NATIONAL QUALIFICATIONS CURRICULUM SUPPORT
Design, Engineering
and Technology
Electrical Engineering
Power Control
[HIGHER]
Edward Boyle
Nacer Tcheir

Acknowledgements
This document is produced by Learning and Teaching Scotland as part of the National
Qualifications support programme for Design, Engineering and Technology.
First published 2003
Electronic version 2003
© Learning and Teaching Scotland 2003
This publication may be reproduced in whole or in part for educational purposes by
educational establishments in Scotland provided that no profit accrues at any stage.
ISBN 1 85955 983 2
TH E TH EO RY O F P E RF EC T CO M PE T I T IO N
CONTENTS
Staff information and support material
Section S1: Outcomes to be covered in this unit
1
Section S2: Teaching and learning advice including how to use
the resource material
3
Section S3: Details of starting points
4
Section S4: Assessment procedures showing what is to be assessed,
when it is to be assessed and result recording methods
5
Section S5: Resource requirements including course notes,
laboratory sheets, book list and audio/visual aids
6
Section S6: Safety
9
Candidate information and support material
Section C1: Outcomes to be covered in this unit
11
Section C2: Assessment instruments for the outcomes
13
Section C3: Course notes and tutorials
– Switchgear
– Power converters
– Power control devices
– AC to DC conversion
– Half-wave uncontrolled rectifiers
– Half-wave controlled rectifiers
– Full-wave rectifier circuits
– DC to AC conversion
– AC to AC conversion
– DC to DC conversion
– Tutorials
– Laboratory experiments
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SECTION S1
Outcomes to be covered in this unit
Outcome 1
Describe the construction, function and interruption capabi lity of switchgear.
Performance criteria
(a) The function and current interruption capability of different types of
switchgear are described correctly.
(b) With the aid of a diagram the process of a plain air -break circuit
breaker opening under fault conditions i s described correctly.
(c) The salient constructional features and interruption process of circuit
breakers are explained correctly.
Note on the range of the outcome
 switchgear: isolator, isolating switch, circuit breaker and auto -recloser
 circuit breaker: air break, air blast, vacuum and sulphur hexafluoride
 constructional features: operating mechanisms, contacts and arc control
devices.
Evidence requirements
Written evidence of the student’s ability to understand the various features of
switchgear.
Outcome 2
Investigate the operation and performance of a static power converter.
Performance criteria
(a) The various types of static power converters are listed correctly.
(b) The principal features and function of static power converters are
described correctly.
(c) Diagrammatic representation of a static power converter is accurate.
(d) Explanation of the operation of the converter is correct.
(e) Evaluation of the key performance characteristics of the converter is
correct.
Note on the range of the outcome
 static power converters: AC to DC, AC to AC, DC to AC and DC to DC.
 converter: phase controlled, cycloconverters, choppers and inverters.
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Evidence requirements
Written and graphical evidence of the student’s ability to interpret the
operation of power converters.
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SECTION S2
Teaching and learning advice including how to use the
resource material
Teaching methods
In general the teaching and learning methods used are very dependent on the
outcomes of the unit and the facilities and expertise available at the
delivering centre. By their very nature, however, the outcomes in the unit
lend themselves to the following teaching methods:
 relate essential theory to practical and industrial requirements
 laboratory learning activities based on a student -centred circuit testing and
analysis approach
 tutorial exercises
 computer simulation activities.
It is important that all the lecturers/teachers working on this unit use
laboratory and computer simulation activities as much as possible. This will
reinforce the essential theory and ensure a good understanding of the
concepts of power control.
Power control unit delivery
Main topics
Delivery suggested
Outcome 1
Construction, function and interruption
capability of switchgear
Outcome 2
Investigate the operation and
performance of a static power converter
Explain basic theory, tutorial exercises,
laboratory demonstration.
Explain theory, tutorial exercises,
laboratory exercise, computer
simulation.
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SECTION S3
Details of starting points
Outcome 1
A brief revision of power generation, transmission and distribution
highlighting the need for the use of switchgear to ensure safe operation of
plant systems.
Outcome 2
Prior to describing the principle of operation of various static converters, it
will be necessary to explain the power conversion concept and the use of
power semiconductor devices for that purpose.
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SECTION S4
Assessment procedures showing what is to be assessed, when it
is to be assessed and result recording methods
The Power Control unit is assessed by two tasks. The majority of the
performance criteria are assessed by structured questions. These are used at
the end of the topic on completion of the teaching relating to Outcomes 1 and
2. Outcome 2 is assessed by structured questions and a laboratory
investigation with a submitted report.
The following table shows how the assessment tasks are related to their
outcomes and performance criteria. It also lists the evidence to be collected.
Outcome
PC
1
a
Task 1: Structured question
Written response
b
Task 1: Structured question
Written/graphical response
c
Task 1: Structured question
Written/graphical response
a
Task 2: Structured question
Written response
b
Task 2: Structured question
Written response
c
Task 2: Structured question
Written/graphical response
d
Task 2: Structured question
Written response
e
Task 2: Laboratory
investigation
Written report
2
Assessment task
Evidence to be collected
The timing and duration of assessment
The unit is divided into two separate topics, namely (i ) switchgear, and (ii)
static power converters. Candidates should be given a formative assessment
prior to the summative assessment at the end of the outcome. This will
reinforce the teaching process while preparing the candidates for assessment.
The suggested time allocation for tasks 1 and 2 is as follows:
 Outcome 1: 60 minutes
 Outcome 2: 60 minutes.
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SECTION S5
Resource requirements including course notes, book list and
visual aid list
Course notes
Candidate notes on Power Control are included in the candidates’s Support
Material. These should be either adopted by the centre or modified to suit the
teaching approach taken and the equipment available.
Laboratory sheets
Some laboratory experiments are included in this support pack. These shoul d
either be adopted by the centre or modified to suit the teaching approach
taken and the equipment available.
Circuit simulation may also be used to reinforce the practical laboratory
work. A suitable product on the market is Electronics Workbench which may
be obtained using the details outlined below.
