conditions.

7

(iii) holding current is zero.

CHAPTER 2

HALF WAVE CONTROLLED RECTIFIERS

8

HALF WAVE CONTROLLED RECTIFIERS

PRINCIPLE OF PHASE CONTROL

2.(i). Single Phase Half Wave Thyristor Circuit with

R-load

The simplest form of controlled rectifier circuits consists of a

single thyristor feeding dc power to a resistive load R as shown in

fig. 2.(i). The source voltage is vs=Vm sin t, Fig.2.(i). An SCR can

conduct only when anode voltage is positive and a gating signal is

applied. As such, a thyristor blocks the flow of load current io until it

is triggered. At some delay angle , a positive gate signal applied

9

between gate and cathode turns on the SCR. Immediately, full

supply voltage is applied to the load as vo, as in Fig. 2.(i). At the

instant of delay angle , vo rises from zero to Vm sin as shown. For

resistive load, current io is in phase with vo. Firing angle of a

thyristor is measured from the instant it would start conducting if it

were replaced by a diode. In Fig. 2.(i), if thyristor is replaced by

diode, it would begin conduction at t = 0, 2, 4 etc ; firing angle

is therefore measured from these instants. A firing angle may thus

be defined as the angle between the instant thyristor would conduct

if it were a diode and the instant it is triggered.

A firing angle may thus be defined as follows: A firing angle

is measured from the angle that gives the largest average output

voltage, or the highest load voltage. If thyristor in Fig. 2.(i) is fired

at t = 0, 2, 4 etc, the average load voltage is the highest; the

firing angle should thus be measured from these instants. A firing

angle may thus be defined as the angle measured from the instant

that gives the largest average output voltage to the instant it is

triggered.

A firing angle may also be defined as the angle measured from

the instant SCR gets forward biased to the instant it is triggered.

Once the SCR is on, load current flows, until it is turned-off by

reversal of voltage at t = 0, , 3, 5 etc. At these angles of , 3,

10

5 etc., load current falls to zero and soon after the supply voltage

reverse biases the SCR, the device is therefore turned-off. It isc seen

from Fig.2.(i) that by varying the firing angle, the phase

relationship between the start of the load current and the supply

voltage can be controlled, hence term phase control is used for these

methods of controlling the load currents.

A single phase half wave circuit is one which produces only

one pulse of load current during one cycle of source voltage. As the

circuit shown in Fig. 2.1 produces only one load current pulse for

one cycle of sinusoidal source voltage, this circuit represents a

single-phase half-wave thyristor circuit.

In Fig.2.(i), thyristor conducts from t = to , (2+) to 3

and so on. Over the firing angle delay , load voltage vo = 0 but

during conduction angle (-), vo = vs. . As firing angle is increased

from zero to , the average load voltage decreases from the largest

value to zero.

The variation of voltage across thyristor is also shown as vT in

Fig. 2.(i). Thyristor remains on from t = to, (2+) to 3 and

so on. During these intervals vT = 0 (strictly speaking 1 to 1.5V). It is

off from t = to (+) , 3 to (4+ ) etc. During these off

11

intervals vT has the waveshape of supply voltage vs. It may be

observed that vs = vo + vT.

As the thyristor is reverse biased for radians, the circuit turn

off time is given by-

tc = (/) sec

where = 2f and f is the supply frequency in Hz.

12

Fig.2.(i).

The circuit turn off time tc must be more than the SCR turn off

time tq as specified by the manufacturers.

Average voltage Vo across load R in Fig. 6.1 for the single –

phase half wave circuit in terms of firing angle is given by-

Vo = (1/2) Vm sin t d (t) = (Vm/2) (1+ cos )

The maximum value of average output voltage Vo occurs at = 0o.

