Turn-to-Turn Fault Protection for Power Transformers
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RIGA TECHNICAL UNIVERSITY Faculty of Power and Electrical Engineering Jevgenijs Kozadajevs Turn-to-Turn Fault Protection for Power Transformers Summary of the Doctoral Thesis Supervisor: Dr. sc. ing., Assoc. Professor Aleksandrs Dolgicers RTU Press Riga 2016
Transcript of Turn-to-Turn Fault Protection for Power Transformers
RIGA TECHNICAL UNIVERSITY
Faculty of Power and Electrical Engineering
Jevgenijs Kozadajevs
Turn-to-Turn Fault Protection for Power Transformers
Summary of the Doctoral Thesis
Supervisor:
Dr. sc. ing., Assoc. Professor
Aleksandrs Dolgicers
RTU Press
Riga 2016
Kozadajevs J. Turn-to-Turn Fault Protection
for Power Transformers. Summary of the
Doctoral Thesis. – R.: RTU Press, 2015. – 50 p.
Printed in accordance with Decision No. 25/16 of
RTU Promotion Council P-05 (Power and
Electrical Engineering) dated 18 January 2015.
The present research has been partly supported by the research programme
within the power engineering project No. 2 LATENERGI: “Optimization of Power
System Development Planning, Energy Production, Selling and Distribution”;
The present research has been partly supported by the research project No. 256/2012 “Power System Risks Management””.
ISBN 978-9934-10-775-7
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DOCTORAL THESIS
PROPOSED TO RIGA TECHNICAL UNIVERSITY FOR THE
PROMOTION TO THE SCIENTIFIC DEGREE OF DOCTOR OF ENGINEERING
To be granted the scientific degree of Doctor of Engineering, the present Doctoral Thesis
will be publicly presented on 11th February 2015 – 1:00 pm, at the Faculty of Power and
Electrical Engineering of Riga Technical University, 12/1 Azenes Street, Room 306.
OFFICIAL REVIEWERS
Dr. habil. sc. ing. Antans Sauhats
Riga Technical University, Institute of Power Engineering, Professor
Dr. sc. ing. Aleksandrs Gavrilovs
JSC Sadales tīkls, Development Department, Senior Engineer
Dr. sc. ing. Virginijus Radziukynas
Lithuanian Institute of Power Engineering, Head of Control and Automation Laboratory
DECLARATION OF ACADEMIC INTEGRITY
I hereby declare that the Doctoral Thesis submitted for the review to Riga Technical University
for the promotion to the scientific degree of Doctor of Engineering is my own and does not
contain any unacknowledged material from any source. I confirm that this Thesis has not been
submitted to any other university for the promotion to any other scientific degree.
Jevgenijs Kozadajevs ................................ (signature)
Date .............................................
The Doctoral Thesis has been written in the Latvian language. The Doctoral Thesis contains an
introduction, 4 chapters, conclusions and proposals, as well as references. The total volume of
the Thesis is 134 pages; it is illustrated by 96 figures and 114 formulas. The list of references
consists of 74 literary sources.
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Contents
INTRODUCTION ........................................................................................................................................... 5
1. THE ROLE OF TRANSFORMERS IN THE POWER SYSTEM AND TRANSFORMER FAULTS.. 10
CONCLUSIONS ................................................................................................................................................... 13
2. TRANSFORMER PROTECTION METHODS ..................................................................................... 14
2.1 TRANSFORMER PROTECTION .................................................................................................................... 14
2.1.1 Gas Protection .............................................................................................................................. 15
2.1.2 Differential Protection of New-Generation Transformers ............................................................ 15
2.2 AN EXAMPLE OF MICROPROCESSOR DIFFERENTIAL PROTECTION – DZL ................................................. 19
2.3 DEVELOPMENT OF DIFFERENTIAL PROTECTION AGAINST TURN-TO-TURN FAULTS ................................. 21
2.3.1 The Negative Sequence Current Protection Method .................................................................... 22
CONCLUSIONS ................................................................................................................................................... 22
3. TURN-TO-TURN FAULTS IN TRANSFORMERS .............................................................................. 23
3.1 THE CAUSES OF TURN-TO-TURN FAULTS AND THEIR PHYSICAL FACTORS .............................................. 23
3.2 THE METHODOLOGY OF PRACTICAL MEASUREMENTS ............................................................................. 26
CONCLUSIONS ................................................................................................................................................... 32
3.3 COMPUTER SIMULATION OF THE TRANSIENT PROCESS IN TRANSFORMERS .............................................. 32
3.3.1 Simulation of a Laboratory Transformer in MATLAB SIMULINK Environment ........................ 33
CONCLUSIONS ................................................................................................................................................... 38
3.4 THE FAULT DETECTION CRITERION ......................................................................................................... 38
CONCLUSIONS ................................................................................................................................................... 40
4. CURRENT TRANSFORMER ERRORS AND UNBALANCE CURRENT .......................................... 40
CONCLUSIONS ........................................................................................................................................... 43
REFERENCES .............................................................................................................................................. 45
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INTRODUCTION
THE TOPICALITY OF THE DOCTORAL THESIS
A critical analysis of the condition of the field of electrical engineering points to the
need to considerably increase the reliability of power transmission and distribution, which is
observed in many studies and official documents [1]. This is mainly due to the increase in the
number of serious emergencies, which cause large economic losses worldwide. The probability
of emergencies is largely determined by the operating conditions. At the conditions of market
economy and shortage of electric power, electric power companies in some regions operate
electric equipment in the maximum operating modes, which are close to the critical modes. This
is stimulated by the development and growing implementation of new means of intensive
electric equipment control, which have been insufficiently studied yet. Doubtlessly, such
operation leads to faster wear and tear of part of electric equipment and a decrease in the
reliability of the power supply system as a whole. This acquires special topicality with regard
to equipment that is close to the end of its normative service life or has exceeded it.
At present, the power industry experiences wide use of transformer equipment: power
transformers, controllable shunt reactors. It is natural that the reliability of the operation of
power networks is in many ways determined by the reliability of the transformer equipment.
Out of the total number of emergencies, about 10 % is made up by transformer faults, which
cause considerable economic losses [3]. This is due to the fact that an emergency repair of a
high-capacity transformer requires considerable financial means and time. Besides, in most
cases after a fire emergency, a transformer cannot be repaired at all but the ensuing emergency
expert examination fails to reveal the initial cause of the fault due to the large amount of
damage; thus, it is not possible to make the required structural changes, the goal of which is to
increase the reliability of the power equipment. During planned repairs of transformer
equipment, it is also complicated to evaluate the condition (the remaining service life) of the
insulation; therefore, increased requirements are set regarding the reliability and effectiveness
of means of relay protection and diagnostics.
Considerable attention has been paid to the development of the relay protection,
automation and control systems of transformers by G. Atabekov, A. Bulychev, V. Vanin,
A. Dmitrenko, A. Drozdov, A. Dyakov, A. Zasypkin, S. Kuzhekov, M. Lint, V. Nagay,
V. Novash, E. Podgorny, A. Fedoseyev, Y. Ulyanitsky, E. Shneyerson and many others.
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The main attention when solving the task of increasing the effectiveness of transformer
protection means is paid to differential protection. The degree of its technical accomplishment
and the reliability of its operation are mainly determined by the quality of input data. In this
connection, one of the possible ways of its development is the improvement of the metrological
characteristics of the measuring equipment and development of methods that take into account
the dynamic properties of the measurements. The accuracy of the measurements of current
transformers, taking into account the non-linearity of their parameters, is a vital task.
