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Differential Protection
for Arbitrary Three-Phase
Power Transformers
Zoran Gajić
Doctoral Dissertation
Department of Industrial Electrical Engineering and Automation
2008
Department of Industrial Electrical Engineering and Automation
Lund University
Box 118
221 00 LUND
SWEDEN
http://www.iea.lth.se
ISBN: 978-91-88934-47-5
CODEN:LUTEDX/(TEIE-1055)/1-226/(2008)
© Zoran Gajić 2008
Printed in Sweden by Media-Tryck, Lund University
Lund 2008
Abstract
This thesis describes how to provide standardized, current based,
differential protection for any three-phase power transformer, including
phase-shifting transformers with variable phase angle shift and
transformers of all construction types and internal on-load tap-changer
configurations. The use of standard transformer differential protection for
such applications is considered impossible in the protective relaying
standards and practices currently applied.
The first part of the thesis provides the background for different types of
power transformers and the differential protection schemes currently
applied. After that a complete mathematical proof for the new, universal
transformer differential protection principle, based on theory of
symmetrical components, is derived. It is demonstrated that it is possible
to make numerical differential protection relays which can properly
calculate differential currents for any power transformer, regardless of
whether it is of fixed or variable phase angle shift construction and
whether current magnitude variations are caused by on-load tapchanger(
s).
It is shown how to correctly calculate differential currents by
simultaneously providing on-line compensation for current magnitude
variations, on-line compensation for arbitrary phase angle shift variations
and settable zero-sequence current reduction on any power transformer
side. By using this method differential protection for arbitrary power
transformers will be ideally balanced for all symmetrical and nonsymmetrical
through-load conditions and external faults. The method is
independent of individual transformer winding connection details (i.e. star,
delta or zigzag), but dependent on having the correct information about
actual on-load tap-changer(s) position if they are built-in within the
protected power transformer.
The implementation and practical use of this new universal principle is
quite simple, as all necessary transformer data is commonly available on
the protected power transformer rating plate. Practical application of the
universal method for the differential protection of standard transformers,
special transformers and phase shifting transformer is presented. Detailed
testing of this new universal differential protection method is given and it
is based on actual field recordings captured by numerical relays in existing
phase-shifting transformer installations and on simulations from the Real
Time Digital Simulator for a practical dual-core, symmetrical phaseshifting
transformer. The implementation of the universal transformer
differential method for analogue and numerical transformer differential
relays is also described.
Problems for the differential protection caused by transformer inrush
currents are discussed. The mathematical relationship between differential
protection and directional protection is derived. Then it is shown that
through the addition of supplementary directional criteria security and
speed of the operation of the transformer differential protection can be
improved. Finally, the use of additional directional criteria to significantly
improve the sensitivity of the differential protection for transformer
winding turn-to-turn faults is suggested. Captured disturbance files from
numerical differential relays in actual power transformer installations,
during internal and external faults, have been used to demonstrate the
performance of additional directional criteria.
v
Acknowledgements
I would like to express my sincere gratitude to Professor Sture Lindahl, my
supervisor, for his guidance and support throughout my studying at Lund
University and also for his help during my relocation and inhabitancy in
Sweden. Furthermore I would like to thank to Dr. Olof Samuelsson,
Dr. Daniel Karlsson and Professor Gustaf Olsson for their help and advice
during my studying at Lund.
Many thanks go as well to my employer ABB AB, Substation Automation
Products for permission to use this work for my thesis and their financial
support for my travelling to Lund. I specially would like to thanks my
direct supervisors Mr. Claudio Marchetti and Mr. Kent Wikström for their
understanding and support during my studies. I would also like to thank
my colleagues Mr. Birger Hillström and Mr. Ivo Brnčić for the many
useful discussions I had with them.
I specially would like to thank Mr. Igor Ivanković from Croatian Power
Utility-HEP for his willingness to share disturbance files captured by
existing numerical differential relays in the first PST installation in
Croatia. From these recordings the first ideas about the presented
differential protection method has been discovered and visualized.
I am also very grateful to Dr. Dietrich Bonmann from ABB AG
Transformatoren, located in Bad Honnef, Germany, for all his patience and
time to discuss with me all details regarding PSTs and his eagerness to
give me his simulation files, rating plates and other design parameters for
practical PSTs and special power transformers.
Finally, I would like to thank my dear wife Dragica and our three children
Ružica, Petar and Maja for all their love, patience, understanding and
support throughout my years of studies. I love you all four so much.
"If you want truly to understand something, try to change it."
Kurt Lewin
"Храбре прати срећа."
Српска народна пословица
Preface - The Whole Story
The author had the privilege to work as a member of the ABB
development team for a numerical, current based, transformer differential
protection relay [11]. The relay was able to automatically compensate for
the power transformer vector group connection and even to compensate for
the current magnitude differences caused by on-load tap-changer (OLTC)
operation. Thus, one could say that I had some good insight into “the
stuff”, or at least I thought so.
Then, sometime at the end of 2002, a customer called me and asked about
the protection of a special transformer. The transformer was a “strange
mix” between an auto-transformer and a phase shifting transformer. “Can
we use standard differential protection?” was their first question. I looked
around and all I could find on the subject was the IEEE/PSRC working
group K1 report [37] regarding protection of phase shifting transformers
(PST). There it is written that standard differential protection can not be
used for a PST. Thus, my first answer was: “No, you probably need to
install buried current transformers within the tank and in one or another
way follow the IEEE rapport”. But the customer came back and said: “But
we have no budget for that. Our phase shift is quite small, around 7o; we
use a different transformer construction than the one presented in the IEEE
paper and we will not install buried CTs. By the way, the transformer
manufacturer is starting with its construction soon. Can we use standard
differential protection? The relay can read the OLTC position!”
Then the work for this thesis started. First, I tried to calculate how big false
differential current would appear if we would apply the differential relay
which reads the OLTC position but only can compensate for the current
magnitude variations (i.e. not for the phase angle variation) caused by
OLTC operation. It took me a while (about a week) to do it. Not much
literature was available. Finally I concluded that it is possible, but the relay
had to be desensitized. Most problems for the relay will of course be for
external single phase to ground faults.
Then the second problem came. From the customer I got steady-state
currents (phasors) calculated for an external single phase to ground fault
by the short-circuit calculation program using the PST model. The
customer asked two questions “Will the differential relay remain stable?
Please check if these currents are properly calculated?”. “Properly
calculated! How I am going to check this? I do not even have source
impedances! Only PST rated quantities! The individual phase currents did
not rotate for just 7o!” were my thoughts. After some thinking I concluded
that the currents seem reasonable, but I was not really 100% sure. After a
while a transformer was manufactured and the first transformer shortcircuits
tests with the connected differential protection were performed in
the transformer manufacturer premises. The differential relay was stable!
My calculations were approximately correct!
As soon as the substation was commissioned, the customer performed the
primary testing of the PST protection by applying close-by primary single
phase to ground faults. The differential relay was stable! For the first time
I got the actual disturbance recordings for an external fault captured on
such a special transformer.
In the mean time some other enquires came for other PST projects and I
got in touch with ABB Transformatoren AG, the ABB centre of excellence
for constructions of special transformers and PSTs. At least I got a
speaking partner for these “strange devices”! I as well got realistic
construction data which were used to simulate such special transformers.
They were also able to provide me with some additional disturbance
recording files from “their existing PST installations”.
Approximately at the same time, more and more often, enquiries for
differential protection of special converter transformers came to my table.
The interesting thing was that most of them had additional phase shift of
7.5o. Almost the same as the maximum phase angle shift of that PST. “Can
we use standard transformer differential protection? Will the error be the
same?”
One day when I was looking for some other information, I by chance
found out that in the old Westinghouse Transmission & Distribution
Reference Book [25] (published in 1950!) there are stated rules of how noload
voltage and load current sequence components (positive, negative and
zero sequence) are transferred across any phase shifting transformer.
“Very useful information! Now I could check if the customer external fault
current calculations were correct. But wait a moment; I could as well
check that these rules were valid by evaluating captured disturbance
recordings! Yes the rules were valid. Good. What about the phase
comparison protection across PST using these rules? Could it be used? Let
me check! Yes it seemed to work based on the data from the available field
recordings!”
“But wait a little bit! I knew how the sequence current components were
transferred across a PST, actually across any three-phase power
transformer in accordance with this old book. If I started from there, I
should be able to derive a relationship between the phase currents from the
two PST sides. I had learned symmetrical components and matrix based
mathematics once upon a time. It should be quite easy to perform such a
task! Yes of course!” Unfortunately it took at least a week to go through
all equations without making any error during the derivation process.
Finally the equation was in front of me.
Then I checked the equation on captured field data. “It works! It works
even for normal standard power transformers! It works for converter
transforms too! It works with phasors but what about inrush currents? Do I
need second and fifth harmonic blocking? I then looked once more into the
matrix.” Surprisingly I realised that the phase angle shift compensation
matrix contained only real numbers. “But, I have started from positive,
negative and zero sequence phasors (i.e. complex numbers)! If only real
numbers are used then I can use it for sampled phase current values from
the two sides! What about sampling rate? Is this matrix transformation
frequency invariant? I checked it on all available recording data. It works!”
Yes, it was so simple!
“And what about turn to turn faults? Yes, I think that I have some good
insight into “the stuff”… Now maybe I just need to wait for another
customer call!?”
Contents
CHAPTER 1 INTRODUCTION..............................................................1
1.1 MAIN PURPOSE OF POWER TRANSFORMERS ...............................1
1.2 OBJECTIVES .................................................................................2
1.3 CONTRIBUTIONS OF THE THESIS..................................................3
1.4 OUTLINE OF THE THESIS..............................................................4
1.5 PUBLICATIONS .............................................................................5
CHAPTER 2 THREE-PHASE POWER TRANSFORMERS ..............7
2.1 GENERAL-PURPOSE POWER TRANSFORMERS..............................7
2.2 CONVERTER TRANSFORMERS....................................................10
2.3 PHASE-SHIFTING TRANSFORMERS.............................................13
2.4 POWER TRANSFORMER AS NONLINEAR DEVICE .......................19
CHAPTER 3 DIFFERENTIAL PROTECTION FOR POWER
TRANSFORMERS..................................................................................21
3.1 DIFFERENTIAL PROTECTION FOR STANDARD TRANSFORMERS.23
3.2 DIFFERENTIAL PROTECTION FOR SPECIAL CONVERTER
TRANSFORMERS.....................................................................................26
3.3 DIFFERENTIAL PROTECTION FOR PST.......................................26
3.4 MAIN CT CONNECTIONS ...........................................................27
CHAPTER 4 NEW UNIVERSAL METHOD ......................................29
4.1 CURRENT MAGNITUDE COMPENSATION ...................................29
4.2 PHASE ANGLE SHIFT ACROSS POWER TRANSFORMER ..............30
4.3 PHASE ANGLE SHIFT COMPENSATION.......................................34
4.4 ZERO SEQUENCE CURRENT COMPENSATION ............................38
4.5 UNIVERSAL DIFFERENTIAL CURRENT CALCULATION METHOD40
4.6 PHASE SEQUENCE AND VECTOR GROUP COMPENSATION.........43
4.7 PROPERTIES OF M AND M0 MATRIX TRANSFORMATIONS ........45
4.8 CORRECT VALUES FOR BASE CURRENT AND ANGLE Θ............47
CHAPTER 5 APPLICATION OF THE METHOD.............................49
5.1 STANDARD TWO–WINDING, YND1 TRANSFORMER ..................49
5.2 AUTO-TRANSFORMERS ..............................................................53
5.3 FOUR – WINDING POWER TRANSFORMER................................. 62
5.4 SPECIAL CONVERTER TRANSFORMER....................................... 65
5.5 24-PULSE CONVERTER TRANSFORMER..................................... 69
5.6 DUAL-CORE, ASYMMETRIC DESIGN OF PST............................. 73
5.7 SINGLE-CORE, SYMMETRIC DESIGN OF PST............................. 75
5.8 COMBINED AUTO-TRANSFORMER / PST IN CROATIA............... 77
CHAPTER 6 EVALUATION OF THE METHOD WITH
DISTURBANCE RECORDING FILES............................................... 81
6.1 PST IN ŽERJAVINEC SUBSTATION, CROATIA............................ 81
6.2 PST INSTALLED IN EUROPE ...................................................... 91
6.3 PST INSTALLED IN SOUTH AMERICA........................................ 94
6.4 PST INSTALLED IN NORTH AMERICA ....................................... 97
CHAPTER 7 EVALUATION OF THE METHOD WITH
SIMULATION FILES.......................................................................... 103
7.1 SETTING UP THE SIMULATION................................................. 103
7.2 SIMULATED FAULTS................................................................ 106
CHAPTER 8 IMPLEMENTATION POSSIBILITIES..................... 129
8.1 MIXED SOLUTION (ANALOGUE + NUMERICAL)...................... 129
8.2 FULLY NUMERICAL IMPLEMENTATION................................... 138
CHAPTER 9 TRANSIENT MAGNETIZING CURRENTS............ 141
9.1 INRUSH CURRENT CALCULATION........................................... 143
9.2 EFFECT OF TRANSFORMER DESIGN PARAMETERS ON THE 2ND
HARMONIC COMPONENT OF THE INRUSH CURRENT........................... 144
9.3 EFFECTS ON TRANSFORMER DIFFERENTIAL PROTECTION...... 147
9.4 INTERNAL FAULTS FOLLOWED BY CT SATURATION.............. 149
9.5 ENERGIZING OF A FAULTY TRANSFORMER............................. 151
CHAPTER 10 DIFFERENTIAL OR DIRECTIONAL PROTECTION
................................................................................................................ 155
10.1 GENERALIZED DIRECTIONAL PRINCIPLE FOR DIFFERENTIAL
PROTECTION........................................................................................ 155
10.2 NEGATIVE SEQUENCE BASED INTERNAL/EXTERNAL FAULT
DISCRIMINATOR.................................................................................. 158
10.3 EVALUATION OF THE DIRECTIONAL COMPARISON PRINCIPLE BY
USING RECORDS OF ACTUAL FAULTS ................................................ 161
CHAPTER 11 TURN-TO-TURN FAULT PROTECTION..............179
11.1 BASIC TURN-TO-TURN FAULT THEORY ..................................180
11.2 TRADITIONAL POWER TRANSFORMER DIFFERENTIAL
PROTECTION ........................................................................................182
11.3 DIRECTIONAL COMPARISON BASED ON NEGATIVE SEQUENCE
CURRENT COMPONENT........................................................................182
11.4 PHASE-WISE DIRECTIONAL COMPARISON ..............................183
11.5 EVALUATION OF THE PROPOSED TURN-TO-TURN FAULT
DETECTION PRINCIPLES.......................................................................184
CHAPTER 12 CONCLUSIONS ..........................................................203
CHAPTER 13 FUTURE WORK.........................................................205
REFERENCES ......................................................................................207
1
Chapter 1
Introduction
In this chapter, a short overview of the thesis is given.
1.1 Main Purpose of Power Transformers
The main principle of a transformer was first demonstrated in 1831 by
Michael Faraday, although he only used it to present the principle of
electromagnetic induction and did not foresee its practical uses. During the
initial years of electricity distribution in the United States, a direct current
based electrical distribution system was used. However, during the "War
of Currents" era (sometimes as well called "Battle of Currents") in the late
1880s, George Westinghouse and Thomas Edison became adversaries due
to Edison's promotion of the direct current (DC) system over an alternating
current (AC) system for electricity distribution advocated by
Westinghouse and Nikola Tesla.
Power is the product of current and voltage ( P =U ⋅ I ). For a given
amount of power, a low voltage requires a higher current and a higher
voltage requires a lower current. Since metal conducting wires have a
certain resistance, some power will be wasted as heat in the wires of the
distribution system. This power loss is given by 2
Loss P = R ⋅ I . Thus, if the
overall transmitted power is the same, and given the constraints of
practical conductor sizes, a low-voltage, high-current based electricity
distribution system will have a much greater power loss than a highvoltage,
low-current based one. This holds true whether DC or AC
electricity distribution system is used.
However, it is quite difficult to transform DC power to a high-voltage,
low-current form efficiently, whereas with AC system this can be done
2 Chapter 1
with a simple and efficient device called a power transformer. Power
transformer can transfer practically all of its input AC power (given by
product U1 ⋅ I1 ) to its output power (given by U2 ⋅ I2 ). However, voltage
and current magnitudes will be changed in accordance with power
transformer design details. Thus, the power transformer was one of the
most important reasons for the success of the AC electrical power system,
which was for the first time commercially used on 1896-11-16. On that
day AC power was sent from the Niagara Falls to industries in Buffalo,
over a distance of 35km, indicating the final triumph of the AC based
distribution system.
Consequently, transformers have shaped the electricity supply industry,
permitting generation (e.g. thermal and hydro power stations) to be located
remotely from points of energy demand (e.g. cities). Today, all but a
fraction of the world's produced electrical power has passed through a
series of transformers by the time it finally reaches the consumer.
Transformers are some of the most efficient electrical machines, with
some large units able to transfer 99.5% of their input power as their output
power. Power transformers come in a range of sizes from a palm-sized
transformer inside mobile telephone chargers to a huge giga-volt-ampere
rated unit used to interconnect parts of national power grid. All of them
operate on the same basic principle of electromagnetic induction, though a
variety of designs exist to perform specialized roles for domestic and
industrial applications [9].
Transformers, just like generators, lines and other elements of the power
system, need to be protected from damages caused by a fault. This task is
performed by relay protection which detects the fault situation and gives
command to the relevant circuit breaker(s) to disconnect the faulty
equipment from the rest of the power system. Power transformers are
normally protected by differential protection relays.
1.2 Objectives
The primary objective of this work is to investigate the possibility to use a
differential protection for standard three-phase power transformers for
protection of special and non-standard three-phase transformers. At the
end of the thesis supplementary criteria are presented which can improve
the performance of the traditional power transformer differential protection
for low level internal faults such as turn-to-turn faults. These
Introduction 3
supplementary criteria can be applied on any type of the three-phase power
transformer.
1.3 Contributions of the Thesis
The main contribution of the work is included in Chapter 4, where the
complete theoretical background for a differential protection for an
arbitrary, three-phase power transformer is presented. It is shown that a
differential protection for standard power transformers can be applied,
with minor modifications, as differential protection for phase shifting
transformers and special converter transformers with fixed, but nonstandard
phase angle shift (e.g. 22.5o). Any previous publications
regarding such use of the differential protection could not be found. Thus,
it seems that this work is unique and completely new in the field of power
transformer protective relaying.
A number of secondary objectives can be enunciated as briefly shown in
the following short list:
♦ better understanding of numerical differential protection principles
to the protective relaying community;
♦ possibility to use standardized differential protection principle for
all types of phase shifting transformers and special converter
transformers;
♦ buried CTs are no longer required for PST protection schemes;
♦ improved principles for detection of transformer winding turn-toturn
faults; and
♦ possibility to check the output calculations from any short-circuit
software package for power systems with PSTs and special
transformers.
Research results from this thesis have resulted in two international patent
applications with the following publication numbers:
♦ WO2007057240
♦ WO2005064759
4 Chapter 1
1.4 Outline of the Thesis
In the Chapter 1 introduction to the thesis is given. The Chapter 2 presents
a brief overview about different types of power transformers used in
modern power systems, in accordance with the IEC standard. In Chapter 3
a brief historical overview about existing differential schemes, currently
used for protection of power transformers, is presented.
In Chapter 4 a complete mathematical proof for the new universal
transformer differential protection method, based on theory of symmetrical
components, is derived. It is shown how to correctly calculate differential
currents by simultaneously providing on-line compensation for current
magnitude variations, on-line compensation for arbitrary phase angle shift
variations and settable zero-sequence current reduction on any power
transformer side. By using this method differential protection for arbitrary
power transformers will be ideally balanced for all symmetrical and nonsymmetrical
through-load conditions and external faults. The method is
independent of individual transformer winding connection details (i.e. star,
delta, zigzag), but dependent on having the correct information about
actual on-load tap-changer(s) position, if they are built-in within the
protected power transformer.
Chapter 5 gives detailed instruction, how to apply the new universal
differential protection method to different types of three-phase, power
transformers. In Chapter 6 evaluation and testing of the new differential
method with disturbance files captured in the field in existing phase
shifting transformer installations is presented. Evaluation and testing of the
new differential method with data files obtained from the Real Time
Digital Simulator is presented in Chapter 7. Practical application and
implementation possibilities of the new universal differential protection
method, for analogue and numerical transformer differential protection
relays, are given in Chapter 8.
Chapter 9 gives insight about transformer inrush currents and problems
encounter by the transformer differential protection because of them. In
Chapter 10 the relationship between differential and directional protection
principles is presented. It as well shows how to use directional protection
as a supplementary criterion in order to improve the performance of the
traditional power transformer differential protection. Chapter 11 gives a
possible solution which improves the sensitivity of the traditional
differential protection for turn-to-turn faults in the power transformer
windings.
Introduction 5
Main conclusions about the performed work are given in Chapter 12, while
the Chapter 13 suggests the possible future work on this subject.
1.5 Publications
This work has resulted in several publications:
Journal Papers:
Z. Gajić, “Universal Transformer Differential Protection, Part I: Theory”,
Submitted to IET Generation, Transmission & Distribution Journal,
Manuscript ID: GTD-2007-0417.
Z. Gajić, “Universal Transformer Differential Protection, Part II:
Application and Testing”, Submitted to IET Generation, Transmission &
Distribution Journal, Manuscript ID: GTD-2007-0419.
Z. Gajić, “Differential Protection for Special Industrial Transformers”,
IEEE Transactions on Power Delivery, Vol. 22, Issue 4, pp. 2126-2131,
Oct. 2007. Paper no. TPWRD-00528-2006. Digital Object Identifier
10.1109/TPWRD.2007.905561.
Conference Papers:
Z. Gajić, “Differential Protection Methodology for Arbitrary Three-Phase
Power Transformers,” IET, The 9th International Conference on
Developments in Power System Protection, Glasgow, UK, March 2008.
Accepted for publishing.
Z. Gajić, S. Holst, D. Bonmann, D. Baars, “Influence of Stray Flux on
Protection Systems,” IET, The 9th International Conference on
Developments in Power System Protection, Glasgow, UK, March 2008.
Accepted for publishing.
Z. Gajić, “Differential Protection Solution for Arbitrary Phase Shifting
Transformer”, International Conference on Relay Protection and
Substation Automation of Modern EHV Power Systems, Moscow –
Cheboksary, Russia, September 2007.
6 Chapter 1
Z. Gajić, I. Ivanković, B. Filipović-Grčić, R. Rubeša, “New General
Method for Differential Protection of Phase Shifting Transformers”, 2nd
International Conference on Advanced Power System Automation and
Protection, Jeju-South Korea, April 2007.
F. Mekic, R. Girgis, Z. Gajić, Ed teNyenhuis, ” Power Transformer
Characteristics and Their Effect on Protective Relays”, 33rd Western
Protective Relay Conference, October 17-19, 2006, Spokane – USA.
Z. Gajić, I. Ivanković, B. Filipović-Grčić, R. Rubeša, “New Method for
Differential Protection of Phase Shifting Transformers”, 15th International
Conference on Power System protection, Bled-Slovenia, September 2006.
I. Brnčić, Z. Gajić, T. Einarson, “Transformer Differential Protection
Improved by Implementation of Negative-Sequence Currents”, 15th
International Conference on Power System protection, Bled-Slovenia,
September 2006.
Z. Gajić, I. Brnčić, B. Hillström, I. Ivanković, “Sensitive Turn-to-Turn
Fault Protection for Power Transformers,” CIGRÉ Study Committee B5
Colloquium, Calgary, Canada, Sep. 2005.
I. Ivanković, B. Filipović-Grčić, Z. Gajić, " Operational Experience with
the Differential Protection of Phase Shifting Transformer", 7th Regional
CIGRÉ Conference, Cavtat, Croatia, November 2005, (in Croatian
language).
Z. Gajić, I. Ivanković, V. Bodiš, “Sensitivity of Transformer Differential
Protection for the Internal Faults”, 7th Regional CIGRÉ Conference,
Cavtat, Croatia, November 2005, (in Croatian language).
Z. Gajić, I. Ivanković, B. Filipović-Grčić, “Differential Protection Issues
for Combined Autotransformer – Phase Shifting Transformer,” IEE
Conference on Developments in Power System Protection, Amsterdam,
Netherlands, April 2004.
7
Chapter 2
Three-Phase Power Transformers
“Power transformer is a static piece of apparatus with two or more
windings which, by electromagnetic induction, transforms a system of
alternating voltage and current into another system of voltage and current
usually of different values and at the same frequency for the purpose of
transmitting electrical power.” (Definition of Power Transformer; taken
from IEC 600761 standard).
Many different types of power transformers are presently used in electrical
power systems worldwide. Short summary of most commonly used types,
as defined by IEC standards, will be given in this Chapter.
2.1 General-purpose Power Transformers
Most commonly used types of general-purpose power transformers will be
described in this section.
Two-winding Transformers
The two-winding power transformer has two separate electrical windings.
It is used to interconnect two electrical networks with typically different
voltage levels. Two-winding power transformers with rating bigger than
5MVA are typically star (wye) connected or delta connected, and less
frequently, zigzag connected. Such power transformers introduce a fixed
phase angle displacement (i.e. phase angle shift) Θ between the two
windings. The phase angle displacement Θ can have a value of 30o n ⋅ ,
where n is an integer between 0 and 11, and depends on the winding
connection details for the specific power transformer. Typically the high
8 Chapter 2
voltage winding is used as reference for the phase angle displacement.
Commonly used connections for two-winding, three-phase power
transformers are shown in Figure 1 (from [58]). More information can be
found in references [9], [58] and [62].
Multi-winding Transformers
The multi-winding power transformer has more than two separate
electrical windings. In practice by far the most used type is a threewinding
power transformer. Such power transformer is used to
interconnect three electrical networks with typically different voltage
levels. The three windings are typically star (wye) connected or delta
connected. Such power transformers introduce a fixed phase angle shift
between each pair of its windings. The phase angle displacement can have
a value of 30o n ⋅ , where n is an integer between 0 and 11, and depends on
the individual winding connection details for the specific winding pair.
Typically the high voltage winding is used as reference for phase angle
displacement. Two examples of three-winding, three-phase power
transformer connections are YNyn0d1 and Yd11d11.
Auto-transformers
An auto-transformer is a power transformer in which at least two windings
have a common part. Auto-transformers are most often used to
interconnect EHV and/or HV networks. It can be shown that they are less
expensive than normal two-winding transformers if the voltage difference
between the two windings (e.g. networks) is relatively small [29]. For
power system applications auto-transformers are typically used with a
third, delta connected winding. Vector group connection for a threewinding
auto-transformer can for example be designated as YNautod5.
Regulating Transformers
Such transformers are typically used to vary the voltage magnitude on one
or more sides of the power transformer. This is achieved by constructing
one (or more) winding with taps. A separate device called Tap-Changer
(TC) is then used to select one of the winding taps and to connect it with
the other electrical parts of the power transformer. Two types of tapchangers
are commonly used:
♦ on-load tap-changer (OLTC) which can change a winding tap
while the power transformer is in service; and
Three-Phase Power Transformers 9
♦ off-circuit tap-changer which can change a winding tap only when
the power transformer is de-energized.
Figure 1: Commonly used connections for two-winding power transformers [58].
10 Chapter 2
More information about tap-changers can be found in IEC 60214 standard.
Note that any previously described type of general-purpose power
transformer can be constructed as a regulating transformer. In such case it
is the most common to use OLTC to select appropriate winding tap. With
such a design it is possible to step-wise regulate the voltage magnitude,
typically on the LV side of the power transformer. The standard OLTC
typically offers in between ±9 and ±17 positions. Each OLTC step can
change the no-load transformer LV side voltage for certain value (typically
1-2%).
