# Chapter 3 Single Phase Fully Controlled Rectifier

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Chapter 3

Single Phase Fully Controlled Rectifier

.

Operation and Analysis of single phase fully controlled converter.

Instructional Objectives

On completion the student will be able to

• Differentiate between the constructional and operation features of uncontrolled and controlled converters.

• Draw the waveforms and calculate their average and RMS values of different variables associated with a single phase fully controlled half wave converter.

• Explain the operating principle of a single phase fully controlled bridge converter.

• Identify the mode of operation of the converter (continuous or discontinuous) for a given load parameters and firing angle.

• Analyze the converter operation in both continuous and discontinuous conduction mode and there by find out the average and RMS values of input/output, voltage/currents.

• Explain the operation of the converter in the inverter mode.

1 Introduction

Single phase uncontrolled rectifiers are extensively used in a number of power electronic based converters. In most cases they are used to provide an intermediate unregulated dc voltage source which is further processed to obtain a regulated dc or ac output. They have, in general, been proved to be efficient and robust power stages. However, they suffer from a few disadvantages. The main among them is their inability to control the output dc voltage / current magnitude when the input ac voltage and load parameters remain fixed. They are also unidirectional in the sense that they allow electrical power to flow from the ac

side to the dc side only. These two disadvantages are the direct consequences of using power diodes in these converters which can block voltage only in one direction. As will be shown in this module, these two disadvantages are overcome if the diodes are replaced by thyristors; the resulting converters are called fully controlled converters. Thyristors are semicontrolled devices which can be turned ON by applying a current pulse at its gate terminal at a desired instance. However, they cannot be turned off from the gate terminals. Therefore, the fully controlled converter continues to exhibit load dependent output voltage /current waveforms as in the case of their uncontrolled counterpart. However, since the thyristor can block forward voltage, the output voltage / current magnitude can be controlled by controlling the turn on instants of the thyristors. Working principle of thyristors based single phase fully controlled converters will be explained first in the case of a single thyristor half wave rectifier circuit supplying an R or R-L load. However, such converters are rarely used in practice. Full bridge is the most popular configuration used with single phase fully controlled rectifiers. Analysis and performance of this rectifier supplying an R-L-E load (which may represent a dc motor) will be studied in detail in this chapter.

2 Single phase fully controlled half wave rectifier

2.1 Resistive load

Figure 1 Single-phase fully controlled half wave rectifier supplying resistive load.

Fig. l(a) shows the circuit diagram of a single phase fully controlled half wave rectifier supplying a purely resistive load. At t= 0 when the input supply voltage becomes positive the thyristor becomes forward biased. However, unlike a diode, it does not turn ON till a gate pulse is applied at t= α. During the period 0 < t≤ α, the thyristor blocks the supply voltage and the load voltage remains zero as shown in fig. 1(b). Consequently, no load current flows during this interval. As soon as a gate pulse is applied to the thyristor at t= α, it turns ON. The voltage across the thyristor collapses to almost zero and the full supply voltage appears across the load. From this point onwards the load voltage follows the supply voltage. The load being purely resistive the load current i0, is proportional to the load voltage. At t= π as the supply voltage passes through the negative going zero crossing the load voltage and hence the load current becomes zero and tries to reverse direction. In the process the thyristor undergoes reverse recovery and starts blocking the negative supply voltage. Therefore, the load voltage and the load current remains clamped at zero till the thyristor is fired again at t= 2π + α. The same process repeats thereafter.

From the discussion above and Fig .1 (b) one can write

Similar calculation can be done for io. In particulars for pure resistive loads FFio = FFvo. 2.2 Resistive-Inductive load Fig 2 (a) and (b) shows the circuit diagram and the waveforms of a single phase fully controlled half wave rectifier supplying a resistive inductive load. Although this circuit is hardly used in practice its analysis does provide useful insight into the operation of fully controlled rectifiers which will help to appreciate the operation of single phase bridge converters to be discussed later.