Electronics Workbench: Circuit simulation and testing
Web address:
http://www.adeptscience.co.uk
E-mail:
info@ adeptscience.co.uk
Telephone:
01462 480055, Fax 01462 480213
Address:
Adept Science plc
6 Business Centre West
Avenue One
Letchworth
Herts
SG6 2HB
Electronics and Electrical Principles
Web address:
http://www.eptsoft.demon.co.uk
E-mail:
sales@ eptsoft.demon.co.uk
Telephone/Fax:
01376 514008
Address:
EPT Educational Software
Pump House
Lockram Lane
Witham
Essex
CM8 2BJ
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Crocodile Clips: Simple simulation of science and technology experiments
Web address:
http://www.crocodile-clips.com/education
E-mail:
sales@ crocodile-clips.com
Telephone:
0131 226 1511, Fax 0131 226 1522
Address:
Crocodile Clips
11 Randolph Place
Edinburgh
EH3 7TA
Book list
Bradley, D A, Fidler, J K and Dorey, A P, Power Electronics, 1994
Flurscheim, Charles H, Power Circuit Breaker Theory and Design, Peter
Peregrinus Ltd on behalf of The Institution of Electrical Engineers (IEE),
1983
Greenwood, Allan, Vacuum Switchgear, 1994
Grigsby, L L, Electrical Power Engineering Handbook, 1999
Lander, Cyril W, Power Electronics, 1993
Lythall, R T, The J. & P. Switchgear Book: Being an Outline of Modern
Switchgear Practice for the Non-Specialist User
Mazda, F F, Power Electronics Handbook, 1997
Ragaller, Klaus, Current Interruption in High Voltage Networks , 1978
Ramshaw, Raymond S, Power Electronics Semiconductor Switches: Solutions
Manual, 1994
Rudman, Jack, Power Electronic Maintainer, 1994
Ryan, H M and Jones, G R, SF6 Switchgear, 1989
Smeaton, Robert W and Ubert, William H, Switchgear and Control
Handbook, McGraw-Hill, 1998
Tyler, Electrical Power Technology, 1998
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Visual aids
The Electrical Engineering laboratory should have an Electrical Safety notice
prominently displayed. These are available from a variety of electrical
wholesale outlets and distributors and are relatively inexpensive. Component
manufacturers and distributors offer wall charts and posters showing many
aspects of Electrical Engineering. They are generally free and available on
request.
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SECTION S6
Safety
The safety of teaching staff and candidates working in the Electrical
Engineering laboratory must be the primary concern of everyone involved.
This aspect has to take precedence over all other activities and be
sustained against all other pressures since electricity can be lethal.
There are many aspects to safety, as follows:






statutory requirements
centre procedures
centre structure
staff training and behaviour
laboratory features
candidate training and behaviour.
It is beyond the scope of this document to provide details of all of these
items, which should be incorporated into a c entre’s safety policy.
Lecturers/teachers must however be content that all appropriate safety
measures are in place before embarking on work within the electrical
engineering laboratory.
Candidate training is a recurrent activity that is likely to be the direct
responsibilty of the lecturer/teacher. While this has to take place on a continuous
basis as work in a laboratory situation proceeds it is helpful to perform specific
safety training at the beginning of the course. Such training might form part o f
the course induction as its relevance extends to all course units. This is
particularly important for electrical engineering candidates as they should be
encouraged to develop their own safety culture; this should become a lifelong
asset.
The lecturer/teacher performing safety training for candidates may find a rich
diversity of available material. Of specific relevance is a teaching package
prepared by the University of Southampton Department of Electrical
Engineering and Technical Support and Media S ervices. The package was
prepared in association with and financially supported by the Health and
Safety Executive. It consists of :
 a handbook for undergraduate electrical teaching laboratories
 a video programme: Not to Lay Blame
 a booklet: Tutor’s Guide.
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SECTION C1
Outcomes to be covered in this unit
Outcome 1
Describe the construction, function and interruption capability of switchgear.
Performance criteria
(a) The function and current interruption capability of different types of
switchgear are described correctly.
(b) With the aid of a diagram the process of a plain air break circuit breaker
opening under fault conditions is described correctly.
(c) The salient constructional features and interruption process of circuit
breakers is explained correctly.
Note on the range of the outcome
 switchgear: isolator, isolating switch, circuit breaker and auto -recloser
 circuit breaker: air break, air blast, vacuum and sulphur hexafluoride
 constructional features: operating mechanisms, contacts and arc control
devices.
Evidence requirements
Written evidence of the student’s ability to understand the various features of
switchgear.
Outcome 2
Investigate the operation and performance of a static power converter.
Performance criteria
(a) The various types of static power converters are listed correctly.
(b) The principal features and function of static power converters are
described correctly.
(c) Diagrammatic representation of a static power converter is accurate.
(d) Explanation of the operation of the converter is correct.
(e) Evaluation of the key performance characteristics of the converter is
correct.
Note on the range of the outcome
 static power converters: AC to DC, AC to AC, DC to AC and DC to DC.
 converter: phase controlled, cyclo, choppers and inverters.
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Evidence requirements
Written and graphical evidence of the student’s ability to interpret the
operation of power converters.
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SECTION C2
Assessment instruments for the outcomes
The unit can be divided into two sections namely:
 switchgear
 static power converters.
Switchgear will be assessed by an end-of-topic test in the form of a structured
question to determine if you understand the construction, function and
interruption capability of switchgear. Assessment time allocation for this
first section is 60 minutes.
Static power converters will be assessed in the form of a laboratory
assignment and a structured question to determine if you understand the
operation and performance of static power converters. A written report of the
practical investigation has to be submitted, which should include the
following:





object
apparatus
circuit diagram
description
results and conclusions.
Assessment time allocation for the second section is 60 minutes.
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SECTION C3
Course notes and tutorials
Switchgear
Protection of the power system is necessary and without it serious damage
coupled with frequent and possibly prolonged shut -downs of services would
result.
Protection can be achieved by using fuses, which are available up to 11kV but
suffer one disadvantage in that when they ha ve cleared a fault they have to be
replaced. Especially at the higher voltages this is extremely costly. An
alternative to the fuse is the circuit breaker which having operated may be re closed once the reason for its operation has been ascertained. Cir cuit
breakers need to have auxiliary devices called relays, which on sensing
abnormal conditions, automatically initiate the opening of the circuit breaker,
disconnecting the fault from the supply.
Auto-recloser
This is a circuit breaker that opens on short-circuit current and automatically
re-closes after a brief time delay. The open/close sequence may be repeated
two or three times. If the short circuit does not clear itself after two or three
attempts to reclose the line the recloser opens permanentl y. A repair crew
must then locate the fault, remove it and reset the recloser.