2.2 Converter Transformers
Converter transformers are power transformers intended for operation with
power electronic converters. A short summary of the most commonly used
types, as defined by IEC 61378 standard, are given in this section.
Transformers for Industrial Applications
This type of transformer is intended for operation with power converters
not exceeding 36kV. They can be of standard construction regarding the
winding connection (e.g. either star or delta) and phase angle displacement
(multiple of 30o), but there are also such transformers with a quite special
construction. Such special industrial power transformers can have a phase
angle shift Θ different from 30º or a multiple of 30º [22]. The overall
phase angle shift Θ differs from the standard 30o n ⋅ shift for additional
angle Ψ (0o < Ψ < 15o). A typical example is a 24-pulse converter
transformer with an additional phase angle shift Ψ of ±7.5o. Such special
transformers typically have three windings, but sometimes even up to five
windings [9], [15]. They are used to supply different electrical equipment
fed by power converter such as MV drives [13], [15] and FACTS devices
[59]. Such power electronic equipment injects significant harmonics into
the utility power system. The application of converter transformers with
special phase angle shift can substantially reduce the current harmonic
content in the utility supply system [6], [36] and [49].
Due to power quality issues, the use of special industrial transformers has
been increased over the last years. Special industrial transformers with
rated power of up to 100MVA have been installed [14]. The additional
phase angle shift Ψ is typically obtained by special connections of the HV
winding [54]. This HV winding is typically connected either as extendedThree-
Phase Power Transformers 11
delta (as shown in Figure 2) or as zigzag (as shown in Figure 3).
Obviously the special “HV winding extensions” are used in both designs
in order to provide the required additional phase angle shift Ψ. Other
converter transformer windings (i.e. LV windings) are connected in the
standard way (e.g. star or delta). Note that the design in Figure 2 is a
variation of a Dy11d0 standard power transformer, and the design in
Figure 3 is a variation of an Yy0d1 standard power transformer.
Ψ Ψ
a) b)
Figure 2: Transformer winding connections for extended delta design.
Ψ Ψ
a) b)
Figure 3: Transformer winding connections for zigzag design.
The phasor diagram for positive sequence quantities for the converter
transformer shown in Figure 2a is given in Figure 4. Figure 4a shows the
phasor diagram which directly corresponds to the winding arrangements
shown in Figure 2a. However, the power transformer phasor diagram is
12 Chapter 2
typically shown with the HV winding positive sequence quantity at
position zero, as shown in Figure 4b. In a similar way the phasor diagrams
for converter transformers shown in Figure 2b, 3a and 3b can be
constructed.
a) b)
Figure 4: Positive sequence phasor diagram for
the special converter transformer shown in Figure 2a.
In the rest of this thesis, power transformers with fixed but non-standard
phase angle displacement will be referred to as “special converter
transformers”.
Transformers for HVDC Applications
This type of transformer is intended for use in station for High Voltage
Direct Current (HVDC) power transmission. Presently, such transformers
are using standard construction regarding the winding connection (either
star or delta) and phase angle displacement (multiple of 30o). Thus,
differential protection can be applied by using the same rules as for
standard multi-winding transformers.
Transformers for Traction Applications
This type of transformer is intended for use in railway substations and
railway locomotives. They are often of a special design, and they are used
to supply one-phase or two-phase railway supply systems. More
information about traction transformers can be found in IEC 60310
standard. Differential protection for such transformers will not be
considered in this thesis.
Three-Phase Power Transformers 13
2.3 Phase-Shifting Transformers
A phase-shifting transformer (PST) is a regulating transformer with one or
more OLTCs which primary task is to regulate the phase angle
displacement across the transformer. Actually, a PST creates a step-wise
variable phase angle shift Θ across its primary (Source) and secondary
(Load) terminals [35]. For a PST one or more OLTCs are used [48] and
[60] to obtain the variable phase angle shift. In practice multiple OLTCs
with as many as 70 combined steps can be used to obtain the PST variable
phase angle shift Θ of up to ±75°. The standard OLTC typically offers in
between ±9 and ±17 positions (i.e. altogether from 19 to 35 positions). If
more positions are required it is necessary to add a second OLTC in series.
Such constructions make the practical design of a PST quite complicated.
The main purpose of the phase-shifting transformer is the real-time control
of the active power flow in a complex power network. The phase angle
shift change governs the flow of active power. Thus, PSTs are typically
used to:
♦ control power exchange between two networks without
influencing power flow to third parties [23];
♦ control load sharing between parallel transmission paths [59];
♦ increase total power transfer through specific interconnection lines
♦ force active power flow on contract path(s) ;
♦ block parasitic power flow due to phase angle differences in
feeding network(s) ;
♦ force power flow from LV to HV side of a power transformer;
♦ distribute power to different customers in a pre-defined way;
♦ avoid circulating power flows in interconnected power systems;
and,
♦ special applications [38].
Phase-Shifting Transformer Design
Phase-shifting transformers have some characteristics in common with
auto-transformers [64]. One of which is that in most practical designs the
primary and secondary terminals are galvanically connected. In addition
the size and therefore also the cost of a PST and auto-transformer is not
only dependent on power rating and voltage. In the case of an autotransformer,
the voltage ratio has a major impact, while for a PST the
14 Chapter 2
maximum possible phase angle shift determines the size of the
transformer.
Note that the maximum transformer rating and phase angle shift, is often
constrained by the availability of an appropriate OLTC [4]. The most
commonly used PST designs in modern power systems are:
♦ single-core design (symmetrical/asymmetrical);
♦ two-core design (symmetrical/asymmetrical); and
♦ special constructions (typically asymmetrical).
A more detailed description of the terms “symmetrical” and
“asymmetrical” might be useful [35]. The term “symmetrical” means that
under no-load condition the absolute values of the source and load voltage
are the same irrespective of the actual phase angle shift Θ. The term
“asymmetrical” means that under no load conditions the voltage
magnitude on the load side is different than the voltage magnitude on the
source side. Typically this difference is bigger as the phase angle shift Θ
increases.
Single-Core PST Design
A simple example for an asymmetric, single-core phase-shifting
transformer is given in Figure 5 (from [64]), which in principle is probably
the simplest type of PST. The advantage of this solution is that it does not
need a separate excitation transformer. On the other hand, the on-load tapchanger
and the regulating windings are connected in series with the
power system. Thus they are directly exposed to system disturbances and
fault currents, which might involve costly OLTC design.
Based on the same principle and with a marginal increase in complexity, a
symmetric design is also possible with the addition of a regulating winding
and an additional OLTC. This design provides for a significant increase in
the maximum possible phase angle shift. The basic design scheme is
shown in Figure 6.
Three-Phase Power Transformers 15
Figure 5: Asymmetric type, single-core PST design [64].
Figure 6: Symmetric type, single-core PST design [64].
Θ
Θ
16 Chapter 2
Additional impedance, typically a series reactor connected to the PST load
side terminals, might be necessary. It is used to protect the OLTCs from
short circuit currents, because no PST impedance is present at phase angle
shift of zero degree.
Two-Core PST Design
The most commonly implemented and “classic” solution is the symmetric,
dual-core PST with separate series transformer and excitation transformer.
The principle scheme for the dual-core PST is shown in Figure 7 (from
[64]). The series transformer primary winding is serially connected with
the primary system in between source and load terminals. This winding is
split into two halves, and the primary winding of the exciting transformer
is connected to the mid point between these two half-windings. Thus, total
symmetry between source and load side no-load voltages is achieved. The
regulating circuit consists of a secondary tapped winding in the excitation
transformer and a delta connected secondary winding in the series
transformer. Ratings of these two windings can be optimized
independently from the main circuit with regard to the voltage level. This
provides more freedom for the selection of the OLTC, which can
sometimes determine the limit for a specific design [4].
Figure 7: Symmetric type, dual-core PST design [64].
Θ
Three-Phase Power Transformers 17
Depending on the rated power, voltage and maximum no-load phase angle
shift of the PST, series and excitation transformers can be designed as:
♦ two three-phase, five-limb transformers located in the same tank;
♦ two three-phase, five-limb transformers located in two separate
tanks interconnected with oil ducts or HV cables; or,
♦ six single-phase transformers located in six separate tanks
interconnected with oil ducts or HV cables.
If one of the two half-windings in the series transformer is omitted, an
asymmetric design can be achieved. Such PSTs are used in practice (see
Section 5.6), but with asymmetric design the maximum phase shift angle is
limited to approximately 20o because otherwise a too big voltage
magnitude difference between the two PST sides will be obtained.
Special PST Design
Special PST constructions are typically based on an auto-transformer
design. As an example the PST installed in the Croatian power system will
be presented [67]. This power transformer is constructed as a conventional
auto-transformer with a tertiary delta-connected, equalizer winding [58].
The OLTC winding is located at the auto-transformer neutral point. The
auto-transformer rating data is 400/400/(130)MVA; 400/231/(10.5)kV;
YNa0(d5). The main difference from the typical auto-transformer
construction is a two position switch located in-between the OLTC
winding and the common auto-transformer winding as shown in Figure 8.
The position of this switch can be changed only when the power
transformer is de-energized.
When this switch position is as shown in Figure 8, the power transformer
is in auto-transformer operating mode. In this operation mode the common
winding, serial winding and OLTC winding, mounted on the same
magnetic core limb, are connected in series. Phase A windings connections
for auto-transformer operating mode and the corresponding power
transformer no-load voltage phasor diagram are shown in Figure 9.
When the switch position is changed, the OLTC winding in phase C
(mounted around the third magnetic core limb) is connected in series with
the common and serial auto-transformer windings in phase A (mounted
around the first magnetic core limb). This switch arrangement converts the
auto-transformer to a phase-shifting transformer. The phase A winding
connections for PST operating mode and the corresponding power
18 Chapter 2
transformer no-load voltage phasor diagram are shown in Figure 10. For
more information about different PST constructions please refer to [35],
[41], [56], [60] and [64].
Figure 8: Construction details for the PST installed in Croatia [67].
EA
EmA
UA
UmA
A
ErA
mA
13
25
g
EA
EmA
UA
U
mA
A
C B
ErA
ErA
Figure 9: Auto-transformer operating mode [67].
Three-Phase Power Transformers 19
EA
E
mA
UA
UmA
A
C B
ErC
ErC
ErC
ϕ
Figure 10: PST operating mode [67].
In Sweden there is only one PST installed in 1988 at Charlottenberg
substation. It is of a special design and is used to interconnect 132kV
networks in Sweden and Norway. More information about it can be found
in [19].
2.4 Power Transformer as Nonlinear Device
All power transformers inherently have a magnetic core. Due to magnetic
properties of the core (e.g. hysteresis, saturation), the whole power
transformer becomes a non-linear device. This non-linearity from the
differential protection point of view manifests itself as a magnetizing
current which is present whenever the power transformer is connected to
the electrical power system. The magnetizing current is used to produce
necessary magnetic flux in the transformer core. The magnetizing currents
can be divided into two categories:
♦ Steady-state magnetizing currents; and
♦ Transient magnetizing current.
Θ
20 Chapter 2
Steady State Magnetizing Currents
The steady state magnetic flux in the core is proportional to the ratio of the
voltage and frequency applied to the power transformer winding, as shown
by the following equation:
U
C
f
Φ = ⋅ (2.1)
where:
♦ Φ is the magnetic flux in the core;
♦ C is a constant dependent on the particular power transformer
construction details;
♦ U is the voltage; and
♦ f is the frequency of the voltage signal.
Typically, a power transformer magnetic core is designed in such way that
it will tolerate 110% of rated U/f ratio being applied to the power
transformer without saturation [58]. Under such steady state operating
condition (e.g. U/f < 110%) the magnetizing current drawn by the power
transformer will be quite small. A typical RMS value of the magnetizing
current is from 0.2% to 0.5% for power transformers with a rating above
30MVA [1]. However, if the 110% over-excitation limit is exceeded the
magnetic core will start to saturate. This will result in a sharp magnitude
increase of the magnetizing current.
Transient Magnetizing Currents
Transient magnetizing currents will appear every time the magnitude or
phase angle of the voltage, applied to the power transformer, is suddenly
changed. Transient magnetizing currents can have quite a big magnitude
(e.g. 300%) and can cause unwanted operation of the protection relays.
Additional information about transient magnetizing currents is given in
Chapter 9.
21
Chapter 3
Differential Protection for Power
Transformers
Current based differential protection has been applied in power systems
since the end of the 19th century [32], and was one of the first protection
systems ever used. Faults are detected by comparing the currents flowing
into and out of the protected object as shown in Figure 11.
Figure 11: Principal connections for transformer differential protection [10].
Within the differential relay two quantities are derived:
♦ the stabilizing current (often as well called bias or restraining
current) which flows through the restraining circuitry “s” shown in
Figure 11; and
♦ the differential current (i.e. the current Id shown in Figure 11).
22 Chapter 3
The magnitudes of these two quantities are typically used in order to
determine whether the differential relay will operate (trip) or restrain from
operation. A typical numerical differential relay tripping characteristic is
shown in Figure 12.
Figure 12: Differential relay tripping characteristic [12].
Typically, differential protection provides for fast tripping with absolute
selectivity for internal, high-level shunt faults when the relay operating
point defined by the current pair [Ibias, Idiff] is above the tripping
characteristic (see Figure 12). Differential relays are often used as main
protection for all important elements of the power system such as
generators, transformers, buses, cables and short overhead lines. The
protected zone is clearly defined by the positioning of the main current
transformers to which the differential relay is connected.
Transformer differential protection is as well quite specific because it has
to cope with non-linearity of the power transformer explained in
Section 2.4. This is traditionally achieved by 2nd and 5th harmonic
blocking/restraining features which are typically found in all power
transformer differential relays [5] and [32].
0 100 200 300 400 500 600 700 800
0
100
200
300
400
500
Bias Current [%]
Diff Current [%]
Restraining
Area
Tripping
Area
Differential Protection for Power Transformers 23
3.1 Differential Protection for Standard Transformers
Current based differential protection for standard power transformers has
been used for decades. It is based on ampere-turn-balance of all windings
mounted on the same magnetic core limb. In order to correctly apply
transformer differential protection it is necessary to properly compensate
for:
♦ primary current magnitude difference on different sides of the
protected transformer (i.e. current magnitude compensation);
♦ power transformer phase angle shift (i.e. phase angle shift
compensation); and provide
♦ zero sequence current elimination (i.e. zero sequence current
compensation).
Static Differential Relays
With static (or even electromechanical) differential relays such
compensations were performed by using interposing CTs or special
connection of main CTs (i.e. delta connected CTs) [10]. Well-known
characteristics for electromechanical or static power transformer
differential relays are as follows:
♦ correct selection of interposing CT ratios, makes it possible to
compensate for current magnitude differences on different sides of
the protected transformer;
♦ correct selection of interposing CT winding connections makes it
possible to compensate for power transformer phase angle shift;
and
♦ the use of interposing CT connections, makes it possible to
remove zero sequence current from any power transformer side.
Maximum power transformer rated apparent power was used to calculate
the interposing CT ratios [10]. However, the interposing CTs could only
be calculated for the mid-position of the on-load tap-changer. Thus, as
soon as the OLTC is moved from the mid-position, false differential
currents would appear. Note as well that all interposing CTs required for
one particular application are calculated by taking the maximum rated
power of all windings within the protected power transformer as a base for
24 Chapter 3
the calculations. A typical differential protection scheme with interposing
CTs is given in Figure 13.
Figure 13: Power transformer differential protection scheme
with interposing CTs [10].
Numerical Differential Relays
The first papers about microprocessor based transformer protection were
published at the beginning of the eighties [7], [45]. With modern
numerical transformer differential relays [11], [12], [17] and [32] external
Differential Protection for Power Transformers 25
interposing CTs are not required because relay software enables the user
to:
♦ compensate for current magnitude differences on the different
sides of the protected power transformer;
♦ compensate for standard power transformer phase angle shift (i.e.
multiple of 30˚); and
♦ use all star connected primary CTs and still remove zero sequence
currents from any transformer side by parameter setting.
In addition to this, it is possible to on-line monitor the OLTC position and
automatically compensate for it in the calculation of differential currents
[11], [12] and [34]. Thus, the numerical differential relay can be ideally
balanced regardless of the actual OLTC position. A typical differential
protection scheme with a numerical differential relay is shown in
Figure 14.
In some recent publications it was suggested to include the voltage
measurement from only one or even from all sides of the protected power
transformer into the differential protection [65], [66]. However, in this
thesis only the current based differential protection will be considered.
Figure 14: Typical connections for modern numerical differential relay.
26 Chapter 3
3.2 Differential Protection for Special Converter
Transformers
Standard three-phase power transformers can be protected without any
external interposing CTs with numerical differential protection as
described in Section 3.1.
However, if the numerical differential relay is directly applied for
differential protection of a special converter transformer, and set to
compensate for the nearest standard transformer vector group, it will not
be able to compensate for additional, non-standard phase angle shift Ψ
caused by special winding connections. As a result a permanent false
differential current would appear. The false differential current magnitude
can be estimated by using the following formula:
_ 2 sin( ) sin( )
2 d false Load Load I I I
Ψ
= ⋅ ⋅ ≈ Ψ ⋅ (3.1)
where:
♦ Id_false is the false differential current magnitude;
♦ ILoad is the through-going load current magnitude; and
♦ Ψ is a non-standard phase angle shift.
For the worst case when Ψ =15o a false differential currents of up to 26%
of the through-load current will appear. As a consequence the minimum
pickup of the differential protection must be increased to at least twice this
value and consequently the differential relay will not be sensitive for the
low level internal faults within the protected power transformer.
3.3 Differential Protection for PST
If a numerical power transformer differential relay is directly applied for
the differential protection of a PST, and set for Yy0 vector group
compensation, the differential relay will not be able to compensate for the
variable phase angle shift Θ caused by OLTC operation. As a result a false
differential current will exist which will vary in accordance with the
coincident PST phase angle shift, as already shown in equation (3.1). As a
consequence the minimum pickup of the differential protection must be
increased and consequently the differential relay will not be sensitive for
the low level internal faults.
Differential Protection for Power Transformers 27
Thus, diverse differential protection schemes for phase-shifting
transformers are presently used [2], [37] and [67]. These schemes tend to
be dependent on the particular construction details and maximum phase
angle shift of the protected PST. A special report has been written by
IEEE-PSRC which describes possible protection solutions for PST
applications [37].
In references [51] and [52] a PST differential protection scheme, based
only on individual positive and negative sequence current components, is
proposed. However such a solution has the following drawbacks:
♦ It can be applied to PSTs with two ends only.
♦ It must be blocked during PST energizing.
♦ It must be blocked when an external fault is cleared (i.e. current
reversal blocking logic shall be used).
♦ It can’t provide the faulty phase indication.
Presently, there is no commercially available differential relay that can
provide complete phase-wise differential protection, in accordance with
Figure 14, for any PST regardless of its construction details.
3.4 Main CT Connections
In some countries (e.g. USA) delta connected main CTs are even used with
numerical differential protection relays. This is not in accordance with IEC
standards due to personal safety related issues, as the delta connected CTs
can not be earthed in the main CT junction box but only in the relay
protection cubicle. The three most typical main CT connections used for
transformer differential protection around the world are shown in Figure
15. It is assumed that the primary phase sequence is L1-L2-L3 (i.e. ANSI
ABC).
For star/wye connected main CTs, secondary currents fed to the
differential relay:
♦ are directly proportional to the measured primary currents;
♦ are in phase with the measured primary currents; and
♦ contain all sequence components including the zero sequence
current component.
For delta DAC connected main CTs (DAC means that the difference
between A and C phase currents is generated as the first phase current by
28 Chapter 3
the main CT delta connection), secondary currents fed to the differential
relay:
♦ are increased 3 times in comparison with star/wye connected
CTs;
♦ lag the primary winding currents by 30o (i.e. this CT connection
rotates currents by 30o in clockwise direction); and
♦ do not contain any zero sequence current component.
For delta DAB connected main CTs (DAB means that the difference
between A and B phase currents is generated as the first phase current by
the main CT delta connection), secondary currents fed to the differential
relay:
♦ are increased 3 times in comparison with star/wye connected
CTs;
♦ lead the primary winding currents by 30o (i.e. this CT connection
rotates currents by 30o in anticlockwise direction)
♦ do not contain any zero sequence current component.
Figure 15: Used CT connections for transformer differential protection.
Note that the influence of delta connected main CTs can be taken into
account in the method shown in Chapter 4, but this is not done in this
thesis. In this thesis it will always be assumed that all main CTs connected
to the differential protection are star/wye connected.
29
Chapter 4
New Universal Method
To provide universal differential protection for all variants of three-phase
power transformers it is necessary to provide three types of compensation
(see Section 3.1), which are described in the following sections.
4.1 Current Magnitude Compensation
In order to achieve current magnitude compensation, the individual phase
currents must be normalized on all power transformer sides by dividing
them by the so-called base current. The base current in primary amperes
can be calculated for each power transformer winding via the following
equation.
_ 3
rMax
Base Wi
rWi
S
I
U
=
⋅
(4.1)
where:
♦ IBase_Wi is winding i base current in primary amperes.
♦ SrMax is the maximum rated apparent power among all power
transformer windings. The maximum value, as stated on the
protected power transformer rating plate, is typically used.
♦ UrWi is winding i rated phase-to-phase no-load voltage; Values for
all windings are typically stated on the transformer rating plate.
For the winding with power rating equal to SrMax the base current is equal
to the winding rated current which is usually stated on the power
transformer rating plate.
Note that when a power transformer incorporates an OLTC, UrWi typically
has different values for different OLTC positions on at least one side of the
power transformer. Therefore the base current will have different values
on that side of the protected power transformer for different OLTC
30 Chapter 4
positions as well. Typically, for the winding where the OLTC is located,
different IBase values shall be used for every OLTC position, in order to
correctly compensate for the winding current magnitude variations caused
by OLTC operation. Once this normalization of the measured phase
currents is performed, the phase currents from the two sides of the
protected power transformer are converted to the same per unit scale and
can be used to calculate the transformer differential currents.
Note that the base current in (4.1) is in primary amperes. Differential
relays may use currents in secondary amperes to perform their algorithm.
In such case the base current in primary amperes obtained from equation
(4.1), shall be converted to the CT secondary side by dividing it by the
ratio of the main current transformer located on that power transformer
side. For an example see Section 5.1.
4.2 Phase Angle Shift across Power Transformer
In order to comprehend the phase angle shift compensation it is important
to understand the property of power transformers described in this section.
Typical voltage and current definitions used for three-phase power
transformers are shown in Figure 16, where:
♦ IL1_W1 is winding 1 (side 1) current in phase L1;
♦ UL1_W1 is winding 1 (side 1) phase-to-earth voltage in phase L1;
♦ IL1_W2 is winding 2 (side 2) current in phase L1; and
♦ UL1_W2 is winding 2 (side 2) phase-to-earth voltage in
phase L1.
UL1_W1
Side 1
Side 2
UL2_W1
UL3_W1
UL3_W2
UL2_W2
UL1_W2
Figure 16: Typical voltage and current reference directions for a transformer.
New Universal Method 31
The common characteristic for all types of three-phase power transformers
is that they introduce a phase angle shift Θ between winding 1 and
winding 2 side no-load voltages, as shown in Figure 17. Note that the
magnitude difference typically induced by the power transformer is not
shown in Figure 17. It can be assumed that voltage phasors are shown in
the per-unit (pu) system.
UL1_W1 UL1_W2
UL3_W2 UL2_W1
UL3_W1 UL2_W2
Θ
Figure 17: Phasor diagram for individual no-load, phase voltages.
The only difference among the variants of three-phase power transformers
is that:
♦ general-purpose three-phase power transformers introduce a fixed
phase angle shift Θ of 30o n ⋅ (n=0, 1, 2, …, 11) between its
terminal no-load voltages;
♦ special converter transformers introduce a fixed phase angle shift
Θ different from 30º or a multiple of 30º between its terminal noload
voltages (e.g. 22.5º); and
♦ phase-shifting transformers introduce a variable phase angle shift
Θ between its terminal no-load voltages (e.g. 0º - 18º in fifteen
steps of 1.2º).
It can be shown [25] that strict rules do exist for the phase angle shift
between the sequence components of the no-load voltage from the two
sides of the power transformer, as shown in Figure 18, but not for
individual phase voltages from the two sides of the power transformer.
32 Chapter 4
Note that the following symbols (abbreviations) will be used for the
sequence quantities:
♦ PS – positive sequence quantity;
♦ NS – negative sequence quantity; and
♦ ZS – zero sequence quantity.
UPS_W1 UPS_W2
Θ
UNS_W2 UNS_W1
-Θ
UZS_W1 UZS_W2
Figure 18: Phasor diagram for no-load positive, negative and zero sequence
voltage components from the two sides of the power transformer.
As shown in Figure 18 the following will hold true for the positive,
negative and zero sequence no-load voltage components:
♦ the positive sequence no-load voltage component from winding 1
(UPS_W1) will lead the positive sequence no-load voltage
component from winding 2 (UPS_W2) by angle Θ;
♦ the negative sequence no-load voltage component from winding 1
(UNS_W1) will lag the negative sequence no-load voltage
component from winding 2 (UNS_W2) by angle Θ; and
♦ the zero sequence no-load voltage component from winding 1
(UZS_W1) will be exactly in phase with the zero sequence noload
voltage component from winding 2 (UZS_W2), when the
zero sequence no-load voltage components are at all transferred
across the power transformer.
However, as soon as the power transformer is loaded, this voltage
relationship will no longer be valid, due to the voltage drop across the
power transformer impedance. However it can be shown that the same
phase angle relationship, as shown in Figure 18, will be valid for the
sequence current components, as shown in Figure 19, which flow into the
power transformer winding 1 and flow out from the winding two [25].
New Universal Method 33
IPS_W2 INS_W1
-Θ
IPS_W1 INS_W2
Θ
IZS_W1 IZS_W2
Figure 19: Phasor diagram for positive, negative and zero sequence
current components from the two sides of the power transformers.
As shown in Figure 19, the following will hold true for the sequence
current components from the two power transformer sides:
♦ the positive sequence current component from winding 1
(IPS_W1) will lead the positive sequence current component from
winding 2 (IPS_W2) by angle Θ (the same relationship as for the
positive sequence no-load voltage components);
♦ the negative sequence current component from winding 1
(INS_W1) will lag the negative sequence current component from
winding 2 (INS_W2) by angle Θ (the same relationship as for the
negative sequence no-load voltage components); and
♦ the zero sequence current component from winding 1 (IZS_W1)
will be exactly in phase with the zero sequence current component
from winding 2 (IZS_W2), when the zero sequence current
components are at all transferred across the transformer (the same
relationship as for the zero sequence no-load voltage components).
Therefore the following equations can be written for positive, negative and
zero sequence current components from the two sides of the power
transformer:
34 Chapter 4
1 j 2 IPS _W e IPS _W = Θ ⋅ (4.2)
1 j 2 INS _W e INS _W = − Θ ⋅ (4.3)
IZS _W1 = IZS _W2 (4.4)
4.3 Phase Angle Shift Compensation
In this section it will be assumed that current magnitude compensation of
individual phase currents from the two power transformer sides has been
performed. Hence, only the procedure for phase angle shift compensation
will be presented.
For a differential protection scheme, currents from all sides of the
protected object are typically measured with the same reference direction
(e.g. towards the protected object), as shown in Figure 14. From this point,
all equations will be written for the current reference direction as shown in
Figure 14.