Vom = (Vm/2) (1+ cos 0o)

Vom = (Vm/2) .2

Vom = (Vm/)

Also, Vo = (Vom /2) (1+ cos )

Average load current, Io = Vo/R = (Vm/ 2R) (1+ cos )

In some types of loads, one may be interested in RMS value of

load voltage Vor. Examples of such loads are electric heating and

incandescent lamps. Rms voltage Vor in such cases is given by-

13

Vor = (1/2) V2m sin2 t d (t) 1/2

Vor = (Vm/2)(-)+ ((sin 2)/2)1/2

The value of rms current Ior is

Ior = (Vor/R)

Power delivered to resistive load = (rms load voltage) (rms load

current) = Vor Ior = (V2or/R) = I2

or R

Input voltamperes = (rms source voltage) (total rms line current)

= Vs Ior = ((2 V2s )/( 2R)) (-)+ ((sin 2)/2)1/2

Input power factor = (Power delivered to load)/ (input VA)

= ( Vor Ior)/( Vs Ior) = (Vor)/( Vs)

Input pf = (1/2 ) (-)+ ((sin 2)/2)1/2

____________________________________________________________________________

2.(ii). 1-Φ Half Wave Thyristor Circuit with RL load

A single-phase half-wave thyristor circuit with RL load is

shown in Fig. 2.(ii). At wt=α, thyristor is turned on by gating signal

14

(not shown). The load voltage Vo at once becomes equal to source

voltage Vs as shown. But the inductance L forces the load, or output,

current io to rise gradually. After some time, io reaches maximum

value and then begins to decrease. At wt=α, Vo is zero but io is not

because of the load inductance L. After wt=π, SCR is subjected to

regverse anode voltage but is will not be turned off as load current io

is not less than the holding current. At some angle β>π, io reduces to

zero and SCR is turned off as it is already reverse biased. After

wt=β, Vo =0 and io =0 and io =0. At wt=2π+α. SCR is triggered

again. Vo is applied to the load and load current develops as before.

turned off as it is already reverse biased. After wt=β, Vo =0and io = o.

At wt=2π+α, SCR is triggered again Vo is applied to the load and

load current develops as before. Angle β is called the extinction

angle and (β-α)=γ is called the conduction angle.

The wave form of voltage VT across thyristor T in Fig. 2.(ii).

reveals that when wt=α, VT = Vm sin α; from wt=α to β, VT =0 and at

wt=β, VT = Vm sinβ. As β>π, VT is negative at wt=β. Thyristor is

therefore reverse biased from wt=β to 2π. Thus, circuit turn-off time

tc=2π-β/w sec. for satisfactory commutation, tc should be more than

tq the thyristor turn-off time.

15

Fig.2.(ii)

The voltage equation for the circuit of Fig.2.(ii), when T is on,

is

Vm sin wt= Rio+ L dio/dt

The load current io consists of two components, one steady-

state component is and the other transient component it. Here is is

given by

is = Vm /(√R2+X2 sin (wt-))

16

where = tan-1(X/R) and X=wL. Here is the angle by which rms

current Is lags Vs

The transient component is can be obtained from force-free

equation.

Rit+L dit/dt =0

Its solution gives, it=Ae-(R/L)t

io = is+ it = [Vm/(z sin (wt-))]+A–(R/L)t ………………..(1)

where, Z=√ R2+X2

Constant A can be obtained from the boundary condition at wt=α.

At this time t = α/w, io = 0. Thus, from Eq. (1),

0=Vm/Z sin (α-) + Ae-Ra/Lw

A= (-Vm /Z) sin (α-) eRα/wL

Substitution of A in Eq. (1) gives

io = Vm /Z sin (wt-) – Vm /Z sin (α-) exp. {-R/wL (wt-α)} …....(2)

for

It is also seen from the waveform of io in fig. 2(ii) that when

wt=β, load current io =0 Substituting this in Eq. (2) gives

17

sin (β-)= sin(α-). exp {-R/wL(β-α) }

This transcendental equation can be solved to obtain the value

of extinction angle β. In case β is known, average load voltage Vo is

given by

Vo = (1/2π) [α Vm sin wt d (wt)] = Vm /[2π (cosα-cosβ)]

Average load current, Io= Vm /2πR (cosα-cosβ)

Rms load voltage, Vor = [1/2π β V2 sin2 wt.d(wt)}1/2

= Vm /2√π [(β-α)-1/2 {sin 2β-sin2α } ] 1/2

_______________________________________________________

2.(iii). 1-Φ Half WaveThyristor Circuit with RL-load &

Freewheeling Diode

A single-phase half wave thyristor circuit with RL-load and

freewheeling diode is shown in Fig. 2 (iii). Line voltage is shown at

the top of Fig. 2 (iii). At t = , thyristor is turned on by the gating

18

signal ( not shown). The load voltage at once becomes equal to

source voltage vs as shown. But inductor L forces the load or output

current io to rise gradually. After some time, io reaches the maximum

value and begins to decrease. At t = , vo is zero but io is not

because of the load inductance L. After t = , SCR is subjected to

reverse anode voltage and it will turn off thyristor. At the same time

FD is forward biased through the conducting SCR. As a result, load

current io is immediately transferred from SCR to FD.