The paper is dedicated to the development of new methods of discerning minimum
internal faults of power transformers, which will make it possible to ensure reliable operation
of protection devices at early stages of such faults. The possibility to integrate the new methods
into existing protection devices will make it possible to increase the effectiveness and reliability
of protection devices without additional costs due to the otherwise required purchase of
expensive equipment.
THE GOAL AND OBJECTIVES OF THE DOCTORAL THESIS
The main goal of the Doctoral Thesis is to increase the sensitivity of power
transformers to turn-to-turn faults.
To achieve this goal, the following main objectives have been set:
1. to analyse the current technical level, methods and techniques of transformer
protection;
2. to analyse the electrotechnical parameters and magnetisation mode of the transformer;
3. to develop a digital model of the saturable transformer;
4. to develop an algorithm for determining a turn-to-turn fault by using the magnetising
inrush current;
5. to verify the digital model of the transformer by using experimental data;
6. to improve the influence of current transformers on the operation of the differential
protection of the transformer; to improve the error of current transformers;
7. to approbate the developed method.
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THE SCIENTIFIC NOVELTY OF THE DOCTORAL THESIS
1. The transformer fault determination methods and techniques currently in use have been
analysed and their deficiencies have been defined.
2. A new method has been synthesized for determining internal transformer faults; the
effectiveness of the method and the possibilities of its implementation have been
proved.
3. A mathematical model has been made for investigating transformer faults and a
methodology has been developed for verifying this model.
4. The factors limiting the measurement errors of current transformers have been studied;
a method of error compensation has been proposed that is to be implemented on a
microprocessor basis in the low-current mode.
THE METHODS AND TOOLS EMPLOYED
1. Power transmission protection methods.
2. Methods for simulating the power transformer transient process.
3. The QuickField electromagnetic process simulation and analysis environment.
4. The Matlab engineering problem solving software.
5. The Simulink simulation library of the Matlab software.
THE PRACTICAL SIGNIFICANCE OF THE DOCTORAL THESIS
The practical significance of the Doctoral Thesis lies in the following:
1. The proposed new fault determination method can be implemented both as a diagnostic
microprocessor device and an additional function for the differential protection terminal
of the transformer.
2. An instrument transformer error correction method has been proposed that can be
implemented by means of microprocessor-based differential protection, which will make
it possible to improve the sensitivity of the protection in the low-current mode.
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THE AUTHOR’S PERSONAL CONTRIBUTION TO THE RESEARCH
CONDUCTED
The foundation of the basic theses to be defended is made up by ideas created in close
co-operation with Associated Professor Aleksandrs Dolgicers and Professor Antans Sauhats,
and Ivars Zālītis. The Doctoral Thesis to be defended can be partly considered a continuation
of long-term research of the professors. Verification of the ideas, the models, the synthesized
software, the numerical experiments and their analysis as well as the recommendations for
efficient use belong personally to the author of this Doctoral Thesis.
APPROBATION OF THE DOCTORAL THESIS
The results of the research have been presented and discussed at seminars and
conferences of various levels:
1. 15th International Scientific Conference “Electric Power Engineering” (EPE 2014),
Brno, the Czech Republic, May 2014.
2. Advances in Information, Electronic and Electrical Engineering (AIEEE’2015),
Vilnius, Lithuania, November 2014.
3. 5th International Conference on Power Engineering, Energy and Electrical Drives,
POWERENG 2015, Riga, Latvia, May 2015.
4. 15th IEEE International Conference on Environment and Electrical Engineering (IEEE
EEEIC 2015), Rome, Italy, June 2015.
5. Powertech Eindhoven 2015, the Netherlands, Eindhoven, June – July 2015.
PUBLICATIONS
The following articles have been published on the investigated subject of the Doctoral
Thesis:
1. Dolgicers, A., Kozadajevs, J. (2014). Improvement of the Sensitivity of Differential
Protection of Power Transformers. Electrical and Data Processing Facilities and Systems,
No. 2, Volume 10. ISSN 1999-5458.
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The following patents have been submitted:
1. Dolgicers, A., Kozadajevs, J., Zālītis, I. Application No. 15047: “A method for the
Diagnosis of Power Transformers and a Device for Detecting Internal Faults”.
STRUCTURE AND CONTENT OF THE DOCTORAL THESIS
The Doctoral Thesis has been written in Latvian; it contains an introduction, four chapters,
conclusions and proposals for further work, as well as a bibliography with 73 reference sources.
The total scope of the Thesis is 134 pages; it has been illustrated by 96 figures and 114 formulas.
The introduction substantiates the topicality of the Thesis and formulates its goals and
objectives. It also reviews the problems solved by the Thesis that have been mentioned at
conferences and in publications and forwarded for the defence of the Doctoral Thesis.
Chapter 1 is dedicated to the role of transformers in the power system; the structural
peculiarities and equipment of various types of transformers; to the problems arising during
their operation; and to the influence of transformer fault on the power system.
Chapter 2 is dedicated to protection devices of power transformers and to differential
current protection in particular, the main function of which is protection from internal faults.
Examples are provided showing the operation of differential protection devices recently
developed by the world’s leading manufacturers, in the prevention of turn-to-turn faults in the
transformer; operation algorithms are analysed and the factors limiting the sensitivity of the
protection devices are found.
Chapter 3 provides a detailed description and approbation of a completely new algorithm
proposed by the author for indicating the presence of a turn-to-turn fault in the transformer,
based on the spectral image of the signal singled out from the magnetising inrush current at the
moment the transformer is energised.
Chapter 4 describes the methodology for using the readings of instrument transformers
for correcting the measurements of current transformers for protection needs, which makes it
possible to improve the sensitivity of differential protection in the case of internal faults at low-
current conditions.
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1. THE ROLE OF TRANSFORMERS IN THE POWER SYSTEM AND
TRANSFORMER FAULTS
Transformers installed at power plants or substations are divided into step-up and step-
down transformers; according to the number of windings, they are divided into two-winding,
three-winding and split-winding transformers. According to the number of phase windings
located on one magnetic core, there are single-phase and three-phase transformers. Three
single-phase transformers make up one three-phase group.
Fig. 1.1. Winding connection diagrams for a two-winding transformer with a split low-voltage
winding (a) and a three-phase three-winding autotransformer.
Split-winding transformers (Fig. 1.1 (a)) are mainly used for diminishing the amount of
short-circuit currents at the network point under consideration. A split-winding transformer is
a transformer with one of the windings consisting of two or more parts, which are not
electrically connected and which have separated outputs. This makes it possible to use each
part independently from the others. If necessary, separate parts of the winding, if their rated
voltage is equal, can be electrically connected and operated in parallel. Each part of the split
winding can also operate if the other one is disconnected. The summary capacity of all the parts
of the split winding is equal to the rated capacity of the transformer.
Split-winding trnasformers are manufactured for voltages of 500...750 kV both in
single-phase and three-phase design. For a single-phase transformer, the high-voltage and low-
voltage branches are located on different cores of the magnetic conductor. In a three-phase
transformer, the branches of the split low-voltage winding of each phase are not located on
different cores but on one core and displaced axially one in relation to the other. The mutual
location of the turns of the windings determines the operational properties and parameters of
the transformer’s equivalent circuit.
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Single-phase transformers with split windings are only used for voltages of
500...700 kV. They are not intended for serial manufacture. Still in the future, the role of this
type of transformers for networks with a voltage of up to 35 kV will increase since the short-
circuit currents in the 0.4...35 kV network increase and they need to be diminished.