Isolator
An isolator is a mechanical device that is capable of making a circuit under
all conditions but only being opened when the circuit is carrying very little or
no current. As the name suggests, an isolator is used to isolate a circuit from
the supply when essential maintenance work is being carried out. The
isolator is usually fitted with an interlocking device to prevent it from being
accidentally operated. Isolators on transmission and distribution systems are
interlocked with an associated circuit breaker so that they cannot be opened
with the circuit breaker in the closed position.
The isolator must be able to:
 carry the full load continuously
 withstand normal and excess voltages
 open and close on no-load.
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Circuit breakers
A circuit breaker is a mechanical device that is capable of making and
breaking an electrical circuit under all conditions. This means that it can be
used to energise a circuit with a short-circuit fault on it without causing
distress to the device as it opens to interrupt very large current. Circuit
breakers are available for circuits with fault levels ranging from a few MVA
at 230V when they are known as miniature circuit breakers, up to 3 5000MVA
at 400kV three-phase.
The fundamental requirements are:
 faults must be cleared with minimum dislocation of the system
 faults must be cleared in the shortest possible time.
Main faults:
 failure of insulation to earth or between phases
 excess or reduction in voltage
 overloads and short circuits.
The circuit breaker must be capable of carrying heavy fault currents until
they are cleared. The equipment must do this without serious overheating
and be able to withstand the large magnetic forces invo lved.
In summary the circuit breaker should:





carry full load continuously
withstand normal and possible excess voltages
make and break the normal rated current
make on to a short circuit
break on short circuit.
Circuit breakers are available for circuits with fault levels ranging from a few
MVA at 230V when they are known as miniature circuit breakers, up to
thousands of MVA at 400kV three-phase.
The main types of circuit breakers used are:





oil circuit breaker (beyond the scope of this unit)
air-blast circuit breaker
air-break circuit breaker (atmospheric pressure)
compressed gas (SF 6 ) circuit breaker
vacuum circuit breaker.
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All types of circuit breakers consist essentially of pairs of mating contacts,
each pair comprising fixed and moving elements. In normal service these
elements are in contact to carry the load current, but under fault conditions
the two elements will part company to interrupt the circuit. At the instant of
separation an arc will be struck between them and will continue until
interrupted. Interruption of the arc depends on aid given either by high
pressure, forced convection, lengthening of the arc, vacuum or by a
combination two or more of these.
Air-break circuit breaker
Figure 1: Elementary arrangement of air-break circuit breaker
This type of circuit breaker employs air as insulant and arc extinguishing
medium. It consists essentially of a pair of mating contacts comprising fixed
and moving elements. In normal service these elements are in contact to
carry the load current, but under fault conditions and on receipt of a tripping
signal, which may be initiated by hand or via a protective device, the two
elements will part company to interrupt the circuit. At the instant of
separation an arc will be struck between them and will continue until
interrupted.
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Interruption is largely due to elongation of the arc, which results in cooling
and de-ionisation by diffusion. Owing to the high temperature of the arc
relative to the surrounding air, the arc is subjected to strong convection
currents, which coupled with the electromagnetic effect of the current loop
cause the arc to rise vertically. It is therefore drawn into the arc chute where
splitter plates assist the cooling and lengthening process so that its length is
much greater than the direct distance between the fully open contacts leading
to successful interruption.
Typical ratings are: 25MVA at 415V; 35MVA at 3.3kV and up to 750MVA at
11kV.
Figure 2: Air-break circuit breaker in closed position with one arc chut e
removed
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Figure 3: Air-break circuit breaker in open position with one arc chute
removed
Air-blast circuit breaker
The air-blast breaker uses air at a high pressure to rapidly cool and blow out
the arc formed as the contacts separate. The basic d ifference in operation
between this type and the natural air type is that the moving contact does not
remain in the open position. It pulls back drawing the arc, which is blown
out and later is forced back into the closed position at high speed.
The interrupting process is aided by an axial blast of air at high pressure
admitted to the arcing chamber. The cold air rapidly cools and blows out the
arc formed. As the air in the blast tube returns to atmospheric pressure after
arc extinction, its dielectric strength in the small gap will be insufficient to
withstand the normal system voltage, and therefore a separate isolating switch
is provided to open automatically after current interruption. When
compressed air is released suddenly in the form of high -velocity jets into a
relatively still atmosphere, the resulting interaction produces sound which is
explosive in nature. When an air-blast circuit breaker opens, such a release
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of air occurs at the exhaust point of each interrupter, and as these multiply
with the size of the breaker the emanating noise can be startling at close
quarters and very annoying even at some distance.
This problem is one of considerable importance if it becomes necessary to
locate substations in residential areas, particularly a t the higher voltages and
where high air pressures are employed. Noise suppression methods must be
used in these areas.
Figure 4: Side view of an air-blast circuit breaker fitted with a silencer
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Various stages in the breaking operation of the above a ir-blast circuit breaker
are shown in Figure 5:
(a)
(b)
(e)
breaker closed
main current interrupted in the extinction chamber after the tripping
command is given
auxiliary spark gap cuts-in low damping resistor when main current has
been interrupted
auxiliary spark is quenched and high resistance is cut-in to limit overvoltages
breaker open; isolator has opened to switch off high resistance.
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Figure 5: Breaking process of an air blast circuit breaker
Key:
1. Isolator blades
2. Extinction chamber
3. Auxiliary spark gap
4. Low resistance
5. High resistance
6. Arc
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Figure 6: 400 kV outdoor substation with air-blast circuit breakers
(courtesy A. Reyrolle & Co. Ltd.)
Sulphur hexafluoride (SF6) circuit breaker
This circuit-breaker type uses SF6 sulphur hexafluoride gas, which is a
particularly good arc-quenching medium in that it rapidly absorbs free
electrons created in an arc. This means that as the current flowing in an arc
passes through a zero, electrons which are present and which would allow the
arc to restrike as the alternating voltage begins to increase in magnitude once
again are absorbed, turning the arc path into an insulating region. The arc
duration time is much shorter in sulphur hexafluoride than it would be in air.
The construction of the sulphur hexafluoride circuit breaker is very similar to
that of the air-blast breaker except that the gas cannot be allowed to escape
into the atmosphere. It is therefore held at high pressure and when the
breaker operates it expands into a larger, l ow-pressure receiver from which it
can be taken and pumped back up to high pressure once more.