The waveform of load current io is improved by connecting a

freewheeling (or flywheeling) diode across load. A freewheeling

diode is also called as by-pass or commutating diode. Voltage drop

across FD is taken almost zero. So load voltage vo is therefore zero

during freewheeling period. SCR is reverse biased from t = to t

= 2. Therefore circuit turn off time is-

tc = (/) sec

The source current is and thyristor currents iT have same

waveforms. Operation of circuit is divided in two modes. In first

mode, called conduction mode, SCR conducts from to , (2 + )

to 3 and so on and FD is reverse biased. The duration of this mode

is for [(-)/] sec. Let the load current at the beginning of mode 1

19

be Io. The expression for current io in mode 1 can be obtained as

follows:

Mode 1:- t

Vm sin t = Rio + L(dio/dt)

Its solution is-

io = [(Vm/Z)(sin (t-)] + A e((-R/L)t)

At t = , io = Io i.e. at t = (/), io = Io

A = [Io – (Vm/Z)( sin (-)) ] e(R/L)

io=(Vm/Z)(sin (t-)+[Io – (Vm/Z)( sin (-)) ]exp{(-R/L)(t-

(/)}

20

Fig.2.(iii).

Mode 2:- t(2+)

This mode is called freewheeling mode, extends from to 2, 3 to

4…. As shown by voltage waveform vT in Fig. 6.3 (b). As the load

current is assumed continuous, FD conducts from to (2+), 3 to

(4+)… Let the current at the beginning of mode 2 be Io1 as shown.

As load current is passing through FD, the voltage equation for

mode 2 is

0 = Rio + L(dio/dt)

21

Its solution is – io = A e((-R/L)t)

At t = , io = Io1

It gives A = Io1 e((-R/L))

Io = Io1 exp [(-R/L) (t-(/))]

Average load voltage Vo = (1/2) Vm sin t d (t)

Vo = (Vm/2) (1+ cos )

Average load current, Io = Vo/R = (Vm/ 2R) (1+ cos )

Load current is contributed by SCR from to , (2 + ) to

3 and so on and by FD conducts from 0 to , to (2+), 3 to

(4+) and so on. Thus the wave shape of iT is identical to io for t

= to , (2 + ) to 3 and so on. Similarly, the wave shape of FD

current ifd is identical with io for t = 0 to , to (2+), 3 to

(4+) and so on.

Load consumes power p1from source for to (both vo and io

are positive) whereas energy stored in inductance L is returned to

the source as power p2 for to (vo is negative and io is positive).

As a result, net power consumed bythe load is difference of these

two powers p1 and p2. Load absorbs power for to , but for to

(2+), energy stored in L is delivered to load resistance R through

22

the FD. As a consequence, power delivered to load, for the same

firing angle, is more when FD is used. As volt-ampere input is

almost the same in both fig. , the input pf = (power delivered to load/

input volt-ampere) with the use of FD is improved.

Thus the advantages of using freewheeling diode are-

(i) input pf is improved

(ii) load current waveform is improved

(iii) load performance is better

(iv) as energy stored in inductor L is transferred to R during

the freewheeling period, overall converter efficiency

improves.

Supply current is taken from the source is unidirectional and is

in the form of dc pulses. Single phase half wave converter thus

introduces a dc component into the line. This is undesirable as

it leads to saturation of the supply transformer and difficulties

(harmonics etc...).

__________________________________________________

23

2.(iv). Single Phase Half Wave Circuit with RLE-load

A single phase half controlled converter with RLE load is

shown in Fig. 2(iv). The counter emf E in the load may be due to a

battery or a dc motor. The minimum value of firing angle is obtained

from the relation Vm sin t = E. This is shown to occur at an angle 1

in Fig. 2. (iv) where

1 = sin-1(E/Vm)

In case thyristor T is fired at an angle <1, then E > Vs, SCR is

reverse biased and therefore it will not turn on. Similarly, maximum

value of firing angle is 2 = (-1), Fig.2.(iv). During the interval

load current io is zero, load voltage vo = E and during the time io is

not zero, vo follows vs curve. For the circuit of Fig. 6.4(a) and with

SCR T on, KVL gives the voltage differential equation as-

Vm sin t = Rio + L(dio/dt)+ E

24

Fig. 2.(iv).

