Major Project, HVDC Thesis - Saurabh Saxena

STUDY OF HVDC BACK-TO-BACK COUPLING
SCHEME WITH CASE STUDY OF
VINDHYACHAL GRID
Project No. – 7
Submitted as a
Major Project for the
Degree of Bachelor of Engineering
Year 2005-2006
Guided by: Submitted by:
Miss Madhu Gupta Rashmi Jain
Saurabh Saxena
Vaseem Mansuree
Department of Electrical Engineering
SHRI VAISHNAVSM INSTITUTE OF TECHNOLOGY AND SCIENCE
INDORE
Project No. – 7: Study of HVDC back-to-back coupling shemes with case study of Vindhyachal Grid
Rashmi jain, Saurabh Saxena & Vaseem Ahmad Mansuree

STUDY OF HVDC BACK-TO-BACK COUPLING
SCHEME WITH CASE STUDY OF
VINDHYACHAL GRID
Major Project
A Dissertation submitted to
Rajiv Gandhi Proudyogiki Vishwavidhyalaya, Bhopal
towards partial fulfillment of the
Degree of Bachelor of Engineering
in
Electrical Engineering
Year 2005-2006
Guided by: Submitted by:
Miss Madhu Gupta Rashmi Jain
Saurabh Saxena
Vaseem Mansuree
INDORE

(57,),$7(

This is to certify that Miss Rashmi Jain (0802EE033D06), Mr. Saurabh Saxena
(0802EE021050) Mr. Vaseem Ahmad Mansuree (0802EE021054) students of Final
Year (VIII Semester), Electrical Engineering Branch, working in a group have successfully
completed the required work for this semester for the major project no. 7 titled “STUDY
OF HVDC BACK-TO-BACK COUPLING SCHEME WITH CASE STUDY OF
VINDHYACHAL GRID”. This project work is a part of the syllabus prescribed by
R.G.P.V. under the subject “Major Project” for the academic year 2005-06.
Project Guide Head of Department
Internal Examiner External Examiner
INDORE

$.12:/('*(0(176

No great tasks can be completed successfully without suitable functional
environment and proper guidance. We are thankful to the board of education for
giving us a chance to apply our theoretical knowledge to develop practical skills
through this project.
We feel immense pleasure and deep feeling of gratitude towards Miss
Madhu Gupta (Lecturer, Department of Electrical Engineering) for encouraging us
in choosing this project and guiding us with constructive and valuable suggestions
and constant motivation, which not merely helped but enabled us to complete the
report. We express our gratitude towards Proff. R. N. Paul (HOD, Electrical
Engineering Department) for his guidance and timely advice for the preparation of
the report.
We are also thankful to Mr. M. C. Sahu (D.G.M., HVDC BTB
Vindhyachal, PGCIL), Mr. A. K. Pandey (Manager, HVDC BTB, Vindhyachal,
PGCIL), Mr. Praveen Ranjan (Dy. Manager, HVDC BTB, Vindhyachal, PGCIL)
for their guidance and providing functional environment during our visit to
Vindhyachal BTB station.
And finally heartfelt appreciation to all those persons, who were directly
and indirectly, helpful in completing this report.
Rashmi Jain
Saurabh Saxena
Vaseem Ahmad Mansuree

Contents
CONTENTS
Page No.
1. Synopsis
1. Aim 1
2. Objectives 2
3. Introduction 3
3.1 Introduction to HVDC 3
3.2 HVDC scenario in India 4
3.3 Selection of voltage level for HVDC transmission 5
3.4 Cost structure of HVDC 7
3.5 HVDC connection schemes 8
4. EHV-AC versus HVDC 11
4.1 Technical considerations 11
4.2 Economical considerations 13
5. HVDC back to back interconnection 15
5.1 Significance 15
5.2 Overview of operation 15
6. Substation configuration 17
6.1 Converter bridge unit 18
6.2 Converter transformer 20
6.3 Smoothing reactor 23
6.4 Filters 23
6.5 Reactive power sources 24
6.6 Transmission medium 25
6.7 DC switchgear 25
6.8 Earth electrode 25
7. Future work to be done 26
8. Utility and application of the project 26
9. Conclusion 27
2. Introductions

Contents
3. Chapter 1: Converter analysis
1.1 Thyristor valve 30
1.1.1 General 30
1.1.2 Valve design consideration 30
1.1.3 Valve firing 31
1.1.4 Recent trends 32
1.2 Choice of converter configuration 32
1.2.1 Valve rating 33
1.2.2 Transformer rating 34
1.3 Analysis of Graetz circuit 34
1.3.1 General 34
1.3.2 Analysis without overlap 36
1.3.3 Analysis with overlap 40
1.3.4 Inversion 48
1.4 Steady state equivalent circuit 51
4. Chapter 2: HVDC control
2.1 Introduction 52
2.2 Principle of DC link control 52
2.2.1 Desired features of control 53
2.3 Voltage–current characteristics for HVDC converter 55
2.3.1 Individual characteristics 55
2.3.2 Combined characteristics 57
2.4 Basic control system 58
2.4.1 Firing angle control 59
2.4.2 Constant minimum ignition angle control 60
2.4.3 Constant current control 60
2.4.3 Constant extinction angle control 62
2.5 Master control 62
2.6 Higher level controllers 62
2.7 System control hierarchy 63
2.8 Reactive power control 64
2.8.1 Introduction 64
2.8.2 Steady state reactive power requirement 65
2.8.3 Sources of reactive power 70

Contents
5. Chapter 3: Harmonics and filters
3.1 Introduction 75
3.2 Generation of harmonics 77
3.2.1 Generation on AC side 77
3.2.2 Generation on DC side 77
3.3 Characteristic harmonics 78
3.3.1 Harmonics at no overlap 79
3.3.2 Harmonics with overlap 81
3.4 Non-Characteristic harmonics 83
3.4.1 Causes 83
3.4.2 Amplification 84
3.4.3 Consequences 84
3.5 Troubles caused by harmonics 84
3.6 Means of reducing harmonics 85
3.6.1 Increased pulse number 85
3.6.2 Application of filter 85
3.7 Filters 86
3.7.1 Purpose 86
3.7.2 Classification 86
3.7.3 Cost 87
3.7.4 AC filters 88
3.7.5 DC filters 89
6. Chapter 4: Converter faults and protection
4.1 Introduction 90
4.2 Converter Faults 90
4.2.1 General 90
4.2.2 Arc-back 91
4.2.3 Arc-through 92
4.2.4 Misfire 92
4.2.5 Quenching (current extinction) 92
4.2.6 Commutation failure 93
4.2.7 Short circuit in bridge 95
4.3 Protection 95
4.3.1 General 95
4.3.2 DC reactor 96
4.3.4 Voltage oscillations and valve dampers 96
4.3.5 Current oscillations and anode dampers 97

Contents
7. Chapter 5: Case study
5.1 Introduction 98
5.2 Location of Vindhyachal HVDC Back-to-Back station 98
5.3 Technical information and data 98
5.4 Nominal ratings 99
5.5 Single line diagram 100
5.6 Equipments 101
5.7.1 Converter transformer 101
5.7.2 Thyristor valve 103
5.7.3 Smoothing reactor 107
5.7.4 Filter and shunt bank 108
5.7 System control and auxiliary power 109
5.7.1 Control hierarchy 109
5.7.2 Control modes 109
5.7.3 Block control 110
7.7.4 Station level controller 111
5.8 Other auxiliaries 112
5.8.1 Valve cooling system 112
5.8.2 D.G. Set 113
5.8.3 PLCC Room 113
5.8.4 Battery Room 114
5.8.5 Battery Charging Room 114
5.8.6 Fire Fighting System 114
5.9 Operations and maintenance 115
8. Conclusions 116
9. Bibliography 117

Synopsis 1
AIM
Study and analysis of HVDC back-to-back coupling scheme
case study of Vindhyachal HVDC back-to-back interconnection
between Western and Northern Regions.

Synopsis 2
OBJECTIVES OF THE PROJECT
¾To understand the basic operation of HVDC interconnection.
¾To study and analyze converter operation.
¾To study the various design considerations of converter transformer
¾To study the problem of harmonics during converter operation
¾To analyze the operation of filters and smoothing reactor
¾To study reactive power requirement and compensation schemes
adopted in HVDC
¾To study and analyze the control parameters governing the
magnitude and direction of power flow.
¾To Study the coupling scheme adopted at Vindhyachal back-to-back
interconnection between Northern region and Western region.