The following advantages accrue from the use of this gas:
 a reduced number of series breaks is required for a given voltage and
rating. The breaker is much less bulky than its air-blast equivalent
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 due to the quicker clearance, burning of contacts is less than in the air
break
 since the gas blast is not released into the atmosphere the operation of the
breaker is much quieter than with air blast which can ofte n be heard a very
long way away.
These breakers are much smaller than other high -voltage breakers and are
less noisy than air-blast breakers. They are extensively used on high -voltage
transmission networks.
Figure 7: Side view of an SF6 circuit breaker
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Figure 8: A cross-sectional view of an SF6 circuit breaker
Key:
1. Moving contact actuator
2. Steel connecting pin
3. Guides
4. Gas compression cylinder supports
5. Arcing chamber
6. Gas compression piston
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7. Gas compression cylinder
8. Moving contact
9. Tungsten-tipped moving contact
10. Moving contact current-collector ring
11. Fixed-contact arcing ring
12. Fixed-contact holder
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Figure 9: 132 kV outdoor substation with GEC SF6 circuit breakers
(courtesy GEC Switchgear Ltd.)
Figure 10: 275 kV outdoor substation with GEC SF6 circuit breakers
(courtesy GEC Switchgear Ltd.)
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Vacuum circuit breaker
The ideal situation in which to interrupt a current might seem to be in a
perfect vacuum and this possibility was investigate d in the early 1920s. At
the time, however, the problems in producing metals that did not contain
dissolved gases seemed insurmountable. When contacts made from metals
interrupt an arc in vacuum the dissolved gases are liberated, thus
contaminating the vacuum. Also without the scouring action of high -velocity
air or oil the contact tended to weld together and any liberated metal vapour
settled on the insulating surfaces.
By careful attention to the geometry of the interior, the problems have been
overcome and the vacuum interruption principle has been developed for very
high voltages. It may be seen as an ideal process for high -performance
circuit breakers.
Figure 11: Constructional features of an 11kV vacuum interrupter
The vacuum chamber is composed of an insulating envelope fitted with an
end plate on each end, maintaining a high degree of vacuum.
Inside the vacuum chamber is a pair of contacts – one stationary, one moving
– fastened to the end of a fixed stem and a moving stem, respectively.
A metallic bellows is provided between the moving rod and its mating end
plate, which enables the contacts to open and close, while a high vacuum is
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maintained. An arc shield is installed around the plates so that the vapour
produced from the contacts during current switching is prevented from
adhering to the inner walls of the insulating envelope. A bellows cover
protects the bellows from direct contact with metal vapour.
The current interruption process consists of separating a pair of current carrying contacts in a high vacuum environment. The current carriers in the
arc are mainly metal ions from the contacts. The arc is shortened by
condensation of these metal ions and vapours on to the contacts and shields,
and the effectiveness of this determines the efficiency of the interrupting
process at the first current zero.
These breakers are hermetically sealed hence they are silent and never
become polluted. They are used considerably on distribution networks.
Another application is for flameproof switchgear for use in situations such as
petrochemical plants or wherever inflammable gases may be present. The
contacts of the vacuum interrupter, being completely enclosed in the vacuum
chamber, are safe in explosive situations.
Figure 12: A cross-sectional view of a vacuum interrupter
The unique properties of the vacuum interrupter offer many advantages.
These include:
 long life and minimum maintenance
 completely enclosed and hermetically sealed
 extremely short and consistent arcing and total brea k times
 no fire risk
 no noise and no emission of air or gas during operation
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 at the end of its life a unit or ‘bottle’ can be changed quickly, removed and
discharged and replaced by a spare.
The vacuum interrupter unit has a long shelf -life, but its main disadvantage is
its relatively high cost.
Figure 13: 132kV outdoor substation with GEC vacuum circuit breakers
(courtesy GEC Switchgear Ltd.)
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Power converters
In recent years, the power control field has experienced a large growth due to
the influence of several factors. There have been revolutionary advances in
microelectronics methods, which have led to the development of linear
integrated circuits and digital signal processors as controllers in power
control systems. Advances in microelectronic fabrication technology have
led to the development of computers, communication systems, and consumer
electronics, all of which require regulated power supplies and often
uninterruptible power supplies. The increasing cost of energy has made it
mandatory that the energy in all these systems be utilised efficiently. Power
control offers the most cost-effective means of achieving efficient energy
utilisation. This increased efficiency is extremely important because of the
cost of wasted energy and the difficulty of removing the heat generated by
wasted energy.
The term power control covers a wide range of electronic circuits in which
the objective is to control the transfer of electrical power from a source to a
load. This control may take many different forms depending on the type of
load. Such control is almost always achieved by using electronic devices
operated as a switch in either an open or closed state.
The power conversion era marks its beginning from the introduction of the
SCR (silicon-controlled rectifier) or thyristor in 1957. Although other
controllable devices such as the mercury arc rectifier certainly had been
available for many years, such devices were large, often required auxiliary
equipment, and were not efficient in low and moderat e voltage circuits. The
introduction of the SCR thus marked the beginning of a period in which
power control shifted largely from rotating machines and static magnetic
amplifiers to electronic devices. During this early period, progress was
slowed by reliability problems, but after the early 1960s the SCR began to be
used in many more applications. The SCR has limitations in terms of power
handling capability and switching speed. To fill some of the shortfalls of
SCRs, other semiconductor devices have been developed for use in the power
industry. They include the triac, the Gate-Turn-Off thyristor (GTO), the
Bipolar Junction Transistor (BJT), the power Metal -Oxide-SemiconductorField-Effect (MOSFET) and the Insulated-Gate Bipolar Transistor (IGBT).
Classification of power converters
A power converter is an operative unit, consisting of semiconductor devices
(electronic valves) and necessary auxiliaries, used for changing one or more
of the characteristics of an electric power system. It can thus chan ge voltage
and current level, and frequency.
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The term ‘converter’ is also used to designate one member of the converter
family, which historically is the most prominent one, namely an apparatus
which links a DC network to an AC one. If the flow of powe r is directed
from the AC side to the DC side, the converter operates as a rectifier. With
the opposite direction of the flow of power, the converter operates as an
inverter.
Several conversion arrangements are used in the majority of power control
applications depending on the types of source and load:
AC–DC: In this case, the AC line-voltage is converted by rectification to a
unidirectional source, which later may be filtered to approximate a DC
source. A controlled rectifier converts the fixed voltag e AC to a variable
voltage DC, in which case one application would be as a source to drive a DC
motor in a variable-speed mode, such as those used in rolling mills.