Fig. 1.2. The winding of a transformer.
An autotransformer differs from other types of transformers in that two of its windings
are electrically connected, which ensures transmission of capacity not only electromagnetically
but also electrically. Autotransformers are widely used in networks with a voltage of
110...330 kV and higher since they are less expensive and with lesser summary losses of active
power in the windings as compared with ordinary transformers of the same capacity. Also,
losses of capacity in the steel of autotransformers are lower than in the steel of other types of
transformers.
Usually in a multiple-winding autotransformer, the high-voltage and medium-voltage
windings are electrically connected whereas the low-voltage winding (the tertiary winding) is
electromagnetically connected with the high-voltage winding (Fig. 1.1 (b)). The three phases
of the high-voltage and medium-voltage windings of an autotransformer are joined in a wye
connection and their common neutral is earthed, whereas the lower-voltage winding is always
joined in a delta connection. Since the windings are electrically connected, the distribution of
power flows in the autotransformer is different than in other types of transformers [5].
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The most widespred type of fault for transformers with a voltage of 110 kV and higher
is a damage of the high-voltage inputs. At present, non-hermetic and hermetic oil-filled inputs
as well as inputs with hard insulations are used.
A widespread type of transformer fault is a damage of on-load voltage regulation
devices. Damage of the contact system may arise due to incorrect regulation of the contacts
(insufficient or excessive pressure, skewing, etc.), which is caused by the formation of oxide
film on the contacts in the case of rare switching as well as by disturbances in the kinematic
diagram.
Much attention is paid to protecting transformers from damage of windings and
interlayer insulation (internal damage). Poorly dried insulation electric cardboard or paper,
polluted or humid transformer oil lead to local weakening of hard insulation accompanied or
not by creeping discharge, followed by breakdown.
Disturbance in the function of hard insulation is also caused by non-observance of
dimensions (distances between the sheets of electric cardboard, etc.), swelling of loosely wound
insulation, disturbance in the function of the cooling system, excessive overloads of the
transformer (overvoltage, overcurrent), etc.
Due to a wide variety of reasons and grave consequences that arise as a result of damage
of windings and interlayer insulation, the most attention is paid to timely detection of this type
of disturbance in the function of transformers.
Protection against internal fault, for example, turn-to-turn faults, is the responsibility of
transverse differential protection as well as gas protection.
Fig. 1.3. Turn-to-turn fault in a transformer.
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Since the power capacities continuously increase, the short-circuit capacities increase
as well. Due to this increase and if the pressing of the windings is weakened, the electrodynamic
stability of the windings under the conditions of external short circuits may be insufficient. As
a result, external short circuits may result in the deformation or rupture of the winding although
its insulation has been in good condition before the fault.
Influence of Transformer Fault on the Power System
The power cut that took place in Chile on 14 March 2010 affected the largest part of the
country’s territory. It set in at 20:44 (23:44 GMT) on Sunday evening and continued into the
following day. The power cut had been caused by a fault of a 500 kV transformer at a substation
in the south of the country, approximately 700 km south of the capital, Santiago. There was a
moment when Santiago received only 8 per cent of the usually required amount of power [1]–
[2]. On 24 September 2012, in Almaty (Kazakhstan), an emergency trip of all the 220 kV
connections of the substation “Almaty-500” occurred. This resulted in loss of power supply to
the whole city and Almaty region, including such important objects as the city underground and
the airport.
Conclusions
At present, transformer equipment is widely used in the power supply: power
transformers, controllable shunt reactors. It is natural that the reliability of the operation of
power grids is in many ways determined by the reliability of the operation of transformer
equipment. Out of the total number of emergencies, approximately 10 per cent is made up by
transformer damage, which causes considerable economic losses [2]. This is due to the fact that
repairing a high-capacity transformer requires considerable financial means and time. In
addition, in most cases after an emergency fire, a transformer is impossible to restore but the
following expert examination fails to indicate the initial cause of the damage due to the large
amount of damage and thus makes it impossible to introduce the required structural changes,
the goal of which is increasing the reliability of the power equipment. During planned repairs
of transformer equipment, it is also complicated to evaluate the condition (remaining service
life) of the insulation; therefore, increased requirements are set regarding the reliability and
efficiency of relay protection and diagnostics means.
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2. TRANSFORMER PROTECTION METHODS
2.1 Transformer Protection
Contemporary power transformers are complex devices that consist of a large number
of structural elements and accessories. Normative documents set a number of requirements
regarding the protection panels of power transformers.
The devices of a transformer protection panel have to be able to ensure base and stand-
by protection of transformers, manual and (sometimes) automatic control of on-load voltage
regulation, measurements and indication of electrical parameters, reflection of the state of high-
voltage switching devices, emergency and warning alarm, and connection to the information
network for the organisation of control systems of various levels.
As an example, let us look at the protection panel of Siemens Sepam transformer:
• differential protection without a time delay (base protection) with regulation on the
basis of the magnetising inrush current and the unbalance currents;
• maximum current protection (standby), which operates separately from the base
protection and which has opeation blocking according to voltage if necessary;
• acceleration of maximum current protection in case of switching on at short circuit;
• current overload protection;
• protection against lowering of oil level (for alarm);
• protection against an increase in oil temperature;
• gas protection (for alarm + for trip);
• gas protection of the on-load regulation device (for trip, with a possibility of switching
over to alarm);
• overheating protection according to a mathematical model;
• zero sequence protection;
• short-circuit tripping reservation at the primary side of the transformer. Besides, the
transformer protection panel ensures operation alarm for each type or protection;
alarm in case of anomalous modes; separate discontinuation of the operation of base
and reserve protection (for checking the operation of the protection devices) as well as
testing units and other devices for testing of protection devices.
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Protection against internal damage, for example, turn-to-turn faults, is the responsibility
of transverse differential protection as well as gas protection [7], [10], [11], [12].
2.1.1 Gas Protection
In case of a turn-to-turn fault, progressing transformer damage emerges, accompanied
by warming to a high temperature; the oil and the hard insulation decompose, forming light
hydrocarbons and gases, which dissolve in the oil and accumulate in the transformer’s gas relay.
The time of gas accumulation in the relay may be relatively long, but the accumulated gas may
differ considerably by its content from the gas collected near the place of release.
Therefore, diagnosis of the fault on the basis of analysis of the gas collected from the
relay is difficult and may even prove belated. All of the above testifies to the fact that gas
protection is not sufficiently sensitive and is not capable of reacting at the early stages of the
fault.
The goal of the present Thesis is to develop protection devices that will be able to react to
an incomplete turn-to-turn fault, which will make it possible to disconnect the transformer in
due time and avoid considerable transformer damage [7], [10], [11], [12].
2.1.2 Differential Protection of New-Generation Transformers
Looking at the recent improvements of differential protection, it has to be taken into
account that the changes are mainly related to those parts of the differential protection that
follow after the current transformers of its “shoulders” since, irrespective of the development
of various non-traditional instrument transformers, it can be forecast that for at least another
5...10 years, the bulk of power engineering facilities will use for differential protection usual
current transformers that are related to diferences in magnetisation, that is, to the unbalance
current between the “shoulders” of the differential protection. This means that the designers of
modern-day differential protection need to deal with the differential protection problems
described in Chapter 2 not only to widen the scope of protection functions, but also to increase
their efficiency [9], [18], [19], [20].