According to the equations (4.2), (4.3) and (4.4) the sequence differential
currents can be calculated with the following equations (note new current
reference directions!):
1 j 2 Id _ PS IPS _W e IPS _W = + Θ ⋅ (4.5)
Positive sequence
differential current
1 j 2 Id _ NS INS _W e INS _W = + − Θ ⋅ (4.6)
Negative sequence
differential current
Id _ ZS = IZS _W1+ IZS _W2 (4.7)
Zero sequence
differential current
By using the basic relationship between sequence and phase quantities the
following matrix relationship can be written for phase-wise differential
currents:
New Universal Method 35
Id _ L1 Id _ ZS
Id _ L2 A Id _ PS
Id _ L3 Id _ NS
= ⋅
(4.8)
where from [21] and [43]:
2
2
1 1 1
1
1
A a a
a a
=
(4.9)
1 2
2
1 1 1
1
1
3
1
A a a
a a
−
= ⋅
(4.10)
120 1 3
120 120
2 2
j a e cos( ) j sin( ) j = ° = ° + ⋅ ° = − + ⋅ (4.11)
2 120 1 3
120 120
2 2
j a e cos( ) j sin( ) j = − ° = − ° + ⋅ − ° = − − ⋅ (4.12)
By combining equations (4.5), (4.6) and (4.7) into equation (4.8) and
doing some basic rearrangements the following equations can be derived:
j
j
Id _ L1 IZS _W1 IZS _W2
Id _ L2 A IPS _W1 A e IPS _W2
Id _ L3 INS _W1 e INS _W2
Θ
− Θ
= ⋅ + ⋅ ⋅
⋅
(4.13)
j
j
Id _ L1 IZS _W1 1 0 0 IZS _W2
Id _ L2 A IPS _W1 A 0 e 0 IPS _W2
Id _ L3 INS _W1 0 0 e INS _W2
Θ
− Θ
= ⋅ + ⋅ ⋅
(4.14)
36 Chapter 4
By further elementary mathematical manipulation and using the basic
relationship between phase and sequence quantities the following
equations can be derived:
j 1
j
Id _ L1 IZS _W1 1 0 0 IZS _W2
Id _ L2 A IPS _W1 A 0 e 0 ( A A) IPS _W2
Id _ L3 INS _W1 0 0 e INS _W2
−
Θ
− Θ
= ⋅ + ⋅ ⋅ ⋅ ⋅ (4.15)
j 1
j
Id _ L1 IL1_W1 1 0 0 IL1_W2
Id _ L2 IL2_W1 A 0 e 0 A IL2_W2
Id _ L3 IL3_W1 0 0 e IL3_W2
−
Θ − Θ
= + ⋅ ⋅ ⋅ (4.16)
The equation (4.16) now represents the basic relationship between phase –
wise differential currents and individual phase currents from the two sides
of the protected object.
To simplify equation (4.16) the new matrix transformation M(Θ) is
defined and further developed in the following equations:
1
1 0 0
0 0
0 0
j
j
M( ) A e A
e
Θ −
− Θ
Θ = ⋅ ⋅ (4.17)
2 2
2 2
1 1 1 1 0 0 1 1 1
1
1 0 0 1
3
1 0 0 1
j
j
M( ) a a e a a
a a e a a
Θ
− Θ
Θ = ⋅ ⋅ ⋅ (4.18)
2 2
2 3 3 4 2
2 2 4 3 3
1 1 1
1
M( )= 1 1 1
3
1 1 1
j j j j j j
j j j j j j
j j j j j j
e e a e a e a e a e
a e a e a e a e a e a e
a e a e a e a e a e a e
Θ − Θ Θ − Θ Θ − Θ
Θ − Θ Θ − Θ Θ − Θ
Θ − Θ Θ − Θ Θ − Θ
+ + + ⋅ + ⋅ + ⋅ + ⋅
Θ ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅
+ ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅
(4.19)
New Universal Method 37
1+2 cos( ) 1 cos( ) 3 sin( ) 1 cos( ) 3 sin( )
1
( ) 1 cos( ) 3 sin( ) 1+2 cos( ) 1 cos( ) 3 sin( )
3
1 cos( ) 3 sin( ) 1 cos( ) 3 sin( ) 1+2 cos( )
M
⋅ Θ − Θ − ⋅ Θ − Θ + ⋅ Θ
Θ = ⋅ − Θ + ⋅ Θ ⋅ Θ − Θ − ⋅ Θ
− Θ − ⋅ Θ − Θ + ⋅ Θ ⋅ Θ
(4.20)
Using the trigonometric relationship
cos( x y ) cos( ± = x ) ⋅ cos( y )m sin( x ) ⋅ sin( y )
the following form can be obtained:
1+2 1 2 120 1 2 120
1
M( )= 1 2 120 1+2 1 2 120
3
1 2 120 1 2 120 1+2
cos( ) cos( ) cos( )
cos( ) cos( ) cos( )
cos( ) cos( ) cos( )
⋅ Θ + ⋅ Θ + ° + ⋅ Θ − °
Θ ⋅ + ⋅ Θ − ° ⋅ Θ + ⋅ Θ + °
+ ⋅ Θ + ° + ⋅ Θ − ° ⋅ Θ
(4.21)
Due to a fact that M(0o) is a unit matrix, the equation (4.16) can be re–
written as follows:
_ 1 1 _ 1 1 _ 2 1 _ 1 1 _ 2
_ 2 2 _ 1 ( ) 2 _ 2 (0 ) 2 _ 1 ( ) 2 _ 2
_ 3 3 _ 1 3 _ 2 3 _ 1 3 _ 2
Id L IL W IL W IL W IL W
Id L IL W M IL W M IL W M IL W
Id L IL W IL W IL W IL W
= + Θ ⋅ = ° ⋅ + Θ ⋅
(4.22)
It shall be observed that Θ is the angle for which the winding two positive
sequence, no-load voltage component shall be rotated in order to overlay
with the positive sequence, no-load voltage component from winding one
side. Refer to Figure 18 for more information. The angle Θ has a positive
value when rotation is in an anticlockwise direction. Note that M(0o) is a
unit matrix, which can be assigned to the first power transformer winding
which is taken as the reference winding for phase angle compensation.
Thus, the reference winding is a winding to which:
♦ all other winding currents are aligned; and
♦ its currents are not rotated (i.e. rotated by zero degrees).
Note that it is as well equally possible to select winding two as the
reference winding for the differential protection phase angle shift
compensation. In that case the negative value for angle Θ shall be
associated with winding one. See Section 5.1 for an example.
38 Chapter 4
4.4 Zero Sequence Current Compensation
Sometimes it is necessary to remove the zero sequence current component
from one or possibly both sides of the protected transformer because the
zero sequence current is not properly transferred from one side of the
transformer to the other. In these cases the following, more general form of
equation (4.22), can be used:
1 2
1 2
1 2
_ 1 1_ 1 _ 1 1_ 2 _ 2
_ 2 (0 ) 2 _ 1 _ 1 ( ) 2 _ 2 _ 2
_ 3 3_ 1 _ 1 3_ 2 _ 2
w w
w w
w w
Id L IL W k IZS W IL W k IZS W
Id L M IL W k IZS W M IL W k IZS W
Id L IL W k IZS W IL W k IZS W
− ⋅ − ⋅
= ° ⋅ − ⋅ + Θ ⋅ − ⋅
− ⋅ − ⋅
(4.23)
where:
♦ IZS_W1 is the zero sequence current on side 1 of the protected
object.
♦ IZS_W2 is the zero sequence current on side 2 of the protected
object.
♦ kw1 and kw2 are setting parameters which can have values 1 or 0
and are set by the end user in order to enable or disable the zero
sequence current reduction on any of the two sides.
By closer examination of equation (4.23) it is obvious that it is actually
possible to deduct the zero sequence currents in the following two ways:
♦ by measuring the zero-sequence current at the winding common
neutral point as described in [44]; or,
♦ by internally calculating zero-sequence current from the
individually measured three-phase winding currents using the
well-known formula from [21] and [43].
1 2 3
3
IL IL IL
IZS
+ +
= (4.24)
When internal calculation of the zero-sequence current is used, it is
possible to include equation (4.24) into the M(Θ) matrix transform by
defining a new matrix transform M0(Θ), which simultaneously performs
the phase angle shift compensation and the required zero sequence current
elimination:
New Universal Method 39
1 1 1
1
0( ) ( ) 1 1 1
3
1 1 1
M M
Θ = Θ − ⋅
(4.25)
cos( ) cos( 120 ) cos( 120 )
2
0( ) cos( 120 ) cos( ) cos( 120 )
3
cos( 120 ) cos( 120 ) cos( )
M
Θ Θ+ ° Θ− °
Θ = ⋅ Θ− ° Θ Θ+ °
Θ+ ° Θ− ° Θ
(4.26)
Therefore now (4.23) can be re-written as follows:
_ 1 1_ 1 1_ 2
_ 2 0(0 ) 2 _ 1 0( ) 2 _ 2
_ 3 2 _ 1 2 _ 2
Id L IL W IL W
Id L M IL W M IL W
Id L IL W IL W
= ° + Θ
(4.27)
Note that equations (4.22) and (4.27) actually have the same form. The
only difference is the matrix transformation (i.e. M(Θ) or M0(Θ)) actually
used. Thus, it is possible to select matrix transformation M0(Θ) to allow
for the removal of the zero sequence currents on the relevant side of the
protected transformer, or to select M(Θ) for phase angle shift
compensation only in the differential current calculations.
Note that matrix transform M0(Θ) is actually the numerical equivalent of
the generalized normalization transform presented in reference [42].
However, when the M0(Θ) matrix transformation is always applied on all
sides of the protected transformer, as suggested in [42]:
♦ the differential protection sensitivity is unnecessarily reduced on
the sides where it is not required to remove the zero sequence
currents; and
♦ the calculation of the instantaneous differential currents can be
unnecessarily corrupted, which can cause problems for proper
operation of the 2nd and 5th harmonic blocking criteria, as shown in
reference [12].
40 Chapter 4
4.5 Universal Differential Current Calculation Method
If now all compensation techniques described in the previous sections are
combined in one equation, the following universal equation for differential
current calculations for any two winding, three-phase power transformer or
PST can be written:
_ 1 2 1_ _ _ 2 1 ( ) 2_ _
_ 3 1 _ 3_ _
Id L IL Wi kWi IZS Wi
Id L M Wi IL Wi kWi IZS Wi i Ib Wi Id L IL Wi kWi IZS Wi
− ⋅
= ⋅ Θ ⋅ − ⋅ Σ=
− ⋅
(4.28)
where:
♦ Id_Lx are phase-wise differential currents;
♦ Ib_Wi is the base current of winding i (it can be a variable value if
the winding incorporates OLTC);
♦ M(ΘWi) is a 3x3 matrix that performs on-line phase angle shift
compensation on winding i measured phase currents (it can have
variable element values for some PST windings depending on the
OLTC location within the PST);
♦ ΘWi is the angle for which winding i positive sequence, no-load
voltage component shall be rotated in order to overlay with the
positive sequence, no-load voltage component from the chosen
reference winding (typically the first star winding as shown in
Section 5.1); ΘWi has a positive value when rotation is performed
in the anticlockwise direction;
♦ ILx_Wi are measured winding i phase currents (primary amperes);
♦ kWi is a setting which determines whether the zero sequence
current shall be subtracted from the winding i phase currents
(settable to zero or one); and
♦ Izs_Wi is either the measured or the calculated winding i zero
sequence current.
By using the superposition principle the most general equation to calculate
the differential currents for any n-winding power transformer or PST can
be written:
New Universal Method 41
_ 1 1_ _
1
_ 2 ( ) 2 _ _
_ 3 1 _ 3_ _
Id L IL Wi kWi IZS Wi n
Id L M Wi IL Wi kWi IZS Wi
i Ib Wi Id L IL Wi kWi IZS Wi
− ⋅
= ⋅ Θ ⋅ − ⋅ Σ=
− ⋅
(4.29)
where:
♦ n is the number of windings of the protected power transformer
(typically n≤6).
Alternatively, when zero sequence reduction is performed by internal
calculations (4.25), the following equation can be written:
_ 1 1_
1
_ 2 2 _
_ 3 1 _ 3_
Id L IL Wi n
Id L MXWi IL Wi
i Ib Wi Id L IL Wi
= ⋅ ⋅ Σ=
(4.30)
where:
♦ MXWi is equal to either M(ΘWi) on sides where zero sequence
current is not removed or M0(ΘWi) on sides where zero sequence
current shall be removed.
A new quantity, DCCWi, described as the Differential Current Contribution
set for winding i, can be defined by the following equation:
_ 1 1_
1
_ 2 2 _
_
_ 3 3_
DCC L IL Wi Wi
DCC DCC L Wi MX IL Wi Wi Ib Wi Wi
DCC L Wi IL Wi
= = ⋅ ⋅
(4.31)
where:
♦ DCC_L1Wi is the phase L1 differential current contribution from
winding i.
Thus, equation (4.30) can now be re-written as follows:
_ 1 _ 1
_ 2 _ 2
_ 3 1 1 _ 3
Id L n DCC L Wi n
Id L DCCWi DCC L Wi
Id L i i DCC L Wi
= Σ = Σ
= =
(4.32)
42 Chapter 4
Note that the elements of the M(Θ) and M0(Θ) matrices are always real
numbers. Therefore, the presented differential current calculation method
can be used to calculate the fundamental frequency phase-wise differential
currents, the sequence-wise differential currents and the instantaneous
differential currents for the protected power transformer [11] and [12].
For example, starting from equation (4.30) the negative sequence
component differential current can be calculated in accordance with the
following equation:
1
_ 1 _
1
_ 2 _
_ 3 1 _ 2
_
_ 1
_ 2
_ 3
n Wi
Wi
i
Wi
IdNS L INS Wi
n
IdNS L MXWi a INS Wi
i Ib Wi IdNS L
a INS Wi
DCCNS L
DCCNS L
DCCNS L
=
= Σ ⋅ ⋅ ⋅ =
= ⋅
Σ (4.33)
where:
♦ IdNS_L1 is the negative sequence differential current for phase L1
♦ INS_Wi is the winding i negative sequence current component in
primary amperes (phase L1 used as reference phase);
♦ DCCNS_L1Wi is the negative sequence differential current
contribution for phase L1 from winding I; and
♦ 120o j a = e is a sequence operator.
Note that the three differential currents based on the negative sequence
current components will have equal magnitudes but they will be phase
displaced by 120o. Thus in practical applications it is sufficient to calculate
the negative sequence component differential current for phase L1 only.
Therefore, by using the concept of differential current contributions
explained above the following equation can be written:
1
_ 1 _ 1
n
Wi
i
IdNS IdNS L DCCNS L
=
= =Σ (4.34)
The above mentioned properties mean that all features of existing
numerical differential protection for standard power transformers [11] and
[12] can be directly applied to the new principle including:
♦ bias current calculation;
♦ operate-restraint characteristic;
♦ unrestraint operational level;
New Universal Method 43
♦ 2nd and 5th harmonic blocking;
♦ waveform blocking;
♦ cross blocking; and
♦ negative sequence based internal/external fault discriminator.
Equation (4.29) is the main innovation in the differential current
measurement system. With numerical technology it is possible to provide
power transformer differential protection, which can simultaneously:
♦ provide on-line current magnitude compensation for every side;
♦ provide on-line phase angle compensation for arbitrary phase shift
between different sides of the protected object;
♦ provide optional zero-sequence current compensation for every
side; and
♦ compensate for multiple OLTCs located within the same power
transformer.
Therefore it will be possible to provide differential protection, in
accordance with Figure 14, for any three-phase power transformer or PST
with arbitrary phase angle shift and current magnitude variations caused by
OLTC(s) operation. This universal method for differential current
calculations eliminates any need for buried current transformers within the
PST tank, as usually required by presently used PST differential protection
schemes [37]. Thus, any PST or special converter transformer can be
protected with this differential protection scheme which is very similar to
the presently used differential protection scheme for general-purpose
three-phase power transformers.
4.6 Phase Sequence and Vector Group Compensation
Declared vector group (e.g. YNd5) on a power transformer rating plate is
always stated with the assumption that the primary phase sequence
connected to this three-phase power transformer is L1-L2-L3 (i.e. ANSI
ABC). In other words, the power transformer vector group is always
declared for the positive sequence system [33], [58].
From the transformer differential protection point of view the most
important thing is that the phase sequence of the currents connected to the
differential relay follows the phase sequence connected to the protected
power transformer. Such arrangement, which is most commonly used in
44 Chapter 4
the protective relaying practice, is shown in Figure 20a. For such
connections the differential relay shall be set to compensate for the vector
group as stated on the protected power transformer rating plate (e.g. YNd5
for application shown in Figure 20a), irrespective of the actual phase
sequence used in this power system (e.g. either L1-L2-L3 or L3-L2-L1).
a) b)
Figure 20: Influence of the primary connections on the differential protection.
Sometimes, due to easier mechanical design, connections as shown in
Figure 20b are used. As shown in this figure, two phases (e.g. L1 and L3
in this example) are swopped on both power transformer sides within the
protected zone of the differential relay. Note that from the power system
New Universal Method 45
point of view the two connections shown in Figure 20a and Figure 20b are
fully equivalent. However the differential relay will not be stable if it is set
to compensate for the YNd5 vector group. The reason is that the phase
sequence connected to the differential relay (e.g. L1-L2-L3) is different on
both sides from the phase sequence connected to the protected power
transformer (e.g. L3-L2-L1). For such connections, the differential relay
shall be set to compensate for the YNd7 vector group in order to remain
stable for all through load conditions. Such setting is required irrespective
of the actual phase sequence used in the power system (e.g. either L1-L2-
L3 or L3-L2-L1).
Thus, for connections shown in Figure 20b, the protected power
transformer vector group effectively becomes equal to twelve minus vector
group number stated on the rating plate. Note that the same rule applies to
all variants of three-phase power transformers (i.e. general-purpose
transformers, converter transformers and phase-shifting transformers).
Connections shown in Figure 20b are taken from an actual installation and
results from the differential protection primary testing are available to
prove the presented principles. The same “setting problem” has been
reported from other sites as well. For another practical example see
Section 10.3/Field Case #1).
In this thesis it will always be assumed that the differential relay
connections and the protected power transformer connections have the
same phase sequence (i.e. as shown in Figure 20a).
4.7 Properties of M and M0 Matrix Transformations
Only three different numerical elements are present in any M and M0
matrix. Thus, the following two equations can be written:
1 2 cos( ) 1 2 cos( 120 ) 1 2 cos( 120 )
1
( ) 1 2 cos( 120 ) 1 2 cos( ) 1 2 cos( 120 )
3
1 2 cos( 120 ) 1 2 cos( 120 ) 1 2 cos( )
o o
o o
M
o o
x y z
z x y
y z x
θ
+ ⋅ Θ + ⋅ Θ+ + ⋅ Θ−
= ⋅ + ⋅ Θ− + ⋅ Θ + ⋅ Θ+
+ ⋅ Θ+ + ⋅ Θ− + ⋅ Θ
= (4.35)
46 Chapter 4
0 0 0
0 0 0
0 0 0
cos( ) cos( 120 ) cos( 120 )
2
0( ) cos( 120 ) cos( ) cos( 120 )
3
cos( 120 ) cos( 120 ) cos( )
x y z
z x y
y z x
o o
M o o
o o
θ =
Θ Θ+ Θ−
= ⋅ Θ− Θ Θ+
Θ+ Θ− Θ
(4.36)
These three numerical elements are interrelated. For the M matrix
transformation elements the following equation is always valid.
x + y + z = 1 (4.37)
For the M0 matrix transformation elements the following equation is
always valid.
x0 + y0 + z0 = 0 (4.38)
The inverse matrix of the M (Θ) transformation is equal to:
1( ) ( ) T ( )
x z y
M M M y x z
z y x
−
Θ = −Θ = Θ = (4.39)
The matrix M0(Θ) is a singular matrix so a unique inverse matrix cannot
be derived. However, it is possible to define the pseudo-inverse matrix
(Moore-Penrose Matrix Inverse) † M0 (Θ) [24]. This matrix can be used to
calculate the three-phase currents if all three differential currents are
known. Note that in such case the calculated phase currents will not
contain any zero-sequence current component.
0† ( )
0 0 0
0( ) 0 ( ) 0 0 0
0 0 0
T M
x z y
M M y x z
z y x
Θ = −Θ = Θ = (4.40)
These matrix transformations have the following interesting properties:
M(Θ1+Θ2) = M(Θ1)⊗M(Θ2) (4.41)
M0(Θ1+Θ2) = M0(Θ1)⊗M0(Θ2) (4.42)
M0(Θ1+Θ2) = M(Θ1)⊗M0(Θ2) = M0(Θ1)⊗M(Θ2) (4.43)
New Universal Method 47
where ⊗ is the symbol for matrix multiplication
The last property of the M and M0 transformations means that in practice
the three-phase currents, which shall be rotated by angle Θ1+Θ2, can first
be rotated by phase angle Θ1 and then subsequently be rotated by phase
angle Θ2. The overall result will be exactly the same as if the rotation by
the overall angle has been performed at once. A practical use of this
property is shown in Section 8.1.
4.8 Correct Values for Base Current and Angle Θ
The proposed differential current calculation method is dependent on the
correct values of the base current and phase angle shift for every power
transformer side being available to the differential protection algorithm.
These values can be obtained in one of the following ways:
♦ as fixed values, determined from the protected power transformer
rated data and vector group, which are entered as setting
parameters by the end user (see Section 5.1 for an example);
♦ from a look-up table which describes the relationship between
different OLTC positions and the corresponding Ibase and Θ
values (see Section 5.6 for an example);
♦ from two, three or more look-up tables, similar to the one
described in the previous point, for devices with more than one
OLTC [19], [48] and [60];
♦ from a two- or three-dimensional look-up table, similar to the one
described in the previous points, for devices with more than one
OLTC [19], [48] and [60];
♦ by an algorithm internal to the differential protection, which
during steady state operating conditions measures the phase angle
difference between the positive sequence no-load voltages from
the two power transformer sides when the transformer is not
loaded, or alternatively by measuring the phase angle difference
between positive sequence currents from the two power
transformer sides when the transformer is loaded. Note that this is
possible only for power transformers with two sides; or
♦ via a communication link from the protected object control system
in case of more complicated FACTs devices.
49
Chapter 5
Application of the Method
Examples of how to calculate the differential currents in accordance with
the new universal method for some practical transformer applications will
be presented in this chapter.
5.1 Standard Two–winding, YNd1 Transformer
The transformer rating data, relevant application data for the differential
protection and the vector diagram for the voltage quantities for this power
transformer are given in Figure 21. The maximum power (i.e. base power)
for this transformer is 20.9MVA, and against this value, the base primary
currents and base currents on the CT secondary side are calculated as
shown in Table 1. Note that the calculation of the base currents on the CT
secondary side is limited to this example and subsequent cases will mainly
be presented with primary base currents.
Table 1: Base current calculations for an YNd1 transformer
Primary Base Current
Base current on CT
secondary side
W1, 69kV-Star
20.9MVA
=174.9A
3×69kV
174.9
=0.583A
300/1
W2, 12.5kVDelta
20.9MVA
=965.3A
3×12.5kV
965.3
=4.827A
1000/5
50 Chapter 5
CT 300/1
Star/Wye
CT 1000/5
Star/Wye
20.9MVA
69/12.5kV
YNd1
(YDAC)
30o
HV_L1
HV_L3 HV_L2
LV_L1
LV_L2
LV_L3
Figure 21: Relevant application data for an YNd1 power transformer.
Regarding phase angle compensation two solutions are possible (in general
for an n-winding transformer at least n possible solutions exist). The first
solution is to take W1 side as the reference side (i.e. with 0o phase angle
shift). The vector group of the protected transformer is Yd1 (ANSI
designation YDAC), thus the W2 (delta winding) positive sequence voltage
component shall be rotated by 30o in an anticlockwise direction in order to
coincide with the W1 positive sequence voltage component. For this first
phase angle compensation solution the required matrices for both windings
are shown in Table 2. Note that the zero sequence current shall be removed
from the W1 side, because the HV star winding neutral point is solidly
grounded.
Application of the Method 51
Table 2: First solution for phase angle compensation for an YNd1 transformer
Compensation matrix Mx
W1, 69kV-Star, selected as
reference winding
2 -1 -1
1
0(0 ) -1 2 -1
3
-1 -1 2
o M
= ⋅
W2, 12.5kV-Delta
0.9107 -0.2440 0.3333
(30 ) 0.3333 0.9107 -0.2440
-0.2440 0.3333 0.9107
o M
=
The second solution is to take W2 side as the reference side (with 0o phase
angle shift). The vector group of the protected transformer is Yd1, thus the
W1 (star winding) positive sequence voltage component shall be rotated
by 30o in a clockwise direction (see Figure 21) in order to coincide with
the W2 positive sequence voltage component. For this second phase angle
compensation solution the required matrices for both windings are shown
in Table 3.
Table 3: Second solution for phase angle compensation for an YNd1 transformer
Compensation matrix Mx
W1, 69kV-Star
1 0 -1
1
0( 30 ) -1 1 0
3
0 -1 1
o M
− = ⋅
W2, 12.5kV-Delta, selected
as reference winding
1 0 0
(0 ) 0 1 0
0 0 1
o M
=
Note that the second solution is identical to the traditionally applied
transformer differential protection schemes that utilize analogue
differential relays and interposing CTs. In such schemes, the y/d connected
interposing CTs are used on star-connected power transformer windings,
while y/y connected interposing CTs are used on delta-connected power
transformer windings.
52 Chapter 5
Note, however, that the first solution correlates better with the physical
winding layout around the magnetic core limbs within the protected power
transformer. In the case of an internal fault in phase L1 of the HV star
connected winding for the second solution, equally large differential
currents would appear in phases L1 and L3 and the differential relay would
operate in both phases. However, for the first solution, the biggest
differential current would appear in phase L1 clearly indicating the actual
faulty phase. It can also be shown that a slightly larger magnitude of the
differential current would be calculated for such an internal fault by using
the first solution (i.e. for phase-to-ground faults, the ratio of the differential
currents will be
2 1
1 _ : 2 _ : 0.667 : 0.577
3 3
st nd Solution Solution = = ). Thus, the
first solution is recommended for the numerical differential protection and
it can be simply formulated using the following guidelines:
♦ the first star (i.e. wye) connected power transformer winding shall
preferably be selected as the reference winding (with 0o phase
angle shift) for the transformer differential protection;
♦ the first delta connected power transformer winding shall be
selected as the reference winding only for power transformers
without any star connected windings;
♦ the first delta connected winding within the protected power
transformer can be selected as the reference winding only if a
solution similar with traditionally applied transformer differential
protection schemes utilizing analogue differential relays and
interposing CTs is required;
♦ for special converter transformers (see Section 5.4 and
Section 5.5), a zigzag connected power transformer winding might
be selected as reference winding; and
♦ for PST applications typically the S-side shall be selected as the
reference side.
The first guideline will be followed for all applications shown in this
document, with exception of Sections 5.2 and 5.8 where still two solutions
for phase angle shift compensation will be presented.
Once the base currents and MX matrices are determined the overall
equation to calculate differential currents can be written in accordance
with equation (4.30). Equation using primary base currents and the first
solution for phase angle compensation will only be presented here.
Application of the Method 53
_ 1 2 1 1 1_ 69
1 1
_ 2 1 2 1
174.9 3 2 _ 69
_ 3 1 1 2
3_ 69
0.9107 0.2440 0.3333 1_12.5
1
0.3333 0.9107 0.2440
965.3 2 _12.5
0.2440 0.3333 0.9107
3_12.5
I
Id L L
Id L I
L
Id L
I
L
I
L
I
L
I
L
− −
= ⋅ ⋅ − − ⋅ +
− −
−
+ ⋅ − ⋅
−
5.2 Auto-transformers
The application of the differential protection to auto-transformers is
somewhat special because the schemes can be arranged in a number of
ways, as described below. The following auto-transformer rating data will
be used for all examples in this section: 300/300/100MVA;
400/115/10.5kV; YNautod5. The maximum power (i.e. base power) for
this auto-transformer is 300MVA. The phase shift between the tertiary
delta winding and the other two windings is 150o.