Figure 2 Single-phase fully controlled half wave rectifier supplying resistive inductive load.

As in the case of a resistive load, the thyristor becomes forward biased when the supply voltage becomes positive at t= 0. However, it does not start conduction until a gate pulse is applied at t= α. As the thyristor turns ON at t= α the input voltage appears across the load and the load current starts building up. However, unlike a resistive load, the load current does not become zero at t= π, instead it continues to flow through the thyristor and the negative supply voltage appears across the load forcing the load current to decrease. Finally, at t= β (β> π) the load current becomes zero and the thyristor undergoes reverse recovery. From this

point onwards the thyristor starts blocking the supply voltage and the load voltage remains zero until the thyristor is turned ON again in the next cycle. It is to be noted that the value of β depends on the load parameters. Therefore, unlike the resistive load the average and RMS output voltage depends on the load parameters. Since the thyristors does not conduct over the entire input supply cycle this mode of operation is called the "discontinuous conduction mode".

From above discussion one can write.

Since the average voltage drop across the inductor is zero. However, Iorms can not be obtained from Vorms directly. For that a closed from expression for io will be required. The value of β in terms of the circuit parameters can also be found from the expression of io.

The equation of the output current io can be used to find out Iorms. To find β it is noted that io|t=β=0

Exercise 1

Fill in the blank(s) with appropriate word(s) : i) In a single phase fully controlled converter the _________ of an uncontrolled converters are replaced by ____________. ii) In a fully controlled converter the load voltage is controlled by controlling the _________ of the converter. iii) A single phase half wave controlled converter always operates in the ________ conduction mode. iv) The voltage form factor of a single phase fully controlled half wave converter with a resistive inductive load is _________ compared to the same converter with a resistive load. v) The load current form factor of a single phase fully controlled half wave converter with a resistive inductive load is _________ compared to the same converter with a resistive load.

Answers:

(i) diodes, thyristors; (ii) firing angle; (iii) discontinuous (iv) poorer; (v) better. 2) Explain qualitatively, what will happen if a free-wheeling diode (cathode of

the diode shorted with the cathode of the thyristor) is connected across the load in Figure 2.(a) Answer 2: Referring to Figure 2(b), the freewheeling diode will remain off till t=π since the positive load voltage across the load will reverse bias the diode. However, beyond this point as the load voltage tends to become negative the freewheeling diode comes into conduction. The load voltage is clamped to zero thereafter. As a result i) Average load voltage increases. ii) RMS load voltage reduces and hence the load voltage form factor reduces. iii) Conduction angle of load current increases as does its average value. The load current ripple factor reduces.

2.3 Pure inductive load:

Figure 3 Single-phase controlled rectifier fed a pure inductive load. (a) The circuit diagram (b) waveform.

Figure 3 (a) shows the connection diagram. When the thyristor turn on at t=α in

the positive half cycle of input voltage, the output voltage will equal the input

voltage according to KVL. The current in the circuit will increase slowly, since the

inductance in the load forces the current to lag the voltage. The inductor is storing

energy in its magnetic field.

When the applied voltage become negative, the thyristor is reversed biased.

However, the energy stored in the magnetic field of the inductor is returned and

maintains a forward-decaying current through the load. The current continues to

flow unit β =2π-α (cut off angle, advance angle or excitation angle), when the SCR

turns off. The voltage across the inductor then changes polarity, and the voltage

across the load becomes negative.

The average output voltage (Vo) becomes zero, because its positive part equal

to its negative part.

The conduction angle is γ=2(π-α)

0

vo vi

0

from 0 to to 2 ( for pure L

(2 ) to 2

The current in the current will follow when the output voltage equal to the

input voltage.