The solution of this equation is made up of two components:-

steady state current component is and the transient current

component it. Let, is= is1 + is2 where is1 is the steady state current due

to ac source voltage acting alone and is2 is that due to counter emf E

acting alone.

is1 = (Vm /Z) sin (t-)

If only E were present, then steady state current is2 would be given

by-

is2 = - (E/R)

The transient current it = A e-(R/L)t

25

Thus total current io = is1 + is2 + it

io = (Vm /Z) sin (t-) - (E/R) + A e-(R/L)t

At t =, io= 0, i.e. at t = (/), io = 0.

This gives A = [(E/R)-(Vm/Z) ( sin (-))] e(R/L)

io = (Vm /Z) = [ (sin (t-))-( sin (-))exp{(-R/L) (t-)}]-(E/R)

[ 1- exp{(-R/L) (t-)}]

This equation is applicable for t. The extinction angle

depends upon load emf E, firing angle and the load impedance

angle. Average voltage across inductance L is zero. Average load

current can be given as-

Io= (1/2R) [(Vm sin t) – E] d (t)

Io= (1/2R) [(Vm (cos -cos ) – E(-)]

Here conduction angle =-. Putting = + gives

Io= (1/2R) [(Vm (cos -cos +) – E()]

Vo = E + IoR

Vo = (1/2)[ (Vm sin t) d (t)+ E(2+-)]

Vo = (1/2)[ (Vm(cos - cos ) + E(2+-)]

26

CHAPTER 3

FULL WAVE CONTROLLED RECTIFIERS

27

Full Wave Controlled Converters

There is large variety of SCR controlled converters (or

rectifiers). They can be classified in different ways.

According to number of supply phases on input side, ac to dc

converters can be-

1. Single phase converters

2. Three phase converters

According to number of load current pulses per cycle of source

voltage, ac to dc converters can be-

1. A Half controlled converters produces only one pulse so called

as single pulse rectifier.

2. A Full controlled converter produces two pulses so called as

two-pulse rectifier.

There are two basic configurations of two pulse rectifier. One

configuration uses an input transformer with two windings for

each input phase winding. This is called as mid-point converter.

28

Second configuration uses SCRs in the form of a bridge

circuit. Single phase two pule bridge converter using 4 SCRs and a

three phase six-pulse bridge converter is shown in figure.

(1-fully-controlled rectifier) (3-fully-controlled rectifier)

(1- 2-pulse mid point converter) (3- 6-pulse mid point converter)

29

(1- 2-pulse bridge converter) (3- 6-pulse bridge converter)

Single Phase Full Wave Converters

In single phase two-pulse (or full wave) converters, voltage at

the output terminals can be controlled by adjusting firing angle delay

of the thyristors. Mid-point or Bridge type circuits may be used for

ac to dc conversion.

3.(i). Single Phase Full Wave Mid Point Converters

(M-2 Connection)

The circuit diagram of a single phase full wave converter using

a centre-tapped transformer is shown in Fig. 3.8 (a). When terminal

a is positive with respect to n, terminal is positive with respect to b.

Therefore, van =vnb or van =-vbn as n is the mid-point of secondary

winding. Assume that load current is continuous and turns ratio from

primary to each secondary is unity.

30

Thyristors T! and T2 are forward biased during positive and

negative half cycles respectably ; these are therefore triggered

accordingly. Suppose T2 is already conducting. After WT=0, van is

positive, T! is therefore forward biased and when triggered at delay

angle α, T1 gets turned on. At this firing angle α, supply voltage 2Vn

sin α reverse biases T2, this SCR is therefore turned off. Here T1 is

called the incoming thyristor and T2 the out going thyristor.

As the incoming SCR is triggered, Ac supply voltage applies

reverse bias across the outgoing thyistors and turns it off. Load

current is also transfer from outgoing SCR to incoming SCR. This

process of SCR turned off by natural reversal of AV supply voltage

is called natural or line commutation.

31

Fig. 3.(i).