Synopsis 3
INTRODUCTION
1. Introduction to HVDC
Early electric power distribution schemes used alternating-current
generators located near the customer's loads. As electric power use became
more widespread, the distances between loads and generating plant
increased. Since the flow of current through the distribution wires resulted in
a voltage drop, it became difficult to regulate the voltage at the extremities
of distribution circuits. A generator connected to a long ac transmission line
may become unstable and fall out of synchronization with a distant ac power
system.
An HVDC transmission link may make it economically feasible to use
remote generation sites. HVDC transmissions make an important
contribution to controlling power transmissions, safeguarding stability and
containing disturbances.
In an HVDC transmission, electric power is taken from a three-phase
.AC network, converted to DC in a converter station, transmitted to the
receiving point by a cable or overhead line and then converted back to AC in
another converter station and injected into the receiving AC network. As the
conversion process is fully controlled, the transmitted power is not dictated
by impedances or phase angle differences, as is the case with AC.
The investment costs for HVDC converter stations are higher than for
high voltage AC substations. On the other hand, the costs of transmission
medium (overhead lines and cables), land acquisition/right-of-way costs are
lower in the HVDC case. Moreover, the operation and maintenance costs are
lower in the HVDC case. Initial loss levels are higher in the HVDC system,
but they do not vary with distance. In contrast, loss levels increase with

Synopsis 4
distance in a high voltage AC system. The following picture shows the cost
breakdown (shown with and without considering losses).
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The breakeven distance depends on several factors, as transmission
medium (cable or OH line), different local aspects (permits, cost of local
labor etc.). When comparing high voltage AC with HVDC transmission, it
is important to compare a bipolar HVDC transmission to a double-circuit
high voltage AC transmission, especially when availability and reliability
is considered.
2. HVDC Scenario in India
In India, HVDC technology is new and presently only seven HVDC
links are under operation and two links are under construction. These are
Commissioned Projects
1. HVDC Back to Back station, Vindhyachal (Madhya Pradesh)
2*250 = 500 MW (Northern region and Western region)
2. HVDC Back to Back station, Sasaram (Bihar)
1*500 = 500 MW (Eastern Region and Northern Region)
3. HVDC Back to Back station, Vijag (Andhra Pradesh)
2*500 = 1000 MW (Southern region and Eastern region)

Synopsis 5
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4. HVDC Back to Back station, Chandrepur (Maharashtra)
2*500 = 1000 MW (Western region and Southern region)
5. HVDC Bipolar line; Chandrapur (MH) to Padeghe (MH)
Ratings: ± 500 kV, 1500 MW, 850 km
6. HVDC bipolar line; Talser to Kollar (Karnataka)
Ratings: ± 500 kV, 2000 MW, 1700 km.
7. HVDC Bipolar Line; Rihand (UP) to Dadri (Delhi)
Ratings: ± 500 kV, 1500 MW, 800 km
Under Commissioning
8. HVDC Bipolar line : Baliya (UP) to Bhivadi
Ratings: ± 500 kV, 2000 MW, ~ 850 km
9. HVDC Bipolar line: Arunachal Pradesh to Agra (UP)
Ratings: ± 800 kV, 3500 MW, 2000 km

Synopsis 6
3. Selection of transmission voltage
Transmission voltage is selected taking into account the line cost and
converter cost. With the increase in voltage level, converter cost increases
gradually on account of increase in voltage rating while the line cost (which
is a function of many parameters) shows the characteristics as shown in
figure.2
Optimum system voltage at which power can be transmitted most
economically is given by the minimum separation between the two curves.
That optimum system voltage may or may not be equal to the optimum line
voltage as shown in figure 3.
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Synopsis 7
2. Cost Structure of HVDC
The cost of an HVDC transmission system depends on many factors,
such as power capacity to be transmitted, type of transmission medium,
environmental conditions and other safety, regulatory requirements etc.
Even when these are available, the options available for optimal design
(different commutation techniques, variety of filters, transformers etc.)
render it is difficult to give a cost figure for an HVDC system.
Nevertheless, a typical cost structure for the converter stations could
be as follows:
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Synopsis 8
HVDC CONNECTION SCHEMES
1. Monopolar Link
Monopolar HVDC system has only one conductor, usually of negative
polarity (pole) and return path is provided by permanent earth or sea. This
system is used only for low power transmission. Earth electrodes are
designed for continuous full-current operation and for overload capacity
required in the specific case.
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2. Homopolar Link
Homopolar link has two or more conductors all having the same
polarity, usually negative; all operates with the ground return. In the event of
fault on one conductor, the entire converter is available for connection to the
remaining conductor or conductors, which have some overload capability,
can carry more than half of the rated, power and perhaps the whole rated
power, at the expense of increased line losses.
It has advantage of lower power loss due to corona and smaller radio
interference due to negative polarity.
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Synopsis 9
3. Bipolar Link
Bipolar link has two conductors, one positive and other negative.
Each terminal has two converter of equal rated voltage. The neutral point of
one or both end is grounded. In the event of fault on one conductor, the other
conductor with ground return can carry up to the half of the rated load. The
voltage between poles is twice that of pole to earth voltage therefore its
typical rating can be expressed as 500 kV, 1500 MW.
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4. HVDC Back-to-Back Coupling Scheme
HVDC coupling scheme is used for interconnection between
adjacent AC networks for the purpose of frequency conversion or for
asynchronous interconnection.
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Rectifier and inverter are connected to form a DC closed loop. There
is no DC transmission line and DC smoothing reactor is connected to de

Synopsis 10
loop. Rectifier and inverter are installed in the same station. The exchange of
power can be controlled, both in direction and magnitude, without can be
controlled without transferring frequency disturbances.
5. Multi-terminal HVDC Scheme
Multi-terminal HVDC scheme is used for asynchronous
interconnection of two or more AC network. This scheme offers an effective
way of large power transfer along with improvement in system stability.

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Synopsis 11
EHV-AC VERSUS HVDC SYSTEM
1. Technical Considerations
1.1 Stability of Transmission System
HVDC gives asynchronous tie and transient stability does not pose
any limit on power transfer. Line can be loaded up to thermal limit of the
line or valves. But in AC system to maintain its stability under transient
condition, it remains in synchronism.
1.2 Short Circuit Level
In AC transmission, when an existing AC system is interconnected
with another AC system, the fault level of both the system increases.
However, when both are interconnected by DC transmission, the short
circuit current is not increased so much as for DC line contributes no current
to an AC short circuit beyond its rated current.
1.3 Corona Losses and Radio Interference
For the same power transfer and same distance, the corona losses and
radio interference of DC system is less than that of AC system, as the
required dc insulation level is lower then corresponding ac insulation.
1.4 Line Loading
The permissible loading of an EHV-AC line is limited by transient
stability limit and line reactance to almost one third of thermal rating of
conductors, no such limit exists in case of HVDC lines.
1.5 Skin Effect
This is absent in dc current, as current density is uniformly distributed
across the cross-section of the conductor while the effective resistance in AC
conductor is increased due to skin effect.

Synopsis 12
1.6 Surge Impedance Loading
Long HVAC lines are loaded to less than 0.8 PN (Surge impedance
loading or natural loading of line). No such condition is imposed on HVDC
line.
1.7 Voltage along the line
Long HVAC line has varying voltage along the line due to absorption
of reactive power. This line remains loaded below its thermal limit due to
the transient stability limit. Such problem does not arise in HVDC line and it
gives almost flat voltage profile.
1.8 Reactive power requirements
HVDC line does not need intermediate reactive power compensation
like in HVAC line but it requires reactive power at converter terminals. The
required reactive power varies with the transmitted power and is about 60 %
of the total active power transferred per converter station. Usually shunt
capacitors or synchronous condenser are installed for supplying reactive
power.
1.9 Skin Effect
This is absent in DC and hence current density is uniformly
distributed across the cross section of the conductor, this leads to reduced
heating effect and optimum conductor utilization
1.10 Rapid power transfer
The control of converter valves permit rapid changes in magnitude
and direction of power flow. Limitation is imposed by power generation and
AC system. For AC line power per phase can be given as
Pac = {[ | V1 | . | V2 | ] Sin d }/ X Watts / phase

Synopsis 13
The AC line can be loaded to transient stability limit which occurs at
d=300 and given by,
Pac = { | V1 | . | V2 | } / 2 X Watts / phase
AC power cannot be changed easily, quickly and accurately as V1 and
V2 should kept around rated and d can not be changed quickly, while power
flow through DC line can be given as
PDC = {Vd1 – Vd2}* Vd / R Watts / pole
By varying Vd1 and Vd2 by means of thyristor converter control and
tap changer control, PDC can be quickly, accurately and easily controlled.
Ramping rate (the rate at which magnitude of power transfer can be varied)
can be as high as 30 MW / minute.
1.11 Transmission through cables
DC transmission can be through underground or marine cables since
charging currents are taken only while energizing the DC link and are not
present continuously. In AC system, there is limit on length of cable
depending upon rated voltage. This limit is about 60 km for 145 kV, 40 km
for 245 kV and 25 km for 400 kV AC line.
2. Economical Considerations
2.1 Substation cost
Substation cost of HVDC is very high owing to costly terminal
equipments like converter, filters, converter transformer, complex control
equipments etc, while initial cost of HVDC terminal substation is very low.
2.2 Number of lines
HVAC needs at least two-three phase lines and generally more for
higher power. HVDC needs at maximum, only one bipolar line for majority
of application.

Synopsis 14
2.3 No of conductors
Bipolar HVDC transmission lines require two-pole conductors to
carry DC power. Hence HVDC transmission becomes economical over ac
transmission at long distance with the saving in overall conductor cost,
losses, towers etc.
2.4 Right of way
Right of way for DC line is low as compared to that of AC transmission
system
2.5 Cost of towers
More number of conductors require high tower strength to stand with
the mechanical forces and weight. This increases the cost of AC towers
while in case of DC tower has to carry only two lines and a compact
structure is sufficient.