During the recent years, the operation algorithms of differential protection are mainly
based on the dependence of the unbalance current on the approximations of the characteristic
curve of the current flowing through the power transformer, Inb=f(IT), as described in the
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theoretical fundamentals of relay protection. The shape of the characteristic curve is shown in
Fig. 2.1 below.
Fig. 2.1. The shape of the dependence of unbalance current on the current flowing through the
transformer.
The characteristic curve of the unbalance current provided in Fig. 2.1 can be divided
into three basic sections, the first one whereof till point a corresponds to the unbalance current
of a weakly loaded power transformer. The next section, from a to b, characterises the
unbalance current for a considerably loaded power transformer. The section after point b is
related to an external short circuit and the unbalance current of magnetising inrush currents.
The differential protection solutions encountered in practice use an approximation of the
characteristic curve of the unbalance current Inb=f(IT) shown in Fig. 2.1 in an analogous plane
of coordinates, where the unbalance current has been substituted by the module of the full
differential current, which according to the basic differential protection diagram could be
expressed as follows:
𝐼𝑑𝑖𝑓 = 𝐼𝑀𝑂 = |𝐼12̇−𝐼22̇ |. (2.1)
On the other hand, the current flowing through the power transformer has been replaced
by the sum of the modules of the secondary currents of the differential protection current
transformers, which also reflects with a sufficient accuracy the size of the current flowing
through the power transformer. The characteristic curves of the more frequently encountered
operation algorithms in these coordinates can be seen in Fig. 2.2 below.
Inb
IT
a b
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Fig. 2.2. Characteristic curves of the operation algorithms of differential protection frequently
encountered nowadays.
These are the characteristic curves used by the modern-day algorithms of differential
protection where A designates the characteristic curve of the unbalance current caused by the
changes in the magnetising properties of the current transformers in the given coordinates. In
principle, the characteristic curve of the protection device should repeat the characteristic curve
of the unbalance current, A, with an unchanging delay reliability area. It is clear that this type
of characteristic curve will be non-linear and difficult to carry out; therefore, a three-degree
approximation B of the unbalance current characteristic curve A is frequently used in practice.
The unbalance current approximation characteristic curve B has a constant operation level,
which corresponds to incomplete loading of the power transformer, and two linearly changing
differential current or operation sections (if necessary, different numbers of linear sections are
used), which characterise considerable loads and external short circuits. These are described by
their inclination factors as seen in Fig. 2.2:
𝑘1 = 𝑡𝑔(𝛼1) =𝑑𝐼𝑑𝑖𝑓1
𝑑(|𝐼12̇ |+|𝐼22̇ |) and (2.2)
𝑘2 = 𝑡𝑔(𝛼2) =𝑑𝐼𝑑𝑖𝑓2
𝑑(|𝐼12̇ |+|𝐼22̇ |). (2.3)
|𝐼12̇| + |𝐼22̇|
dIdif2
dIdif1
𝑑(|𝐼12̇| + |𝐼22̇|)
2
1
INno
I0Max
50Hz
D
B
A
Operation durimg
magnetising inrush
current
Independent operation
C
𝐼𝑑𝑖𝑓 = |𝐼12̇ − 𝐼22̇|
Operation during
external short
circuit
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Correspondingly, if differential current is the largest one at the module of the given
geometrical sum of secondary currents, as foreseen by characteristic curve B, the differential
protection operates and trips the protected element. Algorithms of this kind ensure precise
operation at different unbalance currents of the power transformer as well as optimum
insensitivity in case of unbalance inrush current during external short circuit.
False operations that are due to power transformer magnetisation transient processes are
eliminated by means of the second harmonic blocking methodology, which is based on
complete blocking of DP operation if the amplitude of the filtered-off second harmonic of
differential current relative to the amplitude of the first harmonic exceeds normal mode and
level of short circuits. Usually, the differential protection blocking criterion that characterises
magnetisation inrush current is represented by a level of the content of the second harmonic,
which is equal to starting from 17 percent of the base harmonic, but solutions exist which
additionally use the fifth harmonic or both of these simultaneously. A differential protection
device of this type, as it registers the beginning of the power transformer magnetising process,
becomes completely insensitive. As the differential protection operates in the blocking mode,
it does not react to power transformer damage until the transient process ceases. As a result, a
considerable delay of operation can emerge if there are no additional settings.
Improved relays of this type of differential protection pass over from the unbalance
current characteristic curve approximation B, according to the same criterion of second and/or
fifth harmonic, to a simplified linear differential operation current insensitivity characteristic
curve C, which is displaced in relation to the axis of the argument |𝐼12̇| + |𝐼22̇ | by the maximum
value of the first harmonic of the magnetising current. The displacement of the first harmonic
has been introduced since before arriving in the units of the logical organs, the base harmonic
of the differential current is filtered off by means of a Fourier filter (the characteristic curves
of that harmonic are also provided in Fig. 2.2) and the higher harmonics required for the criteria
are filtered off separately. This kind of improved DP versions still retains a certain level of
sensitivity during magnetisation inrush current of the power transformer, replacing complete
blocking by introduction of additional insensitivity.
To obtain higher stability of operation of the differential protection, some algorithms
determine differential current level INno at which the operation takes place instantaneously
regardless of the operation mode of the power transformer. This kind of solution is to be
regarded as an efficient measure of reliability, particularly for differential protection devices
with complete blocking according to the second and/or fifth harmonic criterion.
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2.2 An Example of Microprocessor Differential Protection – DZL
The initial idea of inhibiting the additional DZL transient processes of DP relays is
based on the increase of the operation differential current Idif no as the inhibiting current Ib
increases, and the accumulation of that increases. If the inhibiting current does not increase, the
additional inhibiting current of transient processes Ipapb is determined on the basis of the
exponential character of the aperiodic component. The testing of the initial model pointed to
the time delay characteristic of the old generation of DP relays before the operation in case of
internal short circuit, which is related to an increase in inhibiting current during short circuit.
The above-described problem leads to an unnecessary decrease in sensitivity and speed. To
prevent loss of sensitivity and speed during internal short circuit, a detector of external short
circuits was installed, which was based on the mutual dependence of differential and inhibiting
current. This detector allows an increase of additional inhibiting current for dampening of
transient processes only if this has been caused by external short circuit or a sharp jump of load.
As the DP current transformers saturate, the current inhibiting the transient processes stops
increasing, yet by this moment, a value of additional current inhibiting transient processes
providing sufficient protection delay has to be accumulated.
The value of the i-th operation current of DZL of differential protection [44] can be
determined as follows by using the inhibiting current and the accumulated additional current
inhibiting transient processes:
𝐼𝑑𝑖𝑓 𝑛𝑜(𝑖) = 𝑓𝑎𝑝𝑟(𝐼𝑏(𝑖)) + 𝐼𝑝𝑎𝑝𝑏(𝑖), (2.4)
where fapr(Ib(i)) stands for the two-stage operation dependence of the standard used in terminal
P543-P546 on the characteristic curve of the inhibiting current shown in figure below:
20
Fig. 2.3. The characteristic curve of the inhibition of terminal P543-P546 and determination
of external short circuits.
