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DISCRIMINATION BETWEEN INRUSH AND
FAULT CURRENTS IN AN UNLOADED
THREE PHASE POWER TRANSFORMER
BASED ON PRE-FLUXING AND HARMONIC
ANALYSIS TECHNIQUES
by
SHANTANU KUMAR
(Achieving international excellence)
This thesis is presented for the degree of Master of Engineering Science
(Research) of The University of Western Australia
Energy System Centre
The School of Electrical, Electronics, and Computer Engineering
2013
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i
Shantanu Kumar
25, Braemount Road,
Darch, Perth, WA 6065
Australia
email : [email protected]
Mobile : +61 4 33399304
The 31st of July, 2013
The Head of the School,
School of Electrical, Electronics and Computer Engineering
The University of Western Australia
Nedlands, WA,6009
Australia
Dear Sir,
I wish to submit this thesis titled :
"DISCRIMINATION BETWEEN INRUSH AND FAULT CURRENTS IN AN
UNLOADED THREE PHASE POWER TRANSFORMER BASED ON PRE-FLUXING
AND HARMONIC ANALYSIS TECHNIQUES"
as part of the requirement for the degree of Master of Engineering Science.
Yours sincerely,
(SHANTANU KUMAR)
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ii
ACKNOWLEDGEMENTS
I express my sincere gratitude to my supervisors, Associate Professor Victor Sreeram
and Associate Professor Tam Nguyen for giving me an opportunity to undertake this
research. Due to their able guidance, constant support and invaluable encouragement
throughout my Master's candidature, I could complete the thesis in spite of my full
time employment.
I specially thank Associate Professor Victor Sreeram and Dr.Sushama Rajaram
Wagh for the pains taken by them to proof read the contents and answer any
technical queries beyond their official duty hours on this thesis
My boundless gratitude to my parents who passed away during the course of my
master's study. They continuously inspired me to pursue academic excellence and
succeed in life. I also thank my wife, Natasha and daughter, Radhika who sacrificed
their precious time and curbed their instinct to undertake holidays, during my
candidature. I also take this opportunity to thank all my brothers, sisters and siblings
in India and other countries who gave me motivation and encouragement to work
towards my objective.
I take this opportunity to express my gratitude to Dr.Van Liem Nguyen for imparting
his knowledge in power system and giving necessary corrections the simulation and
injecting thoughts on new areas to be probed into this research. I also thank my
friend Mr. Paritosh Tripathy who helped me in the presentation of this thesis and
colleagues at Western Power, Mr. Don Wijayasinghe, Mr.Kerry Williams and Mr.
Dilan Amarasinghe who supported me in my academic pursuit.
Finally, I would like to thank Dr. Sato Juniper and other staffs in UWA graduate
research school office, who supported my candidature during my difficult period and
were extremely flexible in allowing me to complete the thesis in spite of having a
challenging personal circumstance.
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ABSTRACT
This thesis is devoted to the application of suitable techniques to mitigate inrush
phenomenon and discriminate inrush from faults in a three phase unloaded power
transformer. Further, this thesis applies appropriate technique to estimate and
eliminate DC component embedded in the inrush and fault wave during the power
transformer energization.
The technique used for mitigating inrush applying pre-fluxing is based on setting the
power transformers residual flux to a known polarity after the transformer has been
de-energized and controlling the incomer circuit breaker closing time. The device
used in the pre-fluxing technique is simple to use and easy to construct and doesn't
require prior flux knowledge of the transformer core. The key driver of this device is
a pre-fluxing device which can operate at a lower voltage level as compared to the
overall voltage of the transformer. Using this model a specific flux pattern is
established in the power transformer, prior to its energization in an unloaded
condition. In the second part of the pre-fluxing technique application, the circuit
breaker associated with the power transformer is energized at a positive or negative
polarity. With the application of this technique, inrush is greatly reduced and is very
close to prospective flux during transformer energization. The motivation to apply
pre-fluxing technique is validated using software wherein the inrush is reduced
considerably with respect to the normal current as opposed to 10 times inrush
without pre-fluxing device.
Having established the pre-fluxing technique method of mitigating inrush in the
fourth chapter, a method to estimate and eliminate unwanted DC component
embedded within inrush and fault is taken up in the fifth chapter, based on harmonic
analysis. The practical problems associated with DC component on the protection
system has been elaborated in this thesis including, the fundamental concept and
initial appearance of DC component. Due to presence of the DC component the
protection system response is slow and usually delays the discrimination ability of
the relay. One of the significant contributions in this thesis is the estimation and
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elimination of DC component appearing as a noise and identifying inrush from fault
condition based on second harmonic ratio to fundamental, of an unloaded power
transformer. In order to eliminate the DC component, a compensating signal is
generated based on Taylor series expansion and Least Square Method (LCM) for the
inrush and fault current. As the second harmonic ratio (SHR) is a dominant feature in
the inrush, discrimination has been carried out by comparing it with a preset value.
Details on SHR are found in the review chapters of this thesis. The algorithm
developed to discriminate inrush from fault current based on harmonic analysis is
validated using MATLAB.