Synopsis 15
HVDC BACK TO BACK INTERCONNECTION
1. Significance of HVDC back-to-back interconnection
Interconnections between grids are desirable because they not only
permit economies through the sharing of reserves, but they also make the
trading of electricity between grids possible. Interconnections allow power
consumers to benefit from generation at the site of lowest incremental cost.
On the downside, however, disturbances can easily spread from one area to
another.
Major blackouts in recent years highlight the vulnerability of large AC
systems and have shown how relatively minor malfunctions can have
repercussions over wider areas. As one link overloads it is tripped,
increasing the strain on neighboring links, which in turn disconnect,
cascading blackouts over vast areas and causing huge productivity losses for
the economy.
HVDC back-to-back coupling scheme play a significant role in
interconnecting the power systems as it not only allows the precise and
reliable transfer of power but also prevent the frequency disturbances to
transfer from one system to another. A HVDC link can fully control
transmission but does not overload or propagate fault currents.
2. Overview of Operation
A back-to-back station is system for power transfer in which both
static inverters are in the same area, usually even in the same building and
the length of the direct current line is only a few meters. Figure 10 shows the
detailed schematic diagram of HVDC back to back coupling scheme,
main components of any such schemes are as follows:

Synopsis 16
• Converter
• Converter transformer
• Shunt compensators
• Smoothing reactor
• AC Filter
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In an HVDC coupling scheme, electric power is taken from one grid
(three-phase AC network), converted to DC in a converter station, fed to the
receiving point (inverter) and then converted back to AC in another
converter station and injected into the receiving AC network. As the
conversion process is fully controlled, the transmitted power is not dictated
by impedances or phase angle difference, as is the case with AC. Earthing is
only for reference, it does not carry any direct current and there are no
problems of galvanic corrosion of substation earth and underground pipes,
structure etc.

Synopsis 17
HVDC SUBSTATION CONFIGURATION
At HVDC converter station, conversion from AC to DC (rectification)
or DC to AC (inversion) is performed. Role of rectifier and inverter can be
reversed using suitable converter control configuration.
A point to point transmission requires two converter stations. While In
a back-to-back station, both rectifier and inverter station are usually installed
in a single valve room with the converter transformer installed on either side
of valve room (Hall) and the DC bushings are taken indside the valve hall
for connection to the valves.
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Figure 11 shows the typical arrangement of the converter substation.
One of the main components of a converter substation is the thyristor
converter, which is usually housed in a valve hall. As seen from figure, the

Synopsis 18
substation also essentially consists of converter transformers. These
transformers transform the ac system voltage based on the dc voltage
required by the converter. The secondary or dc side of the converter
transformers is connected to the converter bridges. The transformer is placed
outside the thyristor valve hall, and the connection has to be made through
the hall wall. This is accomplished in two ways: 1) with phase isolated bus
bars where the bus conductors are housed within insulated bus ducts with oil
or SF6 as the insulating medium, or 2) with wall bushings, and these require
care to avoid external or internal breakdown.
Filters are required on both ac and dc sides since the converters
generate harmonics. The filters are tuned based on the converter operation (6
or 12 pulse). DC reactors are included in each pole of the converter station.
These reactors assist the dc filters in filtering harmonics and mainly smooth
the dc side current ensuring continuous mode of operation. Surge arrestors
are provided across each valve in the converter bridge, across each converter
bridge, and in the dc and ac switches to protect the equipment from over
voltages.
1. Converter Bridge Unit
This usually consists of two three phase converter bridges connected
in series to form a 12 pulse converter unit. The total numbers of valve in
such a unit are twelve. The valves can be packaged as single valve, double
valve or quadrivalve arrangements. Each valve is used to switch in a
segment of an AC voltage waveform. The converter is fed by converter
transformer connected in star/ star and star/delta arrangement.

Synopsis 19
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The valves are cooled by air, oil, and water. Liquid cooling using
deionized water is more efficient and results in the reduction of station
losses. The ratings of valve group are limited by more permissible short
circuit current than steady state load requirement. The design of valve is
based on the modular concepts where each module contains a limited
number of series connected thyristor level.
Valve firing signals are generated in the converter control at ground
potential and are transmitted to each thyristor in the valve through a fiber
optic light guide system. The light signal received at the thyristor level is
converted to an electrical signal using gate drive amplifier with pulse
transformer.

Synopsis 20
2. Converter Transformer
The HVDC converter transformer is a very important component in a
HVDC transmission system. 25 –30 % cost of the converter station is
determined by the cost of converter transformer. In addition to its normal
application to provide transfer of power between two voltage levels, it serves
a number of additional functions like galvanic separation between the AC
and DC systems. A fairly large tapping range permits optimum operation
also for a large variation in load without loss of efficiency.
The converter transformer is generally built with two valve windings
of equal power and voltage ratings. One of the windings is connected in star
and the other in delta. With this arrangement the dominant harmonics from
the converter will be cancelled out. Windings, which are directly connected
to AC system, are termed as line windings while winding connected to the
converter is called valve windings.
The HVDC converter transformer can be built as three-phase or as
single-phase units depending on voltage and power rating. When built as
three-phase transformer there is generally one unit with the valve winding
arranged for star connection and the other delta connection. In single-phase
design the two valve windings are generally built on the same transformer
unit.

Synopsis 21
2.1 Winding Connection
The generation of harmonics is an undesirable feature in the converter
equipment and in order to minimize these, 12 pulse converter is normally
used. It is usual to arrange both star and delta connected valve windings
have a common star connected primary line winding.
2.2 Insulation Design
The insulation design of HVDC converter transformer is determine by
following factors:
1. The AC voltage distribution and DC bias voltage which is a
function of dc system voltage experienced by valve winding
2. The DC voltage experience a voltage polarity reversal when the
direction of power flow is reversed
3. The behavior of insulating materials, paper, pressboard and oil,
differs greatly in its response to DC stress than it does to AC
stress.
In the case of a system subjected to a DC stress the distribution is
determined by material dimension and their resistivity and in case of
converter transformer, as combination of AC and DC stresses occur in
practice.
2.3 Harmonics Consideration
The harmonics add considerably to the stray losses in the transformer
windings, core and structural work and due allowances must be made for
their effect. Reduction is harmonics in line side is achieved by the use of
connecting filters.

Synopsis 22
2.4 Commutating Reactance and Short-Circuit Current
Fault current in the case of converter transformer is likely to contain a
very much greater DC component than is the case for normal transformer
and unlike the in the case of fault in the conventional AC circuit fro which
the DC component decays very rapidly, for converter circuit the high DC
component will continue until the protection operates. The resulting
electromagnetic forces can therefore be very significant. These forces can be
kept within the limits by either higher impedance which result in high
regulation or, the use of tap changers, which in addition to control of valve
firing angle to control the power flow will often have up to 50% grater range
than conventional transformer, so the need to limit the variation of
impedance with tap position becomes an important consideration in
determining the winding configuration.
2.5 Configuration
THE converter transformer can have different configuration (1) three
phase, two winding,(2) single phase , three winding (3) single phase two
winding. The valve side windings are connected in star and delta with
neutral point ungrounded. On the AC side, the transformers are connected in
parallel with neutral ground. The leakage reactance of the transformer is
chosen to limit the short circuit current through any valve.
In back to back links, which are designed for low DC voltage level, an
extended delta configuration can result in identical transformer being used in
twelve pulse converter units. This result in the reduction of the spare
capacity required.

Synopsis 23
3. Smoothing Reactors
The main purpose of a smoothing reactor is to reduce the rate of rise
of the direct current following disturbances on either side of the converter.
Thus the peak current during the dc line short circuits and ac commutation
failure is limited.
For satisfactory current conversion in thyristor-converters and to
eliminate pulses from DC current waveform, a large series inductance (L) is
necessary on DC side. A DC Smoothing reactor (smoothing reactor) is a
high inductance coil connected in series with the main DC pole circuit
between Converter Bridge and DC line-pole. Due to high inductance (L) the
current (Id) stores high energy (e=1/2 L*Id
2) in the reactor coil. The current
in an inductance cannot change instantaneously. Hence the fluctuations and
pulses in the direct current Id are smoothened thus the function of the
smoothing reactor is to eliminate the pulses and fluctuations in DC current
waveform, i.e. to smoothen the DC current.
The reactor blocks the non- harmonic frequencies from being
transferred between two ac systems, and also reduces the harmonics in the
dc line.
4. Filters
There are three types of filter used in HVDC System
4.1 AC Filters
Filters are used to control the harmonics in the network. The filter
banks compensate the reactive power consumed by the converters at both the
ends. For example, in CCC (capacitor commutated converter) reactive power
is compensated by the series capacitors installed between the converter
transformer and the thyristor valves.

Synopsis 24
4.2 DC Filters
The harmonics created by the converter can cause disturbances in
telecommunication systems, and specially designed dc filters are used in
order to reduce the disturbances. Generally, filters are not used for
submarine or underground cable transmission, but used when HVDC has an
overhead line or if it is part of an interconnecting system. The modern filters
are active dc filters, and these filters use power electronics for measuring,
inverting and re-injecting the harmonics, thus providing effective filtering.
4.3 High frequency filter
These are connected between the converter transformer and the station
AC bus to suppress any high frequency current.
5. Reactive Power Sources
Converter station requires power supply that is dependent on the
active power loding. Fortunately, part of this reactive power requirement is
provided by AC filters. In addition, shunt capacitors, synchronous
condensers and static VAR system are used depending on the speed of
control desired. The control of various bus voltage is achieved by supplying
and absorbing the reactive power requirement of respective bus bars by
means of series or shunt compensation. Compensation of reactive power
means supplying/ absorbing reactive volt- amperes. The compensation on
AC side is provided by the following means:
• AC filter capacitors
• AC shunt capacitors
• Synchronous condensers
• Static VAr sources ( SVS )

Synopsis 25
6. Transmission Medium
Transmission medium is not required in Back to Back configuration
as it has ideally zero length and practically only few meters. HVDC cables
are generally used for submarine transmission and overheads lines are used
for bulk power transmission over the land. The most common types of
cables are solid and the oil-filled ones. The development of new power cable
technologies has accelerated in recent years, and the latest HVDC cable
available is made of extruded polyethylene
7. DC Switchgear
This is usually a modified AC equipment used to interrupt small Dc
current. Dc breaker or metallic return transfer breaker are used, if required
for interruption of rated load current.
8. Earth Electrode
Earth electrode is used for providing the return path for the direct
current. This is used in case of Bipolar, Monopolar and Homopolar
configuration but is not required in Back-to-Back system. It is usually
located 5 – 25 KM away from the station to avoid the galvanic corrosion of
substation earthing.