From the equivalent circuit of figure 6.8 (b) it is seen that if

van = Vm sin wt

then vbn = -vnb = -Vm sin wt

and vab = van + vnb = 2Vm sin wt

32

when wt=α, T1 is triggered. SCR T2 is subjected to a reverse

voltage vab = 2Vm sin α as stated before, current is transferred from

T2 to T1 and as a result T2 is turned off. The magnitude of reverse

voltage across T2 can also be obtained by applying KBL to the loop

efghe of the equivalent circuit of fig.3.(i) at the instant T1 is

triggered. Thus

vt2-vbn + van –vt1 = 0

vt2 = vbn-van+vt1

with T1 conducting, vt1=0. therefore the voltage across T2, at the

instant wt=α is given by

vt2 =-Vm sin α – Vm sin α = -2 Vm sin α

this shows that SCR T2 is reverse biased by voltage 2Vm sin α and it

is therefore turned off at wt = α . thyristor T1 conducts from α to π +

α. After wt = π T1 is reversed biased but it will continue conducting

as the forward biased SCR T2 is not get gated. At wt = π + α , T2 is

triggered, T1 is reversed biased by voltage of magnitude 2vm sin α,

current is transferred from T1 to T2, T1 is therefore turned off.

At wt = α , T2 is turned off and it remain reverse biased from wt =α

to π, this can be seen from fig.3.(i). the turned of time provided by

this circuit to SCR T2 is there fore given by

33

tc = [(π-α)/ ] sec…………………….(3.1)

Thyristor T1 is turned off at wt = π + α and fig.3.(i). reveals that T1

is subjected to a reverse voltage from wt = π +α to wt= 2π.

Therefore this circuit provides a turn of time to thyristor T1 as

tc = [2π-(π+α)/] = [(π-α)/]

which is the the same provided to thyristor T2 ; Eq(1)

It is seen from voltage waveform v0, Fig.3.(i), that average value of

output voltage is given by

Vo= 1/π ∫αα+π Vm sin wt . d (wt) = [(2Vm/π) . cos α]

The circuit turn off time tc eq.(1), as provided by this circuit of

Fig.3(i), a must be greater than SCR turn off time tq as given in the

specification sheet. In case tc < tq , commutation failure will occur

and the whole secondary winding will be short circuited. During

commutation failure, if the rate of rise of fault current is high, the

incoming SCR may be damaged in case protective elements do not

clear the fault. Figure. 3.(i) reveals that each SCR is subjected to a

peak voltage of 2Vm.

The following observations can be made from the above studies

I. When commutation of an SCR is desired, is it must be reverse

baised and the incoming SCR must be forward biased.

34

II.

When incoming SCR is gated on, current is transferd from

outgoing SCR to incoming SCR.

III. The circuit turn off time must be greater than SCR turn off

time.

It is seen from above that thyrister commutation achieved by means

of natural reversal of line voltage, called line or natural

commutation, is simple, it is therefore employed in all phase-

controlled rectifiers, Ac voltage controllers and cycloconverters.

_______________________________________________________

3.(ii). Single phase full wave bridge converter

(B-2 Connection)

A single phase full converter bridge using four SCRs is shown in

fig.3.(ii).The load is assumed to be of RLE type, where e is the load

circuit emf. Voltage E may be due to a battery in the load circuit or

may be generated emf of a dc motor. Thyristor pair T1,T2is

simultaneously triggered & π radians later ,pair T3,T4 is gated

together.When a is positive with respect to b, supply voltage

waveform is shown as vab in fig.3.(ii). When b is positive with

respect to a, supply voltage waveform is shown dotted as vba.

Obviously, vab=-vba. The current directions & voltage polarities

shown in fig.3.(ii), are treated as positive.

Load current or output current io is assumed continous over the

working range; this means that load is always connected to the ac

35

voltage sources through the thyristors .Between wt=0 & wt=π;

T1,T2 are forward baised through already conduting SCRs T3 & T4

and block the forward voltage. For continuous current thyristors

T3 ,T4 conduct aftr wt=0 even though these are reverse biased.