Although two case studies of discrimination and mitigation of inrush and fault
currents has been modelled and simulated on a step-up power transformer but this
concept of pre-fluxing and DC component estimation and suppression could be
extended to other vector groups of three phase power transformers in the network
which is a future scope of work for this author.
The notable contributions in this thesis has been the application of the pre-fluxing
technique, mitigation of DC component and application of SHR to discriminate
inrush from the fault
The research can be extended to ultra high voltage rated power transformer
particularly operating at 800kV and 1200kV as the results obtained for inrush by
switching on a 220kV power transformer cannot be extrapolated to that on an 800 kV
transformer which is transmitting power at an ultra high voltage level.
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Table of Contents ACKNOWLEDGEMENTS .............................................................................................. ii
ABSTRACT ..................................................................................................................... iii
Table of Figures ............................................................................................................... 1
List of Tables ................................................................................................................... 3
Chapter 1 Introduction ................................................................................................. 4
1.1 BACKGROUND AND SCOPE OF THE RESEARCH .................................... 4
1.2 OBJECTIVES .................................................................................................... 6
1.3 OUTLINE OF THE THESIS ............................................................................. 7
1.4 CONTRIBUTIONS OF THE THESIS .............................................................. 8
Chapter 2 Power Transformer Protection and its issues ............................................ 10
2.1 INTRODUCTION ............................................................................................ 10
2.2 EQUIVALENT CIRCUIT AND PHASOR DIAGRAMS OF CT .................. 13
2.2.1 Transformation Errors ............................................................................... 19
2.2.2 Current Error (Ratio Error) ....................................................................... 20
2.2.3 Phase Error ................................................................................................ 21
2.2.4 Composite Error ........................................................................................ 21
2.3 TYPICAL CHARACTERSTICS OF AN IDEAL CT ..................................... 23
2.4 CT BURDEN EXPLAINED ............................................................................ 24
2.5 CT CHARACTERSTICS AND ITS EFFECT ON PROTECTION RELAY .. 25
2.6 DIFFERENTIAL PROTECTION .................................................................... 26
2.7 FUNCTION OF INTERPOSING CT (ICT) .................................................... 28
2.8 CT SELECTION AND APPLICATION OF STANDARDS .......................... 28
2.8.1 Accuracy Class .......................................................................................... 30
2.9 FACTORS DETRMINING CT RATIO AND SELECTION .......................... 30
2.10 NEW TRENDS IN CT MANUFACTURE .................................................. 31
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2.11 TRANSIENTS AND ITS EFFECT ON PROTECTION SYSTEMS .......... 32
2.12 EFFECT OF HARMONICS ON POWER TRANSFORMER .................... 34
2.13 PRINCIPLE OF DIGITAL RELAYS .......................................................... 36
2.14 POWER TRANSFORMER PROTECTION ................................................ 43
2.15 SHORT CIRCUIT CURRENTS AND ITS EFFECT ON POWER
TRANSFORMER ....................................................................................................... 44
2.16 EFFECTS OF SHORT CIRCUIT ON POWER SYSTEM AND OTHER
MECHANICAL APPARATUS .................................................................................. 45
2.17 CONCLUSION ............................................................................................. 46
Chapter 3 Algorithms for the Protection of a Power Transformer ............................ 47
3.1 INTRODUCTION ............................................................................................ 47
3.2 OVERVIEW OF THE UNIT PROTECTION SCHEME ................................ 48
3.3 APPLICATION OF ALGORITHMS IN DIGITAL DIFFERENTIAL
RELAYS ..................................................................................................................... 52
3.3.1 Finite duration impulse response filter method (FIR) .............................. 53
3.3.2 Fourier analysis method ............................................................................ 58
3.3.3 Flux based algorithm ................................................................................. 59
3.3.4 Least Square Method................................................................................. 63
3.4 REVIEW OF DIGITAL DIFFERENTIAL PROTECTION ALGORITHM ... 68
3.5 COMMON METHODS FOR DETRMINING INRUSH AND FAULTS ...... 69
3.5.1 Harmonic restraint method ........................................................................ 69
3.5.2 Waveform based restraint method ............................................................ 70
3.5.3 Flux restraint method ................................................................................ 71
3.6 ANALYTICAL EXPRESSION FOR INRUSH CURRENT ........................... 71
3.7 CONCLUSION ................................................................................................ 75
Chapter 4 Mitigation of Inrush Current in a Three phase Power Transformer using
Pre-Fluxing Technique .................................................................................................... 76
4.1 INTRODUCTION ............................................................................................ 76
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4.2 NATURE OF INRUSH TRANSIENTS .......................................................... 78
4.3 PRE-FLUXING TECHNIQUE ........................................................................ 80
4.4 MITIGATION OF INRUSH CURRENT IN TRANSFORMERS USING PRE-
FLUXING ................................................................................................................... 81
4.4.1 Step-1: Pre-fluxing device......................................................................... 82
4.4.2 Step II: Controlled Switching ................................................................... 82
4.5 MODELLING OF TRANSFORMER FOR INRUSH CURRENT STUDY ... 84
4.6 SIMULATION RESULTS ............................................................................... 85