Auto-transformer with not Loaded Tertiary Delta Winding
Quite often the auto-transformer tertiary winding is not loaded and it is
used as a delta-connected equalizer winding [58]. Typical CT locations for
the differential protection of such an auto-transformer are shown in Figure
22. In this scenario the auto-transformer is protected as a two-winding
power transformer. Thus, the base primary currents are calculated as
shown in Table 4.
Table 4: Base current calculations
Primary Base Current
W1, 400kV-Star
300MVA
=433A
3×400kV
W2, 115kV-Star
300MVA
=1506A
3×115kV
54 Chapter 5
Regarding phase angle compensation, two solutions are possible. The first
solution is to take W1 side as the reference side (with 0o phase angle shift).
The vector group of the protected auto-transformer is Yy0, thus the W2
positive sequence, no-load voltage component is in phase with W1
positive sequence, no-load voltage component. Due to the existence of a
tertiary delta winding the zero sequence current must be eliminated from
both sides, thus M0(0o) matrices shall be used on both auto-transformer
sides. The required compensation matrices for both windings are shown in
Table 5.
Figure 22: YNautod5 connected auto-transformer with
unloaded tertiary delta winding.
Application of the Method 55
Table 5: The first solution for the phase angle compensation
Compensation matrix Mx
W1, 400kV-Star, selected
as reference winding
2 -1 -1
1
0(0 ) -1 2 -1
3
-1 -1 2
o M
= ⋅
W2, 115kV-Star
2 -1 -1
1
0(0 ) -1 2 -1
3
-1 -1 2
o M
= ⋅
The second solution is identical to traditionally used solutions with
analogue transformer differential relays and y/d connected interposing
CTs. In the case of an auto-transformer it is only important to take the
same compensation angle on both sides. The vector group of the protected
auto-transformer is Yy0d5, thus both sides can be, for example, rotated by
150o in the clockwise direction in order to prepare for the inclusion of W3
into the differential protection if so would be required in the future. The
required compensation matrices for both windings are shown in Table 6.
Table 6: The second solution for the phase angle compensation
Compensation matrix Mx
W1, 400kV-Star
-1 1 0
1
0( 150 ) 0 -1 1
3
1 0 -1
o M
− = ⋅
W2, 115kV-Star
-1 1 0
1
0( 150 ) 0 -1 1
3
1 0 -1
o M
− = ⋅
The second solution to calculate differential currents for this autotransformer
has the same drawbacks as explained in Section 5.1. Once the
base currents and MX matrices are determined the overall equation to
calculate differential currents can be written in accordance with equation
(4.30).
56 Chapter 5
Auto-transformer with Loaded Tertiary Delta Winding
In some countries the tertiary delta winding is used to provide reactive
power compensation (i.e. shunt reactors or shunt capacitors) to the rest of
the system. Typical CT locations for differential protection of such autotransformers
are shown in Figure 23. In such applications three-winding
differential protection shall be used. Thus, the base primary currents are
calculated as shown in Table 7.
Table 7: Base current calculations
Primary Base Current
W1, 400kV-Star
300MVA
=433A
3×400kV
W2, 115kV-Star
300MVA
=1506A
3×115kV
W3, 10.5kV-Delta
300MVA
=16496A
3×10.5kV
Phase angle compensation matrixes as shown in Table 8 shall be used.
Table 8: Solution for the phase angle compensation
Compensation matrix Mx
W1, 400kV-Star, selected
as reference winding
2 -1 -1
1
0(0 ) -1 2 -1
3
-1 -1 2
o M
= ⋅
W2, 115kV-Star
2 -1 -1
1
0(0 ) -1 2 -1
3
-1 -1 2
o M
= ⋅
W3, 10.5kV-Delta
-0.2440 0.3333 0.9107
(150 ) 0.9107 -0.2440 0.3333
0.3333 0.9107 -0.2440
o M
=
Application of the Method 57
L1 L2 L3
L1 L2 L3
L1
L2
L3
Figure 23: YNautod5 connected auto-transformer with
loaded tertiary delta winding.
Auto-transformer Built from Three Single-phase Units
Due to easier transportation to site and cheaper reserve units big autotransformers
are sometimes built as three single-phase units. Typical CT
locations for differential protection of such auto-transformers are shown in
58 Chapter 5
Figure 24. Note the position of CTs inside the tertiary delta winding. In
such applications three-winding differential protection shall be used. Thus,
the base primary currents are calculated as shown in Table 9.
Table 9: Base current calculations
Primary Base Current
W1, 400kV-Star
300MVA
=433A
3×400kV
W2, 115kV-Star
300MVA
=1506A
3×115kV
W3, 10.5kV-Star
300MVA
=9524A
3×10.5kV
Phase angle compensation matrixes as shown in Table 10 shall be used.
Zero sequence current reduction is not required due to the fact that every
unit has its own magnetic core. The same is also valid for five-limb, threephase
auto-transformers [29].
Table 10: Solution for the phase angle compensation
Compensation matrix Mx
W1, 400kV-Star, selected
as reference winding
1 0 0
(0 ) 0 1 0
0 0 1
o M
=
W2, 115kV-Star
1 0 0
(0 ) 0 1 0
0 0 1
o M
=
W3, 10.5kV-Star
1 0 0
(0 ) 0 1 0
0 0 1
o M
=
Application of the Method 59
L1 L2 L3
L1 L2 L3
L1
L2
L3
Figure 24: YNautod5 connected auto-transformer with
CTs inside the loaded tertiary delta winding.
60 Chapter 5
Auto-transformer Built from Three Single-phase Units and CTs
in the Common Winding Neutral Point
Sometimes CTs are even available in the neutral point of the common
winding of single-phase transformers. CT locations for such differential
protection applications are shown in Figure 25. Three-winding differential
protection shall be used. Thus, the base primary currents are calculated as
shown in Table 11.
Table 11: Base current calculations
Primary Base Current
W1, 400kV-Star
300MVA
=433A
3×400kV
W2, Common
Winding NP-Star 1506-433=1073A
W3, 10.5kV-Star
300MVA
=9524A
3×10.5kV
Phase angle compensation matrixes as shown in Table 12 shall be used.
Zero sequence current reduction is not required due to the fact that every
unit has its own magnetic core. The same is also valid for five-limb, threephase
auto-transformers [29].
Table 12: Solution for the phase angle compensation
Compensation matrix Mx
W1, 400kV-Star, selected
as reference winding
1 0 0
(0 ) 0 1 0
0 0 1
o M
=
W2, Common
Winding NP-Star
1 0 0
(0 ) 0 1 0
0 0 1
o M
=
W3, 10.5kV-Delta
1 0 0
(0 ) 0 1 0
0 0 1
o M
=
Application of the Method 61
L1 L2 L3
L1 L2 L3
L1
L2
L3
Figure 25: YNautod5 connected auto-transformer with CTs inside the loaded
tertiary delta winding and in the common winding neutral point.
Differential protection in this application has increased the sensitivity for
earth-faults within the auto-transformer due to the measuring point in the
common winding neutral point, where increased current during internal
earth-faults will occur.
62 Chapter 5
5.3 Four – winding Power Transformer
The rated quantities for a four winding power transformer are given on the
transformer rating plate shown in Figure 26.
Figure 26: Rating plate for a four-winding transformer.
The rated power for the calculation of the base currents is the maximum
power of all four windings, and it has a value of 55.53MVA. From the
power transformer vector group Yyn0d1d1, stated on the rating plate, the
angles for phase angle compensation can be extracted.
First winding:
Vector group: Y
Phase shift: 0o (this winding is taken as the reference winding)
Rated voltage: 132kV
Rated power: 55.53MVA
Rated current: 242.9A
From this data the base current for the magnitude compensation is
calculated:
b
b_W1
b_W1
S 55.53MVA
I = = =242.9A
3×U 3×132kV
As the first winding is not earthed, then the subtraction of the zero
sequence current is not required. Thus
Application of the Method 63
1
1 0 0
(0 ) 0 1 0
0 0 1
W MX M
= ° =
Second winding:
Vector group: yn0
Phase shift: 0o (the second winding no-load voltage is in phase
with the first winding no-load voltage. Thus there
is no need to rotate these winding currents)
Rated voltage: 7kV
Rated power: 27.765MVA
Rated current: 2290A
The base current is calculated as:
b
b_W2
b_W2
S 55.53MVA
I = = =4580A
3×U 3×7kV
Notice that for the calculation of the base current the maximum rated
power of all windings within the protected transformer is used (in this case
Sb = 55.53MVA).
As the winding is earthed, the zero sequence current must be removed.
2 0(0 )
2 -1 -1
1
-1 2 -1
3
-1 -1 2
W MX = M ° =
⋅
Third winding:
Vector group: d1
Phase shift: 30o (the third winding no-load voltage lags the
first winding no-load voltage. To get the two
windings correlated the third winding voltage has
to be rotated anticlockwise by 30o)
Rated voltage: 7kV
Rated power: 27.765MVA
64 Chapter 5
Rated current: 2290A
The base current is calculated:
b
b_W3
b_W3
S 55.53MVA
I = = =4580A
3×U 3×7kV
As the winding is delta connected the subtraction of the zero sequence
current is not required.
3
0.9107 0.2440 0.3333
(30 ) 0.3333 0.9107 0.2440
0.2440 0.3333 0.9107
W MX M
−
° = −
−
=
Fourth winding:
Vector group: d1
Phase shift: 30o (the fourth winding no-load voltage lags the
first winding no-load voltage. To get the two
windings correlated, the fourth winding voltage
has to be rotated anticlockwise by 30o)
Rated voltage: 11kV
Rated power: 15.0MVA
Rated current: 787.3A
The base current is calculated:
b
b_W4
b_W4
S 55.53MVA
I = = =2914.6A
3×U 3×11kV
As the winding is delta connected the subtraction of the zero sequence
current is not required.
4
0.9107 0.2440 0.3333
(30 ) 0.3333 0.9107 0.2440
0.2440 0.3333 0.9107
W MX M
−
= ° = −
−
Application of the Method 65
Once all these base currents and MX matrices are determined the overall
equation to calculate differential currents can be written in accordance
with equation (4.30).
5.4 Special Converter Transformer
In this case, a design of a special converter transformer will be
demonstrated that is a three–phase converter transformer with four
windings with an additional phase angle shift Ψ of 7.5o. The rating plate of
the transformer is presented in Figure 27.
The necessary data for the calculation of the differential currents can be
easily obtained from the power transformer rating plate data. The vector
group of the transformer is given on the rating plate as
Y-7.5oyn0d1d1. Actually, this transformer vector group shall be given as
Zyn11¾d0¾d0¾. The high voltage zigzag connected winding will be
taken as the reference winding (i.e. with 0º phase shift for differential
current calculation). From the phasor diagram on the rating plate the
angles for phase angle compensation can be extracted.
The rated power for the calculation of the base currents is the maximum
power of the four windings, and in this case it has a value of 61.44MVA.
First winding:
Vector group: Z (i.e. Y on the rating plate)
Phase shift: 0o (this winding is taken as the reference winding)
Rated voltage: 132kV
Rated power: 61.44MVA
Rated current: 268.7A
The base current is calculated:
b
b_W1
b_W1
S 61.44MVA
I = = =268.7A
3×U 3×132kV
66 Chapter 5
Figure 27: Part of the rating plate for a converter transformer.
Application of the Method 67
The zigzag connected winding is not earthed so the subtraction of the zero
sequence current is not required.
1
1 0 0
(0 ) 0 1 0
0 0 1
W MX M
= ° =
Second winding:
Vector group: yn0
Phase shift : -7.5o (the second winding no-load voltage leads
the first winding no-load voltage. To get the two
windings correlated the second winding voltage
has to be rotated clockwise by 7.5o)
Rated voltage: 7.65kV
Rated power: 30.72MVA
Rated current: 2318A
The base current is calculated:
b
b_W2
b_W2
S 61.44MVA
I = = =4636.9A
3×U 3×7.65kV
Because this winding star point is accessible the subtraction of the zero
sequence current is needed.
2
0.6610 -0.2551 -0.4058
-0.4058 0.6610 -0.2551
-0.2551 -0.4058 0.6610
0( 7.5o )
W MX M
= − =
Third winding
Vector group: d1
Phase shift : 30o-7.5o=22.5o (as the third winding vector group
introduces a phase shift of 30o, the phase shift
angle of -7.5o must be taken in consideration so
the total phase shift is 22.5o anticlockwise)
Rated voltage: 7.65kV
Rated power: 30.72MVA
Rated current: 2318A
68 Chapter 5
The base current is calculated:
b
b_W3
b_W3
S 61.44MVA
I = = =4636.9A
3×U 3×7.65kV
As the winding is delta connected the subtraction of the zero sequence
current is not required.
3
0.9493 -0.1956 0.2463
(22.5 ) 0.2463 0.9493 -0.1956
-0.1956 0.2463 0.9493
o
W MX M
= =
Fourth winding
Vector group: d1
Phase shift : 30o-7.5o=22.5o (as the fourth winding vector
group introduces a phase shift of 30o, the phase
shift angle of -7.5o must be taken in consideration
so the total phase shift is 22.5o anticlockwise)
Rated voltage: 11kV
Rated power: 46.68MVA
Rated current: 2450A
The base current is calculated:
b
b_W4
b_W4
S 61.44MVA
I = = =3224.8A
3×U 3×11kV
As the winding is delta connected the subtraction of the zero sequence
current is not required.
4
0.9493 -0.1956 0.2463
(22.5 ) 0.2463 0.9493 -0.1956
-0.1956 0.2463 0.9493
o
W MX M
= =
Application of the Method 69
Once all these base currents and MX matrices are determined the overall
equation to calculate differential currents can be written in accordance
with equation (4.30).
5.5 24-pulse Converter Transformer
In this case, the 24-pulse converter transformer design will be presented.
This 24-pulse converter transformer is quite special because within the
same transformer tank two three-phase transformers, of very similar
design, as shown in Figure 3a and Figure 3b, are put together. The first
internal transformer has the vector group Zy11¾d10¾. The second internal
transformer has the vector group Zy0¼d11¼. Such an arrangement gives
an equivalent five-winding power transformer with a 15o phase angle shift
between the LV windings of the same connection type. For differential
protection this is equivalent to a five winding power transformer with an
additional phase angle shift Ψ of 7.5o. The necessary information to apply
the differential protection is given in Figure 28.
The high voltage, equivalent zigzag connected winding will be taken as the
reference winding with 0º phase shift. The power for the calculation of the
base currents is the maximum power of the five windings, and in this case
it has a value of 2.6MVA.
First winding:
Vector group: Z
Phase shift: 0o (this winding is taken as the reference winding)
Rated voltage: 22kV
Rated power: 2.6MVA
The base current is calculated:
b
b_W1
b_W1
S 2.6MVA
I = = =68.2A
3×U 3×22kV
The zigzag connected winding is not earthed so the subtraction of the zero
sequence current is not required.
70 Chapter 5
1
1 0 0
(0 ) 0 1 0
0 0 1
W MX M
= ° =
Second winding LV1-Y:
Vector group: y
Phase shift : -7.5o (the second winding no-load voltage leads
the first winding no-load voltage. To get the two
windings correlated the second winding voltage
has to be rotated clockwise by 7.5o)
Rated voltage: 705V
Rated power: 650kVA
The base current is calculated:
b
b_W2
b_W2
S 2.6MVA
I = = =2129A
3×U 3×705V
Because this winding star point is not accessible the subtraction of the zero
sequence current is not required.
2
0.9943 0.0782 -0.0725
-0.0725 0.9943 0.0782
0.0782 -0.0725 0.9943
( 7.5o )
W MX M
= − =
Third winding LV1-D:
Vector group: d
Phase shift : -37.5o (the third winding no-load voltage leads the
first winding no-load voltage. To get the two
windings correlated the third winding voltage has
to be rotated clockwise by 37.5o)
Rated voltage: 705V
Rated power: 650kVA
The base current is calculated:
Application of the Method 71
b
b_W3
b_W3
S 2.6MVA
I = = =2129A
3×U 3×705V
Because this winding is delta connected the M matrix shall be used.
3
0.8622 0.4204 -0.2826
-0.2826 0.8622 0.4204
0.4204 -0.2826 0.8622
( 37.5o )
W MX M
= − =
Zy11¾d10¾ Zy0¼d11¼
Figure 28: The 24-pulse converter transformer design.
72 Chapter 5
Fourth winding LV2-Y:
Vector group: y
Phase shift: 7.5o (the fourth winding no-load voltage lags the
first winding no-load voltage. To get the two
windings correlated the fourth winding voltage
has to be rotated anticlockwise by 7.5o)
Rated voltage: 705V
Rated power: 650kVA
The base current is calculated:
b
b_W4
b_W4
S 2.6MVA
I = = =2129A
3×U 3×705V
Because this winding star point is not accessible the subtraction of the zero
sequence current is not required.
4
0.9943 -0.0725 0.0782
0.0782 0.9943 -0.0725
-0.0725 0.0782 0.9943
(7.5o )
W MX M
= =
Fifth winding LV2-D:
Vector group: d
Phase shift : -22.5o (the fifth winding no-load voltage leads the
first winding no-load voltage. To get the two
windings correlated the fifth winding voltage has
to be rotated clockwise by 22.5o)
Rated voltage: 705V
Rated power: 650kVA
The base current is calculated:
b
b_W5
b_W5
S 2.6MVA
I = = =2129A
3×U 3×705V
Because this winding is delta connected the M matrix shall be used.
Application of the Method 73
5
0.9493 0.2463 -0.1956
-0.1956 0.9493 0.2463
0.2463 -0.1956 0.9493
( 22.5o )
W MX M
= − =
Once all these base currents and MX matrices are determined the overall
equation to calculate differential currents can be written in accordance
with equation (4.30).
5.6 Dual-core, Asymmetric Design of PST
In this example the application of the transformer differential protection
method will be illustrated for an actual 1630MVA, 400kV, 50Hz, +18o
PST of asymmetric, two-core design. This type of PST is also known as
the Quad Booster. For such an asymmetric PST design, the base current
and the phase angle shift are functions of OLTC position. All necessary
information for application of the method can be obtained directly from
the PST rating plate. A relevant part of the PST rating plate is shown in
Figure 29.
The first column in Figure 29 represents the available OLTC positions, in
this case 33. From column three it is obvious that the base current for PST
source side is constant for all positions and has a value of 2353A. Column
five in Figure 29 gives the base current variation for the PST load side.
Finally the fourteenth column in Figure 29 shows how the no-load phase
angle shift varies across the PST for different OLTC positions.
Note that the phase angle shift on the PST rating plate is given as a
positive value when the load side no-load voltage leads the source side noload
voltage [35] (i.e. advanced mode of operation). Therefore if the phase
shift from Figure 29 is associated with the load side (i.e. source side taken
as reference side with zero degree phase shift) the angle values from the
rating plate must be taken with the minus sign.
This particular PST has a five-limb core construction for both internal
transformers (i.e. serial and excitation transformer). Therefore the zero
sequence current will be properly transferred across the PST and M(Θ)
matrices shall be used on both PST sides.
74 Chapter 5
Figure 29: Part of rating plate for dual-core, asymmetric PST design.
Application of the Method 75
Thus, for every OLTC position, the appropriate equation for differential
current calculation can now be written. The equation for OLTC position 30
will be given here:
_ 1 1_ 1_
1 1
_ 2 (0 ) 2 _ ( 16.4 ) 2 _ 2353 2257
_ 3 3_ 3_
Id L IL S IL L
Id L M IL S M IL L
Id L I I L S L L
= ⋅ ° ⋅ + ⋅ − ° ⋅
(5.1)
In a similar way this matrix equation can be written for any OLTC position
if appropriate values from Figure 29 are given for the base current and the
phase angle shift on the load side of the PST.
5.7 Single-core, Symmetric Design of PST
In this example the application of the transformer differential protection
method will be illustrated for an actual 450MVA, 138kV, 60Hz, ±58o PST
of symmetric, single-core design. For symmetric PST design, only the
phase angle shift is a function of the OLTC position. All necessary
information for the application of the method can be obtained directly
from the PST rating plate. A relevant part of the PST rating plate is shown
in Figure 30.
The base currents for both sides have the same and constant value
regardless the actual OLTC position. This value can be calculated by using
the following equation:
b
b
b
S 450MVA
I = = =1882.6A
3×U 3×138kV
(5.2)
The fourth column in Figure 30 shows how the no-load phase angle shift
varies across the PST for different OLTC positions. Note that the no-load
phase angle shift shall be used for differential protection phase angle
compensation and not the phase angle shift under load conditions which is
given in column five. The no-load phase angle shift on the PST rating plate
is given with positive values when the load side no-load voltage leads the
source side no-load voltage [35] (i.e. advanced mode of operation).
Therefore if the phase shift from Figure 30 is associated with the load side
(i.e. source side taken as reference side with zero degree phase shift) the
76 Chapter 5
angle values from the rating plate must be taken with the minus sign for
advanced mode of operation.
Figure 30: Part of rating plate for single-core, symmetric PST design.
This particular PST has no internal grounding points, thus the zero
sequence current will be properly transferred across the PST, and M(Θ)
matrices shall be used on both PST sides.
Application of the Method 77
For every OLTC position the appropriate equation for differential current
calculations can now be written. The equation for the OLTC position 8 is
presented here:
_ 1 1_ 1_
1 1
_ 2 (0 ) 2 _ (34.6 ) 2 _ 1883 1883
_ 3 3_ 3_
Id L IL S IL L
Id L M IL S M IL L
Id L I I L S L L
= ⋅ ° ⋅ + ⋅ ° ⋅
(5.3)
In a similar way this matrix equation can be written for any OLTC position
if appropriate angle values from Figure 30 are given for the phase angle
shift on the load side of the PST.
5.8 Combined Auto-transformer / PST in Croatia
In the Croatian Power network a special type of power transformer, which
has two combined operating modes, is installed in the Žerjavinec
substation. This transformer can be used as either a conventional
400MVA, 400/220/(10.5)kV, YNauto(d5) auto-transformer with an onload
tap-changer in the neutral point or as a phase-shifting transformer
connecting 400kV and 220kV networks. The power transformer has a
tertiary, unloaded delta winding. The relevant part of the rating plate in
auto-transformer operating mode is given in Table 13.
In the auto-transformer operating mode no phase shift angle is introduced
between the 400kV and 220kV no-load voltages. Thus, only the
compensation for current magnitude variations caused by the OLTC
movement shall be preformed. All necessary information for application of
the new differential protection method can be obtained directly from the
rating plate.
The first column in Table 13 represents the available OLTC positions, in
this case 25. Column three defines the base current for the transformer
400kV side. The 220kV side base current is constant for all positions and
has a fixed value of 999.7A. Due to the existence of a tertiary delta
winding the zero sequence currents must be eliminated from both sides,
thus M0(0o) matrices shall be used on both power transformer sides. The
equation for auto-transformer mode of operation for OLTC position 19 is
presented here:
78 Chapter 5
_ 1 1_ 400 1_ 220
1 1
_ 2 0(0 ) 2 _ 400 0(0 ) 2 _ 220 607.8 999.7
_ 3 3 _ 400 3_ 220
Id L IL IL
Id L M IL M IL
Id L I I L L
= ⋅ ° ⋅ + ⋅ ° ⋅
(5.4)
Table 13: Rating plate data in auto-transformer operating mode
OLTC 400kV Side 220kV Side 10.5kV Side
Position U[V] I[A] U[V] I[A] U[V] I[A]
1 462 000 499.9 14 310 5 244.1
2 455 100 507.4 13 890 5 404.9
3 448 700 514.8 13 490 5 565.6
4 442 500 521.9 13 110 5 726.3
5 436 800 528.8 12 750 5 887.1
6 431 300 535.5 12 410 6 047.8
7 426 100 542.0 12 090 6 208.5
8 421 200 548.3 11 780 6 369.3
9 416 500 554.5 11 490 6 530.0
10 412 100 560.5 11 220 6 690.7
11 407 800 566.3 10 950 6 851.4
12 403 900 571.8 10 700 7 012.3
13a 400 000 577.4 10 460 7 173.1
13b 400 000 577.4 10 460 7 173.1
13c 400 000 577.4 10 460 7 173.1
14 396 300 582.8 10 230 7 333.8
15 392 800 588.0 10 010 7 494.5
16 389 400 593.1 9 800 7 655.3
17 386 100 598.1 9 600 7 816.0
18 383 000 603.0 9 410 7 976.7
19 380 000 607.8 9 220 8 137.5
20 377 100 612.4 9 040 8 298.2
21 374 300 617.0 8 870 8 458.9
22 371 600 621.4 8 710 8 619.6
23 369 100 625.7 8 550 8 780.4
24 366 600 630.0 8 390 8 941.1
25 364 200 634.1
231 000 999.7
8 250 9 101.8
In this particular installation the existing Main-1 differential relay is using
the traditional approach for differential current calculation, where y/d
connected interposing CTs are used on star-connected power transformer
Application of the Method 79
windings. Thus, this relay is calculating differential currents for OLTC
position 19 as given in the following equation:
_ 1 1_ 400 1_ 220
1 1
_ 2 0( 150 ) 2 _ 400 0( 150 ) 2 _ 220 607.8 999.7
_ 3 3_ 400 3_ 220
Id L IL IL
Id L M IL M IL
Id L I I L L
= ⋅ − ° ⋅ + ⋅ − ° ⋅
(5.5)
Note that for such a solution simply the third winding (i.e. tertiary delta
winding) is taken as reference winding for phase angle compensation. This
is another possible solution to calculate differential currents for this autotransformer,
but with some drawbacks as explained in Section 5.2.
In the PST operating mode the phase angle shift is introduced between the
no-load voltages from the two sides, as shown in Figure 10. Column one in
Table 14 represents the available OLTC positions, in this case 25. Column
three defines the base current for the transformer 400kV side. The 220kV
side base current is constant for all positions and has a fixed value of
999.7A. Finally column eight in Table 14 shows how the no-load phase
angle shift varies across the PST for different OLTC positions.
Note that the phase angle shift on the PST rating plate is given with a
positive value when the 220kV side no-load voltage leads the 400kV side
no-load voltage [35] (i.e. advanced mode of operation). Therefore if the
phase shift from Table 14 is associated with the 220kV side (i.e. the
400kV side taken as reference side with zero degree phase shift) the angle
values from the rating plate must be taken with a minus sign. Due to the
existence of a tertiary delta winding the zero sequence currents must be
eliminated, thus M0 matrices shall be used on both PST sides. The
equation for the PST mode of operation for OLTC position 19 is presented
here:
_ 1 1_ 400 1_ 220
1 1
_ 2 0(0 ) 2 _ 400 0( 3.11 ) 2 _ 220 563.3 999.7
_ 3 3 _ 400 3 _ 220
Id L IL IL
Id L M IL M IL
Id L I I L L
= ⋅ ° ⋅ + ⋅ − ° ⋅
(5.6)
Even in the PST operating mode the traditional approach for transformer
differential current calculation can be used, where y/d connected
interposing CTs are used on star-connected power transformer windings.