DC–AC: A DC source is switched to provide an alternating voltage to a load.
The inverter converts a fixed voltage DC to a fixed (or variable) voltage AC
with variable frequency. The output of such an inverter is not a sinusoid but
instead a rectangular or perhaps stepped waveform, which is suitable for
driving an AC motor in a variable-speed mode by changing voltage and
frequency.
AC–AC: In this case, there are two converters:
 The cycloconverter converts a fixed voltage and fixed frequency AC to a
variable voltage and variable (lower) frequency AC. It can be used to
control the speed of AC motors.
 The AC voltage regulator converts a fixed voltage AC to a variable voltage
AC (fixed frequency). It can be used to control the speed of an induction
motor (voltage control method) and for smooth induction motor starting
(soft starter).
DC–DC: This type converts DC of one level (constant or variable) to another
level (constant or variable). The DC chopper is used to provide a
controllable DC output from a DC source by switching the source on to and
off the load. This converter is primarily used to control the speed of DC
motors.
Applications of power converters
Power conversion finds application wherever a load needs controlled power
modulation. Power semiconductors are used in a wide range of applications.
The following gives only a representative sample:
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 Industrial applications consist primarily of two areas, motor control and
power supplies. The motors that are controlled vary from the very large
type as used in steel mills, to the relatively smaller ones, such as in
machine tools. Power supplies too come in many shapes and sizes, such as
for battery charging, induction heating, electroplating and welding.
 Consumer applications cover many different areas in the home, such as
audio amplifiers, heat controls, light dimmers, ballasts, motor c ontrol for
food mixers, washing machines, as well as hand power tools and security
systems.
 Transportation applications include electric vehicles, locomotives, and
fork-lift trucks. Equally important are non-motor drive applications, such
as DC power transmission, traffic signal control, vehicle electronic
ignition and vehicle voltage regulation.
 Aerospace and defence applications include VLF transmitters, power
supplies for space and aircraft; Uninterruptible Power Supplies for vital
loads, and switching using solid-state relays and contactors.
The control of electric drives may involve the glamour areas of robotics,
computer disk drives, space applications or it may be associated with more
conventional loads like fans, compressors, pumps and hoists. Wha tever the
mechanical load, the power semiconductor converter lends itself to the
control of adjustable speed drives, which may be DC or AC drives.
DC drives require voltage control. This is provided by controlled rectifiers or
by choppers, depending upon what kind of source is available. The DC drive
is expensive and the rectifier is inexpensive.
AC drives require voltage and frequency control inverters and sometimes
cycloconverters accomplish this task. The AC drive is inexpensive and the
inverter is expensive. The choice of type of drive depends on cost and
versatility.
In general, DC drives are found useful in many applications. However, AC
drives are becoming prominent as inverter technology continues to improve.
Whatever load is to be controlled, there is usually one semiconductor device
that is best suited for the application.
Power control systems are being installed throughout the world using the
previously mentioned devices of ever -increasing ratings. Some examples of
large systems in the UK are:
 The cross-channel link that connects together the AC electricity supply
systems of England and France via a high -voltage DC link to enable power
to be transferred in either direction. The DC side is at 270kV, 2000MW
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and the AC side is 400kV at 50Hz. The devices in the inverter are
thyristors.
 The Eurostar locomotive, on the Channel Tunnel route, uses induction
motors driven by Gate-Turn-Off inverters with more than 1MW of power
available for driving the motors. In France and in the tunnel, th e DC link
voltage is 1900V. In England the DC link is 750V.
The above applications are some examples of spectacular power control
developments.
Choice of power device
The selection of a power device for a particular application depends not only
on the required voltage and current levels but also on cost, rating and the ease
with which it can be turned ‘on’ and ‘off’.
Transistors and GTOs provide control of both turn -on and turn-off, SCRs of
turn-on but not turn-off, and diodes of neither.
MOSFETs and IGBTs have the simplest driving requirements; they are
voltage controlled and the gate current is virtually zero during the ‘on’
period. However, they lack the reverse blocking capability that makes the
SCR, Triac and GTO so suitable for AC mains power a pplications. With DC
link inverters, the DC side means that turning off thyristors requires a forced
commutation circuit, and GTOs are better suited for that. However, if
MOSFETs are available with the correct rating then these, with reverse
conducting diodes for inductive loads, would be a simpler choice.
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Power control devices
Diodes
Diodes are mainly used in rectification circuits where fixed voltage DC is
required. The diode conducts once the anode polarity is positive with respect
to the cathode. When the anode polarity is negative with respect to the
cathode, the diode ceases to conduct. The diode has the highest rating of all
the semiconductor devices and is the cheapest, but it cannot regulate the
magnitude of the rectified voltage. Diodes with out a heat-sink are available
up to about 3A. For higher currents the diodes are fitted with heat -sinks or
they are of stud-type to be mounted on a heat-sink.
Figure 14: Diode package types
Figure 15: Diode terminal identification
Figure 16: Diode symbol
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Figure 17: Heat sink
Thyristors
Thyristors are electronic switches used in circuits where control of switch
turn-on is required. Thyristors are a family of three -terminal devices, which
includes the Silicon-Controlled-Rectifier (SCR), the triac, and the Gate-TurnOff (GTO) thyristor. The three terminals are the anode, cathode, and gate.
Thyristor and SCR are terms that are sometimes used synonymously.
Thyristors are capable of carrying large currents and large blocking voltages
for use in high-power applications, but switching frequencies are limited to
about 10 to 20kHz.
For the SCR to begin to conduct, it must have a gate current applied while it
has a positive anode-to-cathode voltage. After conduction is established, the
gate signal is no longer required to maintain anode current. The SCR will
continue to conduct as long as the anode current remains positive and above a
minimum value called the holding level.
The GTO thyristor like the SCR, is turned on by a short -duration gate current
if the anode-to-cathode voltage is positive. However, unlike the SCR, the
GTO can be turned off with a negative gate current. The GTO is therefore
suitable for some applications where control of both turn -on and turn-off of a
switch is required. The negative GTO current can be of brief duration (a few
microseconds), but its magnitude must be very large compared to the turn -on
current. Typically, gate turn-off current is one-third the on-state anode
current.
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Figure 18: SCR symbol
Figure 19: SCR construction
A triac is a bidirectional thyristor, i.e. it has two blocking/forward directions.