In order to determine the additional inhibiting current Ipapb of DZL in differential
protection relays, the speed of change of the differential current is first determined, which will
be designated by dIdif as the mode changes. This will be determined, finding the differences
between the differential current and the inhibiting current:
Δ𝐼𝑑𝑖𝑓(𝑖) = 𝐼𝑑𝑖𝑓(𝑖) − 𝐼𝑑𝑖𝑓(𝑖 − 1), (2.5)
Δ𝐼𝑏(𝑖) = 𝐼𝑏(𝑖) − 𝐼𝑏(𝑖 − 1). (2.6)
Then, the speed of the i-th change of the differential current can be determined as follows:
𝑑𝐼𝑑𝑖𝑓(𝑖) =Δ𝐼𝑑𝑖𝑓(𝑖)
Δ𝐼𝑏(𝑖). (2.7)
Using the determined speed of differential current change, the additional transient
process inhibiting i-th current value Ipapb(i) is determined according to the algorithm described
below:
If dIdif(i)< Kn and 𝛥𝐼𝑏(𝑖)>0, external short circuit is detected with a change of inhibiting
current in the overall characteristic curve section with inclination factor Kn. If this condition is
fulfilled, the additional inhibiting current is increased according to the following expression:
𝐼𝑝𝑎𝑝𝑏(𝑖) = 𝐷𝐼𝑝𝑎𝑝𝑏(𝑖 − 1) + 𝑆𝐼𝑏(𝑖), (2.8)
where D — stands for the damping factor (D<1);
S — the scale factor.
[Ib(i),Idif(i)]
[Ib(i),Idif(i)]
[Ib(i-1),Idif(i-1)]
K1
K2
1
2
Idif
Ib
Internal short
circuit or
saturation of
current
transformers
dIdif>K2 External short
circuit dIdif<K2
21
In other cases, the accumulated content of additional transient process inhibiting current
slowly decreases:
𝐼𝑝𝑎𝑝𝑏(𝑖) = 𝐷𝐼𝑝𝑎𝑝𝑏(𝑖 − 1) (2.9)
The discrete time algorithm of the DZL DP relay terminal MiCOM P543-546 operates
with a discretisation frequency of 400 Hz, or 8 measurements over a period, operating in a
50 Hz network. If the first condition of the algorithm is not fulfilled (as an internal short circuit
occurs, the current transformers saturate or an external short circuit passes over to an internal
one), over one period, which in a 50 Hz network corresponds to 20 ms, the transient process
additional inhibiting current according to the expression decreases to D8 Ipapb(t=0). The damping
factor used in practice is D = 0.8, according to which we arrive at D8 Ipapb(t=0)=
0.88Ipapb(t=0)0.1678Ipapb(t=0), or approximately 17 % of the initial additional transient process
inhibiting current. Such a fast damping of the additional inhibiting current makes it possible to
avoid a protection operation delay, which was detected in the testing of the initial models. Of
particular interest is a DZL relay with an additional transient process inhibiting algorithm,
which has been tested by O.I.Bagleybter. The co-authors of the DZL relay description widely
used the simulation unit of the MATLAB software. As a result, the incorrect operation of the
old DZL algorithm during external short circuit has been successfully eliminated. This does not
preclude the possibility of using a similar solution for magnetising inrush currents as well. In
addition, using the second and/or fifth harmonic criterion, the required component against
magnetising inrush currents should be added to the additional transient process inhibiting
current or the expression should be changed in some other way.
2.3 Development of Differential Protection Against Turn-to-Turn Faults
Over the recent years, the development of microprocessor technology has been
accompanied by the development of differential protection. However, the attempts to increase
the sensitivity of transformer differential protection against internal turn short circuits have still
been unsuccessful. Only in the recent ten years, the world’s leading manufacturers, for example,
ABB and General Electric, have proposed new principles of protection operation, which has
enabled considerable advances, increasing sensitivity against turn-to-turn faults. Let us have a
closer look at the newest developments in this direction.
22
2.3.1 The Negative Sequence Current Protection Method
The method is based on the theory of symmetrical components, more specifically, on
the use of negative sequence current, and is widely used in the differential protection devices
of ABB [50]. According to the information provided by the manufacturer, this method allows
detecting even the damage of a small number of turns — up to 1 per cent of the total number
of turns. The sensitivity limit of the method corresponds to the upper limit of the value of the
negative sequence current, which is due to the error of the measuring equipment and the
asymmetry of the magnetic system (Fig. 2.4).
B
P1 P2 P3
S1 S2 S3
Fig. 2.4. The asymmetry of the magnetic system of a three-core transformer.
Conclusions
This chapter discussed the main principles of the operation of the differential protection
of transformers from the point of view of protection from internal turn fault. Over recent years,
many improvements have been developed for protection against false operations and increasing
sensitivity to minimal damage.
However, it has to be pointed out that notwithstanding the evident progress, attempts to
achieve sufficient sensitivity to incomplete turn damage as well as to turn damage in which the
number of damaged turns is less than 1 per cent have been unsuccessful. The next chapter
provides a cardinally new method for detecting turn fault, which shows considerably better
results regarding sensitivity as compared the methods described before.
23
3. TURN-TO-TURN FAULTS IN TRANSFORMERS
3.1 The Causes of Turn-to-Turn Faults and Their Physical Factors
A transformer no-load equivalent circuit is provided in Fig. 3.1.
Fig. 3.1. An equivalent circuit of a transformer with a turn-to-turn short circuit.
Fig. 3.2. No-load mode of a transformer with short-circuited turns.
U1
I1
E1
E`Mwk
=EM1
E`wk
I1R
1
R1
R`wk
I`wk
I
0
jX1 jX`
wk
jXM
R0
I`wk
R`wk
W1
i1
u1
iwk
Kw
Φo
Φwk
Core
Core
Φ
Wk
24
When a short circuit occurs between some of the turns of a transformer’s winding,
according to Lenz’s law, demagnetising current flows in these turns, striving to eliminate its
cause. This results in magnetomotive force of the short circuited turns Fwk=iwkwk and, as shown
in Fig. 3.2, a flow Φwk that is opposite to the no-load flow Φ0 of the primary winding. The
opposite flow diminishes the induction degree of the magnetic field and displaces the working
point along the hysteresis loop B = f(H) from B1 to B2 (see Fig. 3.3), which results in an opposite
electromotive force of the lower voltage primary winding. Since the primary voltage is
determined by the grid and practically unchanging, it can be seen that it is necessary for the
voltage drop i1R1, or the current i1, to increase for the grid voltage to be balanced. Such a
development influences the hysteresis loop, namely, the intensity of the magnetic field
increases, which can be seen from the magnetic field intensity formula:
𝐻 =𝑖𝑤
𝑙 , (3.1)
where l — stands for the length of the magnetic circuit (const);
w — the number of turns (practically unchanging for a small number of short-circuited
turns);
i — the current flowing in the turns.
Both changes that influence the hysteresis loop are characteristic both in a steady state
and in transient processes; their overall influence compresses the hysteresis loop along the
magnetic field induction (B) axis and extends it along the mangetic field intensity (H) axis. As
a result of the above deformations of the hysteresis loop, it increasingly resembles an oval as
the number of short-circuited turns increases. This is explained by an increase of the total
electromotive force induced in the short-circuited turns whereas the resistance increase is small,
as a result of which the current of the short-circuited turns and its magnetomotive force increase.
These changes are depicted in general form in Fig. 3.3.
25
Fig. 3.3. Changes of the hysteresis loop in case of short circuits in the transformer.