Synopsis 26
UTILITY APPLICATION OF THE PROJECT
Utility
To make the back-to-back coupling system more familiar to people
Applications
1. As an asynchronous tie between two regional grid for precise and
reliable power transfer.
2. For interconnecting the two or more systems operating at different
frequencies.
3. In some cases it may be for transferring the energy generated by
windfarms to the backbone network
FUTURE WORK TO BE DONE IN THE PROJECT
¾Detailed study and analysis of converter
¾Analysis of control schemes adopted in converter station.
¾Study of reactive power requirement in converter operation and
compensation schemes adopted.
¾Study of protection schemes in HVDC
¾Study of Valve halls and switchyard
¾Case study of Vindhyachal HVDC back-to-back interconnection
between northern and western grid.

Synopsis 27
CONCLUSION
In the present scenario of energy crisis it becomes very
important to effectively utilize the available energy. In a way to achieve
this, HVDC back to back Interconnection play very important role in
connecting the power systems by providing the asynchronous tie and
enabling the precise exchange of power along with consolidation to the
stability of the existing AC network.
.
In HVDC Back-to-Back coupling, the great advantage of
avoiding synchronization between AC power systems to grid helps in
power transfer smoothly. Our study on the subject should reveal new
facts, which will be helpful in power system stability analysis.
With a lot of advantages over conventional (AC) connection
schemes, due to very high cost consideration of equipments required
and complexity of operation, the realization of scheme is restricted to
few places in our country and is scarcely used in other countries except
the developed countries except the developed countries.

Introduction
INTRODUCTION
While the very first practical applications of electricity were based on
direct current, this technology was quickly replaced by three-phase
alternating current because of various advantages. Still, in spite of the
principal use of alternating current in power systems, there are some
applications for which direct current is the better not only from the point of
view of technical performance but, even taking into account the economic
consideration.
With today’s power systems being operated closer to their stability
limits, and particularly in view of the vulnerability of AC system to faults,
there is an increasing need to understand how the HVDC technology can
play in important role in improving the dynamic performance of the existing
AC network. The thesis is organized as follows:
First of all the thesis gives, a brief overview of HVDC technology,
various transmissions schemes and presents a technical comparison with the
existing AC system. This also gives some introduction to HVDC Back-to-
Back interconnection and typical substation configuration and shows the
significance of the project from the utility and application point of view.
Secondly, it reviews with the basic converter elements i.e thyristor valve
followed by the analysis of converter and concludes with the equivalent
electrical model of a HVDC scheme.
With the various control strategies adopted for the efficient power
transmission It also cites the necessity of reactive power requirement and

Introduction 29
various compensation techniques. The next chapter presents the harmonics
generation phenomenon in converter operations, their effects and
introduction to AC and DC filters for elimination of those harmonics. Also
brief study of faults during converter operation and protection schemes is
carried out
Case-study of Vindhyachal HVDC Back-to-Back station demonstrates
the practical implementation of the so far theoretically known operation and
control of link. And finally a conclusion has been drawn citing the
significance of the technology for the existing AC system presenting the
back to back interconnection as a solution to many challenging situation.

Converter Analysis
Chapter 1
CONVERTER ANALYSIS
1.1 THYRISTOR VALVE
1.1.1 General
A thyristor Valve is made up of number of devices connected in series
to provide the required voltage rating and also of devices connected in
parallel to provide the required current rating. Device ratings, transient
overvoltages and protection philosophy determine number of series and
parallel-connected thyristor.
The valves are usually placed indoor in a valve hall for the protection
purpose and are base mounted in single, double or quadric-valve
configuration. These are usually air insulated and cooled using air, water, oil
or Freon. The water flowing in ducts cools heat sinks and damping resistor.
1.1.2 Valve design consideration
The valve design must consider the voltage and current stresses that
occur during normal and abnormal operating conditions such as over voltage
(which may occur due to switching action or as a result of external cause) or
over current, which may arise from short circuit across a valve or a converter
bridge.
The losses in a valve includes
i. The losses during on-state and switching losses
ii. Damper and grading circuit losses
iii. Losses due to auxiliary power requirement of cooling

Converter Analysis 31
The reduction in short circuit ratio (SCR) tends to reduce the maximum
value of fault current in a valve. The low SCR can also result in non-sinusoidal
voltage at the converter bus, which can give rise to commutation
failures.
The valve can be subjected to high stress commutation resulting from high
di/dt the discontinuous conduction can also result in high over voltages
across a valve. The control of electrostatic and electromagnetic fields
surrounding a valve is essential to avoid corona discharge and interference
with sensitive electronic circuits.
1.1.3 Valve firing
The basic valve-firing scheme is shown in Fig.1.1. The valve control
generates the firing signals. Each thyristor lever receives the signal directly
from a separate fiber-optic cable making each thyristor level independent.
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The valve control unit also indicates many monitoring and protective
function. The return pulse system coupled with short pulse firing scheme is
used in present day valve control unit. A separate light guide is used to send
a return pulse whenever the voltage across a thyristor is sufficient and the
power supply unit is charged. If at that time, firing pulses are demanded
from the valve control, the light signals are sent to all the thyristor control
units simultaneously.
During normal operation, one set of the light pulses are generated in a
cycle for each valve. However, during operation at low direct current, many
light pulses are generated due to discontinuous current.
1.1.4 Recent Trends
The recent developments are expected to improve reliability and
reduce the cost of HVDC valves. These are mainly:
• Development in high power semiconductor devices these include
direct light triggered thyristor and metal oxide semiconductor
controlled thyristor.
• Better cooling techniques such as forced vaporization as a means of
reducing thermal resistance between the heat sink and the ambient.
• Suspension of quadrivalve assembly from ceiling to withstand
seismic forces.
1.2 CHOICE OF CONVERTER CONFIGURATION
The configuration for a given pulse number is selected in such a way
that both the valve and transformer utilization are maximized. The basic
commutation group defines a converter configuration and the number of
such groups connected in series and parallel.


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If there are ‘q’ valves is a basic commutation group and r of these are
connected in parallel and s of them are connected in series, then
p = q*r*s …………1.1
1.2.1 Valve Rating
The valve voltage is specified in terms of peak inverse voltage (PIV)
it has to withstand, The ration of PIV to the average DC voltage is an index
of valve utilization. The average maximum DC voltage across the converter
is given by
Vd0 = VTŒ(PVLQŒT) …………1.2

The peak inverse voltage (PIV) across a valve can be obtained as
follows:
The valve utilization factor is given by
PIV / Vd0 = 2ŒVTVLQŒT

@ (for q odd)
For a six-pulse Graetz circuit, valve utilization factor comes out to be
1.047, which is one of the min. VUF obtained for various combinations.
1.2.2 Transformer Rating
The current rating of a valve is given by
IV = ID /[r ¥T@
Where, ID is the DC current assumed to be constant. The transformer rating
on the valve side (in volt ampere) is given by
STV = p EM IV / ¥
The transformer utilization factor (STV/ Vd0 ID) for q = 3 is obtained as
1.481, while for Graetz circuit it is equal to 1.047. Thus it is clear from the
above discussion that both from valve and transformer utilization
consideration, Graetz circuit is best circuit for six pulse converter.
1.3 ANALYSIS OF GRAETS CIRCUIT
1.3.1 General
Converters used in HVDC system are of various types six pulse, twelve
pulse etc, here we are considering a six-pulse converter, whose circuit
diagram is shown in the figure 1.3 with the notation adopted. Following
assumptions are made regarding the voltage source, current nature,
frequency etc to simplify the analysis:

Assumption
1. Power source (or sink) consisting of balanced sinusoidal EMFs of
constant voltage and frequency in series with equal lossless
inductances.
2. Constant ripple free direct current
3. Valves with no forward resistance and infinite inverse resistance
4. Ignition of valve at equal interval of one-sixth cycle (600)
)LJXUH%ULGJHRQYHUWHUVFKHPDWLFFLUFXLWIRUDQDOVLV
The instantaneous line-to-neutral EMFs are taken as:
……… 1.3

Corresponding line-to-line emfs are
………1.4
1.3 ANALYSIS WITHOUT OVERLAP
At any instant, two valves are conducting in the bridge, one from the
upper commutation group and second from the lower commutation group.
The firing of the next valve in a particular group results in the turning off the
valve that is already conducting.
One period of AC supply voltage has six intervals corresponding to
conduction of pair of valves.
)LJXUH%ULGJHRQYHUWHUZLWK9DOYHVDQGRQGXFWLQJ
Fig 1.4 shows the typical waveforms of the converter if the ac
inductance LC is neglected. In the top graph the ac line-to-neutral voltages
are drawn in thin lines and, in heavy lines, the potentials of the positive and
negative dc terminals with respect to ac neutral. The middle graph shows the
ac line-to-line voltages and, in a heavy line, the instantaneous direct voltage
VD (or Ud). The bottom graph shows the constant dc current and, in a heavy
line, the ac line current Ia.