80 Chapter 5
In that case the relay can calculate the differential currents for OLTC
position 19 as given in the following equation:
_ 1 1_ 400 1_ 220
1 1
_ 2 0( 150 ) 2 _ 400 0( 153.11 ) 2 _ 220 563.3 999.7
_ 3 3_ 400 3_ 220
Id L IL IL
Id L M IL M IL
Id L I I L L
= ⋅ − ° ⋅ + ⋅ − ° ⋅
(5.7)
Table 14: Rating plate data in PST operating mode
400kV Side
220kV Side 10.5kV Side
OLTC Angle
Position
U[V] I[A] U[V] I[A] U[V] I[A] Θ[deg]
1 375 100 615.7 9 030 8 307.2 -4.48
2 377 200 612.2 9 150 8 201.4 -4.19
3 379 400 608.8 9 270 8 097.3 -3.89
4 381 500 605.4 9 390 7 995.1 -3.57
5 383 600 602.2 9 510 7 895.0 -3.24
6 385 800 598.7 9 630 7 796.8 -2.89
7 387 900 595.4 9 750 7 700.6 -2.52
8 390 000 592.2 9 870 7 606.8 -2.14
9 392 000 589.1 9 990 7 515.1 -1.75
10 394 100 586.0 10 110 7 426.0 -1.33
11 396 100 583.0 10 230 7 339.0 -0.91
12 398 100 580.2 10 350 7 254.7 -0.46
13a 400 000 577.4 10 460 7 173.1 0.00
13b 400 000 577.4 10 460 7 173.1 0.00
13c 400 000 577.4 10 460 7 173.1 0.00
14 401 900 574.7 10 580 7 093.9 0.48
15 403 700 572.1 10 690 7 017.7 0.97
16 405 400 569.7 10 810 6 944.5 1.48
17 407 000 567.4 10 920 6 874.1 2.01
18 408 600 565.3 11 030 6 806.8 2.55
19 410 000 563.3 11 130 6 742.7 3.11
20 411 300 561.5 11 230 6 681.9 3.69
21 412 500 559.8 11 330 6 624.4 4.28
22 413 600 558.4 11 420 6 570.2 4.88
23 414 500 557.1 11 510 6 519.6 5.49
24 415 300 556.1 11 600 6 472.7 6.12
25 416 000 555.2
231 000 999.7
11 670 6 429.4 6.76
81
Chapter 6
Evaluation of the Method with
Disturbance Recording Files
The new method for calculation of the differential currents has been
evaluated on a number of disturbance recording (DR) files captured in the
field in pre-existing PST installations.
6.1 PST in Žerjavinec Substation, Croatia
This 400MVA, 400/220kV PST has been in full commercial operation in
Žerjavinec Substation since July 2004. Since then numerous disturbance
records have been captured by existing numerical differential relays during
external faults and normal through-load conditions. These records have
been used to check the stability of the new differential protection method.
The current recordings presented below were captured by a numerical
differential relay with a sampling rate of twenty samples per power system
cycle. More information about this PST can be found in Section 2.3 and
Section 5.8.
An overview of the relevant part of the Croatian power grid and locations
of the four presented external faults are shown in Figure 31.
82 Chapter 6
Figure 31: Location of external faults around Žerjavinec Substation.
Table 15 provides a summary of the presented DR files.
Table 15: Summary of the presented DR files
Type of captured DR file
Ext. Fault
#1
Ext. Fault
#2
Ext. Fault
#3
Ext. Fault #4
Through-
Load
Type of
Fault
L3-Ground L1-Ground L2-Ground L2L3-Ground NA
Fault
Position
Cirkovce
OHL
Mraclin
OHL
Heviz 1
OHL
110kV
Busbar
NA
OLTC
Position
25 25 18 13 1
Θ 6,76o 6,76o 2,55o 0o -4,48o
Ib400 555,2A 555,2A 565,3A 577,4A 615,7A
Ib220 999.7A 999.7A 999.7A 999.7A 999.7A
Evaluation of the Method with Disturbance Recording Files 83
The recorded currents were imported into a MATLAB® (MATLAB is a
trade mark registered by The MathWorks; additional information can be
found at www.mathworks.com ) model and the following figures show the
result of the calculation with the new differential protection method.
In the following five figures, for every presented DR file from this PST
installation, the following waveforms are given:
♦ 400kV current waveforms;
♦ 220kV current waveforms;
♦ differential currents as seen by the numerical differential relay
(equation (5.4)), which compensates for the current magnitude
variations but is not able to compensate for the phase angle shift
variations (i.e. it can only provide the magnitude compensation for
different OLTC positions);
♦ differential currents in accordance with the new method (i.e.
equation (5.6)); and
♦ phase angle difference between the positive and negative sequence
current components from the two PST sides.
Note that on these figures there is a significant difference between y-axis
scales used on sub-figures showing the RMS values of the differential
currents calculated in accordance with the new method (e.g. 0-2%) and the
differential currents as seen by the existing differential relay using
equation (5.4) (e.g. 0-50%).
84 Chapter 6
Figure 32: External Fault #1, OHL Cirkovce, OLTC is on position 25.
Evaluation of the Method with Disturbance Recording Files 85
Figure 33: External Fault #2, OHL Mraclin, OLTC is on position 25.
86 Chapter 6
Figure 34: External Fault #3, OHL Heviz 1, OLTC is on position 18.
Evaluation of the Method with Disturbance Recording Files 87
Figure 35: External Fault #4, 110kV Busbar, OLTC is on position 13.
88 Chapter 6
Figure 36: Normal through-load condition, OLTC is on position 1.
The DR files have also been captured at the moment of the OLTC position
change in the PST operating mode. The following two figures provide
information about the behaviour of the new differential protection method
under such operating conditions. For both presented DR files, the
following waveforms are given:
♦ 400kV current waveforms;
♦ 220kV current waveforms;
♦ differential currents in accordance with the new method (i.e. by
using equation in accordance with (5.6)); and
♦ phase angle difference between the positive and negative sequence
current components from the two PST sides.
Evaluation of the Method with Disturbance Recording Files 89
3.6 3.65 3.7 3.75 3.8 3.85 3.9
-100
0
100
Waveforms of 400kV Currents
[%]
[sec]
iL1
iL2
iL3
3.6 3.65 3.7 3.75 3.8 3.85 3.9
-100
0
100
Waveforms of 220kV Currents
[%]
[sec]
iL1
iL2
iL3
3.6 3.65 3.7 3.75 3.8 3.85 3.9
0
0.5
1
1.5
RMS Diff Currents by Using New Method
[%]
[sec]
IdL1
IdL2
IdL3
3.6 3.65 3.7 3.75 3.8 3.85 3.9
0
1
2
[sec]
[deg]
Angle Difference between 220kV & 400kV Sides
PosSeq Currents
NegSeq Currents
Figure 37: OLTC tapping from position 16 to position 15.
Where:
♦ Number 1 indicates the instant of OLTC mechanism tapping from
position 16 to position 15.
♦ Number 2 indicates the instant when the new differential method
changes internal compensation to the values which correspond to
the new OLTC position 15.
1 2
90 Chapter 6
3.4 3.45 3.5 3.55 3.6 3.65 3.7
-100
0
100
Waveforms of 400kV Currents
[%]
[sec]
iL1
iL2
iL3
3.4 3.45 3.5 3.55 3.6 3.65 3.7
-100
0
100
Waveforms of 220kV Currents
[%]
[sec]
iL1
iL2
iL3
3.4 3.45 3.5 3.55 3.6 3.65 3.7
0
0.5
1
1.5
RMS Diff Currents by Using New Method
[%]
[sec]
IdL1
IdL2
IdL3
3.4 3.45 3.5 3.55 3.6 3.65 3.7
0
1
2
[sec]
[deg]
Angle Difference between 220kV & 400kV Sides
PosSeq Currents
NegSeq Currents
Figure 38: OLTC tapping from position 14 to position 15.
Where:
♦ Number 1 indicates the instant of OLTC mechanism tapping from
position 14 to position 15.
♦ Number 2 indicates the instant when the new differential method
changes internal compensation to the values which correspond to
the new OLTC position 15.
From all presented DR files it can be concluded that the new differential
protection method is stable for such special PST construction.
1 2
Evaluation of the Method with Disturbance Recording Files 91
6.2 PST Installed in Europe
In this section the DR files recorded on two identical PSTs positioned at
the beginning of two parallel 380kV overhead lines (OHL) in Europe are
presented. The transformers are of asymmetrical type, dual-core design.
The captured incident involved two simultaneous single-phase to ground
faults. On OHL #1 it was a phase L2 to ground fault and on OHL #2 it
was a phase L1 to ground fault. Existing protection schemes on both PSTs
maloperated during this incident. The first scheme maloperated because of
the Buchholz relay operation caused by the PST tank vibrations and the
second scheme maloperated because of the operation of the existing
differential protection relay. The rated quantities for these two identical
PSTs are listed below:
♦ Rated power: 1630MVA;
♦ Rated voltages: 400/400kV;
♦ Frequency: 50Hz;
♦ Angle variation: 0º - 18º (at no-load)
More information about this PST can be found in Section 5.6. The OLTC
was in position 30 when the faults occurred. Thus, from Figure 29 all
necessary information about the compensation values can be extracted.
The base current for this type of transformer is different on the two PST
sides and for this tap position their values are IBase_S= 2353A and IBase_L=
2257A. The PST no-load phase angle shift was 16.4o. For the exact
equation see (5.1).
The presented recordings were made by two existing numerical differential
relays having sampling rates of twelve samples per power system cycle.
The S- and L-side currents recorded by the relay were run in the
MATLAB model and the following figures show the result of the
calculation from the new differential protection method.
In the following two figures, for every presented DR file from this
installation, the following waveforms are given:
♦ S-side and L-side current waveforms;
♦ instantaneous differential currents waveforms calculated in
accordance with the new method;
♦ RMS differential currents calculated in accordance with the new
method; and
92 Chapter 6
♦ phase angle difference between the positive and negative sequence
current components from the two PST sides.
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
-20
-10
0
10
Waveforms of S-side Currents
[pu]
[sec]
iS1
iS2
iS3
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
-10
0
10
20
Waveforms of L-side Currents
[pu]
[sec]
iL1
iL2
iL3
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
-0.5
0
0.5
Waveforms of Diff Currents
[pu]
[sec]
IdL1
IdL2
IdL3
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
0
0.1
0.2
RMS Diff Currents
[pu]
[sec]
IdL1
IdL2
IdL3
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
-20
0
20
[sec]
[deg]
Angle Difference L-S
X: 0.4433
Y: -16.02
PosSeq
NegSeq
Figure 39: Evaluation of DR file for the first PST.
Evaluation of the Method with Disturbance Recording Files 93
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
-10
0
10
20
Waveforms of S-side Currents
[pu]
[sec]
iS1
iS2
iS3
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
-20
-10
0
10
Waveforms of L-side Currents
[pu]
[sec]
iL1
iL2
iL3
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
-0.5
0
0.5
Waveforms of Diff Currents
[pu]
[sec]
IdL1
IdL2
IdL3
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
0
0.1
0.2
RMS Diff Currents
[pu]
[sec]
IdL1
IdL2
IdL3
0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
-20
0
20
X: 0.4433
Y: -15.69
[sec]
[deg]
Angle Difference L-S
PosSeq
NegSeq
Figure 40: Evaluation of DR file for the second PST.
The two figures show that for this severe external fault the differential
current amplitude, calculated by using the new method, remains within
0.15pu (15%), while the bias current is bigger than 6pu (600%). That
clearly indicates that the new differential relays will remain stable during
this special external fault (see Figure 12).
94 Chapter 6
6.3 PST Installed in South America
In this section the differential current calculation will be made for a PST in
South America during an external fault. The transformer is of symmetrical
type, dual-core design. The rated quantities of the PST are listed below:
♦ Rated power: 400MVA;
♦ Rated voltages: 138/138kV;
♦ Frequency: 60Hz;
♦ Angle variation: ±21.66º (at no-load);
♦ Main CT ratio: 2000/1A; and
♦ Main CTs are connected in delta on both PST sides.
The PST has two protection schemes, as recommended by [37]. In the
Main-1 protection scheme the current transformers are star connected,
while in the Main-2 protection scheme the S- and L-side CTs are delta
connected. The PST transformer Main-1 protection scheme is shown in
Figure 41, and the Main-2 protection scheme is shown in Figure 42. Note
that in both figures protection device designations in accordance with
IEEE C37.2-1996 standard have been used.
Figure 41: Main-1 protection scheme of the transformer.
Evaluation of the Method with Disturbance Recording Files 95
Figure 42: Main-2 protection scheme of the transformer.
The transformer is of a symmetrical type, dual-core design. The base
current for this type of transformer is equal for the source and load side.
The currents measured in the relay are in secondary amperes, so in the
calculation of the base current the current transformer ratio must be
included as well as the fact that the main CT’s are delta connected. This is
compensated in the algorithm of the new universal differential protection
by multiplying the base secondary current by 3 .
b
400MVA 1
I = × × 3=1.449A
3×138kV 2000
The main CTs are externally connected in delta on both sides of the
transformer, meaning that they do not change the phase angle shift
between S- and L-side CT secondary currents. The external fault occurred
while the PST phase angle shift was at 5.47o.
96 Chapter 6
The current recording presented was made by a numerical Main 2
differential relay with twelve samples per power system cycle. The
differential relay maloperated during this external fault.
The S- and L-side currents recorded by the relay were run in the
MATLAB model and Figure 43 shows the result of the calculations made
by the new differential protection method.
In this figure the following waveforms are given:
♦ S-side and L-side current waveforms;
♦ instantaneous differential currents waveforms calculated in
accordance with the new method;
♦ RMS differential currents calculated in accordance with the new
method; and
♦ phase angle difference between the positive and negative sequence
current components from the two PST sides.
The figure shows that the new RMS differential currents remain within
0.025pu (2.5%), indicating that the differential relay using the new method
would remain stable during this external fault.
Evaluation of the Method with Disturbance Recording Files 97
0.04 0.06 0.08 0.1 0.12 0.14 0.16
-4
-2
0
2
4
Waveforms of S-side Currents
[pu]
[sec]
iS1
iS2
iS3
0.04 0.06 0.08 0.1 0.12 0.14 0.16
-4
-2
0
2
4
Waveforms of L-side Currents
[pu]
[sec]
iL1
iL2
iL3
0.04 0.06 0.08 0.1 0.12 0.14 0.16
-0.1
0
0.1
Waveforms of Diff Currents
[pu]
[sec]
IdL1
IdL2
IdL3
0.04 0.06 0.08 0.1 0.12 0.14 0.16
0
0.05
RMS Diff Currents
[pu]
[sec]
IdL1
IdL2
IdL3
0.04 0.06 0.08 0.1 0.12 0.14 0.16
-5
0
5
X: 0.1
Y: -5.729
Angle Difference L-S
[deg]
[sec]
PosSeq
NegSeq
Figure 43: Evaluation of DR file from the PST installed in South America.
6.4 PST Installed in North America
In this section the differential current calculation will be made for a PST in
North America during different operating conditions. The transformer is of
symmetrical type, single-core design. In order to limit the through going
short circuit currents one three-phase series reactor is installed within the
PST tank. The ratings of the PST are listed below:
♦ Rated power: 450MVA;
♦ Rated voltages: 138/138kV;
♦ Frequency: 60Hz;
♦ Angle variation: ±58.0º (at no-load); and,
♦ Number of OLTC steps: 33 (i.e. ±16).
98 Chapter 6
More information about this PST can be found in Section 5.7. The base
current for this transformer is 1883A primary and is equal for the source
and the load side. The recordings were captured by an existing PST
numerical differential protection relay at a sampling rate of 20 samples per
power system cycle.
In the following three figures, for every presented DR file from this PST
installation, the following waveforms are given:
♦ S-side and L-side current waveforms;
♦ instantaneous differential currents waveforms calculated in
accordance with the new method; and
♦ RMS differential currents calculated in accordance with the new
method.
Energizing of the PST Together with a 138kV Cable
This PST is connected in series with a 138kV cable on the S-side. This
causes the energizing currents to have special wave shapes. Note that
manufacturer recommendations required that this PST is always energized
with 0o phase shift (i.e. tap position 17). The recorded S- and L-side
currents were run in the MATLAB model and the results of the
calculations are presented in Figure 44.
The individual phase inrush currents are obviously rich in harmonics but
the calculated differential current waveforms have properties of “classical
power transformer inrush currents”. Thus, the traditional methods (i.e.
second harmonic blocking or waveform blocking) can be used to restrain
the differential protection during inrush conditions.
Evaluation of the Method with Disturbance Recording Files 99
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18
-100
0
100
S-side Current Waveforms
[%]
[sec]
L1
L2
L3
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18
-200
0
200
L-side Current Waveforms
[%]
[sec]
L1
L2
L3
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18
-200
0
200
Diff Current Waveforms
[%]
[sec]
L1
L2
L3
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18
0
50
100
RMS Diff Currents
[%]
[sec]
L1
L2
L3
Figure 44: Energizing of the PST and a cable.
Off-rated Frequency
This PST was involved in the USA blackout on 2003-08-14. During the
final stages of this blackout a recording was captured, which shows that
the PST was overloaded and that the frequency of the captured current
waveform was much lower than the 60Hz what is the rated power system
frequency. From the captured current waveforms, by using the current
zero-crossings, the frequency of the current signal can be estimated to be
around 53.5Hz. Consequently it can be concluded that the frequency of the
voltage signal was even lower in some parts of the surrounding network.
Note that during this disturbance the OLTC was in the mid-position (i.e. 0o
phase shift). The recorded S- and L-side currents were run in the
MATLAB model and results of the calculations are presented in Figure 45.
100 Chapter 6
0.04 0.05 0.06 0.07 0.08 0.09 0.1
-200
0
200
S-side Current Waveforms
[%]
[sec]
L1
L2
L3
0.04 0.05 0.06 0.07 0.08 0.09 0.1
-200
0
200
L-side Current Waveforms
[%]
[sec]
L1
L2
L3
0.04 0.05 0.06 0.07 0.08 0.09 0.1
-2
0
2
Diff Current Waveforms
[%]
[sec]
L1
L2
L3
0.04 0.05 0.06 0.07 0.08 0.09 0.1
0
1
2
RMS Diff Currents
[%]
[sec]
L1
L2
L3
Figure 45: Off-nominal frequency through load condition.
The calculated differential current waveforms demonstrate that the new
differential protection method was not influenced by the off-ratedfrequency
condition. It is as well interesting to note that the IEC standards
typically suggest the operation range of the protection relays shall be
within ±5Hz from the rated power system frequency.
Evaluation of the Method with Disturbance Recording Files 101
Through Load Condition
Finally, the through load condition for a 4o phase angle shift (the PST in
advanced operating mode) is shown in Figure 46.
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14
-100
0
100
S-side Current Waveforms
[%]
[sec]
L1
L2
L3
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14
-100
0
100
L-side Current Waveforms
[%]
[sec]
L1
L2
L3
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14
-2
0
2
Diff Current Waveforms
[%]
[sec]
L1
L2
L3
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14
0
1
2
RMS Diff Currents
[%]
[sec]
L1
L2
L3
Figure 46: Through load condition for a 4o phase angle shift for the PST in
advance operating mode.
The new differential protection method also performs well in this case.
103
Chapter 7
Evaluation of the Method with
Simulation Files
Simulation of a symmetrical, dual-core PST (see Section 2.3) will be
presented based on data from an actual PST installation in Europe.
7.1 Setting up the Simulation
The simulation was preformed with the Real-Time Digital Simulator,
RTDS® (RTDS is a trade mark registered by RTDS Technologies;
additional information can be found at www.rtds.com). A single line
diagram (SLD) of the simulated network, together with the PST rated data,
is shown in Figure 47. Note that a path parallel with the PST is included in
the simulation model, but is not shown in Figure 47.
TS 400 kV; 50 kA
400 kV nadzemni vod
20 km
1400 MVA
±25°
transformator s regulacijom
kuta
400 kV nadzemni vod
10 km
TS 400 kV; 50 kA
Figure 47: SLD for the simulated power system.
400kV OHL
10km
400kV OHL
20km
400kV; 50kA 400kV; 50kA
±25o
PST
104 Chapter 7
PST Data
The simulated PST is of symmetric type, dual-core design. Due to its size
it consists of six single-phase transformers. Each single-phase transformer
is located in its own tank. The tanks are interconnected with oil ducts.
The main PST data used for the simulation is shown below:
♦ Rated power: 1400MVA;
♦ Rated voltages: 400/400kV;
♦ Angle variation: ±25o (at no-load).
Each PST phase was simulated as two separate single-phase transformers.
The data applied for the series transformers included:
♦ series unit primary winding with a rated voltage of 100kV (i.e.
50kV for each of the two split windings);
♦ delta connected, secondary winding of the series unit with rated
voltage of 138.6kV;
♦ rated power of one phase series transformer 609.10MVA;
♦ leakage reactance of the transformer set to 0.3pu; and,
♦ no load losses of 0.000106pu.
The data applied for the excitation transformers included:
♦ exciter unit primary winding with a rated voltage of 225kV and a
fixed number of turns;
♦ exciter unit secondary winding with a rated voltage of 80kV and a
variable number of turns (0% - 100%);
♦ rated power of one phase excitation transformer 594.7MVA;
♦ leakage reactance of the transformer set to 0.6pu; and,
♦ no load losses of 0.0093pu.
A detailed SLD of the PST is shown in Figure 49.
Overhead Line Data
The simulated PST was connected to the rest of the system via two quite
short 400kV overhead lines. The line on the source side of the transformer
was 10km long, and on the load side of the transformer the line was 20km
long. Both of the lines can be heavily loaded up to 2100MVA in real life.
Evaluation of the Method with Simulation Files 105
In the simulation case the lines were simulated with a T – line model. The
loading of the lines in the simulation was higher, due to the fact that the
transformer was simulated for overload conditions. The parameters entered
for the first line are shown in Figure 48. The parameters for the second line
are the same with only exclusion for the length of the line.
Figure 48: 400kV OHL data.
Sources and Loads
Two sources are used in the simulation; the first source feeds the first line
on the source side of the PST, and the second source is located at the end
of the second line on the load side of the PST. Both sources are 400kV
with an initial phase shift of 0o. The source impedance type was R/L, with
the positive sequence impedance set to 8 and the zero sequence
impedance set to 16. Each source is connected to a bus, loaded with a
resistive load of 1200/phase.
Parallel Path
In order to demonstrate the influence of the phase shift of the PST a
parallel path had to be introduced in the circuit connecting the two buses
(i.e. in parallel with the PST and two 400kV OHLs). The parallel line is
simulated with a PI section model.
106 Chapter 7
7.2 Simulated Faults
Once the simulation case was built and compiled, the simulation could be
started. The main goal of the simulation was to obtain current waveforms
on both sides of the transformer during a fault (external or internal) for
different phase shift angles between the transformer ends. The current
measurement was performed on circuit breakers on both sides of the
transformer. In this simulation case the current transformers were not
simulated, so the influence of the CT saturation during a fault could not be
obtained.
The external faults (F1 and F2) are simulated on the source and load bus.
The internal faults (F3 and F4) are simulated on the series transformer as
well as on the regulating (i.e. boosting) transformer. The simulated fault
points are shown in Figure 49. For each fault point four different fault
types are simulated: L1–L2–L3, L1–L2, L2–L3–Ground and L3–Ground.
Once the currents for each fault are obtained the next step involved
calculation of the differential currents. The calculations were made with
the MATLAB model of the new differential current measurement
technique explained in Section 4.5. The sampling rate of 400 samples per
power system cycle was used in output files from the simulator.
The first group of faults was simulated for a 25o no-load phase angle shift
in the advanced operating mode. This is the highest phase angle shift that
could be obtained for this particular PST. All above mentioned fault types
in all four fault location points are simulated.
The second group of faults is simulated for a 15o no-load phase angle shift
in the advanced operating mode. All above mentioned fault types in all
four fault location points are simulated.
The third group of faults is simulated for a 2.5o no-load phase angle shift
in the advanced operating mode. All above mentioned fault types in all
four fault location points are simulated. For this phase shift angle it can be
shown that the new differential protection may not be sensitive enough for
an internal single-phase to ground fault at location F3, as described in the
following section.
Evaluation of the Method with Simulation Files 107
Figure 49: SLD for the simulated PST and simulated fault locations.
Selected results are presented in the following figures.
108 Chapter 7
External Faults on the Source Bus (fault point F1) for a 25o
Phase Shift in the Advanced Operating Mode
External L1-L2 fault at F1, Θ=25o
4 5 6 7 8 9 10 11 12
500
0
500
IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
500
0
500
IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 50: Individual phase currents during this ph-ph external fault
Evaluation of the Method with Simulation Files 109
4 5 6 7 8 9 10 11 12
4
2
0
2
4
id_A
id_B
id_C
Diff Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
1
2
3
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 51: Differential currents during this ph-ph external fault
The above waveforms show that the RMS differential currents remain
within approximately 0.02pu (2%), indicating that the differential relay
using the new method would remain fully stable during this external fault.
110 Chapter 7
External L1-L2-L3 fault at F1, Θ=25o
4 5 6 7 8 9 10 11 12
1000
0
1000
IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
1000
500
0
500
1000
IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 52: Individual phase currents during this external three-phase fault
Evaluation of the Method with Simulation Files 111
4 5 6 7 8 9 10 11 12
4
2
0
2
4
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
0.5
1
1.5
2
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 53: Differential currents during this external three-phase fault
The above waveforms show that the RMS differential currents remain
within 0.015pu (1.5%), indicating that the differential relay using the new
method would remain fully stable during this external fault.
112 Chapter 7
External L2-L3-Ground fault at F1, Θ=25o
4 5 6 7 8 9 10 11 12
500
0
500 IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
500
0
500 IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 54: Individual phase currents during this external fault
Evaluation of the Method with Simulation Files 113
4 5 6 7 8 9 10 11 12
4
2
0
2
4
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
1
2
3
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 55: Differential currents during this external fault
The above waveforms show that the RMS differential currents remain
within 0.025pu (2.5%), indicating that the differential relay using the new
method would remain fully stable during this external fault.
114 Chapter 7
External L3-Ground fault at F1, Θ=25o
4 5 6 7 8 9 10 11 12
500
0
500 IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
500
0
500 IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 56: Individual phase currents during this external fault
Evaluation of the Method with Simulation Files 115
4 5 6 7 8 9 10 11 12
4
2
0
2
4
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
0.5
1
1.5
2
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 57: Differential currents during this external fault
The above waveforms show that the RMS differential currents remain
within 0.017pu (1.7%), indicating that the differential relay using the new
method would remain fully stable during this external fault.
116 Chapter 7
Internal faults on the Secondary Side of the Excitation
Transformer (fault point F3) for a 25o Phase Shift in the
Advanced Operating Mode
Internal L1-L2 fault at F3, Θ=25o
4 5 6 7 8 9 10 11 12
200
0
200 IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
200
0
200 IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 58: Individual phase currents during this internal fault
Evaluation of the Method with Simulation Files 117
4 5 6 7 8 9 10 11 12
200
0
200
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
100
200
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 59: Differential currents during this internal fault
The above waveforms show that the RMS differential currents are big
during the internal fault (183%), indicating that the differential relay using
the new method would operate for this internal fault.
118 Chapter 7
Internal L2-L3-Ground fault at F3, Θ=25o
4 5 6 7 8 9 10 11 12
200
0
200 IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
200
0
200 IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 60: Individual phase currents during this internal fault
Evaluation of the Method with Simulation Files 119
4 5 6 7 8 9 10 11 12
350
0
350
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
100
200
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 61: Differential currents during this internal fault
The above waveforms show that the RMS differential currents are big
during the internal fault (190%), indicating that the differential relay using
the new method would operate for this internal fault.
120 Chapter 7
Internal L3-Ground fault at F3, Θ=25o
4 5 6 7 8 9 10 11 12
200
0
200 IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
200
0
200 IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 62: Individual phase currents during this internal fault
Evaluation of the Method with Simulation Files 121
4 5 6 7 8 9 10 11 12
250
0
250
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
50
100
150
200
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 63: Differential currents during this internal fault
The above waveforms show that the RMS differential currents are big
during the internal fault (160%), indicating that the differential relay using
the new method would operate for this internal fault.