When forward biased SCRs T1,T2 are triggered at wt=π, they get

turned on. As a result supply voltage Vm sin α immediately appears

across thyristors T3,T4 as a reveres bias , these are therefore turned

off by natural, or line , commutation. At the same time, load current

io flowing through T3,T4 is transferred to T1,T2 at wt=α. Note that

when T1,T2 are gated at wt=α, these SCRs will get turned on only if

Vm sin α> E. Thyristors T1,T2 conduct from wt=α to π+α. In other

words, T1,T2 conduct for π radian. Likewise, waveform of current it1

through T1 (or it2 through T2) is shown to flow π radians in fig.3.

(ii). At wt=π+α, forward biased SCRs T3,T4 are triggered. The

supply voltage turns off T1,T2 by natural commutation & the load

current is transferred from T3,T4 .

Voltage across thyristors T1, T2 is shown as uT1=uT2 and that

across T3, T4 as uT3=uT4. Maximum reverse voltage across, T1,

T2, T3 or T4 is Vm, and at the instant of triggering with firing angle

α, each SCR is subjected to a reverse voltage of Vm sin α. Source

current is treated as positive in the arrow direction . Under this

assumption, source current is shown positive when T1, T2 are

conducting and negative when T3, T4 are conducting, Fig.3.(ii).

36

Fig.3.(ii)

During α to π, both vs and is are positive, power therefore flows

from ac source to load During the interval π to (π + α), is negative

but is positive, the load therefore returns some of its energy to the

37

supply system, But the net power flow is from ac source to dc load

because (π – α)>α om Fig. 6.10 (b.

The load terminal voltage, or full-converter output voltage, vo

is shown in Fig.3.(ii).

The average value of output voltage Vo is given by

Vo = (1/π)π+Vmsin(wt).d(wt)

= [(2Vm/) cos α] …(3.2)

rms value of output voltage for single-phase M-2, or B-2,

controlled converter can also be obtained as under.

Vor = [(1/π) π+α Vm

2 sin(2wt) d (wt)

= (Vm2/2π ) [wt-{1/2 sin (2 wt)|} π+α

α] = Vm2/2 =V2

s

Vor = Vs

_______________________________________________________

3.(iii). Line-Commutated Inverter

38

Eq. (3.2) shows that if α > 90o, vo is negative. This is illustrated in

Fig.3. (iii)., where α is shown greater than 90o. In this figure,

average terminal voltage Vo is negative, If the load circuit emf E is

reversed, this source E will feed power back to ac supply. This

operation of full converter is known as inverter operation of the

converter. The full converter with firing angle delay greater than

90o is called line-commutated inverter. Such an operation is used

in the regenerative braking mode of a dc motor in which case then E

is counter emf of the de motor.

During 0 to α, ac source voltage vs is positive but ac source

current is is negative, power therefore flows from dc source to ac

source. From α to π, both Vs and is are positive, power therefore,

flows from ac source to dc source. But the net power flow is from dc

source to ac source, because (π – α) < α in Fig.3. (iii).

In converter operation, the average value of output voltage Vo

must be greater than load circuit emf E. During inverter operation,

load circuit emf when inverted to ac must be more than ac supply

voltage. In other words, de source voltage E must be more than

inverter voltage Vo, only then power would flow from de source to

ac supply system. But in both converter and inverter modes,

thyristors must be forward biased and current through SCRs must

flows in the same in the same direction as these are unidirectional

devices. This is the reason output current io is shown positive in

39

Fig.3. (iii). As before, source current is is positive when T1, T2 are

conducting.

Fig.3. (iii).

40

The variation of voltage across thyristors T1, T2 T3 or T4

reveals that circuit turn-off time for both converter and inverter

operations is given by

tc = [(π-α)/] sec

As both the types of phase-controlled converter have been

studied, the advantages of single-phase bridge converter over single-

phase mid-point converter can now be stated:

(i) SCRs are subjected to a peak inverse voltage of 2

Vm in mid-point converter an Vm in full converter.

Thus for the same voltage and current ratings of

SCRs, Power handled by mid-point configuration is

about half of that handled by bridge configuration.

(ii) In mid-point converter, each secondary should be

able to supply the load power. As such the

transformer rating in mid-point converter is double

the load rating. This, however, is not the case in

single-phase bridge converter.

41

(iv). Single-phase semiconverter

A single-phase semiconverter bridge with two thyristors and

three diodes is shown in fig.3. (iv). The semiconverter are T1, T2;

the two diodes are D1, D2; the third diode connected across load is

freewheeling diode FD. The load is of RLE Type as for the full

converter bridge. Various voltage and current waveforms for this

converter are shown in Fig.3. (iv), where load current is assumed

continuous over the working range.