At any given instant, one valve of the upper commutation group and
one of the lower rows are conducting. Therefore, the instantaneous direct
voltage at any time equals one of the six line-to-line voltages. The instant at
which the direct voltage changes to another line-to-line voltage is controlled
via the firing angle ‘.¶
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SKDVHDOLQHFXUUHQW
Average direct voltage Vd (or Ud)
It is assumed that the valves are fired at equal intervals. Hence, Ud
consists of six identical segments of 600 width each, and so the average
direct voltage can be found by averaging the direct voltage over any 600
interval. LCC models average direct voltage is given by

……………1.5
Where
……………1.6
is the so called ideal no-load direct voltage.
DC voltage harmonics
The dc voltage waveform contains a ripple whose fundamental
frequency is six times the supply frequency. This can be analyzed in Fourier
series and contains harmonics of the order
h = np
Where,
p is the number of pulse and n is integer.

The rms value of hth order harmonic in DC voltage is given by
Vh = Vd0 * ¥K2 – 1) Sin2 .@1/2 / [h2 – 1] ………………1.7
$OWKRXJK.FDQYDUIURP-1800 , the full range cannot be utilized. In
order to ensure the firing of all the series connected thyristors, it is necessary
to provide a minimum limit of .greater than zero. Also in order to allow for
the turn-off time of a valve, it is necessary to provide an upper limit less than
1800. The delay angle .is not allowed to go beyond (1800 - ) where is
called the extinction angle (also called margin angle). The minimum value
of extinction angle is typically 100, although in normal operation as an
inverter, it is not allowed to go below 150 or 180.
AC current waveform
As it is assumed that the direct current has no ripple (or harmonics).
The AC currents flowing through the valve (secondary) and primary
windings of the converter transformer contains harmonics.
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The waveform of the current in a valve winding is shown in fig.1.6
The rms value of the fundamental component of the current is given by
I1 = ¥Œ
,D …………1.8
Whereas the rms value of the current is
I = ¥

The Power Factor
The AC power supplied to the converter is given by
PAC = ¥(LL I1FRV3 ¥(LL * (¥Œ)* IDFRV3««««
Where,
FRV3 the power factor of ac side
ELL line to line voltage on AC side
I1 rms value of fundamental component
ID value of direct current on DC side
The DC power fed must match the AC power ignoring the losses in
the converter. Thus, ignoring losses we get
PDC = VD*ID = 3¥(LL*I1 cos .Œ ………... 1.11
Where,
VD value of direct voltage on DC side
Equating the above two equations we get
FRV3 FRV. …………1.12
From the above equation it is clear that the reactive power
UHTXLUHPHQW YDULHV LQ GLUHFW SURSRUWLRQ WR ILULQJ DQJOH . +HQFH LW LV
recommended to operate the rectifier at low firing angle with suitable safety
margin.
1.3.3 ANALYSIS WITH OVERLAP
1.3.3.1 General concept of overlap
Because of the AC source inductance and converter transformer
leakage reactance, transfer of current from one phase to another can’t be
instantaneous but requires finite time called commutation time or overlap
time where is the overlap angle. In normal operation it is less than 600:
typical full load values are 20 - 250.

With the increase in overlap angle, number of conducting valves at a given
time increases.
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Each interval of the period can be defined by two subintervals. In the
first subintervals two valves are conducting and in the second subintervals,
three valves are conducting. As the overlap increases to 600, there is no
instant when only two valves are conducting. As the overlap angle increases
beyond 600, there is a finite period during an interval when four valves
conduct and the rest of the interval during which three valve conduct. Thus
there are three modes of the converter as follows:
1. Mode 1 – Two and three valve conduction ( 600)
2. Mode 2 – Three valve conduction ( = 600)
3. Mode 3 – Three and four valve conduction ( 600)
For the simplicity of analysis, we will discuss here only Mode-1 of
operation, which is most usually encountered during the operation.
ANALYSIS WITH OVERLAP LESS THAN 600
Since a new commutation begins every 600 and lasts for angle the
angular interval when two valve conducts is 600 – The sequence of
conducting valve is 12, 123, 23, 234, 34, 345, 45, 456, 56, 561, 61, 612 and
so on.

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D

SKDVHDDQGEOLQHFXUUHQWV

Consider the situation when valve 1 and 2 were conducting initially.
At W ., when valve 3 is ignited, the effective circuit is as shown in
fig.1.10 with valve 1, 2 and conducting.

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During this interval direct current is transferred from valve 1 to valve 3.
Hence, at beginning (W .

i1 or ia = ID and i3 or ib = 0 …………1.13
At end (W . /):
i1 = 0 and i3 = ID …………1.14
1.3.3.2 Average Direct Current
The mesh equation for the loop N31N can be given as
The emf in this loop known as commutating EMF, which is
ea – eb = ¥(PVLQW …………1.15
The sum of ia and ib during commutation equals direct current
and equation 1.15 becomes
¥(PVLQW /C dib / dt = 2LC di3 / dt

Integration during commutation period (from W . to W /) gives
And finally inserting the boundary conditions in the LHS of the above
equation, we get
Id = ¥/CFRV.–FRV/

…………1.16
Equation 1.14 shows that i3, the current in the incoming valve during
commutation, consists of a constant (dc) term and a sinusoidal term which
lags the commutation voltage by 900. And has a crest value which is that of
the current in a line-to-line short circuit on the AC source.
From this equation the extinction angle d (and ultimately the overlap
angle ) can easily be determined for a given firing angle .. It also allows
the calculation of the ideal maximum firing angle .MAX for which the
commutation will succeed in a converter with ideal valves. Since
For any angle /
And
………… 1.17

1.3.3.3 Average Direct Voltage
During commutation the two impedances in the commutation loop act
as a voltage divider that sets the potential of the positive converter terminal
to the average of the two line voltages. It is only after the commutation that
the terminal potential recovers to the voltage of the on-going phase.
The consequence is that an area Aμ as shown in Fig. decreases the
voltage/angle-area A derived in Eq. 1.17. This results in a voltage drop ¨Ud
of the average direct voltage,
…………1.18
…………1.19
Comparison of equation 3.17 and 3.20 shows that voltage drop is
directly proportional to the DC current
¨8d Œ
/C ID …………1.20
The total average direct voltage is thus given by
= Udi0 cos.– RC Id ………... 1.21

Where,
RC Œ
/C
‘RC’ is called the equivalent commutation resistance. It accounts for
the voltage drop due to commutation. However, it is not a real ohmic
resistance and thus consumes no active power.
With Eq 1.21 the average direct voltage could also be written as
= Udi0
FRV.FRV/

…………1.22
1.3.3.4 Equivalent circuit of rectifier
From the equation 1.22, equivalent circuit of the rectifier can be
drawn as
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1.3.3.5 DC voltage waveforms
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Figure 1.11 shows the waveforms of the voltage across the converter
bridge VD. The valve voltage (not shown in figure) has various jumps that
occur at the firing and the turning off of the valve. This voltage jumps results
in extra losses in the damper circuit.
1.3.3.6 AC Current Magnitude and Phase
Approximate analysis:
Due to the overlap the ac currents are no longer rectangular blocks.
Instead, their shape is that of a deformed trapezoidal Still, Eq.3.24 is a good
approximation for the fundamental frequency component of the ac current:
I1 = 2¥Œ
,d ……… ... 1.23
By assumption, the converter is lossless and therefore the ac active
power must equal the dc power:
3/2 Em I1FRV3§8di0 Id
FRV.FRV/

«««
Where,3 denotes the angle by which fundamental component of the
line current lags the applied voltage. On simplification, equation 1.24 gives,
FRV3 §FRV.FRV/

……… ...1.25
another expression for the power factor FRV3can be given as
FRV3 §8d / Udi0
§FRV.– Rc Id / Udio ………...1.26
shows that with increasing load the power factor decreases and
accordingly the phase shift between the fundamental ac current and the ac
voltage increases.
Reactive power on the AC side may be found from
4 3DWDQ3 ………...1.27
Where, Eq.1.26 or 1.27 gives3. Of course, there is no reactive power on the
DC side.

1.3.4 Inversion
1.3.4.1 General
Because the valves conduct in only one direction, the current in a
converter cannot be reversed, and power reversal is obtained only by the
reversal of average direct voltage VD. The voltage then opposes the current
is called counter voltage.
Ideally the inversion occurs in the region 900 . 0, but in
practical case, there is always some overlap and the vaOXHRI.DWZKLFK
inversion begins is given as:
. Œ–/ Œ-@ …………1.28
Which is always less than 900.
Moreover, /ought to be less than Œby at least an angle corresponding
to the time required for the de-ionization of the arc, which is 1 – 80.
Synchronous machines connected to AC side furnish the commutation
voltage for the HVDC inverter. If the AC system receiving power from DC
link has no generators, a synchronous condenser is used.
Notations for Ignition and Extinction Angle
In inverter theory, commoner practice is to define LJQLWLRQDQJOH
and H[WLQFWLRQDQJOH by their advance with respect to the instant when the
commutation voltage is zero and decreasing. Referring to figure 1.12 this
parameters can be described.