122 Chapter 7
Internal Faults on the Secondary Side of the Excitation
Transformer (fault point F3) for a 2.5o Phase Shift in the
Advanced Operating Mode
Internal L3-Ground fault at F3, Θ=2.5o
4 5 6 7 8 9 10 11 12
20
0
20 IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
20
0
20 IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 64: Individual phase currents during this internal fault
Evaluation of the Method with Simulation Files 123
4 5 6 7 8 9 10 11 12
4
0
4
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
1
2
3
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 65: Differential currents during this internal fault
It can be seen from the above waveforms that for the internal earth-fault on
the secondary side of the excitation transformer for a very small no-load
phase angle shift, the differential current magnitudes are smaller than
2.5%. The main reason is the small number of active turns on the
secondary side of the excitation transformer. Thus, additional protection
relays like excitation transformer secondary side neutral point earth-fault
protection shall be used to detect and clear such faults. For an alternative
solution refer to Chapter 11.
124 Chapter 7
Internal Faults on the Primary Side of the Excitation
Transformer (fault point F4) for a 2.5o Phase Shift in the
Advanced Operating Mode
Internal L3-Ground fault at F4, Θ=2.5o
4 5 6 7 8 9 10 11 12
900
0
900
IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
900
0
900
IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 66: Individual phase currents during this internal fault
Evaluation of the Method with Simulation Files 125
4 5 6 7 8 9 10 11 12
1700
0
1700
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
500
1000
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 67: Differential currents during this internal fault
The above waveforms show that the RMS differential currents are quite
big during this internal fault (11.5pu), indicating that the differential relay
using the new method would operate for this internal fault.
126 Chapter 7
External Faults on the L Side Bus (fault point F2) for a 2.5o
Phase Shift in the Advanced Operating Mode
External L3-Ground fault at F2, Θ=2.5o
4 5 6 7 8 9 10 11 12
400
0
400
IS1
IS2
IS3
S-Side Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
400
0
400
IL1
IL2
IL3
L-Side Current Waveforms
Cycles
Current [%]
Figure 68: Individual phase currents during this external fault
Evaluation of the Method with Simulation Files 127
4 5 6 7 8 9 10 11 12
2
0
2
id_A
id_B
id_C
Differential Current Waveforms
Cycles
Current [%]
4 5 6 7 8 9 10 11 12
0
0.5
1
ID_A
ID_B
ID_C
RMS Differential Currents
Cycles
Current [%]
Figure 69: Differential currents during this external fault
The above waveforms show that the RMS differential currents remain
within 0.01pu (1.0%), indicating that the differential relay using the new
method would remain fully stable during this external fault.
129
Chapter 8
Implementation Possibilities
In this chapter, implementation possibilities for the presented differential
protection method will be discussed.
8.1 Mixed Solution (Analogue + Numerical)
In the previous part of this document the following items were discussed:
♦ special converter transformers (Figure 2);
♦ problems which arise when standard numerical differential
protection is applied for differential protection of such special
converter transformers (Section 3.2); and,
♦ properties of M and M0 matrix transformations (Section 4.7).
If these three elements are combined it is possible to design improved
differential protection for special converter transformers by using a
mixture of analogue and numerical techniques.
If one is able to provide rotation, in the appropriate direction, of the threephase
currents externally to compensate for the additional, non-standard
phase angle shift Ψ, the net transformer connection as seen by the
numerical differential relay reverts back to the standard power transformer
vector group. This allows for protection of the converter transformer as if
it did not have special “HV winding extensions”. The standard numerical
transformer differential relay software features can then be used in the
usual way to provide differential protection for this special converter
transformer, as if it were of a standard vector group design (e.g. Dy11d0
for the special converter transformer shown in Figure 2a).
130 Chapter 8
Rotation of Three-Phase Currents by Angle Ψ, by Using
Analogue Technique
Busbar protection summation type design has been used by different relay
manufacturers for decades. The auxiliary summation CT used for this type
of design has three primary windings and one secondary winding. It was
found out that by using a set of three identical auxiliary summation CTs
one can provide external rotation by angle Ψ without changing the main
CT secondary current magnitude (e.g. with an overall ratio 1/1A or 5/5A).
The necessary connections, for the external rotation of the three-phase
currents by angle Ψ in the anticlockwise direction are shown in Figure 70.
In the left-hand side of Figure 70, wiring comes from the main CT and
wiring from the right-hand side of Figure 70 shall be connected to the
numerical differential relay.
Figure 70: Auxiliary CT set connections for anticlockwise
(i.e. positive) rotation by angle Ψ.
Implementation possibilities 131
By using ampere-turn balancing, the following equation can be written for
the auxiliary summation CT connections shown in Figure 70.
1_ 1 2 3 1_
1
2 _ 3 1 2 2 _
4
3_ 2 3 1 3_
IL DR N N N IL CT
IL DR N N N IL CT
N
IL DR N N N IL CT
− −
= ⋅ − − ⋅
− −
(8.1)
where:
♦ IL1_CT is the main CT secondary current in phase L1;
♦ IL1_DR is the phase L1 current, rotated by angle Θ in an
anticlockwise direction, which shall be connected to the
differential relay; and,
♦ N1, N2, N3 and N4 are turn numbers of the four windings within
each auxiliary summation CT.
Obviously if one can choose the auxiliary summation CT turn numbers in
such a way that:
1 2 3
1
3 1 2 0( )
4
2 3 1
N N N
N N N M
N
N N N
− −
⋅ − − = Ψ
− −
(8.2)
the connections shown in Figure 70 will provide the necessary rotation of
the three-phase currents by angle Ψ in an anticlockwise (i.e. positive)
direction without changing the main CT secondary current magnitude (e.g.
with overall ratio 1/1A or 5/5A). Sometimes, within the same application,
the rotation in clockwise direction by angle Ψ is needed as well. By using
the properties of the M0 matrix transformation, it can be shown that the
same auxiliary summation CT set can be used, but it shall be connected as
shown in Figure 71. Thus, the connection shown in Figure 71 will provide
the necessary rotation of the three-phase currents by angle Ψ in a
clockwise (i.e. negative) direction.
132 Chapter 8
Figure 71: Auxiliary CT set connections for clockwise
(i.e. negative) rotation by angle Ψ.
Table 16 gives example of possible design solutions regarding the turn
numbers within auxiliary summation CTs for the most typical, additional
phase angle shifts Ψ from converter transformers used in practice.
Table 16: Auxiliary summation CT design details
Auxiliary
Summation CT
Turn Numbers
Auxiliary Summation
CT Performance
Design
Phase
Angle
Shift Ψ N1 N2 N3 N4
Achieved
Overall
Ratio
Achieved
Rotation
Angle
±7.5o 26 16 10 39 1/1.009 ±7.59o
±15o 26 19 7 40 1/1.009 ±14.92o
Implementation possibilities 133
Small CT secondary current magnitude errors of less than 1% and small
phase angle errors of approximately 0.1o caused by imperfection in the
auxiliary summation CT design will not cause any significant false
differential current in practical installations.
Note that auxiliary summation CTs are designed to remove the zero
sequence current from the protected power transformer side where they are
connected. Thus, the zero sequence currents will not be available within
the differential relay from that power transformer side.
Differential Protection Solution for a Transformer with Ψ=15o
The overall differential protection solution and all relevant data for this
transformer application (including power transformer vector diagram) are
shown in Figure 72. Review of the power transformer vector diagram
shows that the LV side no-load voltages shall be rotated by 15o in an
anticlockwise direction in order to be in phase with the HV side no-load
voltages. Thus, the same rotation shall be provided for the LV side
currents for the differential protection when the HV side is selected as the
reference winding. To do that, one set of auxiliary summation CTs that
provide current rotation by 15o in anticlockwise direction are required.
This auxiliary CT set is used in order to put the transformer overall phase
shift, as seen by the differential relay, back to the standard Yy0 vector
group. The main CT secondary current magnitudes are not altered at all on
the LV side. The numerical differential relay software features can then be
used in the usual way to compensate for this special converter transformer,
as if it were a standard two-winding transformer with vector group Yy0.
All other relevant application data such as main CT ratios and power
transformer rated power, rated currents and rated voltages shall be used as
they are in the actual installation to derive the differential relay settings.
134 Chapter 8
Figure 72: Differential protection solution for a transformer with 15o phase shift.
Differential Protection Solution for a 24-pulse Converter
Transformer
This converter transformer is quite special because within the same
transformer tank, two three-phase transformers, of similar design as shown
in Figure 3, are put together. The first internal transformer has vector
group Zy11¾d10¾. The second internal transformer has vector group
Zy0¼d11¼. Such an arrangement gives an equivalent five-winding power
transformer with a 15o phase angle shift between LV windings of the same
connection type. The power transformer construction details and
corresponding phasor diagram for positive sequence no-load voltages are
shown in Figure 73.
Implementation possibilities 135
Zy11¾d10¾ Zy0¼d11¼
HV1-Z
LV1-Y LV1-D LV2-Y LV2-D
HV2-Z
HV2-Z
LV2-D
LV2-Y
HV1-Z
LV1-D
LV1-Y
0
1
2
11
10
0
1
2
11
10
Figure 73: 24-pulse converter transformer with positive sequence phasor diagram.
From the transformer phasor diagram it can be seen that:
♦ LV1-Y and LV1-D sides shall be rotated by 7.5o in a clockwise
direction; and
♦ LV2-Y and LV2-D sides shall be rotated by 7.5o in an
anticlockwise direction,
in order to put the 24-pulse converter transformer overall phase shift, as
seen by the differential relay, back to the standard Yy0d11y0d11 vector
group.
136 Chapter 8
For such transformers, four sets of auxiliary summation CTs that provide
current rotation by 7.5o are required. Two sets, connected for current
rotation in a clockwise direction shall be applied on the two LV sides of
the first internal transformer. Two sets, connected for current rotation in an
anticlockwise direction shall be applied on the two LV sides of the second
internal transformer. These auxiliary CTs are used in order to put the 24-
pulse converter transformer overall phase shift, as seen by the differential
relay, back to the standard Yy0d11y0d11 vector group. Note that all
twelve pieces of auxiliary summation CTs used for this application are
exactly the same. The main CT secondary current magnitudes are not
altered on any of the four LV sides. Hence, the numerical differential relay
software features can now be used in the usual way to compensate for this
special converter transformer, as if it were a standard five-winding
transformer with vector group Yy0d11y0d11. All other relevant
application data like main CT ratios and 24-pulse converter transformer
windings rated power, rated currents and rated voltages shall be used as
they are stated on respective equipment rating plates to derive the
differential relay settings. The overall differential protection solution is
shown in Figure 74. Note that in this figure, protection device designations
in accordance with IEEE C37.2-1996 standard have been used.
Summary about Mixed Solution
Standard numerical power transformer differential relays can be used to
provide differential protection for the special converter transformers with
non-standard, but fixed, phase angle shift. The only pre-request is that the
external auxiliary CTs are used to compensate for the additional phase
angle shift Ψ, typically caused by special arrangements of the converter
transformer HV winding. Once this compensation is done externally, the
numerical differential relay shall be set and applied as if the special
converter transformer was designed with the standard vector group
connection.
Using the presented solution, the differential relay is ideally balanced
during all through load conditions and for all types of external faults.
Hence, no false differential current will be measured by the differential
relay. This will enable the end user to set the minimum differential
protection pickup to a quite sensitive level (e.g. 15-20%), ensuring
sensitive protection for low-level transformer internal faults such as
interturn faults. The approach presented is not dependent on the particular
Implementation possibilities 137
special converter transformer construction details, and by using the
described principle, it is possible to provide differential protection for any
three-phase power transformer with non-standard, but fixed phase angle
shift, which can not be directly covered by the setting facilities of the
numerical transformer differential protection relays.
Zy11¾d10¾ Zy0¼d11¼
HV1-Z
LV1-Y LV1-D LV2-Y LV2-D
HV2-Z
87T
50/51
50/51
50/51
50/51 49
50N/51N
50BF
50/51
Diff
Relay
Set Yy0d11y0d11
Four Aux
CT Sets
+7.5o
+7.5o
-7.5o
-7.5o
Figure 74: Overall protection solution for 24-pulse converter transformer.
138 Chapter 8
8.2 Fully Numerical Implementation
The first possibility for numerical implementation would be to mimic the
mixed solution presented in the previous section. The only difference from
the mixed solution would be that the functionality of the summation
interposing CTs is implemented in the relay software for processing the
analogue input values, while the traditional transformer differential
function is still used inside of the numerical relay in order to execute the
differential protection algorithm.
The second possibility for numerical implementation would be to perform
all compensation within the differential protection function itself. One
such possible solution for a PST application is shown in Figure 75, and a
corresponding flow chart is given in Figure 76.
The following abbreviations are used in Figure 75:
♦ DFF = “Digital Fourier Filter”;
♦ A/D = “Analogue to digital converter”;
♦ Max = “Maximum of”;
♦ BCD = “Binary Coded Decimal”; a group of five or six binary
signals, coded in a special way, in order to monitor the OLTC
position; and
♦ mA = “milli-Ampere”; a low level current signal (e.g. 4-20mA)
used in practice as an alternative solution for monitoring of the
OLTC position.
Implementation possibilities 139
1
_ 1
1_ 1 1 _ 1
2_ 1 1 _ 1
2_ 1 1 _ 1
1
( ) W
b W
L W W ZS W
L W W ZS W
L W W ZS W
I
I k I
M I k I
I k I
− ⋅
⋅ Θ ⋅ − ⋅
− ⋅
2
_ 2
1_ 2 2 _ 2
2_ 2 2 _ 2
2_ 2 2 _ 2
1
( ) W
b W
L W W ZS W
L W W ZS W
L W W ZS W
I
I k I
M I k I
I k I
− ⋅
⋅ Θ ⋅ − ⋅
− ⋅
1_ 1
2 _ 1
3_ 2
IL W
IL W
IL W
1_ 2
2 _ 2
3 _ 2
IL W
IL W
IL W
Figure 75: Fully numerical implementation for PST differential protection.
140 Chapter 8
Figure 76: Flow chart for complete numerical implementation
of the PST differential protection.
141
Chapter 9
Transient Magnetizing Currents
As stated in Section 2.4 any abrupt change of the power transformer
terminal voltage will result in a transient current into the power
transformer. This transient current is generally termed inrush current and is
typically caused by:
♦ initial energization of the power transformer (initial inrush);
♦ voltage recovery after the clearing of an external, heavy short
circuit in the surrounding power system (recovery inrush);
♦ energization of another, parallel power transformer (sympathetic
inrush); or,
♦ out-of–phase synchronization of a generator-transformer block
with the rest of the power system.
Initial inrush is a form of over-current that occurs during the energization
of a transformer and is a large transient current which is caused by part
cycle saturation of the magnetic core of the transformer. For power
transformers, the magnitude of the initial inrush current has a typical value
of two to five times the rated load current. By use of some additional
devices (e.g. pre-insertion resistors or point on wave switching relays) the
magnitude of the inrush current can be reduced. However, the influence of
such devices will not be considered in this thesis.
The inrush current slowly decreases from the initial peak value by the
effect of oscillation damping due to the winding and magnetizing
resistances of the transformer, as well as the impedance of the system it is
connected to, until it finally reaches the normal exciting current value.
This process typically takes several minutes and as a result, the inrush
current could be mistaken for a short circuit current and the transformer
142 Chapter 9
can be erroneously taken out of service by the overcurrent, earth-fault or
differential relays.
Special transformers have similar properties regarding inrush current as
standard three-phase power transformers. Actual field recordings of inrush
currents into a phase-shifting transformer are shown in the following two
figures. Note that PSTs are typically energized at an OLTC position which
corresponds to 0o phase angle shift.
0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22
-1.5
-1
-0.5
0
0.5
1
[sec]
[pu]
Waveforms of S-side Currents
iS1
iS2
iS3
Figure 77: Recorded initial inrush into 600MVA, 232kV, 50Hz,
dual-core, symmetrical PST.
Transient Magnetizing Currents 143
0.1 0.12 0.14 0.16 0.18 0.2
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
[sec]
[pu]
Waveforms of S-side Currents
iS1
iS2
iS3
Figure 78: Recorded sympathetic inrush into 600MVA, 232kV,
50Hz, dual-core, symmetrical PST.
9.1 Inrush Current Calculation
The simplified equation often used to calculate the peak value of the first
cycle of the inrush current is given in [61] as follows:
N R S
pk 2 2
N
2×U 2×B +B -B
I = ×( )
(ω×L) +R B
(9.1)
where:
♦ Ipk = Peak inrush current in [Primary Amperes];
♦ U = Applied voltage in [Volts];
♦ L = Air core inductance of the energized winding in [Henry];
♦ R = Total DC resistance of the transformer windings in [Ohms];
♦ BR = Remanent flux density of the transformer core in [Tesla];
144 Chapter 9
♦ BS = Saturation flux density of the core material in [Tesla]; and,
♦ BN = Normal rated flux density of the transformer core in [Tesla].
In reality, equation (9.1) will not give sufficient accuracy, since a number
of transformer and system parameters exist that effect the magnitude of the
inrush current significantly, are not included in the calculation. The above
equation neglects the following important transformer and system
parameters which can have as much as 60% impact [61] on the magnitudes
of the inrush current:
♦ inductance of the air-core circuit adjusted for the transient nature
of the inrush current phenomenon;
♦ impedance and short circuit capacity of the system; and
♦ core geometry and winding configurations and connections (e.g.,
1- vs. 3-phase; Y- vs. Delta winding connections; Grounded vs.
non grounded Y connections; etc.).
9.2 Effect of Transformer Design Parameters on the
2nd Harmonic Component of the Inrush Current
The design of power transformers has changed slightly over time [61], and
at the same time, more modern materials have been used. These factors
will influence the power transformer inrush current and consequently the
differential protection design.
Effect of Design Flux Density
The inrush current peak increases as the design induction level increases.
This is caused by core saturation for a greater part of the voltage cycle. For
the same reason, the minimum percentage of the 2nd harmonic / peak
inrush current ratio decreases with the induction. Modern transformers
generally operate at higher flux density values with the increased use of
higher grain oriented steels. This results in modern transformers having
higher inrush currents due to the higher rated design induction value but
lower minimum percentage of 2nd harmonic / peak inrush current ratio
[61]. A typical example for a 36MVA, three-phase transformer is given in
Figure 79.
Transient Magnetizing Currents 145
Figure 79: Typical 2nd harmonic / peak inrush current ratio [61].
Effect of Core Material
A new feature of modern transformers is the use of highly grain oriented
and domain – refined electrical steel type materials that have a higher
value of saturation flux density, a larger linear portion of the magnetization
curve, and a lower remanent flux density compared to regular grain
oriented type materials.
Thus, these higher grain orientation materials are associated with higher
minimum percentage of 2nd harmonic / peak inrush current ratios. For the
same flux density, the new, modern materials have an appreciably greater
minimum percentage of 2nd harmonic / peak inrush current ratio than
Regular Grain Oriented (RGO) material [61].
Effect of Core Joint Type
Until a decade or two ago, a non step-lap (e.g. conventional) type joint was
commonly used in transformer cores, however modern transformers use a
step-lap type joint, as shown in Figure 80 (from [9]). Because of the high
146 Chapter 9
reluctance of the core joints, the remanent flux density levels of a
transformer core are significantly lower than the flux density level of the
core material itself. As the conventional joint has a greater reluctance than
a step-lap joint, it follows that a core with the step-lap joint would have a
much lower minimum percentage of 2nd harmonic / peak current ratio than
those of a core with a conventional joint [61].
Figure 80: Three-leg magnetic core with conventional or step lap joint [9].
Effect of Winding Connection Type
In a three–phase power transformer, the connection of the primary and
secondary windings and the grounding of any star connected winding will
dictate the distribution of the inrush current generated in one winding to
the other phases and line currents. For instance the line current of a star
connected primary winding will see the full winding inrush current, while
the line current for a delta connected primary winding will be reduced
since the inrush current can enter the other phases.
The percentage of the second harmonic will not be affected by the winding
connection or number of phases [61]. It is only a function of the rated flux
density, core material parameters (saturation flux density, the remanent
flux density) and lap joints.
Transient Magnetizing Currents 147
9.3 Effects on Transformer Differential Protection
Knowledge about transformer inrush currents significantly influences the
design of protection relays. The main impact of the inrush current is the
increased risk of unwanted operation for instantaneous overcurrent, earthfault
and transformer differential protection elements within the relay. The
transformer differential function must be blocked to prevent unwanted
operation in the case of inrush currents.
Inrush Detection by Harmonic Analysis of Instantaneous
Differential Currents
The most commonly used method involves the detection of the 2nd
harmonic content of the inrush currents which is used to block the
differential function [11], [12], [17] and [32]. Typically, when the ratio of
the second harmonic current component with respect to the fundamental
current component exceeds a preset level (e.g. 15%), the transformer
differential protection in that phase is blocked.
The instantaneous differential currents are calculated by using equation
(4.30), with the only difference being that the currents used in the equation
are instantaneous values (i.e. samples) from all transformer sides. Note
that it is quite important to measure the second harmonic content in the
instantaneous differential current and not in the individual winding phase
currents. The main reasons are:
♦ the possibility of high harmonic current content in the individual
winding phase currents, especially in industrial applications;
♦ the content of the fundamental current component is typically
much bigger in the individual winding phase currents than in the
respective differential currents during sympathetic and recovery
inrush; and,
♦ the lack of distinct correlation between phases within differential
protection and individual winding phase currents.
Practice has shown that although using the second harmonic blocking
approach may prevent false tripping during inrush conditions, it may
sometimes increase fault clearance time for heavy internal faults followed
by CT saturation. On the positive side, the second harmonic
restrain/blocking approach will increase the security of the differential
relay for a heavy external fault with CT saturation.
148 Chapter 9
Inrush Detection by Waveform Analysis of Instantaneous
Differential Currents
The waveform blocking criterion is a good complement to the harmonic
analysis. The waveform blocking is a pattern recognition algorithm that
searches for intervals within each fundamental power system cycle with
low magnitude of the inrush current. In the inrush current waveform there
is a period of time, within each power system cycle, during which very
low magnetizing currents flow. Thus, an inrush condition can be identified
when a low rate of change of the instantaneous differential current exists
for at least a quarter of the fundamental power system cycle, as shown in
Figure 44. This figure is as well excellent example why it is mandatory to
perform such analysis in the instantaneous differential current waveforms
and not in the individual phase current waveforms. This criterion can be
mathematically expressed for phase L1 as:
Diff_L1 Diff_L1 i pi
C1
t pt
∂
≈ ≤
∂
(9.2)
where, iDiff_L1 is the instantaneous differential current in Phase L1, t is a
time and C1 is a constant, fixed in the relay algorithm.
Cross-blocking Between Phases
The basic definition of cross-blocking is that one of the three-phases can
block the operation (i.e. tripping) of the other two phases of the differential
protection due to the properties of the instantaneous differential current in
that phase (i.e. waveform analysis or 2nd harmonic content). This principle
increases the security of the differential protection during power
transformer energizing.
Transient Magnetizing Currents 149
9.4 Internal Faults Followed by CT Saturation
A primary fault current typically does not contain any 2nd harmonic
component. However, in the case of DC saturation of the CTs, the
secondary fault current will temporarily contain a 2nd harmonic. For heavy
internal transformer faults followed by CT saturation, the distorted CT
secondary current may contain a quite high level of the second harmonic.
As a consequence, delayed operation of the restrained differential
protection might occur.
Inrush Detection by Adaptive Techniques
The term “Adaptive Relaying” has been defined in [8]. The combination of
the 2nd harmonic and waveform analysis methods, allows the relay
designer to optimize the detection of inrush currents while avoiding some
of the potential drawbacks. One possible way, with good field experience
[11], is to combine these methods as follows:
♦ employ both the 2nd harmonic and the waveform criteria to detect
the initial inrush condition;
♦ one minute after power transformer energizing, the 2nd harmonic
criterion can be disabled in order to avoid long clearance times for
heavy internal faults and the waveform criterion alone can take
care of the sympathetic and recovery inrush scenarios; and,
♦ temporarily enable the 2nd harmonic criterion for six seconds when
a heavy external fault has been detected, to gain additional
security for external faults.
The behaviour of the differential protection under such operating
conditions was tested. First the differential protection relay was setup in
the traditional way, with a second harmonic blocking level set at 15% and
always active. This resulted in slow operation of the differential relay for
an internal fault followed by CT saturation as shown in Figure 81.
150 Chapter 9
Figure 81: Slow differential protection operation due to
traditional use of 2nd harmonic blocking.
After this test, the differential relay was set to adaptively use the second
harmonic. No other setting parameter was changed. Then the operation of
the differential function for internal faults was not effected at all by the
presence of the second harmonic due to distorted CT secondary current, as
shown in Figure 82. These tests show that modern numerical differential
protection relays can adaptively use the second harmonic blocking criteria.
The protection system can utilize the 2nd harmonic criterion as a restrain
quantity during inrush conditions, but disregard its delaying influence
during internal faults. This feature ensures much faster operation of the
differential function for internal faults followed by CT saturation.
Transient Magnetizing Currents 151
Figure 82: Fast differential protection operation
with adaptive 2nd harmonic blocking.
9.5 Energizing of a Faulty Transformer
When a faulty transformer is energized the fault current might contain a
high percentage of second harmonic. As a consequence, delayed operation
of the restrained differential protection might occur. Modern numerical
differential protection [12] might incorporate adaptive features in order to
ensure faster operation for such faults. Some other solutions for the same
problem have been proposed in the literature [16] and [47]. Two recorded
field cases of energizing a faulty transformer will be presented.
Field Case #1
This field case was captured on a three-winding power transformer with
the following rating data 25MVA; 115/38.5/6.6kV; Yy0d11; 50Hz, in
accordance with IEC terminology [58]. The transformer suffered an
internal turn-to-turn fault within the 35kV winding in phase L2, as shown
152 Chapter 9
in Figure 108. After correct tripping by the differential protection the
operator tried to energize again the faulty transformer. The DR file was
captured during this transformer energizing attempt by the existing
differential relay having a sampling rate of 20 samples per power system
cycle. In Figure 83 the following waveforms, either extracted or calculated
from this DR file, are presented:
♦ 110kV current waveforms;
♦ instantaneous differential current waveforms; and,
♦ RMS values of the differential currents.
2 3 4 5 6 7 8
-300
-200
-100
0
100
200
300
400
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
-300
-200
-100
0
100
200
300
400
Diff Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
0
50
100
150
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 83: Captured DR file during energizing of a faulty 25MVA transformer.
Note that the 110kV winding currents do not have typical inrush
waveforms. For example, typical current gaps, as shown previously are no
longer present. This characteristic can be used within numerical
differential protection to speed up the relay operation.
Transient Magnetizing Currents 153
Field Case #2
This field case was captured on a three-winding power transformer with
the following rating data 20MVA, 110±13*1,15%/21/10,5kV, YNyn0(d5),
50Hz. Note that the transformer tertiary winding is not loaded and it is
used as a delta-connected equalizer winding. The 110kV winding neutral
point is directly grounded while the 20kV winding neutral point is
grounded via a 40r resistor. The transformer suffered an internal fault in
the 110kV winding in phase L2, as shown in Figure 111. After correct
tripping by the differential protection relay the operator tried again to
energize the faulty transformer. The DR file was captured during this
transformer energizing attempt by the existing differential relay having a
sampling rate of 20 samples per power system cycle. In Figure 84 the
following waveforms, either extracted or calculated from this DR file, are
presented:
♦ 110kV current waveforms;
♦ instantaneous differential current waveforms; and,
♦ RMS values of the differential currents.
154 Chapter 9
0 2 4 6 8 10 12
-200
0
200
400
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
0 2 4 6 8 10 12
-300
-200
-100
0
100
200
300
400
Diff Current Waveforms
[%]
[Cycles]
L1
L2
L3
0 2 4 6 8 10 12
0
50
100
150
200
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 84: Captured DR file during energizing of a faulty 20MVA transformer.
Note that the 110kV, phase L2 winding current has a close to sinusoidal
waveform while the other two phases have typical inrush current
waveforms. Current waveforms generated by such operating conditions
can cause delayed operation of the transformer differential protection.