After wt = 0, thyristor T1 is forward biased only when source

voltage Vm sin > E. With T1 on, load gets connected to source

through T1 and d1. For the period wt = α to π, load current io flows

through RLE, D1, source and T1 and the load terminal voltage vo is

the same wave shape as the ac source vs. Soon after wt = π, load

voltage vo tends to reverse as the ac source voltage changes polarity.

Just as vo tends to reverse (at wt = π+), FD gets forward biased and

starts conducting. The load, or output, current io, is transferred from

T1, D1 to FD. As SCR T1 is reverse biased at wt = π+ through FD,

T1 is turned off at wt = π+. The waveform of current iT1 through

thyristor T1 is shown in Fig.3. (iv). It flows α to π, (2π+α) to 3π and

so on for an interval of (π-α) radians. The load terminals are short

circuited through FD, therefore load, or output, voltage vo is zero

during π<wt>(π+a). After wt=π, during the negative half cycle, T2

will be forward biased only when source voltage more than E.

42

At wt = (π+α), source voltage exceeds E, T2 is therefore

triggered. Soon after (π+α), FD is reverse biased and is therefore

turned off; load current now shift form FD to T2, D2. At wt = 2π,

FD is again forward biased and output current io is transferred from

T2, D2 to FD as explained before. The source current is in positive

from α to π when T1, D1 conduct and is negative from (π + α) to 2π

when T2, D2 conduct, see Fig.3.(iv).

During the interval α to π, T1 and D1 conduct and ac source

delivers energy to the load circuit. This energy is partially stored in

inductance L, partially stored as electric energy in load-circuit emf E

and Partially dissipated as heat in r. During the freewheeling period

π to (π + α), energy stored in inductance is recovered and is partially

dissipated in R and partially added to the energy stored in load emf

E. No energy is fed back to the source during freewheeling period.

For semiconverter, the average output voltage Vo, from Fig.3.

(iv), is given by -

Vo = (1/π) απ Vm sin wt. d(wt)

= (Vm/π) (1+cos α) ….(3.3)

and rms value of output voltage is

Vor = [(1/π) απ Vm2 sin(2wt) d (wt)

= (Vm2/2π ) [ wt-{sin2wt/2} π α] = (Vs/π) [(π-α)+(sin2α)/2]

= Vs [(1/π) {(π-α) + (sin 2α)/2}]1/2

43

Fig.3. (iv)

The variation of voltage across across T1 and T2 is also

depicted in Fig.3. (iv). It is seen from these waveforms that circuit-

turn off time for the semiconverter is

tc=π-α/w sec

_______________________________________________________

44

3.(v). Single-phase Full Converter Drives

Two full converters, one feeding the armature circuit and other

feeding the field circuit of a separately-excited de motor, are shown

in Fig.3.(v). This scheme offers two-quadrant drive, Fig.3.(v) and its

use is limited to about 15 kW. For regenerative braking of the motor,

the power must flow from motor to the ac source and this is feasible

only if motor counter emf is reversed because then eaia would be

negative. Note that direction of current cannot be reversed as SCRs

are unidirectional devices. So, for regenerative breaking, the polarity

of ea must be reversed which is possible by reversing the direction of

motor field current by making delay angle of full converter 2 more

than 90o . In order that current in field winding can be reversed, the

field winding must be energised through single-phase full converter

as in Fig.3.(v).

45

Fig.3.(v).

For the armature converter 1, Vo= Vt = 2 Vm /π cos α For 0<α>π

……(3.4)

For the field converter 2, Vf = (2 Vm /π) cos α1 for 0< α1>π

.. ...(3.5)

46

From the waveforms in Fig.3.(v), it is seen that

rms value of source current, Isr=√ Ia 2 . π/π = Iα

rms value of thyristor current, ITr = [Iα 2 . π/2π]1/2 = Iα/ √2 …..(3.6)

From Eq. (3.4), input supply pf= Vt . Iα / Vs . Isr= 2 Vm /π cosα. Iα . /2/ Vm . Ia

= 2√2/π cos α …..(3.7)

It is seen from Eq.3.7 that pf depends on the firing angle α

only under the assumptions of constants armature current.