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The relations among the several inverter angles are as follows:
Œ– . ………..1.29(a)
Œ–/ ………..1.29(b)
/– . – ………..1.29(c)
1.3.4.2 Equivalent Circuit
Equations for Average Direct Current and Voltage
General equations 1.16 and 1.17can be changed to inverter equations
by changing the sign of VD and putting
FRV. –FRV and FRV/ –FRV,
with these results
ID = IS2FRV-FRV

…………1.30
VD = VD0 [cos .FRV@ …………1.31
For constant ignition advance angle , equation 1.31 becomes
VD = VD0FRV5C ID
Because the inverters are commonly controlled so as to operate at
constant current advanced angle it is useful to have relations between ID
and VD for this condition.
VD = VD0FRV– RC ID

Under this condition, the equivalent commutation resistance is – RC
and is negative. This is the reason why inverter is said to posses a negative
commutation resistance. The equivalent circuit of the inverter is shown in
the figure 1.14
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1.4 STEADY STATE EQUIVALENT CIRCUIT
From the ongoing discussion, equivalent circuit of the for the steady
state operation of two terminal DC link can be drawn as shown in fig 1.15.
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The effect of leakage reactance in producing drop of direct voltage is
accounted for by the equivalent commutating resistance and subscripts ‘r’
and ‘i’ signifying rectifier and inverter.

HVDC Control
Chapter 2
HVDC CONTROL
2.1 INTRODUCTION
A well known technical advantage of HVDC is it s inherent ability for
control of transmitted power. The voltage across valve-bridge can be
changed nearly instantaneously. The speed of response of the control is
limited only by the maximum voltage available, the dynamics of the DC side
circuit and the sped of change of power which the connected AC networks
can stand
The fact that the reactive power consumed by the HVCD converter is
dependent on the values of the control angles means also that reactive power
of the converter station and the AC network can be controlled and the AC
voltage can be stabilized.
This chapter covers the control fundamentals for the HVDC converter.
Starting with the general discussion of control characteristics of the
converter, the report deals with the different stages in control hierarchy.
2.2 PRINCIPLE OF DC LINK CONTROL
By incorporating the equivalent circuit of the converter shown in
figure 1.15, the direct current ID in the DC line can be given as
……………2.1
From the above equation it is clear that
ID µ Voltage drop
µ 1 / (total resistance)

HVDC Control 53
Direct voltage and thus current ID can be controlled by control of
internal voltage which then can be controlled by
1. Grid Controlling
Grid control, delaying the ignition angle . (time .), reduces the
internal voltage from the ideal no-load voltage VD0 by the factor FRV..
2. Control of alternating voltage
The alternating voltage is usually controlled be tap changing on the
converter transformer.
Grid control is rapid (1 to 10 ms), but tap changing is slow (5 to 6
seconds per step). Both these means of voltage control are applied
cooperatively at each terminal. Grid control is used initially for rapid action
and is followed by tap changing for restoring certain quantities (ignition
angle in the rectifier or voltage in the inverter) to their normal values.
2.2.1 Desired features of control
The following features are desirable:
• Limitation of the maximum current so as to avoid damage to
valves and other current carrying devices.
• Limitation of the fluctuation of current due to the fluctuation of
alternating voltage.
• Keeping the power factor as high as possible.
• Prevention of commutation failures of the inverter.
• Prevention of arc back of the rectifier valves.
• In multi-anode valves, providing a sufficient anode voltage before
ignition occurs.
• Controlling the power delivered or the frequency at one end.
• Provided better voltage regulation.

HVDC Control 54
There are four reasons for keeping the power factor high, two
concerning the convertor itself and the other two concerning the ac system to
which it is connected. The first reason is to keep the rated power of the
converter as high as possible for given current and voltage rating of valves
and transformer. The second reason is to reduce the stresses on the valves
and damping circuits. The third reason is to minimize the required current
rating and copper losses in the ac lines to the converter. The fourth reason is
to minimize voltage drops at the ac terminal of the converter as its loading
increases. The last two reasons apply to any large ac loads.
The p.f. can be raised by adding shunt capacitor, if this is done , the
disadvantages becomes the cost of the capacitors and switching them as the
load on the converter varies. The p.f. of the converter itself is
FRV3 §FRV.FRV.

…………2.2
for rectifier and
FRV3 §FRVFRV

…………2.3
for an inverter.
In a rectifier, we can make .= 0 for which FRV. = 1. In an inverter it
is more difficult. In order to avoid a commutation failure, commutation must
be completed before the commutating voltage reverses at , hence y
must be greater than zero by some margin. Because of some inaccuracy in
the computation of and a possibility of changes indirect current and
alternating voltage even after commutation has began, sufficient
commutation margin above the minimum angle required for de-ionization of
the mercury arc must be allowed. The easy and safe way would be to choose
a larger value of . This way lowers the power factor and raises the stresses
on the valves.

HVDC Control 55
2.3 V-I CHARACTERISTICS OF HVDC CONVERTERS
2.3.1 Individual characteristics of Rectifier and Inverter
These are plotted in rectangular coordinates of direct current Id and
direct voltage Vd. If the rectifier be equipped with constant-current regulator,
ideal characteristics will be a vertical line AB, but in practice it has a high
negative slope which can be shifted horizontally by adjusting current
command.
If the inverter be equipped with C.E.A. regulator, then inverter
characteristics is a line with slightly negative slope (under the assumption
that commutating resistance RC2 is somewhat higher than line resistance RL)
given by
VD = VD02FRV5l – RC2) * ID …………2.4
Operating point of the system is the point of intersection of rectifier
and inverter characteristics.
It may be said with fair accuracy that rectifier direct current and
inverter controls direct voltage. But control of one parameter at one end
affects both the current and voltage settings due to non ideal characteristics.

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HVDC Control 57
If the inverter voltage changes, rectifier voltage must be change by
equal amount in order to keep current constant which can be done quickly by
current regulator till . Rectifier voltage can be increased further only by
taps on the rectifier transformer.
2.3.2 Combined Characteristics of Rectifier and Inverter
In many dc transmission links each converter must function
sometimes as a rectifier and other times as an inverter therefore each
converter is given a combined characteristics consisting of three linear
portions: C.I.A., C.C. and C.E.A.
)LJXUHRQYHUWHUFRQWUROOHUFKDUDFWHULVWLFV

HVDC Control 58
With the characteristics shown by solid lines, power is transmitted
from converter-1 to converter-2 and with the characteristics shown by
broken lines, direction of transmission is reversed by reversal of direct
voltage with direction of current being the same.
Usually the current setting of constant current characteristics of the
two converter are separated by û,d called current margin to account to
maintain positive margin in spite of errors in the current measurement and
regulation as the operation of the two steep CC characteristics, with both
current regulators would be highly unstable.
There can be three modes of operation of the link (for the same
direction of power flow) depending on the point of intersection of the two
characteristics.
1. CC at rectifier and CEA at the inverter (normal mode of operation)
2. With the slight dip in the AC voltage, the point of intersection drift
which implies minimum .at rectifier and minimum at inverter.
3. With the lower AC voltage at the rectifier, the mode of operation
again shifts which implies CC at the inverter with minimum . at the
rectifier.
2.4 BASIC CONTROL SYSTEM
As the current order to the inverter is lower by the current margin that
in the rectifier, current delivered by the rectifier is higher than demanded by
the inverter, latter tries to counteract that by increasing and the counter emf
VHWXSDJDLQVWWKHUHFWLILHUDQGLQYHUWHU.WHQGVWRUHDFKLWVmaximum value
determined by the minimum commutation margin and the CFC will operate
in another mode, the commutation margin control (CMC).

HVDC Control 59
)LJXUH%DVLFFRQWURORI+9'FRQYHUWHU
The next step in our study of the control of a converter is to examine in
more detail how each of the three straight-line segments of the combined
characteristics can be obtained
1. Constant minimum ignition angle
2. Constant current characteristics
3. Constant extinction angle
2.4.1 Firing Angle Control
The objective of convertor firing control (CFC) system is to generate
control pulses to all valves within the convertor in correct phase position and
inside the interval. = .MIN to . = . MAX., The latter being determined by a
minimum commutation margin limit. The output form the CFC is issued to a
control pulse generator (CPG), which forms individual gate control pulse
signals for all the valves within the convertor.

HVDC Control 60
Types of firing control systems
The firing angle control systems can be broadly referred into two categories:
• Individual Phase Control
In this, phase positions of gate control signals are determined
VHSDUDWHOIRUHDFKYDOYHDQG.RUZLOOEHHTXDOHYHQLIWKH$
network is unbalanced.
This scheme generates higher amount of harmonics.
• Equidistance Pulse Control
.-order in current control can be turned into a gate pulse signal in
correct phase position by using a phase-controlled oscillator. Firing
pulses are generated in steady state at equal interval of 1/pf through a
ring counter. This removes the risk of harmonics. This is the control
principle used in all modern HVDC systems.
2.4.2 Constant Minimum Ignition Angle Control
Normally rectifier is operated at ‘Constant minimum ignition angle’
to minimize the reactive power requirement as it varies in direct proportion
to ignition angle at rectifier side. To maintain a minimum delay angle say .0
following method is used.
Voltage across each valve is measured, if it is found less than a pre-specified
voltage say ¥9M Sin .0 the constant current control is prevented
form igniting the valve. In practice, secondary voltage of control transformer
is used rather than the voltage across the valve by any suitable arrangement.
2.4.3 Constant Current Control
Under normal operation system is made to operate at constant current
control setting of the rectifier end. In this mode short-circuit current are
ideally limited to the value of the load current and in practice to about twice
rated current