Using adaptive features within numerical differential relays [12] makes it
possible to speed-up the operation of traditional differential protection for
such cases.
155
Chapter 10
Differential or Directional
Protection
Directional protection monitors the phase angle difference between two
phasors in order to determine whether protection operation should occur or
not. A similar concept of α- and β- plane for the differential protection was
introduced in [5], however it was only defined for protected objects with
two ends and mainly used for line/feeder differential protection. In its
basic form these two planes define the phase angle relationship between
the currents from two sides of a protected object, which makes a
directional principle inherent to the differential protection scheme.
Recently an α-plane based concept was used for the design of a numerical
line differential protection [26], [27] and [28].
10.1 Generalized Directional Principle for Differential
Protection
The directional principle is also inherent to equation (4.32). In order to be
better understood, the directional principle equation (4.32) can be rewritten
in the following form:
_ 1 _ 1 _ 1 1
_ 2 _ 2 _ 2
1
_ 3 2 _ 3 _ 3
1
Id L DCC L DCC L W n Wi
Id L DCC L DCC L
W Wi
Id L i DCC L DCC L
W Wi
= + Σ =
(10.1)
156 Chapter 10
On the right-hand side of equation (10.1) we have two terms, which offer
the possibility to represent an n-winding transformer with an equivalent
two-winding transformer. The first term is the differential current
contribution from the winding one side, as defined in equation (4.31). The
second term represents the differential current contribution from the
equivalent second winding. If we now assume that magnitude and phase
angle corrections are ideally performed, the total differential current shall
be equal to zero for all symmetrical or non-symmetrical through-load
conditions including external faults. Thus, if we assume that the all three
differential currents are approximately zero the following formula can be
written:
_ 1 _ 1
1
_ 2 _ 2
1
2
_ 3 _ 3
1
DCC L DCC L
W n Wi
DCC L DCC L
W Wi
i
DCC L DCC L
W Wi
≈ − Σ
=
(10.2)
Note that this formula is only valid during all through-load conditions (i.e.
not during internal faults). Consequently for every one of the three-phases
the resultant phasors from the left and right hand side of formula (10.2)
should have equal magnitude and shall be in phase (i.e. with phase angle
shift of 0o between them). Theoretically, any phase angle other than 0o
between these two phasors would mean the existence of a differential
current and consequently the presence of an internal fault. In the case of
an ideal internal fault, these two phasors would be 180o out of phase. If
this directional rule is applied, the differential protection is converted to a
directional comparison protection by the simple analysis of the phase angle
shift between the two phase-wise phasors defined in formula (10.2).
Note the minus sign on the right hand side of formula (10.2). In practice,
this minus sign means that the CT reference direction, shown in Figure 14,
is reversed for the equivalent second winding. This inversion ensures the
zero degree phase angle shift between the two phasors during all throughload
conditions.
It is possible to re-write equation (10.1) in the following way:
Differential or Directional Protection 157
_ 1 _ 1 1 _ 1
_ 2 _ 2 _ 2
1
2 _ 3 _ 3 _ 3
1
DCC L DCC L Id L n Wi W
DCC L DCC L Id L
Wi W
i Id L DCC L DCC L
Wi W
− Σ = − =
(10.3)
If (10.3) is now inserted into (10.2) the following formula is obtained:
_ 1 _ 1 _ 1 1 1
_ 2 _ 2 _ 2
1 1
_ 3 _ 3 _ 3
1 1
DCC L DCC L Id L W W
DCC L DCC L Id L
W W
DCC L DCC L Id L
W W
≈ −
(10.4)
Note that this formula is only valid during all through-load and external
fault conditions when all three differential currents are approximately zero
(i.e. not valid during internal faults). Now the directional comparison can
be performed on two phase-wise phasors obtained from the left and the
right hand side of the formula (10.4). From a mathematical point of view
formulas (10.4) and (10.2) are equivalent. However, in practice it is much
easier to implement formula (10.4) within a numerical differential relay.
At the same time formula (10.4) can be easily applied on any protected
power transformer side by simply exchanging the differential current
contribution from the winding one side with the differential current
contribution from the winding side were formula (10.4) shall be applied.
For power transformer differential protection, the negative-sequence
current component based differential currents are calculated by using
equation (4.34). Thus the directional comparison criterion obtained from
formula (10.4) for phase-wise differential currents can be applied in a
similar manner for negative sequence current components and it is given in
the following formula:
1 1 _ 1 _ 1 W W DCCNS L ≈ DCCNS L − IdNS (10.5)
This formula is only valid during all through-load conditions (i.e. not
during internal faults). Note that a similar formula can be constructed for
the positive sequence current components as well.
158 Chapter 10
10.2 Negative Sequence Based Internal/External Fault
Discriminator
The use of negative sequence quantities for transformer protection has
been proposed in the literature [30], [46]. The existence of a relatively high
negative-sequence current component is in itself proof of a disturbance on
the power system, and possibly of a fault in the protected power
transformer. The negative-sequence current components are measurable
indications of abnormal conditions, similar to the zero-sequence current
components. One advantage of the negative-sequence current component
compared to the zero-sequence current component is that it provides
coverage for phase-to-phase faults as well, not only for phase-to-earth
faults. Theoretically, the negative sequence current component does not
exist during symmetrical three-phase faults. However the negative
sequence current component appears during the initial stage of such faults,
as shown in [39], for a period of time long enough for the numerical
differential relay to make a proper directional decision. Further, the
transfer of the negative sequence current component through the power
transformer is not prevented by Yd or Dy winding connections. The
negative sequence current component is always properly transformed to
the other side of any power transformer, regardless of its phase angle shift
and type of external disturbance. Finally, the negative sequence current
component is typically not affected by fully symmetrical through-load
currents. The algorithm of the internal/external fault discriminator is based
on the theory of symmetrical components. In [21] and [43] it has been
stated that the:
♦ source of the negative-sequence currents is at the point of fault;
♦ negative-sequence currents distribute through the negativesequence
network; and,
♦ negative-sequence currents obey the first Kirchhoff’s law.
Imagine a power transformer with a turns ratio equal to 1, and a zero
degree phase displacement, e.g. a transformer of the connection group
Yy0. For an external fault the fictitious negative sequence source will be
located outside the differential protection zone at the fault point. Thus the
negative sequence current component will enter the healthy power
transformer on the fault side, and leave it on the other side, properly
transformed. According to the current direction definitions in Figure 14,
the negative sequence current components on the respective power
Differential or Directional Protection 159
transformer sides will have opposite directions. In other words, the
internal/external fault discriminator sees these currents as having a relative
phase displacement of exactly 180o, as shown in Figure 85.
Relay
ENS
ZNSS1 ZNSS2
Yy0; 1:1
INSS1 INSS1 INSS2
INSS1 INSS1
Negative Sequence
Zero Potential
Figure 85: Flow of Negative Sequence Current Components during external fault.
For an internal fault (with the fictitious negative sequence voltage source
within the protected power transformer) the negative sequence current
components will flow out of the faulty power transformer on both sides.
According to the current direction definitions in Figure 14, the negative
sequence currents on the respective power transformer sides will have the
same direction. In other words, the internal/external fault discriminator
sees these currents as having a relative phase displacement of zero
electrical degrees, as shown in Figure 86. In reality, for an internal fault,
there might be some small phase shift between these two currents due to
the possibility of having different negative sequence impedance angles for
the source equivalent circuits on the two power transformer sides.
Relay
ENS
Yy0; 1:1
ZNSS1 ZNSS2
INSS2 INSS1
INS INSS2 S1
Negative Sequence
Zero Potential
Figure 86: Flow of Negative Sequence Current Components during internal fault.
160 Chapter 10
However, if a power transformer has a non-zero phase displacement, a
non-unity turns ratio and a multi-winding arrangement, the
internal/external fault discriminator can be instead based on a directional
comparison method, as defined by formula (10.5). When this directional
comparison method is used, a similar 0o/180o rule is again valid between
the two negative sequence current component phasors defined by formula
(10.5). Thus, for any unsymmetrical external fault, the two negative
sequence current component phasors defined by formula (10.5) will be in
phase regardless of the power transformer turns ratio, phase angle
displacement or number of windings, while for any internal fault these two
phasors will be approximately 180o out of phase.
In order to perform the internal/external fault algorithm (e.g. directional
comparison), the magnitude of the two negative sequence phasors must be
high enough. Both negative sequence phasor magnitudes must exceed a
certain minimum limit before the directional comparison is permitted. On
the other hand, in order to obtain a good sensitivity of the internal/external
fault discriminator, the value of this minimum limit must not be too high.
In the algorithm this limit is made settable in the range from 1% to 20% of
the differential protection base, with a nominal value of 4%. If either of the
negative sequence current component phasors to be compared is too small
(less than the pre-set minimum limit), no directional comparison is made
in order to avoid the possibility of an incorrect decision. This magnitude
check will also guarantee the stability of the algorithm when the power
transformer is energized.
Once both negative sequence current component phasors exceed the preset
minimum limit the directional comparison is performed. An internal
fault is declared if the phase angle between the two phasors is between 120
and 240 degrees. This is done in order to ensure proper operation of the
phase angle comparator during external faults followed by CT saturation.
The internal/external fault discriminator is actually a very powerful and
reliable method. It detects even minor faults, with high sensitivity and
speed, and at the same time discriminates with a high degree of
dependability between internal and external faults. Thus it can be added as
the second criterion for the operation of the traditional power transformer
differential relay. If the operating point of the differential relay is above
the traditional operating characteristic and simultaneously the
internal/external fault discriminator confirms that the fault is internal, the
Differential or Directional Protection 161
trip signal can be issued immediately without any additional time delay
typically needed to check for second and fifth current components as
described in Section 9.4. Thus, extremely fast tripping is achieved for most
internal faults.
Note that the internal/external fault discriminator has the following
shortcomings:
♦ it requires that the protected transformer is loaded (i.e. connected
to the rest of the power system on at least two sides); and,
♦ it doesn’t provide clear indication about the faulty phase.
10.3 Evaluation of the Directional Comparison
Principle by Using Records of Actual Faults
The performance of the internal/external fault discriminator and phasewise
directional comparison principle will be evaluated by using
recordings of actual faults captured in the field.
Field Case #1
This field case was captured on a three-winding transformer with the
following rating data 16/8/8MVA; 115/6.3/6.3kV; Yd5d5; 50Hz. This
transformer is protected by a numerical, three-winding differential
protection. However, due to special connections, as explained in
Section 4.6, the phase shift compensation shall be performed as if the
transformer were with the vector group Yd7d7.
In order to calculate the differential currents in accordance with equation
(4.30) the base currents and compensation matrixes as shown in Table 17
shall be used.
162 Chapter 10
Table 17: Compensation data for 16/8/8MVA; 115/6.3/6.3kV; Yd7d7 Transformer
Base Current Ib Compensation Matrix MX
W1,
115kV 80.3A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2, 6.3kV 1466.7A
-0.244 0.911 0.333
( 150 ) 0.333 -0.244 0.911
0.911 0.333 -0.244
o M − =
W3, 6.3kV 1466.7A
-0.244 0.911 0.333
( 150 ) 0.333 -0.244 0.911
0.911 0.333 -0.244
o M − =
The two 6.3kV networks are passive (i.e. without installed generation) and
have high-impedance grounded neutral points. The 110kV star point of
this transformer is directly grounded. The disturbance file was captured
during an external earth-fault in the 110kV network at a sampling rate of
600Hz (i.e. 12 samples per cycle). Note that this is an excellent example of
why zero sequence current reduction is absolutely necessary on the 110kV
side. Without it, the power transformer differential relay would maloperate
for this external fault due to the massive zero sequence current component
on the 110kV side, which is not at all present on the other two delta sides.
In Figure 87 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1, W2 and W3 individual phase current waveforms;
♦ RMS values of the differential currents; and,
♦ phase angle between the two negative sequence phasors, as
defined in formula (10.5).
Differential or Directional Protection 163
2 3 4 5 6 7 8
-400
-200
0
200
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
-50
0
50
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
-50
0
50
W3 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
0
1
2
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
-10
0
10
Neg Seq Angle
[deg]
[Cycles]
Figure 87: External fault on 110kV side.
Therefore, regardless of the different grounding methods of the two
networks, the internal/external fault discriminator will categorize this
disturbance as an external fault. In Figure 88 the phasor diagram for the
“usual” negative sequence current components from all three sides of the
protected transformer are shown at the time instant which corresponds to
time 5.5 cycles shown in Figure 87. Note that certain magnitude
differences and phase angle shifts do exist between the negative sequence
current components from the two delta sides.
164 Chapter 10
10
20
30
40
30
210
60
240
90
270
120
300
150
330
180 0
Neg Seq Wndg Components
W1
W2
W3
Figure 88: Negative sequence current components at t=5.5 cycles.
Field Case #2
This field case was captured on a symmetrical type, dual-core PST with
the following rating data 600MVA; 232kV; ±35o in 57 steps; 50Hz. This
PST is protected with the classic IEEE protection scheme [37]. In order to
calculate the differential currents in accordance with equation (4.30) the
base currents and compensation matrixes as shown in Table 18 shall be
used. The fault happened in full retard position (i.e. tap position one). The
disturbance file was captured during an external three-phase fault on the Lside
of the PST at a sampling rate of 1000Hz (i.e. 20 samples per cycle).
In Figure 89 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ S- and L-side individual phase current waveforms; and,
♦ phase angle between the two negative sequence phasors, as
defined in formula (10.5).
Differential or Directional Protection 165
Table 18: Compensation data for the 600MVA; 232kV; ±35o double-core PST
Base Current Ib Compensation Matrix MX
S-side,
232kV 1493A
1 0 0
(0 ) 0 1 0
0 0 1
o M
=
L-side,
232kV
1493A
0.879 -0.271 0.391
(35 ) 0.391 0.879 -0.271
-0.271 0.391 0.879
o M
=
0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-400
-200
0
200
400
Waveforms of S-side Currents
[%]
[sec]
iS1
iS2
iS3
0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-400
-200
0
200
400
Waveforms of L-side Currents
[%]
[sec]
iL1
iL2
iL3
0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
-10
-5
0
5
10
[sec]
[deg]
Neg Seq Angle
NegSeq
Figure 89: External three-phase fault on the L-side of a 600MVA, 232kV PST.
166 Chapter 10
Note that the internal/external fault discriminator could determine that this
fault is external during the first and last cycle of the fault, regardless of the
fact that this is a symmetrical three-phase fault.
Field Case #3
This field case was captured on a three-winding transformer with the
following rating data 40/40/10MVA; 110/36.75/10.5kV; Yy0d5; 50Hz.
Note that this transformer tertiary winding is not loaded and it is used as a
delta-connected equalizer winding. This transformer is protected with a
numerical, two-winding differential protection. In order to calculate the
differential currents in accordance with equation (4.30) the base currents
and compensation matrixes as shown in Table 19 shall be used.
Table 19: Compensation data for the 40MVA; 110/36,75/10.5kV transformer
Base Current Ib Compensation Matrix MX
W1, 110kV 201A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2, 36,75kV 628.4A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
The 35kV network is passive (i.e. without installed generation) and with
resistance grounded neutral point. The earth-fault current in the 35kV
network is limited to 300A primary. The 110kV star point of this
transformer is directly grounded. The disturbance file is captured during an
evolving fault at the 35kV busbar, caused by an animal climbing into the
busbar. The fault started as L3-to-ground, then it evolved into L2-L3-toground
and finally it became a three-phase fault. Note that the captured
recording starts during the L3-to-ground fault, therefore the pre-fault
current waveforms are not available. The sampling rate in the file is
1000Hz (i.e. 20 samples per cycle).
Differential or Directional Protection 167
In Figure 90 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1- and W2-side individual phase current waveforms; and,
♦ RMS differential currents.
2 4 6 8 10 12 14 16 18 20 22
-1000
-500
0
500
1000
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 4 6 8 10 12 14 16 18 20 22
-1000
-500
0
500
1000
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 4 6 8 10 12 14 16 18 20 22
0
1
2
3
4
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 90: External evolving fault on the 35kV side.
In Figure 91 the following waveforms, calculated from this DR file, are
presented:
♦ phase angle difference between the two negative sequence and the
two positive sequence phasors respectively as defined by equation
(10.5); and,
♦ phase angle difference between the phase-wise phasors, as defined
in the equation (10.4).
168 Chapter 10
2 4 6 8 10 12 14 16 18 20 22
-10
-5
0
5
10
Sequence-Wise DCC Angle Directional Comparisson
[deg]
[Cycles]
Pos Seq
Neg Seq
2 4 6 8 10 12 14 16 18 20 22
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Phase-Wise DCC Angle Directional Comparisson
[Deg]
[Cycles]
L1
L2
L3
Figure 91: Directional comparison during an external evolving 35kV fault.
Note that the negative sequence based internal/external fault discriminator
could determine that this fault is external at the beginning of the fault.
However after the fault becomes a three-phase fault, the negative sequence
phase angle starts to deviate from the theoretical value of zero degrees.
The reason is that negative sequence quantities had quite small magnitudes
while the fault was the three-phase fault. Such behaviour of the negative
sequence quantities made it difficult to precisely determine the phase angle
between them. At the same time positive sequence and phase-wise
directional comparisons can securely determine that this fault is external
for the entire fault duration.
Differential or Directional Protection 169
Field Case #4
This field case was captured on an auto-transformer with the following
rating data 160/160/50MVA; 220/126/10.5kV; YNautod11; 50Hz, in
accordance with the IEC terminology [58]. It shall be noted that this autotransformer
tertiary winding is not loaded and is used as a delta-connected
equalizer winding. The transformer was protected with one two-winding
differential relay.
In order to calculate the differential currents for this transformer in
accordance with equation (4.30) the base currents and compensation
matrixes as shown in Table 20 shall be used.
Table 20: Compensation data for the 160MVA; 220/126/10.5kV auto-transformer
Base Current Ib Compensation Matrix MX
W1,
220kV
420A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2,
126kV
733A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
The disturbance file was captured by the numerical differential relays and
stored directly in secondary amperes. The CT on the 220kV side was
600/1 and on the 126kV side 1000/1. Thus, these ratios must be taken in
the account during the analysis of the secondary quantities from the DR
file. This external fault was captured during the primary testing of the
relay. The fault was intentionally applied for testing purposes as a singlephase
L1 fault on the 126kV side. Phases L2 and L3 on 126kV side were
left open circuited during the test, after which the transformer 126kV CB
was directly closed onto the fault. The sampling rate in the file is 600Hz
(i.e. 12 samples per cycle).
170 Chapter 10
In Figure 92 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1- and W2-side individual phase current waveforms;
♦ RMS values of the differential currents; and,
♦ phase angle between the two negative sequence phasors, as
defined in formula (10.5).
Note that the incomplete circuit on the 126kV side (i.e. open L2 and L3
phases) did not adversely influence the proper operation of the negative
sequence based internal/external fault discriminator.
4 5 6 7 8 9 10 11 12 13 14
-1000
0
1000
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
4 5 6 7 8 9 10 11 12 13 14
-1000
0
1000
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
4 5 6 7 8 9 10 11 12 13 14
0
5
10
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
4 5 6 7 8 9 10 11 12 13 14
-5
0
5
Neg Seq Angle
[deg]
[Cycles]
Figure 92: External L1-Ground fault on the 126kV side
of a 160MVA auto-transformer.
Differential or Directional Protection 171
Field Case #5
This field case is a repeat of the primary test presented above under Field
Case #4. The only difference is that an additional resistance was added in
the CT secondary circuit in phase L1 on the 126kV side. This was done in
order to check the performance of the relay for CT saturation.
In Figure 93 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1- and W2-side individual phase current waveforms; and
♦ RMS values of the differential currents.
2 3 4 5 6 7 8 9 10 11 12
-500
0
500
1000
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8 9 10 11 12
-1000
-500
0
500
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8 9 10 11 12
0
50
100
150
200
250
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 93: External L1-Ground fault on the 126kV side
of a 160MVA auto-transformer with CT saturation.
172 Chapter 10
In Figure 94 the following waveforms, calculated from this DR file, are
presented:
♦ phase angle difference between the two negative sequence and the
two positive sequence phasors respectively as defined by equation
(10.5); and,
♦ phase angle difference between the phase-wise phasors, as defined
in equation (10.4).
2 3 4 5 6 7 8 9 10 11 12
-10
0
10
20
30
40
Sequence-Wise DCC Angle Directional Comparisson
[deg]
[Cycles]
Pos Seq
Neg Seq
2 3 4 5 6 7 8 9 10 11 12
-10
0
10
20
30
40
Phase-Wise DCC Angle Directional Comparisson
[Deg]
[Cycles]
L1
L2
L3
Figure 94: Directional comparison during an external L1-Groung fault.
Note that the CT saturation of the 126kV CT caused an angle deviation
from the theoretical 0o for all directional comparison principles applied in
this case. However, this deviation is only temporary while the CT is
saturated. Note that before CT saturation the relay could measure this
angle equal to zero and thus easily conclude that this fault is external. The
transient angle deviation of 40o is still far away from the theoretical angle
for internal fault of 180o.
Differential or Directional Protection 173
Field Case #6
This field case was captured on a three-winding transformer with the
following rating data 20/20/10MVA; 110/36.75/10.5kV; Yy0d5; 50Hz.
Note that this transformer tertiary winding is not loaded and is used as a
delta-connected equalizer winding. This transformer is protected with a
numerical, two-winding differential protection. In order to calculate the
differential currents in accordance with equation (4.30) the base currents
and compensation matrixes as shown in Table 21 shall be used.
Table 21: Compensation data for the 20MVA; 110/36,75/10.5kV transformer
Base Current Ib Compensation Matrix MX
W1, 110kV 101A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2, 36,75kV 314A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
The 35kV network is passive (i.e. without installed generation) and with a
resistance grounded neutral point. The earth-fault current in the 35kV
network is limited to 300A primary. The 110kV star point of this
transformer is directly grounded. The disturbance file was captured when
an operator had erroneously tried to open the disconnector under-load in
the 35kV transformer bay. The fault was therefore an external fault for the
transformer differential protection, which started as an L1-L2 fault and
evolved into a three-phase fault. During this fault the 35kV CTs went into
extremely heavy saturation that ultimately caused the maloperation of the
existing differential relay. The sampling rate in the file is 1000Hz (i.e. 20
samples per cycle).
In Figure 95 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1- and W2-side individual phase current waveforms; and,
♦ RMS values of the differential currents.
174 Chapter 10
4 5 6 7 8 9 10 11 12
-2000
-1000
0
1000
2000
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
4 5 6 7 8 9 10 11 12
-2000
-1000
0
1000
2000
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
4 5 6 7 8 9 10 11 12
0
100
200
300
400
500
600
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 95: External L1-L2 fault evolving into
a three-phase fault on the 35kV side.
In Figure 96 the following waveforms, calculated from this DR file, are
presented:
♦ phase angle difference between the two negative sequence and the
two positive sequence phasors respectively as defined by equation
(10.5); and,
♦ phase angle difference between the phase-wise phasors, as defined
in equation (10.4).
Differential or Directional Protection 175
4 5 6 7 8 9 10 11 12
-100
-50
0
50
100
Sequence-Wise DCC Angle Directional Comparisson
[deg]
[Cycles]
Pos Seq
Neg Seq
4 5 6 7 8 9 10 11 12
-100
-50
0
50
100
Phase-Wise DCC Angle Directional Comparisson
[Deg]
[Cycles]
L1
L2
L3
Figure 96: Directional comparison during the external fault on the 35kV.
Note that saturation of the 35kV CTs caused an angle deviation from the
theoretical 0o for all directional comparison principles. However, deviation
of the negative sequence angle is by far the biggest one due to CT
secondary current distortions caused by the evolving three-phase fault.
Note that before the CT saturation, the relay could measure this angle
equal to zero and thus easily conclude that this fault was external.
176 Chapter 10
Field Case #7
This field case was captured on an auto-transformer with the following
rating data 150/150/30MVA; 220/115/10.5kV; YNautod5; 50Hz, in
accordance with IEC terminology [58]. It shall be noted that this autotransformer
tertiary winding was not loaded and is used as a deltaconnected
equalizer winding. This auto-transformer is protected with two
numerical, two-winding differential protections from different
manufacturers, in accordance with the utility protection philosophy.
In order to calculate the differential currents for this transformer in
accordance with equation (4.30), the base currents and compensation
matrixes as shown in Table 22 shall be used.
Table 22: Compensation data for the 150MVA; 220/115/10.5kV auto-transformer
Base Current Ib Compensation Matrix MX
W1,
220kV
394A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2,
115kV
753A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
The disturbance file is captured during an internal phase-to-ground fault,
which occurred on the connection between the 110kV phase L2 winding
and the 110kV phase L2 bushing within the auto-transformer tank. The
sampling rate of the file is 1000Hz (i.e. 20 samples per cycle).
In Figure 97 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1- and W2-side individual phase current waveforms; and,
♦ RMS values of the differential currents.
Differential or Directional Protection 177
9 10 11 12 13 14 15
-500
0
500
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
9 10 11 12 13 14 15
-2000
-1000
0
1000
2000
3000
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
9 10 11 12 13 14 15
0
500
1000
1500
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 97: Internal L2-ground fault on the 110kV side of
a 150MVA auto-transformer.
In Figure 98 the following waveforms, calculated from this DR file, are
presented:
♦ phase angle difference between the two negative sequence and the
two positive sequence phasors respectively as defined by equation
(10.5); and,
♦ phase angle difference between phase-wise phasors, as defined in
equation (10.4).
178 Chapter 10
9 10 11 12 13 14 15
160
165
170
175
180
185
190
195
200
Sequence-Wise DCC Angle Directional Comparisson
[deg]
[Cycles]
Pos Seq
Neg Seq
9 10 11 12 13 14 15
160
165
170
175
180
185
190
195
200
Phase-Wise DCC Angle Directional Comparisson
[Deg]
[Cycles]
L1
L2
L3
Figure 98: Directional comparison during internal fault.
Note that all directional comparison methods could determine that this
fault is internal. But the comparison based on negative sequence quantities
could operate in less than half a cycle from the point of fault inception.
179
Chapter 11
Turn-to-Turn Fault Protection
A study of the records for modern transformer breakdowns that have
occurred over a period of years indicates that between 70% and 80% of the
total number of transformer failures are eventually traced to internal
winding insulation failure [63]. If not quickly cleared, these turn-to-turn
faults usually develop into more serious, and costly to repair earth-faults,
involving the power transformer iron core. Alternatively, turn-to-turn
faults cause arcing within the power transformer tank, making significant
damage until tripped by the Buchholtz relay.
These winding faults are mostly a result of the degradation of the
insulation system due to thermal, electrical, and mechanical stress,
moisture, and other factors. Degradation means reduced insulation quality,
which will eventually cause a breakdown in the insulation, leading to
adjacent winding turns being shorted (turn-to-turn fault) or to a winding
being directly shorted to earth (winding to earth failure). Most often the
insulation undergoes a gradual aging process before such a fault happens.
Ageing of the insulation reduces both the mechanical and dielectric
withstand strength. Under external fault conditions, power transformer
windings are temporarily subjected to high radial and compressive forces.
As the load increases with system growth, the operating stresses increase.
In an ageing transformer the conductor insulation is weakened to the point
where it can no longer sustain any additional stress. Under increased
stress, for example due to external fault, the insulation between adjacent
turns suffers a dielectric failure and a turn-to-turn fault may develop.
A short circuit of a few turns in the power transformer winding (i.e. turnto-
turn fault) will give rise to a heavy fault current in the short-circuited
turns. However, changes in the transformer terminal currents will be quite
small because of the high ratio of transformation between the whole
winding and the short-circuited turns. For that reason, traditional power
transformer differential protection has typically not been sensitive enough
180 Chapter 11
to detect such winding turn-to-turn faults before they develop into more
serious and costly to repair earth-faults. Such faults can also be detected by
Buchholtz (gas operated) relays. However, the detection interval for such
low-level faults is in the order of hundreds of milliseconds or even
seconds, which often allows the fault to evolve into a more serious one.