From to 2

di vo 2V sin(t) L

dt

2V sin(t)dt di

L

t 2V sin(t)

i

dt such that

L

2V i (cos( ) cos(t))

L

The average current of the output current

1 2V

io

(cos( ) cos(t))dt

2 L

1 i

2V ( ) cos( ) sin( )

o

XL

The rms of the output voltage is given by:

V0rms

1 2 2V sin(t dt 2

1 1 Vorms V sin(2 )

2 2 4

The average output power equal to zero and it is given by:

1 2 1 2 2V

P0

vo idt

( 2V sin(t) (cos( ) cos(t)))dt 0

2 2 L

Note that:

The maximum current occurs at t=π, where the output voltage equal to zero

di

di

vo L

L 0 but

0 give I max

dt

dt

The instant time that it occurs the maximum current equal to:

1 to sec onds

2f F

2.4 The load circuit with pure L in series with Back EMF.

The effect of introducing a direct Electro-Motive Force into the load circuit in

series with pure inductance of a half wave controlled rectifier is investigated. Fig.

4(a) shows the connection diagram. Such a circuit can be employed to charge a

battery or to excite the armature circuit of a de motor. In general the load circuit is

expected to posses both resistance and inductance.

In analyzing the circuit shown in figure 4a, the earliest point in the cycle of the ac source at which conduction can begin is given by:

=sin-1(Vc /V2) If a pulse is applied at t= α, where a ≥, then conduction will begin, and the

resulting current can be considered being made up of two components, one due to

the ac source and the other due to the dc source.

Figure 4. The single phase controlled half wave rectifier fed pure inductance in series with EMF.

The thyristor conducts from α to β. In this period the output voltage will equal to

the positive supply voltage, the inductance is stored energy in its magnetic field

and the current increases slowly until t=π-α. At that point, the thyristor becomes

reverse-biased. However, the energy stored in the magnetic field of the inductor is

returned and maintains a forward-decaying current through the load. The current

continues to flow unit β, when the SCR turns off. The voltage across the inductor

then changes polarity, and the voltage across the load becomes negative.

Vc vo vi

Vc

from 0 to from to

to 2

From to

di vo 2V sin(t) L Vc

dt

di ( 2V sin(t) Vc )dt L

Single Phase Fully Controlled Rectifier

.

Operation and Analysis of single phase fully controlled converter.

Instructional Objectives

On completion the student will be able to

• Differentiate between the constructional and operation features of uncontrolled and controlled converters.

• Draw the waveforms and calculate their average and RMS values of different variables associated with a single phase fully controlled half wave converter.

• Explain the operating principle of a single phase fully controlled bridge converter.

• Identify the mode of operation of the converter (continuous or discontinuous) for a given load parameters and firing angle.

• Analyze the converter operation in both continuous and discontinuous conduction mode and there by find out the average and RMS values of input/output, voltage/currents.

• Explain the operation of the converter in the inverter mode.

1 Introduction

Single phase uncontrolled rectifiers are extensively used in a number of power electronic based converters. In most cases they are used to provide an intermediate unregulated dc voltage source which is further processed to obtain a regulated dc or ac output. They have, in general, been proved to be efficient and robust power stages. However, they suffer from a few disadvantages. The main among them is their inability to control the output dc voltage / current magnitude when the input ac voltage and load parameters remain fixed. They are also unidirectional in the sense that they allow electrical power to flow from the ac

side to the dc side only. These two disadvantages are the direct consequences of using power diodes in these converters which can block voltage only in one direction. As will be shown in this module, these two disadvantages are overcome if the diodes are replaced by thyristors; the resulting converters are called fully controlled converters. Thyristors are semicontrolled devices which can be turned ON by applying a current pulse at its gate terminal at a desired instance. However, they cannot be turned off from the gate terminals. Therefore, the fully controlled converter continues to exhibit load dependent output voltage /current waveforms as in the case of their uncontrolled counterpart. However, since the thyristor can block forward voltage, the output voltage / current magnitude can be controlled by controlling the turn on instants of the thyristors. Working principle of thyristors based single phase fully controlled converters will be explained first in the case of a single thyristor half wave rectifier circuit supplying an R or R-L load. However, such converters are rarely used in practice. Full bridge is the most popular configuration used with single phase fully controlled rectifiers. Analysis and performance of this rectifier supplying an R-L-E load (which may represent a dc motor) will be studied in detail in this chapter.