It is capable of conducting current in either direction. The triac is
functionally equivalent to two anti-parallel SCRs (in parallel but in opposite
directions) with a common gate. Turn-on can, however, be performed by a
positive as well as a negative pulse. The fact that the triac is bi -directional
and only needs one heat-sink and one trigger pulse circuit, implies that it is
possible to make a simple, cheap electrical and mechanical design especially
for low power ratings. Triacs are used in light -dimmer circuits and for
controlling the power for heating elements.
Figure 20: Triac symbol
Figure 21: Triac construction
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Figure 22: SCRs and Triacs – physical appearance
Power transistors
Transistors operate as switches in power control circuits. Transistor drive
circuits are designed to have the transistor either in fully -on or fully-off state.
This is unlike other transistor applications, such as an amplifier circuit, where
the transistor operates in the active or linear region. Transistors have the
advantage of providing control of turn-off as well as turn-on, as opposed to
the SCR, which has control of turn-on only. Types of transistors used in
power control circuits include BJTs, MOSFETs, and IGBTs. Figures 10 and
11 show the circuit symbols.
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Power BJTs are available in ratings up to 1200V and 400A. They are
commonly used in converters operating up to approximately 10kHz. Power
BJTs generally are available in higher voltage and current ratings than
MOSFETs.
The MOSFET is a voltage-controlled device. A sufficiently large gate -tosource voltage will turn the device on, resulting in a small drain -to-source
voltage. The drive circuit to turn a MOSFET on and off is usually simpler
than that for a BJT. MOSFET ratings are up to 1000V and 50A and as their
switching speed is faster than BJTs they are used in converters operating up
to and beyond the 100kHz range.
The IGBT is an integrated connection of a MOSFET and a BJT. The drive
circuit for the IGBT is like that of the MOSFET, while the on -state
characteristics are like that of the BJT. IGBTs are suitable for switching
speeds up to about 20kHz and have replaced BJTs in many applications.
Figure 23: Transistors – physical appearance
Figure 24: Transistors – terminal connections
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AC to DC conversion
In the UK, generation and transmission of electrical power are by means of
alternating current. The power stations use synchronous alternators to
generate a voltage at about 11kV, or higher, at a frequency of 50Hz. The
voltage is then stepped up using transformers to a value considered economic
for transmission; this can be 132kV (the grid), or 275kV and 400kV (the
super grid).
Grid switching stations are used to interconnect the various voltage levels.
Grid supply points have transformers to reduce the voltage to 33kV.
Substations reduce the voltage to 415/240V for distribution to homes and
factories (there are also other voltage levels).
Some electrical equipment can use AC directly, e.g. lamps, space and water
heating, cookers, fans, drills, and vacuum cleaners, etc. Other applications
require that AC be changed to DC. These include radio and TV sets,
computers, battery chargers, TTL and CMOS logic circuits, laboratory power
supplies, public transport traction drives, high voltage DC links, etc. The
process of changing AC to DC is called rectification. Where the application
requires fixed voltage DC, the switching device is a diode. Where the
application requires variable voltage DC, controlled rectifiers (SCRs) are
used.
Rectification is the process of converting a bi -directional (alternating) current
or voltage into a unidirectional (direct) current or voltage. This conversion
can be achieved by a variety of circuits based on and using any of the
switching devices discussed previously, with the use of diodes probably the
most common. By using thyristors, power transistors, power MOS, e tc.,
additional control over the magnitude of the direct voltage can be achieved by
varying the point-on-wave at which the device is placed into the conducting
state. The operation of rectifiers and converters ranging from a simple half wave rectifier using a single diode to complex full-wave bridge circuits
employing several thyristors will be described.
The rectifier circuits can be separated broadly into three classes:
uncontrolled, fully-controlled and half-controlled. An uncontrolled rectifier
uses only diodes and the DC output voltage is fixed in amplitude by the
amplitude of the AC supply. The fully-controlled rectifier uses thyristors as
the rectifying elements and the DC output voltage is a function of the
amplitude of the AC supply voltage and the point-on-wave at which the
thyristors are fired. The half-controlled rectifier contains a mixture of diodes
and thyristors, allowing a more limited control of the DC output voltage level
than the full-wave controlled rectifier. The half-wave controlled rectifier is
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cheaper than a full-wave controlled rectifier of the same rating but has
operational limitations.
Thyristor converters are used to control the speed and torque of DC motors
driven from AC mains. For applications requiring motor ratings of about 10
kW or so, single-phase supplies can be used. For larger power applications,
three-phase supplies are used. The separately excited DC motor is used in
these drives, allowing separate control of field and armature circuits.
The field supply is derived from a diode bridge rectifier and the field current
is held constant. The armature is supplied from a thyristor -controlled bridge,
which can be half-controlled if only forward control of speed and torque is
required. It must be fully controlled if regeneration is required, and there
must be two fully controlled full-wave bridges connected in inverse parallel if
forward and reverse control of speed and torque are required.
Half-wave uncontrolled rectifiers
Resistive load
When a diode is connected as shown in Figure 25, current flows in the circuit
when the anode of the diode is positive with respect to the cathode; that is,
current flows in the positive half-cycles of the supply voltage waveforms. In
the negative half-cycles the diode blocks the flow of current in the circuit.
Since current only flows during positive half -cycles, the circuit is described
as a half-wave rectifier circuit. The voltage waveforms across the source,  s ,
load,  0 , and diode,  d are shown in Figure 26.
When an ideal diode conducts it has no forward resistance, and no voltage is
dropped across it. Similarly, when it is in its reverse blocking mode, it has
infinite resistance, and no current flows throu gh it. In the latter case, all of
the negative half-cycle of the supply appears across the diode, and the reverse
blocking voltage rating of the diode must be at least equal to the peak supply
voltage. The maximum voltage across the diode when it is block ing is known
as the peak inverse voltage.
The rectifier circuit therefore converts the alternating supply voltage into a
unidirectional DC voltage across the load.
In practice the ideal diode does not exist. When conducting, a practical diode
has some resistance, and there is small voltage drop across it. When it is in
its reverse mode, there is some leakage current, and a small value of negative
voltage across the load.
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Figure 25: Half-wave uncontrolled rectifier circuit with resistive load
Figure 26: Voltage waveforms for a half-wave uncontrolled rectifier with
resistive load
Resistive-inductive load
Industrial loads typically contain inductance as well as resistance. Current
flow will commence directly when the supply voltage goes positive, but the
presence of the inductance will delay the current change, the current still
flowing at the end of the half-cycle, the diode remains on, and the load sees
the negative supply voltage until the current drops to zero.