From the active resistance of the short-circuited turns, which is forecast to be higher
than the inductance, an additional active resistance is introduced to the circuit to be connected
with a squared transformation ratio. As a result, Q factor of the circuit will diminish and the
aperiodic component will decrease at a faster rate, which is also characterised by the time
constant Ta used for characterising transient processes:
𝑇𝑎 =𝑥𝐿
𝜔𝑅=
𝐿
𝑅. [5] (3.2)
Mainly only the periodic electromotive force will be induced in the short-circuited turns
since 𝑑Φ𝑎
𝑑𝑡≪
𝑑Φ𝑝
𝑑𝑡 , that is, the change of the aperiodic flow over time is considerably slower
than that of the periodic flow. Correspondingly, a practically periodic current flows in the short-
circuited turns and the opposite flow most of all inhibits the periodic flow component brought
about by the primary magnetomotive force.
Taking into account such an inhibition of the period flow and the accelerated damping
of the aperiodic component, in the transient process it can be expected that the flow jump after
the first half-period will be smaller and also the saturation degree during the transient process
will be less. This means that the magnetising inrush current amplitudes or peaks will be smaller,
which in combination with a lower saturation level would be characterised by a lower content
of the higher harmonics in the current consumed by the transformer. The form of the peaks
themselves, most probably, will not change considerably.
The visual changes of the consumed current, which also mean changes in its harmonic
content, are more probable to be observed in the negative sections of the instantaneous current
characteristic curve, the shape of which is usually closer to a sinusoid since in these sections
B
H
B2
B1
-B1
-B2
H
B
26
the saturation level is lower (Bpal in case of unipolar character of the magnetising current). In a
normal magnetising transient process, along with a considerable degree of saturation, the lower
sections of the current characteristic curve usually have a shape similar to stationary no-load
current with sharp projections in the minima, which will most probably be partly or fully
smoothed off due to the influence of the opposite flow Φwk on the hysteresis loop and the total
flow as well as due to a decrease in the saturation degree [1]–[2].
3.2 The Methodology of Practical Measurements
In order to confirm the phenomenon described above, a laboratory experiment was
conducted.
The measurements were made by means of a transformer from the series ТАН 125-
127/220-50, which connected both primary windings in series and was intended for a 220 V;
50 Hz network (shown in Fig. 3.4 and designated by T1 in the measurement circuit). Additional
turns were added to the examined transformer, which could be short-circuited or disconnected
by means of switches.
In addition, in order to observe new changes in the transformer connection transient
process, the initial phase of the voltage and the remanent induction need to be equal in these
trials. The whole connection diagram is provided below, Fig. 3.4.
As could have been expected, the changes in the magnetic flow have influenced the
shape of the magnetising inrush current. Based on the obtained results, an algorithm was
developed to single off the signal containing information about the presence of internal damage
from the magnetising inrush current.
The developed algorithm is shown in Fig. 3.6 [69], [70]. In order to confirm the change
in the hysteresis loop described in theory in case of a turn-to-turn fault, experiments were
conducted with an undamaged transformer as well as a transformer with one/ two/ three
damaged windings.
27
Fig. 3.4. Measurement connection diagram.
The results are shown in Fig. 3.5. As can be seen, the practical experiment fully confirms
the theory, and the higher the number of damaged turns, the more significant the changes of the
hysteresis loop.
a b
Fig. 3.5. A hysteresis loop for (a) an undamaged transformer; (b) a transformer with two
damaged (short-circuited) turns.
-1,5
-1
-0,5
0
0,5
1
1,5
-1500 -1000 -500 0 500 1000 1500
B, T
H, A/m
SF1 SA1 K1.1
K1.2
K1.3
K1.4
SB1 K1
C1
R1
R2
T1
Tos 220V
220V
220V
To the oscillograph
To the oscillograph
-1,5
-1
-0,5
0
0,5
1
1,5
-1000 0 1000 2000
B, T
H, A/m
28
Fig. 3.6. A MATLAB algorithm flow diagram for analysing magnetising inrush currents.
Measurement
array A1
Smoothing off disturbances with
average instantaneous value
Smoothed-off array
A
Determining I0Max and its index
Yes
No
Inversion
of A and
A1
I0Min determined
Indices of I0 minima
determined
Approximation of the
aperiodic component by
Lagrange polynomial
B(i)=A1(i)-LA(i)
Aperiodic component
approximation array LA
Vai I0<0
Yes
No
Array of I0 minima
EKSi
B(i)=0
Array B to be
processed
Discrete Fourier decomposition
of array B for 15 harmonics
Start
Relative amplitude array
H for 15 harmonics,
displacement angle array
AlfaR
End
MIN
29
This algorithm has been described in more detail below:
The size of the input data matrix A1 is determined and by using the instantaneous
average value of the number disturbances of the input signal are smoothed off, obtainining array
A;
The value largest by module in the whole smoothed-off array A is determined (the
largest current peak or amplitude) with its index; after that, the values of the arrays A and A1 of
current i0 are inverted or the current characteristic curves are inverted if the largest peak is
directed downwards, for the sake of convenience in further processing;
The minimum value of magnetising current i0 is determined, which will be the departure
point for determining the aperiodic component;
Approximation of the lower sections of the magnetising current characteristic curve is
done by the Lagrange polynomial, for the last minimum, the last but one, and the fourth one
from the end;
The whole array of the smoothed-off current is browsed and in case of positive values
counting of indices is continued whereas for negative values, also the index of the minimum
value is determined and stored in the array of smoothed-off current minima EKSi;
An additional processing array B is formed, in which the values of the negative sections
of the last three full magnetising inrush currents are recorded, from which the values of the
aperiodic component are subtracted and which are brought closer to the index axis for more
precise analysis of the very lowest sections;
For array B, discrete Fourier decomposition is conducted and the following is
determined for the first fifteen harmonics: amplitudes, angles, relative values of amplitudes in
relation to the first harmonic as well as the relative displacement angles in relation to the first
harmonic;
All the analysis graphs are output, consecutively providing characteristic curves of the
instantaneous values of magnetising current (A1), the Lagrange approximation instantaneous
values [48] (LA), the instantaneous values of the current sections to be processed (array B),
using instead of time since all the measurements have the same discretisation frequency. These
are followed by a layout of all the decomposition harmonics in three-dimensional space, where
the horizontal axis of the front plane contains the numbers of the harmonics, the second
horizontal axis contains the relative displacement angles and the vertical axis, the relative
values of the amplitudes of the harmonics. The last two graphs show a separate two-dimensional
division of the relative amplitudes and displacement angles of the harmonics.
30
As can be seen, the operation of the algorithm results in a spectral image — the first
fifteen harmonics of the signal singled out from the magnetising inrush current. The need to
single off the aperiodic component of signal should be pointed out once more.
Analysis of the Experiment Results
The first example to be considered is a specimen of output data for the transformer
without turn-to-turn faults chosen as the point of departure:
Time, r.v.
Current, r.v.
0 1000 2000 3000 4000 5000 6000 7000 8000 9000-0.2
-0.1
0
0.1
0.2
0.3
a b
Current, r.v.
0 500 1000 1500 2000 2500 3000 35000.05
0.07
0.08
0.075
0.065
0.06
Time, r.v.
c d
e
Fig. 3.7. The output data of the algorithm for analysing the magnetising transient process of
an undamaged transformer: (a) the magnetising inrush current; (b) the singled-out aperiodic
component; (c) the singled-out negative half-periods; (d) the harmonic composition (the
amplitudes); (e) the harmonic composition (the amplitudes and the angles).
Harmonic Nr.
%from basic harmonic
0.4
0.2
0.6
0.8
1
00 5 10 15
Current, r.v.