HVDC Control 61
Constant-current control involves the following:
1. Measurement of direct current.
2. Comparison of direct current Id with the set (or reference) value IdS.
3. Amplification of difference IdS
- Id called error.
4. Application of output signal of the amplifier to a phase-shift circuit
that alters the ignition angle . in proper direction for reducing error.
)LJXUH6FKHPDWLFGLDJUDPRIFRQVWDQWFXUUHQWUHJXODWRU
If the measured current in a rectifier is less than the set current, .must
be decreased in order to increase FRV. and thus raise the internal voltages of
the rectifier VDO FRV . The difference between the internal voltages of
rectifier and the inverter is thereby increased, and the direct current is
increased proportionally. A decrease in . increases the algebraic internal
voltage VDO FRV.This means that a same constant current controller can be
used on a given converter without change of connections during both
rectification and inversion.
In practice, however, the same current setting is transmitted to both
terminals of a DC line, and the current margin is subtracted from the current
setting of the inverter; that is, the error signal for the inverter’s current
regulator is
0 = IDS – ¨,D – ID

HVDC Control 62
The current regulator is a simple kind of feedback amplifier
characterized by gain and time constant. Its differential equation is
…………2.5
Where,
V = instantaneous voltage
T = R2C = time constant
K = gain of amplifier and phase shift circuit
0 (UURUVLJQDO
2.4.4 Constant Extinction-Angle Control
Each inverter must be ignited at such a time that extinction occurs at a
later time, which, how ever must be earlier by an adequate margin than the
time when commutation voltage reverses. The easy and safe way is to
FKRRVHDODUJHYDOXHRI7KLVZDKRZHYHUORZHUVWKHSRZHUIDFWRUDQG
rises the stresses on the valve. The better way is to compute the firing angle
UHTXLUHGWRREWDLQDFRQVWDQWH[WLQFWLRQDQJOH7KLVFDOFXODWLRQLVGRQH
using a analog computer obtaining input from the AC side of inverter and
current in the DC link.
2.5 MASTER CONTROL
Master control generates the current order to be issued to the current
control systems of both converter stations, from instance the power order set
by the operator, and it includes control functions for modulation of the
transmitted power when the HVDC link is used for stabilization of
connected AC network.
2.6 HIGHER LEVEL CONTROLLERS
The HVDC transmission can be used for stabilization of AC system
by modulating the power flow in accordance with the variations in some AC

HVDC Control 63
system quantities, usually frequency. The link can also be used to directly
control the frequency of an AC network connected to one of the substation.
2.7 SYSTEM CONTROL HIRARCHY
The control functions required for the HVDC link are performed using
the hierarchical control structure shown in Fig. 2.5. The master controller for
a bipole is located at one of the terminals and is provided with the power
order (PREF) from the system controller (from energy control center). It also
has other information such as AC voltage at the converter bus, DC voltage,
etc. the master controller transmit the current order (IREF) to the pole control
units, which in turn provide a firing angle order to the individual valve
groups (converters). The valve group or converter control also oversees
valve monitoring and firing logic through the optical interface; it also
includes bypass pair selection logic, commutation failure protection, tap
changer control, converter start/stop sequences, margin switching and valve
protection circuits.
)LJXUH+LHUDUFKLFDOFRQWUROVWUXFWXUHVIRUD'OLQN

HVDC Control 64
2.8 REACTIVE POWER CONTROL
2.8.1 Introduction
The converter in HVDC stations are line commutated, which implies
that the current initiation in the valve can only be delayed with reference to
the zero crossing of the converter bus AC voltage. This result in lagging
power factor operation of the converters, requiring reactive power sources
connected at the converter bus for better voltage control. Figure 2.6 shows
the typical phase displacement of the line side current waveform phase with
that of AC voltage with the firing angle as a parameter.
)LJXUH5HODWLRQEHWZHHQLJQLWLRQGHODDQGSKDVHGLVSODFHPHQW

HVDC Control 65
Figure 2.6 illustrates that fundamental line current lags the line to
neutral source by an angle equal to its firing angle. Hence it is advised to
keep the ignition angle low. Statistical data shows that at each converter
station, reactive power requirement is around 60% of the active power
transferred.
2.8.2 Reactive Power Requirement in Steady State
2.8.2.1 Conventional Control Strategies
Under normal operation, a DC link is operated with current control at
the rectifier side and minimum extinction angle control at the inverter. This
method of control leads to minimum reactive power requirement at both
ends.
The equation for the reactive power as a function of the active power
is conveniently expressed in terms of per unit quantities. Average bridge
voltage across the converter bridge is given by
VD = 9FRV.– RC*ID (for rectifier) …………2.6(a)
VD = 9FRV– RC*ID (for inverter) …………2.6(b)
Where,
VD = voltage on DC side (in per unit value)
ID = current on DC side (in per unit value)
The power factor is given by
RV3 §VD / 9

FRV. – (RC*ID/V) …………2.7
The power and reactive power in per unit are given by the following
equations:
PD = V*IDFRV3 …………2.8(a)
QD = V*IDVLQ3 …………2.8(b)
Also, the power factor of the converter can be given by equation
FRV3 FRV.FRV.

HVDC Control 66
Thus, from the above equations, variation of reactive power demand
with the active power demand as a function of firing angle can be shown as
in figure 2.7
)LJXUH9DULDWLRQRI4'ZLWK3'
From the figure, it is clear that
• Under normal operation (.”0), reactive power at any station is
around 0.6 times the rated active power.
• Increase in firing angle .leads to sharp increase in reactive power
demand with the increase in active power supplied, hence it is
recommended to maintain low firing angles in steady state.
However, too low values of .can result increased frequency of mode
shifts and too low values of can result in increased incidence of the
commutation failure.
The reactive power is also affected by the magnitude of AC voltage.
The reduction in V leads to increase in QD, however on-load tap changer can
control V within limits.

HVDC Control 67
2.8.2.2 Alternate Control Strategies
The region of operation of a converter bridge is bounded by the limits
on the DC current and firing angle. Neglecting minimum current limit, the
operating region of a bridge in PD – QD plane is shown in fig. 2.8
)LJXUH2SHUDWLQJUHJLRQRIDEULGJHLQ3'4'SODQH
Which is drawn for a constant (rated) AC voltage. This region is
bounded by three regions:
i. minimum . characteristics
ii. minimum characteristics
iii. constant rated DC current
In general the locus for a constant DC current in part of a circle in the
3'4' plane and the constant DC voltage characteristic is a straight line
passing through the origin.
The operation at constant DC voltage implies constant power factor
characteristics at the converter bus. At the rectifier, the characteristic is that
of a load with lagging power factor, while at the inverter, this can be viewed
as a generator with leading power factor operation.

HVDC Control 68
)LJXUH6LPSOLILHGVVWHPGLDJUDPD

LQYHUWHU
This is shown from the analysis of a simplified system shown if
Figure 4.10 In Fig 2.9 (a), the rectifier is shown as a constant (lagging)
power factor load while Fig. 2.9 (b) is applicable to the inverter operation.
The phasor diagram for both the cases are shown in Fig 2.10.
)LJXUH3KDVRUGLDJUDPD

LQYHUWHU
It can be shown by the phasor diagram that
9 (FRV/3

FRV3 …………2.10
Where, 3 is the power factor angle.
The power expression is given by
P = VEBVLQ/ …………2.11
Substituting Eq. 2.10 into Eq. 2.11, we get
P = E2%FRV/3

VLQ/FRV3 …………2.12
From the above equation, it can be shown that maximum power transfer is
obtained when,
/ –3

HVDC Control 69
The maximum power (for 3 0) is given by
Pmax = 0.2887 E2 B …………2.13
This is much less than what can be obtained in the case with 3 -30 or V = E.
To modify the power rating, the provision of a shunt capacitor (having
succeptance, BC) at the converter bus results in the modification of the
maximum power expression from equation 2.10 to 2.13
Pmax = 0.2887 E2 B / (1 – BC/B) …………2.14
The above analysis shows that there is a need to modify the reactive
power characteristics of the converter station by either
i. choice of reactive power sources
ii. adjustment in the converter control characteristics
When the DC link involves long distance transmission, the
minimization of power losses in the line dictates operation at constant DC
voltage and flexibility of converter operation is not feasible. However, with
back-to-back links, the operation at constant voltage is not critical and
alternate converter control strategies, as shown in Fig. 4.12 can be adopted.
These are
1. Constant reactive power characteristics
2. Constant leading power factor characteristics
)LJXUH$OWHUQDWHUHDFWLYHSRZHUFRQWUROVWUDWHJLHV

HVDC Control 70
It is to be noted that by providing a constant reactive power source of
QN at the converter bus, the characteristics ab or a’b results in unity power
operation of the converter. Similarly, by providing reactive source of 2QN,
the power factor angle is changed from 3to -3
2.8.3 SOURCES OF REACTIVE POWER
The reactive power requirement of the converter are met by one or
more of the following sources:
• AC system
• AC filters
• Shunt Capacitors
• Synchronous Condenser
• Static VAR system
These are shown schematically in Fig. 2.12
)LJXUH5HDFWLYHSRZHUVRXUFHVDWDFRQYHUWHUEXV
The voltage regulation at the converter bus is desirable not only from
the voltage control viewpoint but also from the minimization of loss and

HVDC Control 71
stability considerations. This requires adjustable reactive power source,
which can provide variable reactive power as demanded.
2.8.3.1 AC System
Figure 2.13 shows the reactive power drawn by AC system at the
inverter bus, as a function of PD. At low values of delivered power, reactive
power supplied by AC system is positive while with the increase in PD it
goes negative.
)LJXUH5HDFWLYHSRZHUVXSSOLHGEWKH$VVWHP
This value is more negative when the short circuit ratio (SCR) is
lower for the same amount of power transfer PD.
2.8.3.2 AC Filters
AC filters, that are provided at the converter bus for filtering out AC
current harmonics, appears as a capacitors at the fundamental frequency and
thus provide reactive power. These filters are mechanically switched and
suffer from the inability of continuous control. Also they can cause low
order resonance with the network impedance, resulting in harmonic
overvoltages.