The load current, i 0 , and voltage waveforms across the source,  s , load,  0 ,
resistance,  R , inductance,  L and diode,  d are shown in Figure 34.
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Figure 27: Half-wave uncontrolled rectifier circuit with resistive -inductive
load
Figure 28: Voltage waveforms for half-wave uncontrolled rectifier with
resistive-inductive load
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Fly-wheeling diode
Many circuits, particularly those which are half - or uncontrolled, include a
diode across the load as shown in Figure 29. This diode is variously
described as a free-wheeling, flywheel, or bypass diode, but it is best
described as a commutating diode, as its main function is to to commutate or
transfer the load current away from the rectifier whenever the load voltage
goes into a reverse state.
The commutating diode serves one or both of the two functions: one is to
prevent reversal of load voltage (except for the small diode voltage -drop) and
the other to transfer the load current away from the main rectifer, thereby
allowing all of its thyristors to regain their blocking state. When the diode is
turned on at t = 0, the load voltage, v 0 , is the same as the supply voltage, v S .
The load current, i 0 , builds up. When the diode is turned off, the load current
freewheels through diode D2 and v 0 = 0 and when the diode is turned on
again, the cycle repeats itself. The correspo nding voltage and current
waveforms are shown in Figure 30.
Figure 29: Half-wave uncontrolled rectifier circuit with fly-wheeling diode
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Figure 30: Load voltage and current waveforms for half -wave uncontrolled
rectifier circuit with fly-wheeling diode
Half-wave rectifier with a capacitor filter
The half-wave rectifier shown in Figure 31 has a parallel R -C load. The
purpose of the capacitor is to reduce the variation in the output voltage,
making it more like DC. The resistance may represent an e xternal load, and
the capacitor may be a filter, which is part of the rectifier circuit.
Assuming the capacitor is initially uncharged and the circuit is energised at
t = 0, the diode becomes forward-biased as the source becomes positive.
With the diode on, the output voltage is the same as the source voltage, and
the capacitor charges.
The capacitor is charged to V m when the input voltage reaches its positive
peak at t =


. As the source decreases after t = , the capacitor
2
2
discharges into the load resistor. At some point, the voltage of the source
becomes less than the output voltage, reverse biasing the diode and isolati ng
the load from the source. The output voltage is a decaying exponential with
time constant  = RC while the diode is off.
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The point when the diode turns off is determined by comparing the rates of
change of the source and the capacitor voltages. The diode turns off when the
downward rate of change of the source exceeds that permitted by the t ime
constant of the R-C load.
When the voltage comes back up to the value of the output voltage in the next
period, the diode becomes forward biased, and the output again is the same as
the source voltage. The angle at which the diode turns on in the sec ond
period, t = 2 + , is the point where the sinusoidal source reaches the same
value as the decaying exponential output. The corresponding voltage
waveforms are represented in Figure 32.
Figure 31: Half-wave uncontrolled rectifier with R-C load
Figure 32: Voltage waveforms for half-wave uncontrolled rectifier R-C load
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Half-wave controlled rectifiers
Resistive load
The thyristor is a device which blocks the flow of current when the anode is
negative with respect to the cathode, and can be triggered int o conduction at
any point when the anode is positive (Figure 33).
The load is connected in series with the thyristor, which is triggered into
conduction by a pulse generator connected between its gate and cathode. The
pulse generator produces a short pulse of a few microseconds duration at an
angle known as the firing angle, , with respect to the commencement of the
supply voltage waveform. The firing angle, , can be changed from zero to
, which will change the output voltage. Note that at  = 0, the thyristor
circuit behaves like a diode circuit and the output voltage will be maximum.
However, if the thyristor is fired at  =  the output voltage will be zero.
Since the point in the waveform at which the gate pulse is applied is a
function of the phase angle, the circuit is said to be phase controlled.
Even if the anode is positive with respect to the cathode, the thyristor does
not conduct until the gate pulse is applied. Once it has been applied, the
thyristor turns on and conducts; from this p oint onwards in the positive halfcycle, the circuit operates as though it were a half -wave rectifier circuit. If
the load is resistive, the current waveform follows the supply waveform.
When the anode becomes negative with respect to the cathode, the th yristor
enters its reverse blocking mode, and current no longer flows through it. It
remains in this state until the next pulse is applied.
The voltage waveforms across the source,  s , load,  0 , and thyristor,  SCR are
shown in Figure 34.
Figure 33: Half-wave controlled rectifier circuit with resistive load
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Figure 34: Voltage waveforms for half-wave controlled rectifier with resistive
load
Resistive-inductive load
A thyristor rectifier circuit with a load consisting of a resistance and an
inductance is shown in Figure 35. The thyristor is fired at an angle, ,
meaning it starts to conduct at t = . The inductance in the load forces the
current to lag the voltage and therefore the current decays to zero at t = 
instead of t = , which would have been the case if the load was purely
resistive. The voltage waveforms across the source,  s , resistance,  R , load,
 0 , and thyristor,  SCR , are shown in Figure 35. The current waveform is
similar to the voltage waveform across the resistance,  R .
Figure 35: Half-wave controlled rectifier with resistive-inductive load
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Figure 36: Voltage waveforms for half-wave controlled rectifier with
Resistive-inductive load
Full-wave rectifier circuits
Bi-phase rectifier circuit
The bi-phase rectifier circuit is so named because it is energised by a centre tapped secondary winding of a two-winding transformer. The two halves of
the secondary winding have emfs induced in them, which act in the same
direction. Consequently, during the positive half -cycle of the waveform,
diode D1 is forward biased and conducts, while diode D2 is reverse biased
and blocks the flow of current. In the negative half -cycle, the polarity of the
induced voltage in the secondary winding reverses, so that D1 blocks the flow
of the current and D2 conducts. The waveforms in Figure 38 illustrat e the
general result.
Since the bi-phase circuit needs a transformer, the DC output voltage can be
selected by means of the turns ratio of the transformer. Moreover, since the
transformer electrically isolates the secondary winding from the primary, the
circuit is particularly useful where safety is important. While these features
may be advantageous, it has the disadvantage of the cost, size and weight of
the transformer. Moreover, the transformer will reduce the electrical
efficiency of the circuit.
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Figure 37: Full-wave uncontrolled rectifier circuit with resistive load
Figure 38: Waveforms for full-wave uncontrolled rectifier with resistive load
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Bridge rectifier circuit
The bridge rectifier does not need a transformer, but one may be necessa ry if
both the DC and AC sides of the circuit must be separately earthed.