2 Single phase fully controlled half wave rectifier

2.1 Resistive load

Figure 1 Single-phase fully controlled half wave rectifier supplying resistive load.

Fig. l(a) shows the circuit diagram of a single phase fully controlled half wave rectifier supplying a purely resistive load. At t= 0 when the input supply voltage becomes positive the thyristor becomes forward biased. However, unlike a diode, it does not turn ON till a gate pulse is applied at t= α. During the period 0 < t≤ α, the thyristor blocks the supply voltage and the load voltage remains zero as shown in fig. 1(b). Consequently, no load current flows during this interval. As soon as a gate pulse is applied to the thyristor at t= α, it turns ON. The voltage across the thyristor collapses to almost zero and the full supply voltage appears across the load. From this point onwards the load voltage follows the supply voltage. The load being purely resistive the load current i0, is proportional to the load voltage. At t= π as the supply voltage passes through the negative going zero crossing the load voltage and hence the load current becomes zero and tries to reverse direction. In the process the thyristor undergoes reverse recovery and starts blocking the negative supply voltage. Therefore, the load voltage and the load current remains clamped at zero till the thyristor is fired again at t= 2π + α. The same process repeats thereafter.

From the discussion above and Fig .1 (b) one can write

Similar calculation can be done for io. In particulars for pure resistive loads FFio = FFvo. 2.2 Resistive-Inductive load Fig 2 (a) and (b) shows the circuit diagram and the waveforms of a single phase fully controlled half wave rectifier supplying a resistive inductive load. Although this circuit is hardly used in practice its analysis does provide useful insight into the operation of fully controlled rectifiers which will help to appreciate the operation of single phase bridge converters to be discussed later.

Figure 2 Single-phase fully controlled half wave rectifier supplying resistive inductive load.

As in the case of a resistive load, the thyristor becomes forward biased when the supply voltage becomes positive at t= 0. However, it does not start conduction until a gate pulse is applied at t= α. As the thyristor turns ON at t= α the input voltage appears across the load and the load current starts building up. However, unlike a resistive load, the load current does not become zero at t= π, instead it continues to flow through the thyristor and the negative supply voltage appears across the load forcing the load current to decrease. Finally, at t= β (β> π) the load current becomes zero and the thyristor undergoes reverse recovery. From this

point onwards the thyristor starts blocking the supply voltage and the load voltage remains zero until the thyristor is turned ON again in the next cycle. It is to be noted that the value of β depends on the load parameters. Therefore, unlike the resistive load the average and RMS output voltage depends on the load parameters. Since the thyristors does not conduct over the entire input supply cycle this mode of operation is called the "discontinuous conduction mode".

From above discussion one can write.

Since the average voltage drop across the inductor is zero. However, Iorms can not be obtained from Vorms directly. For that a closed from expression for io will be required. The value of β in terms of the circuit parameters can also be found from the expression of io.

The equation of the output current io can be used to find out Iorms. To find β it is noted that io|t=β=0

Exercise 1

Fill in the blank(s) with appropriate word(s) : i) In a single phase fully controlled converter the _________ of an uncontrolled converters are replaced by ____________. ii) In a fully controlled converter the load voltage is controlled by controlling the _________ of the converter. iii) A single phase half wave controlled converter always operates in the ________ conduction mode. iv) The voltage form factor of a single phase fully controlled half wave converter with a resistive inductive load is _________ compared to the same converter with a resistive load. v) The load current form factor of a single phase fully controlled half wave converter with a resistive inductive load is _________ compared to the same converter with a resistive load.