HVDC Control 72
2.8.3.3 Shunt Capacitor
For slow variation in load, switched capacitors or filters can provide
some control, which may cause voltage flicker owing to discrete control,
unless the size of unit, which is switched is made sufficiently small.
2.8.3.4 Synchronous Condenser
Synchronous condenser provides continuous control of reactive power
and can follow fast load changes. It has following advantages
1. The availability of voltage source for commutation at the inverter
even if the connection to the AC system is temporarily interrupted.
2. Increase in SCR as the fault level is increased.
3. Better voltage regulation during a transient due to the maintenance
of flux linkages in the rotor windings.
But still there are some disadvantages to its part such as – (i) high
maintenance and cost (ii) possibility of instability due to machine going
out of synchronism.
2.8.3.4 Static VAR Systems (SVS)
In HVDC converter station, the provision for SVS mainly helps to
have fast control of reactive power flow, thereby controlling voltage
fluctuations and also to overcome the problem of voltage instability. There
are basically three types of SVS schemes:
i) Variable impedance type SVS
ii) Current source type SVS
iii) Voltage source typr SVS
The variable impedance type is most common in power system
applications and will be described next.

HVDC Control 73
Thyristor Controlled Reactor (TCR)
)LJXUH6LQJOHSKDVHWKULVWRUFRQWUROOHGUHDFWRU
Single phase TCR is shown in Fig. 2.14 By controlling firing angle of
the back-to-back connected thyristor, the current in the reactor can be
controlled. A TCR is usually operated with fixed capacitor (FC) to provide
the variation of reactive power consumption form inductive to capacitive.
The schematic FC-TCR is shown in Fig. 2.15.
)LJXUH7KHVFKHPDWLFGLDJUDPRI)75

HVDC Control 74
Thyristor Switched Capacitor
Thyristor switching is faster than mechanical switching. A reactor is
usually connected in series with the capacitor to reduce the rate of change of
the inrush current.
)LJXUH$VLQJOHSKDVH76

Harmonics and Filters
Chapter 3
HARMONICS AND FILTERS
3.1 INTRODUCTION
HVDC converter introduces AC and DC harmonics that are injected
into AC system and DC line side respectively. A converter of pulse number
p generates harmonics principally of the order of
h = p*q (on the DC side) …………3.1
And
h = p*q ± 1 (on the AC side) …………3.2
Where, q is an integer.
Most of the HVDC converters have pulse number 6 or 12 and thus
produce the harmonics of the order given in table 3.1
Table 3.1 Orders of the Characteristics Harmonics
The amplitude of the harmonics decrease with increasing order: the
AC harmonic current of order h is less than I1/h where I1 is the amplitude of
the fundamental current.
There are several problems associated with the injection of harmonics
and these are listed below:

Harmonics and Filters 76
• Telephone interference
• Extra power losses and consequent heating in machines and
capacitance connected in the system.
• Over voltage due to resonance.
• Instability of converter control, primarily with individual phase
control scheme of firing pulse generation.
• Interference with ripple control system used in load management.
AC filters are invariably used to filter out AC current harmonics
which are critical. These filters are of band pass or high pass type and also
supply reactive power. DC smoothing reactor along with DC filter perform
the function of filtering DC harmonics.
In addition to the harmonics, which cause telephone interference, the
harmonics at the carrier and radio frequencies are also generated by the
converter and may require suitable filters.
Principal means of diminishing the harmonic output of converter are
1. Increase the pulse number
2. Installation of filters
In general, converters with pulse number greater than 12 are not used
as the complexity of operation and control overshadows the significant
advantages of higher pulse number. It is also found that for HVDC converter
use of filter is more economical than the use of higher pulse number (greater
than 12). AC filters serves the dual purpose of diminishing the AC
harmonics and supply reactive power at the fundamental frequency.

3.2 GENERATION OF HARMONICS
3.2.1 Generation of Harmonics in AC Side
The line current and phase voltage waveforms under the condition of
no overlap are as shown in figure 3.1
)LJXUH/LQHFXUUHQWZDYHIRUP
Line current waveform under the condition of no-overlap is the series
of equally spaced rectangular pulses with alternately positive and negative
value.
3.2.2 Generation of DC Harmonics on DC Side
DC voltage waveforms contains ripple whose fundamental frequency
is six times the supply frequency.
)LJXUH/LQHFXUUHQWZDYHIRUP
This voltage is analyzed in Fourier series and contains harmonics of the
order of h
h = n*p
Where, p is the number of pulse and n is an integer.
The rms value of the hth order harmonic can be given as
Vh = Vd0 * ¥K2 – 1) Sin2.@1/2 / [h2 – 1] …………3.3

Normally, a DC reactor of large inductance is used in the DC side so
that the DC current is almost constant and can be considered free from
ripples hence it can be said that on DC side there are voltage harmonics
predominately while on AC side, current harmonics predominates.
Besides these, some harmonics also occur owing to imbalance in the
AC supply waveform, difference in firing angle etc. These harmonics can be
categorized namely Characteristics Harmonics and Non- characteristics
Harmonics
3.3 CHARACTERISTICS HARMONICS
Characteristics harmonics are those which can e predicted by
mathematical analysis and are generally predominate. These are present
even under ideal operating conditions like balanced AC voltage,
symmetrical three-phase network and equidistant pulses. Characteristics
harmonics are those of orders given by equations 3.1 3.2.
Assumptions:
The following assumptions are made as bases for deriving the orders,
magnitude and phases of the characteristics harmonics of a six-pulse
converter:
• The alternating voltage are three phase, sinusoidal, balanced, and of
positive sequence.
• The direct current is absolutely constant that is without ripple. Such
current would be the consequence of having a dc reactor of infinite
inductance.
• The valves are ignited at equal times interval of one-sixth cycle that
is, at constant delay angle measured from the zeros of the respective
commutating voltage. By assumption 1, these zeros are equally spaced
in time.

• The commutation inductances are equal in the three phases.
3.3.1 Harmonics at No Overlap
The wave shape of alternating voltage and currents confronting with
the assumptions made above are equidistant rectangular pulses assuming that
direct current has no harmonics, current waveforms for the primary side of
converter transformer are drawn for an ignition delay of .without overlap
( = 0).
3.3.1.1 For six-pulse Converter
The line current waveforms at no overlap are a series of equally space
rectangular pulses, alternately negative and positive. Fourier analysis of such
wave shape, for finding the characteristics harmonics can be carried out
under the following steps:
Consider the pulse of unit height and width w radian that is of
duration w/ seconds.
iA = (2¥p) IdFRVt – (1/5) cos 5t + (1/7) cos 7t
– (1/11) cos 11t + (1/13) cost -….] …………3.4
The rms value of the hth order harmonic in DC voltage is given by
equation 3.3.
3.3.1.2 For 12-pulse Converter
A 12-pulse group in a HVDC converter is composed of two 6-pulse
group fed from sets of valve side transformer winding having a phase shift
of 300 between fundamental voltages. Since . is same for both 6-pulse
group, the fundamental valve side currents have the same phase difference
as the voltages, and fundamental network-side currents are in phase with one
another. The schematic diagram for a 12-pulse converter unit is shown in
figure 3.3

)LJXUH6FKHPDWLFGLDJUDPRIDSXOVHFRQYHUWHU
Neglecting overlap, the current in the primary side of star-star
connected transformer (assuming turns ratio of 1:1) is given by the equation
3.5. Similarly, assuming that the delta-star connected transformer has turns
ratio of ¥IA2 can be given as
iA2 = (2¥p) IdFRVt + (1/5) cos 5t - (1/7) cos 7t –
(1/11) cos 11t + (1/13) cost -.…] …………3.5
The current IA can be given by the summation of IA1 and IA2 or,
IA = IA1 + IA2
IA = (4¥p) IdFRVt – (1/11) cos 11t + (1/13)
cost – (1/23) cos 23 W

FRVW«] …………3.6
From the above expression, it can be observed that
I10 = (2¥Œ

,D
Iho = I10 / h
Where I10 and Ih0 are rms values of the fundamental component and
harmonic of the order of ‘h’. The second subscript shows that the overlap
angle is considered zero.

The magnitude of the characteristics harmonics is also a function of the load
current. This is shown in the Fig. 3.4
)LJXUH+DUPRQLFPDJQLWXGHVZLWKYDULDWLRQRI'FXUUHQW
3.3.2 AC and DC Harmonics with Overlap
Because of overlap (owing to inductive nature of transformer winding
and inductance of AC network seen through the converter) valve current in
valve winding is distorted.
)LJXUH$DQG'FXUUHQWZDYHIRUPXQGHURYHUODS
Thus, expressions for the fundamental component of the AC current
derived for the case with no overlap is not valid. The actual expression for
the current can be derived from Fourier analysis and is given by
I1 = [I11
2 + I12
2] ½ …………3.7

Where,
I11 = I1FRV3 ¥Œ,dFRV.FRV.

/@ …………3.8
I12 = I1 VLQ3 ¥Œ,dVLQ.–VLQ/

@
Where, 3 is the power factor and / .
From the above expression, the power factor angle can be obtained as
WDQ3 VLQ.–VLQ/

…………3.10
The harmonic components in the AC current are also altered. These
are reduced from the value calculated with no overlap. The expression can
be given as
Ih = Ih0 [A2 + B2 –$%FRV.

@ 1/2FRV.–FRV/@«««.11
Where,
$ VLQ^K

Major Project, HVDC Thesis - Saurabh Saxena

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