In operation (Figure 39), diagonally opposed pairs of rectifiers conduct.
During the positive half-cycles, diodes D1 and D2 conduct while D3 and D4
block the flow of current. In the negative half-cycle, D1 and D2 are reverse
biased while D3 and D4 are forward biased. The supply and output
waveforms are shown in Figure 40.
Figure 39: Full-wave uncontrolled rectifier bridge with resistive load
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Figure 40: Voltage waveforms for uncontrolled rectifier bridge with resistive
load
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DC to AC conversion
The inverter provides AC load voltage from a DC voltage source. The power
devices can be thyristors (SCRs), MOSFETS, IGBTs, etc. The choice of
power switch depends on rating requirements and the ease with which the
device can be turned on and off. The output frequency of the inverter is
controlled by the rate at which the switches are turned on and off, in other
words by the pulse repetition frequency of the base, or gate, driver circuit.
Thyristors would only be used in very high -power inverters as commutation
circuits would be required to turn the thyristors off.
Converters that modulate power from a DC source to provide AC power to a
load are called inverters. The two parameters of importance in inverters are
the output voltage and the output frequency.
The switch-mode inverter is the most commonly used. Power semiconductor
switches, in different configurations, chop the DC supply waveform so that
the load experiences rectangular waves that periodically change polarity to
give an alternating voltage. Concern is given to the quality of power
absorbed by the load. In most cases a sinewave of a single frequency is
desired to minimise losses produced by other harmonics. In s witch-mode
inverters there are always some harmonics because the output waveform is
synthesised digitally from the rectangular waveforms. Techniques to produce
a near-sinewave are called pulse-amplitude modulation (PAM) or pulse-width
modulation (PWM) methods.
There are two types of switch-mode inverters. They are the voltage -type and
the current-type. As its name implies, the voltage -type inverter is fed from a
constant voltage source. The voltage chopping to create changing intervals of
constant voltage at the load causes the current to change. This type is the one
most commonly used. The current-type inverter supplies a constant source
current that is not interrupted. The pattern of switching changes the voltage
across the load in this case. Current-type inverters are used in some large AC
motor drives.
If it is important to have an inverter with no harmonics, then, instead of
switched-mode inverters, resonant inverters can be used. Resonance of
energy between a capacitor and an inductor at the required output frequency
will provide a good sinewave output.
Current-source inverters are derived by taking the dual of the voltage -source
inverters. Current sources replace voltage sources. Current -filter inductors
replace voltage-filter capacitors, and series diodes (to block reverse voltages
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at the switches) replace inverse-parallel diodes (to conduct reverse current
that a switch would block).
AC–AC conversion
Cycloconverters
The cycloconverter synthesises its output voltage waveform by switc hing
between the phases of the AC supply and provides an alternative to the
inverter where the output frequencies are restricted to being less than the
supply frequency. The simplest form of cycloconverter produces an output in
which each half cycle of the output waveform is made up of a whole number
of half-cycles of the single-phase supply waveform. By using a multi -phase
supply an output waveform can be produced which approximates to a square
wave. By altering the point-on-wave at which the individual phases are
switched to form the output waveform, an output voltage can be obtained in
which the fundamental is emphasised. This approach also means that the
output is no longer restricted to frequencies, which can be made up from
integer numbers or cycles or parts of cycles of the AC source frequency.
Voltage regulators (Phase control)
Two antiparallel thyristors connected in series with a load to an AC voltage
give a simple example of a direct converter for controlling, for instance, active
power. The control can be performed by phase control or by sequence control.
The phase control implies a change of the output waveform by letting a
thyristor block a smaller or greater part of the half -cycle. With sequence
control the ratio between blocked and unblocked half-cycles is varied.
DC–DC conversion
The power source for the chopper could be a battery or rectified AC. The
purpose of the chopper is to provide a variable DC voltage from a fixed
voltage DC source. Applications of choppers are in drives f or electric
vehicles, in the DC link for variable frequency inverters and in switched
mode power supplies.
The power switch used can be a power transistor (MOSFET or IGBT). These
require base, or gate driver, circuits to turn the switch on, and they turn off
when the driver pulse is removed. The power switch could be a thyristor
(SCR), but on DC a separate ‘turn-off’ circuit is required and this
complication tends to rule out the thyristor for all but very high -power
applications.
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Tutorials (Electronics Workbench)
Diodes
1.
Draw a 12V battery on the left-hand side of the screen, and two 12V
bulbs on the right. Label the bulbs R for red and G for green. Add a
suitable switch next to the battery to make a ‘signal controller’. The
controller must be able to light either the red bulb only, or the green
bulb only. This can be achieved with only two wires linking the
controller to the bulbs by adding diodes to the circuit.
2.
Draw a circuit diagram consisting of 3 bulbs (rated at 12V), 3 switches,
a 10V battery and any necessary diodes. Arrange it so that:
(a)
(b)
(c)
3.
Switch 1 makes only bulb 1 light up
Switch 2 makes only bulbs 1 and 2 light up
Switch 3 makes all 3 bulbs light up.
Design a power supply that can be plugged into the UK mains supply of
240V, and which produces a smooth DC output of 12V. Take the
following steps:
(a)
(b)
(c)
(d)
Draw the circuit
Calculate the AC output voltage required (i.e. the RMS value)
from the transformer that causes 12V to develop across the
smoothing capacitor
Calculate the transformer turns ratio required
Check your calculations on Workbench.
Note:
You should select the POWER IDEAL transformer (by double -clicking on the
symbol). Now click on EDIT and change the turns ratio to the value you have
calculated.
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Thyristors
4.
(a)
(b)
(c)
5.
(a)
(b)
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Design a simple circuit that shows a thyristor employed to switch
a lamp on or off. Use a 12V AC supply, and a 20V lamp. Control
the thyristor with a switch.
When the switch is closed, why does the bulb appear to flash on
and off?
If the switch is opened just after the bulb has lit, there is a delay
before the bulb switches off. What causes the delay?
Design a simple circuit that employs a triac to control a lamp.
Again, use a 12V voltage source, a 20V lamp and control the triac
with a switch.
What is the main difference between the action of this circuit and
that of the previous one?
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Laboratory experiments
Some laboratory experiments (using Electronics Workbench) that could be
used to consolidate the theory are given below:
1.
2.
3.
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4.
5.
6.
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