_______________________________________________________

47

CHAPTER 4

THREE PHASE CONVERTERS

48

THREE PHASE CONVERTERS

If all the diodes of fig.3.39 are replaced by thyristors , a three

phase full converter bridges as shown in fig.4.(i) is obtained. The

three phase input supply is connected to terminals A,B,C & the load

RLE is connected across the output terminals of converter as shown.

As in a single phase converter full converter, thyristor power circuit

of fig.6.26 works as a three phase ac to dc converter for firing angle

delay 0o < α < 180o . A three phase full converter is therefore

preferred where regeneration of power is required. The numbering

of SCRs in Fig. 6.26 is 1, 3, 5 for the positive group and 4(=1+3),

6(=3+3), 2(=5+3-6) for the negative group. This numbering scheme

is adopted here as it agrees with the sequence of gating of the six

thyristors in a 3-phase full converter.

49

Fig. 4.(i).

50

For α=0o; T1, T2,…..T6 behave like diodes. This is shown in

fig.4.(i). The sequence of conduction of SCRs T1 to T6 is also

indicated in this figure. Note that for α=0o, T1 is triggered at wt =

π/6, T2 at 90o, T3 at 150o and so on. The load voltage has, therefore,

the waveform as shown in Fig.4.(i). For α = 60o, the conduction

sequence of thyristors T1 to T6 is shown in fig.4.(i). Here T1 is

triggered at wt=30o + 60o = 90o , T2 at 90 + 60= 150o and so on. If

the conduction interval of various thyristors T1, T2, …… T6 is

shown first, then it becomes easier to draw the voltage and current

waveforms. Note that each SCR conducts for 120o, when T1 is

triggered, reverse biased thyristor T5 is turned on. T6 is already

conducting. As T1 is connected to A and T6 to B, voltage Vab

appears across load. It varies form 1.4 Vm to zero as shown. Here Vmp

is the maximum value of phase voltage. When T2 is turned on,T6 is

commutated from the negative group. T1 is already conducting. As

T1 and T2 are connected to A and C respectively, voltage Vac appears

across load. Its value varies from 1.5 Vmp to zero as shown. This

sequence of triggering is continued for other SCRs.

Note that positive group of SCRs are fired at an interval of

120o. Similarly, negative group of SCRs are fired with an interval of

120o amongst them. But SCRs from both the groups are fired at an

interval of 60o. This means that commutation occurs every 60o

51

alternatively in upper and lower group of SCRs. Each SCR from

both groups conducts for 120o . At any time, two for SCRs, one from

the positive group and the other from negative group, must conduct

together for the source to energise the load. For ABC phase sequence

of the three-phase supply, thyristors conduct in pairs; T1 and T2, T2

and T3, T3 and T4 and so on.

CHAPTER 5

SIMULATION DESIGN AND ANALYSIS

52

2.(i). Single Phase Half Wave Thyristor Circuit with

R-load

Source voltage Vs = 100V

Load resistance R = 100

Firing angle = 450

53

54

2.(ii). Single Phase Half Wave Thyristor Circuit with

RL-without FD

Source voltage Vs = 100V

Load resistance R = 100 and inductance L = 0.01H

Firing angle = 450

55

56

2.(iii). Single Phase Half Wave Thyristor Circuit with

RL- FD load

Source voltage Vs = 100V

Load resistance R = 100 and inductance L = 0.01H

Firing angle = 450

57

2.(iv). Single Phase Half Wave Thyristor Circuit with

RLE load

Source voltage Vs = 100V

Load resistance R = 100 and inductance L = 0.01H

Back emf E = 50V

Firing angle = 450

58

59

3.(i). Single Phase Full Wave Mid Point Converters

(M-2 Connection)

Source Vs1 = 100V Vs1 = 100V

Load resistance R = 100 and inductance L = 0.01H

Back emf E = 50V

Firing angle = 450

60

3.(ii). Single phase full wave bridge converter

(B-2 Connection)

61

62

3.(iii). Line-Commutated Inverter

63

64

(iv). Single-phase semiconverter

65

66

67

3.(v). Single-phase Full Converter Drives in

continuous mode of operation

68

69

3.(vi). Single-phase Full Converter Drives in

discontinuous mode of operation

70

71

4.(i).THREE PHASE CONVERTERS

72

73

REFERENCES

74