0-0.05
-0.04
-0.03
-0.02
-0.01
500
0
1000 1500 2000 2500 3000 3500Time, s
Amplitude of harmonic
Harmonic Nr.H
arm
onic
ang
le
31
current, r.v.
time, r.v.
-0.05
-0.04
-0.03
-0.02
-0.01
0
0 500 1000 1500 2000 2500 3000 3500
From Fig. 3.7 it can be seen that after the elimination of the aperiodic component, the
zoomed-in negative sections of the magnetising current really are characterised by a sharp shape
at the minimum point and outspokenly steep edges, which, on the whole, as can be seen in the
graph of the relative amplitudes, corresponds to a considerable content of higher harmonics.
Current, r.v.
Time, .r.v.
-0.2
-0.1
0
0.1
0.2
0.3
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
a b
c d
Harmonic Nr.H
arm
onic
ang
le
Harmonic amplitude
e
Fig. 3.8. The output data of the algorithm for analysing the magnetising transient process of a
transformer with one short-circuited turn: (a) the magnetising inrush current; (b) the singled-
out aperiodic component; (c) the singled-out negative half-periods; (d) the harmonic
composition (the amplitudes); (e) the harmonic composition (the amplitudes and the angles).
Current, r.v.
Time, r.v.
0 500 1000 1500 2000 2500 3000 3500
0.08
0.095
0.105
0.1
0.09
0.085
0.075
% from basic harmonic
Harmonic Nr.
0.4
0.2
0.6
0.8
1
00 5 10 15
32
The observations allow us to conclude that during a magnetising transient process, a
considerable saturation of the magnetic circuit is reached and the shape of the magnetising
current is considerbly distorted.
Further, let us look at identical output data for a transformer with one short-circuited
turn (Fig. 3.8).
The processed graph of the magnetising inrush current minima shown in Fig. 3.8 shows
an evident smoothing-off of the shape of this current, as compared to the shapes of the
magnetising current minima for an undamaged transformer. Such a character confirms the
forecast changes of the shapes of magnetising current regarding a further increase of short-
circuited turns as well as the character of change in the shapes on the whole.
The measurement has also been analysed by using numerical output data of the program:
the relative amplitudes and the relative displacement angles of the harmonics as compared to
the amplitude and angle of the first harmonic.
Conclusions
The obtained spectral image of the singled-out signal makes it possible to analyse the
changes related to the emergence of the fault, however, this is not enough for developing a
criterion, on the basis of which the protection will react to faults. In order to develop such a
criterion, a much larger amount of statistical data is required regarding various faults in various
transformers. As has been pointed out before, the peculiarities of the magnetic system as well
as the gravity and location of the fault strongly influence the character of change in the spectral
image of the magnetising current, which creates difficulties when determining the criterion for
the operation of the protection device.
3.3 Computer Simulation of the Transient Process in Transformers
The main objective of the present Thesis is to protect power transformers from turn-to-
turn faults. Since it is impossible to conduct experiments on an energised megawatt transformer,
it becomes necessary to create a precise computer model of the transient process in the
transformer. Since we have the results of full-scale experiments conducted on a laboratory
33
transformer, it would be useful to create a model of that transformer, obtaining simulation
results that are identical to the experimental ones. After verifying the model of the laboratory
transformer, it can be affirmed that the model of a power transformer created by the same
principle will also be correct. On the basis of the above criteria, two simulation environments
were chosen: QuickField and Matlab+Simulink+Simscape+SimPowerSystem. Further, we will
provide the results of the simulation and describe the problems which were encountered.
A significant advantage of the special software lies in the built-in mathematics. The
software is equipped with the so-called solvers, which, by using various numerical methods —
the Euler, Heun, Runge–Kutta methods — solve systems of differential equations describing
physical processes. [48].
3.3.1 Simulation of a Laboratory Transformer in MATLAB SIMULINK Environment
Simulink [60]–[61], [66] makes it possible to work with ready-made models where only
the nominal parameters need to be entered. By using the nameplate data and the results of the
experiment, we create a model as follows (Fig. 3.9).
It should be noted that in the choice of the parameters of the model, an enormous role is
played by the type of the solver, i.e. the numerical method, by which the differential equations
describing the model will be solved. The most widespread model — OD4 –, which is based on
the Runge-Kutta method, does not provide a solution for this model. The shape of the hysteresis
loop resembles the graph of a discontinuous function, which leads to a divergence of the Runge-
Kutta method. The best choice for this model is to use the trapezoidal method or Heun’s method,
which yields the most stable solution.
34
Fig. 3.9. The model of a laboratory transformer in MATLAB SIMULINK environment.
For comparing the obtained results, let us use the spectral distribution of the singled-out
signal, which is described in Chapter 3.2.
Current, r.v.
Time, s
0.02 0.04 0.06 0.08 0.1
0
0.2
Fig. 3.10. The simulated magnetising inrush current for an undamaged laboratory transformer
TAH-125.
35
Time, s.
Current, r.v.
0.02 0.04 0.06 0.08 0.1
0
0.2
Fig. 3.11. The simulated magnetising inrush current for laboratory transformer TAH-125 with
one short-circuited turn.
0 5 10 15
0.2
0.4
0.6
0.8
1
Harmonic Nr.
% from basic harmonic
Fig. 3.12. The harmonic composition of the magnetising inrush current for an undamaged
laboratory transformer TAH-125.
0.2
0.4
0.6
0.8
1
Harmonic Nr.
% from fundamental harmonic
Fig. 3.13. The harmonic composition of the magnetising inrush current for laboratory
transformer TAH-125 with one short-circuited turn.
36
Current, r.v.
time, s
0.02 0.04 0.06 0.08 0.1
0.2
0
a
time, s
0.02 0.04 0.06 0.08 0.1
0.02
0
Current, r.v.
b
time, s
0.02 0.04 0.06 0.08 0.1
0.02
0
Current, r.v.
c
Fig. 3.14. The simulated magnetising inrush current of a three-phase transformer: (a)
magnetising inrush current in phase A; (b) magnetising inrush current in phase B; (c)
magnetising inrush current in phase C.
As can be seen in Figs. 3.12 and 3.13, the results are practically identical, which enables
us to conclude that the model is correct. Thus, by means of this program, we can create the
model of a three-phase trasnformer and use it for the approbation of the proposed methodology.
Taking into account that damage can occur in any of the phases, it is necessary to conduct model
experiments with the transformer with a turn-to-turn fault in phase A/ B/ C. The simulation
results of the three-phase 300 VA transformer are provided in Fig. 3.14.
37
Current, r.v.
Time, s
a
b
c
Fig. 3.15. The simulated magnetising inrush current of a three-phase transformer with a short-
circuited turn in phase B: (a) magnetising inrush current in phase A; (b) magnetising inrush
current in phase B; (c) magnetising inrush current in phase C.
Current, r. v.
Time, s.
Current, r.v.
Time, r.v.
38
Conclusions
Upon analysing the obtained results, it can be concluded that using the changes in
amplitude or angle of harmonics provides an insufficient criterion for detecting the presence of
a fault. On the basis of statistical data, this Thesis proposes using the changes of the plane where
the harmonics are located on the complex plane as the criterion for the presence of a fault.