Answers:

(i) diodes, thyristors; (ii) firing angle; (iii) discontinuous (iv) poorer; (v) better. 2) Explain qualitatively, what will happen if a free-wheeling diode (cathode of

the diode shorted with the cathode of the thyristor) is connected across the load in Figure 2.(a) Answer 2: Referring to Figure 2(b), the freewheeling diode will remain off till t=π since the positive load voltage across the load will reverse bias the diode. However, beyond this point as the load voltage tends to become negative the freewheeling diode comes into conduction. The load voltage is clamped to zero thereafter. As a result i) Average load voltage increases. ii) RMS load voltage reduces and hence the load voltage form factor reduces. iii) Conduction angle of load current increases as does its average value. The load current ripple factor reduces.

2.3 Pure inductive load:

Figure 3 Single-phase controlled rectifier fed a pure inductive load. (a) The circuit diagram (b) waveform.

Figure 3 (a) shows the connection diagram. When the thyristor turn on at t=α in

the positive half cycle of input voltage, the output voltage will equal the input

voltage according to KVL. The current in the circuit will increase slowly, since the

inductance in the load forces the current to lag the voltage. The inductor is storing

energy in its magnetic field.

When the applied voltage become negative, the thyristor is reversed biased.

However, the energy stored in the magnetic field of the inductor is returned and

maintains a forward-decaying current through the load. The current continues to

flow unit β =2π-α (cut off angle, advance angle or excitation angle), when the SCR

turns off. The voltage across the inductor then changes polarity, and the voltage

across the load becomes negative.

The average output voltage (Vo) becomes zero, because its positive part equal

to its negative part.

The conduction angle is γ=2(π-α)

0

vo vi

0

from 0 to to 2 ( for pure L

(2 ) to 2

The current in the current will follow when the output voltage equal to the

input voltage.

From to 2

di vo 2V sin(t) L

dt

2V sin(t)dt di

L

t 2V sin(t)

i

dt such that

L

2V i (cos( ) cos(t))

L

The average current of the output current

1 2V

io

(cos( ) cos(t))dt

2 L

1 i

2V ( ) cos( ) sin( )

o

XL

The rms of the output voltage is given by:

V0rms

1 2 2V sin(t dt 2

1 1 Vorms V sin(2 )

2 2 4

The average output power equal to zero and it is given by:

1 2 1 2 2V

P0

vo idt

( 2V sin(t) (cos( ) cos(t)))dt 0

2 2 L

Note that:

The maximum current occurs at t=π, where the output voltage equal to zero

di

di

vo L

L 0 but

0 give I max

dt

dt

The instant time that it occurs the maximum current equal to:

1 to sec onds

2f F

2.4 The load circuit with pure L in series with Back EMF.

The effect of introducing a direct Electro-Motive Force into the load circuit in

series with pure inductance of a half wave controlled rectifier is investigated. Fig.

4(a) shows the connection diagram. Such a circuit can be employed to charge a

battery or to excite the armature circuit of a de motor. In general the load circuit is

expected to posses both resistance and inductance.

In analyzing the circuit shown in figure 4a, the earliest point in the cycle of the ac source at which conduction can begin is given by:

=sin-1(Vc /V2) If a pulse is applied at t= α, where a ≥, then conduction will begin, and the

resulting current can be considered being made up of two components, one due to

the ac source and the other due to the dc source.

Figure 4. The single phase controlled half wave rectifier fed pure inductance in series with EMF.

The thyristor conducts from α to β. In this period the output voltage will equal to

the positive supply voltage, the inductance is stored energy in its magnetic field

and the current increases slowly until t=π-α. At that point, the thyristor becomes

reverse-biased. However, the energy stored in the magnetic field of the inductor is

returned and maintains a forward-decaying current through the load. The current

continues to flow unit β, when the SCR turns off. The voltage across the inductor

then changes polarity, and the voltage across the load becomes negative.

Vc vo vi

Vc

from 0 to from to

to 2

From to

di vo 2V sin(t) L Vc

dt

di ( 2V sin(t) Vc )dt L

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