Regarding the turn-to-turn fault detection, in the current literature, the
most advanced methods are utilizing either wavelet or artificial neural
network [3], [18], [40], [50], [53], [55] and [57]. However, in this thesis,
methods to improve standard differential protection in order to detect turnto-
turn faults are suggested.
11.1 Basic Turn-to-Turn Fault Theory
Operation of the transformer differential protection is based on Ampereturn-
balance for all coils located on one magnetic core. Let us consider the
simplest case of a two winding, single-phase transformer as shown in
Figure 99, with its relevant phasor diagram.
Figure 99: Single-phase, two-winding transformer.
The phasor diagram, shown in Figure 99, neglects the existence of
magnetizing current which is necessary to create a magnetic flux in the
transformer core. A differential relay would measure currents I1 and I2
scale them appropriately using equation (4.30), and then find a negligible
differential current during normal through-load conditions.
Turn-to-Turn Fault Protection 181
Note that power transformers are primarily used to transfer active power
between two networks. Thus, it is reasonable to assume that the winding
current and voltage are approximately in phase. That means that for power
transformers used in a power system, the resultant flux is lagging
approximately 90o behind the current phasors [9].
Let’s assume that a turn-to-turn fault has happened in winding two,
involving Nx turns, as shown in Figure 100. Note that for practical turn-toturn
faults Nx<
Figure 100: Single-phase, two-winding transformer with an internal
turn-to-turn fault.
The induced voltage in the short-circuited turns will cause the additional
current component Ix, which is not measured by the differential relay, to
circulate through the shorted turns. Because the impedance of the shorted
turns is mostly inductive, the current Ix will lag the voltage by
approximately 90o. However, the Ampere-turn-balance principle for all
coils located on one magnetic core must still be fulfilled, irrespective of
the existence of a turn-to-turn fault. In order to fulfill this requirement, two
measured currents will get a certain phase angle shift δ, as shown in Figure
100, but not necessarily any sufficient magnitude increase, in order to
compensate for the additional ampere-turn component Nx.Ix.
A differential relay will see the component Nx.Ix as a differential current.
However, for a turn-to-turn fault, involving just a few turns, the resultant
differential current magnitude might be quite small and certainly not
within the tripping region of the differential relay operating characteristic.
However, if the differential relay would instead look into the phase angle
shift between the two measured currents the turn-to-turn faults can be
182 Chapter 11
detected. Note that the previous explanation for a single-phase, twowinding
transformer is still valid in the case of a three-phase power
transformer, if the differential relay monitors the phase angle shift between
the differential current contributions from different power transformer
sides, as explained in Section 10.1.
11.2 Traditional Power Transformer Differential
Protection
The problem with classical transformer differential protection is that lowlevel
faults such as turn-to-turn faults can not be detected. The differential
relay minimum pickup current in the first section of the relay operate –
restraint characteristic is traditionally set to a value between 30% and 40%.
When a minor turn-to-turn fault, at fault inception, causes a differential
current of 15%, it cannot be detected until it evolves into a more severe
fault with bigger differential currents.
However, the opportunity to perform complete magnitude and phase angle
shift compensation, as described in Chapter 4, allows for greater sensitivity
in the minimum pickup value (e.g. 15%) of the traditional differential
protection. This sensitive pickup value enables the traditional differential
protection to be more capable in detecting turn-to-turn faults, as illustrated
in the examples presented at the end of this chapter.
11.3 Directional Comparison Based on Negative
Sequence Current Component
The existence of negative sequence current components during turn-to-turn
fault conditions allows the use of the internal/external fault discriminator,
described in Section 10.2, for detection of such faults. The sensitive,
negative sequence current based turn-to-turn fault protection
independently detects low-level faults not detected by the traditional
transformer differential protection. The essential part of this sensitive
negative sequence protection is the internal/external fault discriminator
previously described. In order to be activated, the sensitive protection
doesn’t require any pickup signal from the power transformer biased
differential protection, based on phase currents. If the magnitudes of the
Turn-to-Turn Fault Protection 183
contributions to the negative sequence differential current are above the
minimum limit (e.g. 4%), then their relative phase displacement is
determined. If the disturbance is characterized as an internal fault, then a
separate trip request will be placed. Any decision regarding a final trip
request must be confirmed several times in succession in order to cope
with possible CT transients, causing a short additional operating time
delay. Trustworthy information on whether a fault is internal or external is
typically obtained in about ten milliseconds after the fault inception,
depending on the magnitudes of the fault currents. For low-level turn-toturn
faults the overall response time of this protection can be in the order
of 30 milliseconds. At heavy through-load conditions this feature shall be
temporarily blocked, in order to prevent maloperation during secondary
CT transients.
This protection principle for turn-to-turn faults has, however, the following
drawbacks:
♦ Requires the presence of relatively high negative sequence current
components on at least two sides of the protected power
transformer;
♦ might be desensitized by the presence of unsymmetrical throughload
currents; and,
♦ doesn’t provide any indication about the faulty phase.
11.4 Phase-Wise Directional Comparison
As described in Section 10.1, the differential protection can be converted
to the directional comparison principle. Thus, if this directional
comparison principle is applied in a phase segregated way, a sensitive
detection of turn-to-turn faults can be achieved as explained at the end of
Section 11.1.
In the case of a turn-to-turn fault in any winding on one magnetic core
limb, the phase shift between the two phasors from the same phase as
defined by equation (10.4) will not be any more zero degrees. Instead, they
will have some other arbitrary phase angle shift, caused by the quite high
current in the shorted turns, as shown in Figure 100.
184 Chapter 11
Therefore, by continuously monitoring the phase angle between these two
phasors in a phase-wise fashion, sensitive, but simple, protection against
turn-to-turn faults can be achieved. In order to avoid maloperation of this
algorithm for heavy through-fault currents, it can be disabled when the
level of the stabilizing current exceeds the pre-set level (e.g. 170% of the
power transformer rating). Captured recordings from the field, show that
possible trip levels for this type of detection can be set from 3 to 5 degrees,
which will ensure a very sensitive turn-to-turn fault detection.
The following additional checks can also be made:
♦ check that negative sequence differential current is bigger than a
pre-set level (e.g. 4%);
♦ check that different phase angle shifts exist in all three-phases. If
the phase angle shift is exactly the same in all three-phases it is
most probably caused by incorrect compensation of the OLTC
position in case of a PST. It will typically indicate loss of tapposition
compensation in the case of differential protection for a
phase-shifting transformer. In such a case a separate alarm can be
issued; and,
♦ check that the highest phase differential current doesn’t have
excessive second harmonic content.
11.5 Evaluation of the Proposed Turn-to-Turn Fault
Detection Principles
The performance of the proposed methods to detect turn-to-turn faults will
be evaluated on four actual winding faults captured in the field and one
RTDS simulated internal winding fault for a symmetrical, double core
PST.
Field Case #1
This field case was captured on an auto-transformer with the following
rating data 300/300/100MVA; 400/115/10.5kV; YNautod5; 50Hz, in
accordance with IEC terminology [58]. It should be noted that this autotransformer
tertiary winding is not loaded and is used as a delta-connected
Turn-to-Turn Fault Protection 185
equalizer winding. This auto-transformer is protected with two numerical,
two-winding differential protections from different manufacturers, in
accordance with the utility protection philosophy. In this particular
installation both numerical differential relays utilize the traditional
principle for differential current calculation where y/d connected
interposing CTs are used on star-connected power transformer windings,
as described in Section 5.1. Due to this reason, lower differential currents
were measured during the turn-to-turn fault than the differential currents
which are shown in this document. The existing differential relays
minimum pickup current is set to 30% of the auto-transformer rating.
Within approximately one year the utility had four incidents with this autotransformer
as stated below:
On 2003-04-27 at 09:39:51.199 hours, the auto-transformer 400kV
bushing in phase L3 exploded causing a heavy internal fault. The fault was
tripped extremely quickly by the unrestrained differential protection stage
in less than one power system cycle. The fault current contribution from
the 400kV network was 2500% and the fault current contribution from the
110kV network (i.e. fault current through the auto-transformer windings)
was up to 500% of the auto-transformer rating. Due to fast tripping, the
auto-transformer windings were not damaged. After on-site bushing
replacement the auto-transformer was put back into service on 2003-05-08.
On 2004-01-04 at 00:35:07.189 hours, a nearby external fault on the
110kV side in phase L1 appeared. The auto-transformer through-fault
current was around 280% of its rating. Both auto-transformer differential
protections were stable.
On 2004-05-04 at 05:10:30.614 hours, a nearby external fault on the
110kV side in phase L3 happened. The auto-transformer through-fault
current was around 310% of its rating. Both auto-transformer differential
protections were stable.
On 2004-05-04 at 05:28:46.736 hours, approximately eighteen minutes
after the external fault previously mentioned, the auto-transformer was
tripped by the Buchholtz relay. Both numerical differential protections did
not operate, and no other current or impedance measuring backup
protection had started. By oil analysis it was confirmed that extensive and
long-lasting electrical arcing within the auto-transformer tank had caused
186 Chapter 11
the Buchholtz relay operation. The auto-transformer was shipped to the
factory for repair and during inspection, a winding fault in phase L3 was
found. It was concluded that it was a turn-to-turn fault which had involved
only four turns at the auto-transformer neutral point in the common
winding of phase L3. Figure 101 shows the affected common winding part
in phase L3.
Figure 101: Common auto-transformer winding internal fault
in phase L3 at the winding neutral point.
In order to calculate the differential currents for this auto-transformer in
accordance with equation (4.30), the base currents and compensation
matrixes as shown in the following table, shall be used.
Turn-to-Turn Fault Protection 187
Table 23: Compensation data for the 300MVA; 400/115kV auto-transformer
Base Current Ib Compensation Matrix MX
W1,
400kV
433A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2,
115kV
1506A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
The disturbance recordings, from all aforementioned fault cases for the
auto-transformer were available from the two numerical differential relays.
By merging the disturbance recording files for fault cases three and four,
one overall disturbance file has been made. This merged disturbance file,
with 20 samples per power system cycle, was used to specifically test the
proposed algorithms for turn-to-turn fault detection.
In Figure 102, relevant instantaneous currents are shown. During the entire
turn-to-turn fault, all measured phase currents are smaller than 60% of the
auto-transformer rating. Therefore the traditional differential currents were
smaller than the pre-set differential minimum operational level, and
traditional differential protection could not operate for this fault. However,
from Figure 103 it is obvious that the low-level turn-to-turn fault was
definitely internal. Operation of the internal/external fault discriminator
consistently indicates an internal fault. This independent but sensitive
negative-sequence-current-based differential protection detects the fault
and characterizes it as internal.
In Figure 102 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1- and W2-side individual phase current waveforms; and
♦ RMS values of the differential currents.
188 Chapter 11
64 66 68 70 72 74 76
-50
0
50
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
64 66 68 70 72 74 76
-50
0
50
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
64 66 68 70 72 74 76
0
5
10
15
20
25
30
35
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 102: Current waveforms during turn-to-turn fault field case #1.
In Figure 103 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ phase angle between the two negative sequence phasors, as
defined in formula (10.5);
♦ phase angle between the two phase-wise phasors, as defined in
formula (10.4); and,
♦ phase angle between the two phase-wise phasors, very similar to
the one defined in formula (10.4), but with only M type
compensation matrices applied on all sides of the protected
transformer.
Turn-to-Turn Fault Protection 189
64 66 68 70 72 74 76
170
180
190
Neg Seq DCC Angle Directional Comparisson
[deg]
[Cycles]
Neg Seq
64 66 68 70 72 74 76
0
20
40
Pos Seq DCC Angle Directional Comparisson
[deg]
[Cycles]
Pos Seq
64 66 68 70 72 74 76
0
20
40
Phase-Wise DCC Angle Directional Comparisson
[Deg]
[Cycles]
L1
L2
L3
64 66 68 70 72 74 76
0
20
40
60
Phase-Wise DCC Angle Special Compenasation
[Deg]
[Cycles]
L1
L2
L3
Figure 103: Directional comparison during turn-to-turn fault field case #1.
Note that all types of directional comparison can detect that something is
wrong with the protected power transformer. However only the negative
sequence based directional comparison has seen the complete angle
inversion (i.e. angle of 180o) during this winding fault. What is quite
interesting is that the phase-wise directional comparison based on M
matrices, being used on all transformer sides can clearly identify the faulty
phase.
190 Chapter 11
Field Case #2
This field case was captured on an auto-transformer with the following
rating data 300/300/100MVA; 400/115/10.5kV; YNautod5; 50Hz. It
should be noted that this auto-transformer tertiary winding is not loaded
and is used as a delta-connected equalizer winding. This auto-transformer
is protected with one numerical, two-winding differential protection. The
differential relays minimum pickup current is set to 20% of the autotransformer
rating.
A serial auto-transformer winding internal fault occurred in phase L2 close
to the 110kV connection point as shown in Figure 104. The exact turn-toturn
fault location in one winding disc of the serial winding is shown in
Figure 105.
Figure 104: Serial auto-transformer winding internal fault in phase L2
was close to the 110kV connection point.
Turn-to-Turn Fault Protection 191
In order to calculate the differential currents for this auto-transformer in
accordance with equation (4.30), the base currents and compensation
matrixes as shown in Table 24 shall be used.
Figure 105: Exact location of the internal turn-to-turn fault in phase L2.
Table 24: Compensation data for the 300MVA; 400/115kV auto-transformer
Base Current Ib Compensation Matrix MX
W1,
400kV
433A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2,
115kV
1506A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
192 Chapter 11
In Figure 106 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1- and W2-side individual phase current waveforms; and
♦ RMS values of the differential currents.
9 10 11 12 13 14 15 16 17
-200
-100
0
100
200
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
9 10 11 12 13 14 15 16 17
-150
-100
-50
0
50
100
150
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
9 10 11 12 13 14 15 16 17
0
10
20
30
40
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 106: Current waveforms during a turn-to-turn fault, field case #2.
In Figure 107 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ phase angle between the two negative sequence phasors, as
defined in formula (10.5);
♦ phase angle between the two phase-wise phasors, as defined in
formula (10.4); and
♦ phase angle between the two phase-wise phasors, very similar to
the one defined in formula (10.4), but with only M type
compensation matrices applied on all sides of the protected
transformer.
Turn-to-Turn Fault Protection 193
9 10 11 12 13 14 15 16 17
160
180
200
Neg Seq DCC Angle Directional Comparisson
[deg]
[Cycles]
Neg Seq
9 10 11 12 13 14 15 16 17
-10
0
10
20
Pos Seq DCC Angle Directional Comparisson
[deg]
[Cycles]
Pos Seq
9 10 11 12 13 14 15 16 17
-10
0
10
20
30
Phase-Wise DCC Angle Directional Comparisson
[Deg]
[Cycles]
L1
L2
L3
9 10 11 12 13 14 15 16 17
-10
0
10
20
30
Phase-Wise DCC Angle Special Compenasation
[Deg]
[Cycles]
L1
L2
L3
NOT POSIBLE TO BE DETERMINED DUE TO LOW NEG SEQ
COMPONENT ON 110kV SIDE
Figure 107: Directional comparison during a turn-to-turn fault, field case #2.
Note that all types of directional comparison, except the one based on the
negative sequence current components, could detect that something is
wrong within the protected power transformer. The reason for failure of
the negative sequence directional comparison is no change of currents on
the 110kV side during this fault. While other directional comparison
methods could determine that something is wrong only the one where M
matrices are used (i.e. without the zero sequence current reduction) on all
transformer sides could clearly identify the faulty phase.
194 Chapter 11
Field Case #3
This field case was captured on a three-winding power transformer with
the following rating data 25MVA; 115/38.5/6.6kV; Yy0d11; 50Hz, in
accordance with IEC terminology [58]. It shall be noted that all three
windings are loaded. Because the transformer is installed in an industrial
complex, quite high harmonic content is present in individual phase
currents during normal through-load conditions. This transformer was
protected with a numerical, three-winding differential protection. The
35kV winding internal fault occurred in phase L2 as shown in Figure 108.
Figure 108: 35kV winding internal fault in phase L2.
Turn-to-Turn Fault Protection 195
In order to calculate the differential currents in accordance with equation
(4.30), the base currents and compensation matrixes as shown in Table 25
shall be used.
Table 25: Compensation data for a 25MVA; 115/38.5/6.6kV; Transformer
Base Current Ib Compensation Matrix MX
W1,
115kV 125.5A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2,
38.5kV
374.9A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W3,
6.6kV
2186.9A
0.911 0.333 -0.244
( 30 ) -0.244 0.911 0.333
0.333 -0.244 0.911
o M
− =
In Figure 109 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1-, W2- and W3-side individual phase current waveforms; and
♦ RMS values of the differential currents.
196 Chapter 11
2 3 4 5 6 7 8
-200
0
200
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
-100
0
100
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
-20
0
20
W3 Current Waveforms
[%]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
0
100
200
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 109: Current waveforms during a turn-to-turn fault, field case #3.
In Figure 110 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ phase angle between the two negative sequence phasors, as
defined in formula (10.5);
♦ phase angle between the two phase-wise phasors, as defined in
formula (10.4); and,
♦ phase angle between the two phase-wise phasors, very similar to
the one defined in formula (10.4), but with only M type
compensation matrices applied on all sides of the protected
transformer.
Turn-to-Turn Fault Protection 197
2 3 4 5 6 7 8
160
180
200
Neg Seq DCC Angle Directional Comparisson
[deg]
[Cycles]
Neg Seq
2 3 4 5 6 7 8
-50
0
50
100
150
Pos Seq DCC Angle Directional Comparisson
[deg]
[Cycles]
Pos Seq
2 3 4 5 6 7 8
-50
0
50
100
150
Phase-Wise DCC Angle Directional Comparisson
[Deg]
[Cycles]
L1
L2
L3
2 3 4 5 6 7 8
-50
0
50
100
150
Phase-Wise DCC Angle Special Compenasation
[Deg]
[Cycles]
L1
L2
L3
Figure 110: Directional comparison during a turn-to-turn fault, field case #3.
Note that all types of directional comparison could detect that something is
wrong with the protected power transformer. Due to the relatively big fault
current, all directional methods could see a quite big phase angle change
for this fault. However, the phase-wise directional comparison, based only
on M matrices being applied to all transformer sides, could not clearly
identify the faulty phase in this case.
198 Chapter 11
Field Case #4
This field case was captured on a three-winding transformer with the
following rating data 20MVA, 110±13*1,15%/21/10,5kV, YNyn0(d5),
50Hz. Note that this transformer tertiary winding is not loaded and is used
as a delta-connected equalizer winding. The 110kV winding neutral point
is directly grounded while the 20kV winding neutral point is grounded via
a 40r resistor. This transformer was protected with a numerical, twowinding
differential protection. The differential relay minimum pickup
current is set to 23% of the transformer rating. The 110kV winding
internal fault occurred in phase L2 when the OLTC was four steps from
the mid-position.
In order to calculate the differential currents in accordance with equation
(4.30), the base currents and compensation matrixes as shown in Table 26
shall be used.
Table 26: Compensation data for the 20MVA transformer
Base Current Ib Compensation Matrix MX
W1,
110kV
100.5A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
W2, 21kV 550A
2 1 1
1
0(0 ) 1 2 1
3
1 1 2
o M
− −
= ⋅ − −
− −
In Figure 111 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ W1- and W2-side individual phase current waveforms; and,
♦ RMS values of the differential currents.
Turn-to-Turn Fault Protection 199
12 13 14 15 16 17 18 19 20
-300
-200
-100
0
100
200
300
W1 Current Waveforms
[%]
[Cycles]
L1
L2
L3
12 13 14 15 16 17 18 19 20
-50
0
50
W2 Current Waveforms
[%]
[Cycles]
L1
L2
L3
12 13 14 15 16 17 18 19 20
0
50
100
150
Diff RMS Currents
[%]
[Cycles]
L1
L2
L3
Figure 111: Current waveforms during a turn-to-turn fault, field case #4.
In Figure 112 the following waveforms, either extracted or calculated from
this DR file, are presented:
♦ phase angle between the two negative sequence phasors, as
defined in formula (10.5);
♦ phase angle between the two phase-wise phasors, as defined in
formula (10.4); and,
♦ phase angle between the two phase-wise phasors, very similar to
the one defined in formula (10.4), but with only M type
compensation matrices applied on all sides of the protected
transformer.
200 Chapter 11
12 13 14 15 16 17 18 19 20
140
160
180
200
220
Neg Seq Angle
[deg]
[Cycles]
Neg Seq
12 13 14 15 16 17 18 19 20
0
20
40
60
80
Phase-Wise DCC Angle Standard Compenasation
[Deg]
[Cycles]
L1
L2
L3
12 13 14 15 16 17 18 19 20
-10
0
10
20
30
40
50
Phase-Wise DCC Angle Special Compenasation
[Deg]
[Cycles]
L1
L2
L3
NOT POSSIBLE TO BE DETERMINED DUE TO LOW NEG SEQ
COMPONENT ON 20kV SIDE
Figure 112: Directional comparison during a turn-to-turn fault, field case #4.
Note that all types of directional comparison except the one based on
negative sequence current components could detect that something is
wrong within the protected power transformer. The reason for failure of
the negative sequence directional comparison is no change in currents on
the 20kV side during this internal fault. While all other directional
comparison methods could determine that something is wrong, only the
one where M matrices are used on all transformer sides could clearly
identify the faulty phase.
For this case, large phase L2 110kV current and differential currents
appeared during the fault. However, it is interesting to note practically no
change in 20kV currents during this internal fault. Similar observations
were reported in [30] and [31]. Thus it can be concluded that the phasewise
directional criteria seems to be more dependable in detecting winding
Turn-to-Turn Fault Protection 201
turn-to-turn faults than the negative sequence component based directional
criterion.
Case #5
This case is the same test case as presented in Figure 64 and Figure 65,
Section 7.2. It is a single-phase to ground fault on the secondary side of the
regulating transformer for 2.5o phase angle shift across a PST. It was
shown that standard differential protection alone was not sufficiently
sensitive to detect this fault. However, by using the directional comparison
principle, it is actually possible to detect that something is wrong within
the protected PST.
In Figure 113 the following waveforms, from this simulation file, are
presented:
♦ phase angle between the two negative sequence phasors, as
defined in formula (10.5); and,
♦ phase angle between the two positive sequence phasors, as defined
in formula (10.5).
4 6 8 10 12 14
-2
0
2
4
6
8
10
12
[cycles]
[deg]
Sequence-wise DCC Angle Directional Comparisson
Pos Seq
Neg Seq
Figure 113: Sequence-wise directional comparison.
202 Chapter 11
In Figure 114 the following waveforms, from this simulation file, are
presented:
♦ phase angle between the two phase-wise phasors, as defined in
formula (10.4).
4 6 8 10 12 14
-4
-2
0
2
4
6
8
10
[cycles]
[deg]
Phase-wise DCC Angle Directional Comparisson
L1
L2
L3
Figure 114: Phase-wise directional comparison.
Note that all types of directional comparison have indicated a deviation
from a value of zero degrees, which in principle shall suggest existence an
internal fault. However, the negative sequence based internal/external fault
discriminator did not completely reverse (i.e. theoretically it should have a
value close to 180o). The phase-wise directional comparison in phase L3
had the biggest deviation from 0o phase shift and can therefore be used to
detect that something is wrong within the protected PST. It should also be
noted that the individual phase currents are in the order of 10-14% of the
PST rating during this fault.
203
Chapter 12
Conclusions
The equations (4.29) and (4.30) represent the universal method to calculate
the differential currents for an arbitrary three-phase power transformers.
This new method can be used to calculate:
♦ differential currents, in accordance with Figure 14, for any multiwinding,
standard or non-standard power transformers and PSTs
with arbitrary phase angle shifts and current magnitude variations;
♦ differential currents for overall differential protection of two or
more series connected power transformers and/or PSTs; and,
♦ differential currents, in accordance with Figure 14, for any FACTS
device, which comply with the assumptions for sequence no-load
voltages and load currents, shown in Figure 18 and Figure 19.
The presented method provides a clear relationship between the sequence
and the phase quantities for an arbitrary three-phase power transformer. By
using this method the differential protection for arbitrary three-phase
power transformers will be ideally balanced for all symmetrical and nonsymmetrical
through-load conditions and external faults, irrespective of
the actual OLTC position. Note that inrush and over-excitation
stabilization (e.g. 2nd and 5th harmonic blocking) is still required for such
differential protection.
The method is also not dependent on individual winding connection details
(i.e. star, delta, zigzag), but it might be dependent on correct information
regarding the actual OLTC position. On-line reading of the OLTC position
and compensation for phase current magnitude variations caused by OLTC
movement has been used for numerical power transformer differential
protection relays since 1998 [11]. This approach has shown an excellent
track record and is the de-facto industry standard in many countries. In this
thesis the feasibility of advanced on-line compensation for non-standard or
variable phase angle shifts across a power transformer has been
204 Chapter 12
demonstrated. Thus, differential protection for an arbitrary three-phase
power transformer can be provided in accordance with Figure 14. By
doing so, simple but effective differential protection for special converter
transformers and PSTs can be achieved, which is very similar to already
well-established numerical differential protection relays for standard
power transformers [11] and [12]. The only difference is that elements of
M(Θ) or M0(Θ) matrices used to provide the phase angle shift
compensation and the zero sequence current reduction are not standard or
fixed, but instead dynamically calculated based on the actual OLTC
position. Due to the relatively slow operating sequence of the OLTC, these
matrix elements can be computed within the differential relay on a slow
cycle (e.g. once per second). That should not pose any additional burden
on the processing capability of modern numerical differential protection
relays.
The presented method has been extensively tested by using disturbance
files captured in actual PST installations and RTDS simulations based on
practical PST data. All tests indicate excellent performance of this method
for all types of external and internal faults.
Any previous publications regarding such a differential protection relay
could not be found. Thus, it seems that this work is unique and completely
new in the field of power transformer protective relaying.
The presented differential method can also be used to check the output
calculations from any short circuit and/or load flow software packages for
power systems, which incorporate arbitrary power transformers and/or
PSTs. Finally, the method can be used in software packages of modern
secondary injection test equipment, in order to make automatic testing
routines for the differential protection of any power transformer.
It has also been shown that by using supplementary directional criteria the
dependability and the security of the traditional power transformer
differential protection can be improved. At the same time, these directional
criteria significantly improve the sensitivity of the power transformer
differential protection for low level transformer internal faults such as
turn-to-turn faults.
205
Chapter 13
Future Work
From the theoretical point of view it would be interesting to look further
into the possibility to apply this universal differential protection method
for an m-phase power transformer (m ≠ 3) and subsequently to derive
the equivalent M and M0 matrix transformations for such multi-phase
transformers. Afterwards, the possibility to use the presented method for
transformer differential protection of special railway transformers, which
convert a three-phase power system into a two-phase power system (e.g.
Scott and Le-blanc transformers), can be tested.
From the practical application point of view it would be interesting to
investigate the influence of incorrect OLTC position feedback from a
PST on the presented differential protection method and a way to
automatically detect such a condition. Further the behaviour of the
presented differential protection for PST series transformer saturation
during heavy external faults can be investigated.
For the differential protection of standard power transformers it can be
interesting to look further into the presented possibility to arrange the
phase angle compensation for a protected power transformer in more than
one way. Especially the behaviour of the different phase angle
compensation possibilities during transformer initial inrush, sympathetic
inrush and evolving faults can be further investigated.
Finally, the influence of the modern FACTS devices (such as HVDC
connections and series capacitors installed in the vicinity of the protected
power transformer or PST) on the operation of the presented universal
transformer differential protection method can be further investigated.
207
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