3.4 The Fault Detection Criterion
Upon analysing the results obtained after the simulation of faults, it becomes clear that
it is practically impossible to forecast a particular change in the spectral image, namely, the
degree of change of particular harmonics. Therefore, this study proposes using a complex
approach. After singling out the signal, it proposes using Fourier decomposition into complex
harmonics consisting of real and imaginary parts. Each harmonic is depicted on the complex
plane in relation to the base harmonic. Let us discuss this type of spectral image for various
types of faults. The results are shown in Figs. 3.16–3.17. Upon reviewing various faults, we see
a clear tendency towards the displacement of the harmonics towards the region of the second
harmonic, in other words, the density of harmonics in the area round the second harmonic
increases.
Considering that the operating criterion needs to be determined on the equipment level,
the most effective approach will be to assume the origin of coordinates on axis X as the
reference point and compare the number of harmonics that are situated in the half-plane with
the second harmonic. If the number of harmonics in the half-plane of the second harmonic
increases as compared with the number corresponding to an undamaged transformer, it means
that the transformer is damaged.
This approach presupposes that at the installation moment, the spectral image of the
harmonics is recorded into the memory of the protection device, which serves as an etalon.
Considering the errors contributed by the measuring instruments, it is expedient to introduce a
correction, i.e. for reliable operation, the change in the number of harmonics in the half-plane
of the second harmonic has to exceed two. The above-mentioned considerations let us use these
phenomena as reliable criteria for turn-to-turn fault detection.
39
a b
Fig. 3.16. The spectral composition of laboratory transformer TAH-125 (the distribution of
harmonics 1 to 15) on the complex plane: (a) in undamaged condition; (b) with one
short-circuited turn.
a b
Fig. 3.17. The spectral composition of phase B of a three-phase transformer (the distribution
of harmonics 1 to 15) on the complex plane: (a) in undamaged condition; (b) with one short-
circuited turn.
40
Conclusions
Upon analysing the changes in the spectral image of the laboratory transformer TAH-
125, it can be seen that even in case of one damaged turn, which corresponds to less than 1 %
of the total number of turns in the winding, a considerable displacement of the harmonics into
the half-plane in the direction of the second harmonic is observed. As the number of the
damaged turn increases, the harmonics are displaced in the half-plane around the second
harmonic. The type and severity of the damage have a varying influence on the displacement
trajectory of the harmonics; however, all of these displacements take place around the second
harmonic. Exactly the same tendency is observed in case of turn-to-turn faults in a three-phase
transformer. In case of a turn-to-turn fault in one of the phases, the spectral image of all the
phases changes.
These changes are insignificant in the undamaged phases and considerable in the
damaged phase. Due to this, as compared to a single-phase transformer, in case of a fault of the
same degree of severity, the changes in the spectral image of the damaged phase of a three-
phase transformer are less significant. However, the tendency for the harmonics to be displaced
into the half-plane with the second harmonic remains outspoken, which makes it possible to use
this phenomenon as a reliable criterion for determining the presence of a minimal internal fault.
4. CURRENT TRANSFORMER ERRORS AND UNBALANCE
CURRENT
One of the ways to improve the operation of differential protection in the low-current
mode is to increase the accuracy of current measurements. In case of an ideal transformer, the
secondary current is proportional to the primary current — ''
''''
w
wII
—
yet in case of a real-
life transformer, it is necessary to take into account the non-linear properties of the transformer
steel. As an example, let us consider the error characteristic curve for a current transformer with
a core manufactured from this type of steel (Fig. 4.1) [29].
Good current transformer design makes optimum use of the linear sections of the
magnetising curve of the core. At present, two basic types of current transformers are
manufactured — for relay protection needs and for measurements, the latter of which are mainly
41
adapted for commercial metering needs. Instrument transformers are manufactured with an
accuracy class of 0.2 and 0.5 and a measuring range of up to double rated current.
Fig. 4.1. The limits of current transformer error.
Transformers for relay protection needs are manufactured with an error class of 5P and
10P, which correspond to an error of 5 % and 10 %, respectively. The graph shown in Fig. 4.2
demonstrates the dependence of this current difference on the primary current.
Fig. 4.2. The difference of the secondary current of an instrument transformer and a relay
protection transformer depending on the primary current.
4.5 Ohm
0
5
10
15
20
25
0 20 40 60 80 I, A
del
ta,
%
4.5 Ohm
42
As can be seen, a relay protection current transformer has a relatively low error in the
region below the nominal current, yet even an error of 2...3 % considerably limits the ability of
the protection to detect an incomplete turn-to-turn fault in time, before it has developed into a
more serious fault.
As has been mentioned before, simply using instrument transformers for protection
needs is not acceptable due to the unavoidable saturation, which is often considered necessary
in order to protect the measurement devices from damage or overcurrent. However, the
information obtained from instrument current transformers can be used (of course, when
needed) for correcting the errors of unit instrument transformers.
A microprocessor device can “teach” itself, creating in its memory an error correction
table, based on a comparison of the output data in normal operating mode. In case of a fault,
the device can operate with a much higher sensitivity, thus detecting a fault at an early stage.
At normal conditions, the protection “learns”; the comparatory module creates a tabular
corrections function IfKc . This module has two inhibiting inputs, the first of which
precludes “unsuccessful” learning caused by magnetising inrush current.
The second inhibiting input is activated by a signal that interrupts the “learning” if the
current flowing through the current transformer exceeds 120 %–150 % of the rated value, thus
preventing the “poisoning” of the correction table with data from the saturated measuring core.
After the device has been in operation for some time, a correction table is formed in the
memory of the device, containing values of the correction factor CK as a tabular function of
the value of the current, and the device can start operating by using the corrected values of the
currents I and ''I . It has to be pointed out that the correction table contains discrete values of
CK and the device needs an interpolation module that is able to return a value of CK for any
intermediate value of current.
For the protection to have a minimum tripping time, the interpolation module has to
operate within minimum possible time; due to this, a linear interpolation module in the space I,
., cmce KJKR was chosen. The data contained in the correction table can be graphically
represented as shown in Fig. 4.3 (one phase is demonstrated).
43
Im(KC)
Re(KC)
I
K’CK’’C
a
b
K*C
d
0
I’
I’’
Im(K’’C)Im(K’C)
KC1
KC2
KC3
Im(KC)
Re(KC)
I
Fig. 4.3. A graphical representation of the correction table.
Usage of measuring transformers as a correction source for main current transformers
allows reducing the “appearing” value of unbalance current from 2–3 % to 0.2–0.3 % of the
nominal. As a result, the protective device will become much more sensitive towards an inter-
winding fault, maintaining a good robustness level in case of other types of fault.
Conclusions
Turn-to-turn faults are the most difficult type of fault for determination by the
differential protection of the transformer.
Failure to disconnect the transformer in due time leads to considerable economic losses;
therefore, correct operation of the protection is of major importance.
An analysis of the hitherto known protection devices has shown insufficient sensitivity
to turn-to-turn faults in the transformer.
Current at the moment when the transformer is energised contains information about
the presence of an internal fault and can be used for detecting a turn-to-turn fault.
The use of mathematical modelling makes it possible to create a precise model of the
transformer reflecting the transient process at the moment when the transformer is
energised. This was confirmed by a practical experiment.
Development of a precise transformer model is a mathematically complicated task,
which requires special approaches.
44
The proposed method makes it possible to detect a turn-to-turn fault with a high degree
of probability.
The error of current transformers in the low-current mode considerably diminishes the
sensitivity of the differential protection.
By means of the proposed error correction method, it is possible to improve the
operation of the differential protection.
The use of more powerful microprocessor devices makes it possible to use more
efficient algorithms for the operation of protection devices.
45
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