4.6.1 Inrush current in power transformer without using pre-fluxing device .... 85
4.6.2 Harmonic analysis without filters ............................................................. 87
4.6.3 Inrush current in transformer using pre-fluxing ........................................ 89
4.6.4 Inrush current using pre-fluxing in transformer with filter ....................... 92
4.7 CONCLUSION ................................................................................................ 94
Chapter 5 Elimination of DC Component and Discrimination of Inrush and Fault
based on Harmonic Analysis method .............................................................................. 95
5.1 INTRODUCTION ............................................................................................ 95
5.2 BACKGROUND OF DC COMPONENT ....................................................... 96
5.3 DISCRIMINATION OF INRUSH FROM SHORT CIRCUIT AND
ELIMINATION OF DC COMPONENT .................................................................... 98
5.4 MODELLING OF THE INRUSH CURRENT .............................................. 100
5.4.1 Estimation of DC component from inrush current .................................. 100
5.4.2 Estimation of DC component from fault current .................................... 102
5.4.3 Discrimination between inrush and fault current .................................... 104
5.5 SIMULATION RESULTS ............................................................................. 106
5.5.1 Case I : Discrimination between inrush and fault current ....................... 106
5.5.2 Case II: Three phase power transformer under fault condition............... 111
5.6 CONCLUSION .............................................................................................. 112
Chapter 6 Conclusions and Future Work ................................................................. 113
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viii
6.1 CONCLUSIONS ............................................................................................ 113
6.2 FUTURE WORK ........................................................................................... 115
Bibliography .................................................................................................................. 118
Appendix A: Determination of DC and AC Components during transients of an
unloaded Transformer ................................................................................................... 121
Appendix:B Publications ......................................................................................... 126
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Table of Figures
Figure 2.1 Current transformer and impedance burden [8] ............................................. 14
Figure 2.2 Equivalent circuit referred to primary [8] ...................................................... 15
Figure 2.3 Equivalent circuit as refrerred to Secondary [8] ............................................ 16
Figure 2.4 Phasor diagram of a CT referred to the secondary [8] .................................. 17
Figure 2.5 Phasor diagram of CT having inductive burden [8] ...................................... 18
Figure 2.6 CT open circuit excitation characteristics [8] .............................................. 23
Figure 2.7 Burden connected to a secondary circuit of a CT [8] .................................... 25
Figure 2.8 Biased differential relay with interposing CT [8] .......................................... 27
Figure 2.9 Incorrect switching time leads to inrush [12] ................................................ 34
Figure 2.10 No inrush occurrence due to correct switching time [12]............................ 34
Figure 2.11 Block diagram of a typical digital relay [15] ............................................... 40
Figure 2.12 Surge protection circuit [15] ........................................................................ 41
Figure 2.13 Characteristics of an (a) ideal filter response (b) practical filter response of a
low pass filter [15] .......................................................................................................... 42
Figure 2.14 Time course of AC voltage [16] .................................................................. 45
Figure 3.1 Basic unit protection scheme of a transformer [7]......................................... 49
Figure 3.2 Three phase delta-star transformer with bias set on the differential relay [7]51
Figure 3.3 Typical dual slope bias characteristics of a differential relay [7] .................. 51
Figure 3.4 Impulse responses of FIR filters [15] ............................................................ 56
Figure 3 5 Magnitude of the frequency response of filters [15] ..................................... 57
Figure 3.6 Two winding Transformer [15] ..................................................................... 61
Figure 3.7 Transformer magnetising curve [15] ............................................................. 62
Figure 3.8 Fault and non fault regions in dψ/di- i plane [15] .......................................... 63
Figure 3.9 Least square curve fitting method [15] .......................................................... 64
Figure 3.10 Block diagram for determining the Second Harmonic Ratio (SHR) [15] ... 67
Figure 3.11 Transformer Equivalent Circuit ................................................................... 72
Figure 3.12 Simplified two slope saturation curve ........................................................ 72
Figure 4. 1 Pre-fluxing device ......................................................................................... 81
Figure 4. 2. Connection of pre-fluxing device in a three phase power transformer ...... 82
Figure 4.3 Three - phase simultaneous controlled switching with phase voltage. ......... 83
Figure 4.4 MATLAB model to determine inrush current in an unloaded transformer .. 84
Figure 4.5 Inrush current and fluxes in individual phase and collectively .................... 87
Figure 4.6 Magnitude of harmonics without filters ....................................................... 88
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Figure 4. 7 (a), (b) and (c) Inrush current in Phase A,B and C, ...................................... 91
Figure 4. 8 (a), (b), (c) Harmonics in different phases with pre-fluxing......................... 93
Figure 5.1 Status of DC component during closing of an inductive circuit .................... 98
Figure 5. 2 Single line diagram of the network simulated ............................................ 102
Figure 5.3 MATLAB model for harmonic analysis of inrush and fault current .......... 107
Figure 5.4 Magnitude of inrush current at zero degree energization ........................... 108
Figure 5. 5 Harmonic contents present in phase ‘A’ inrush current ............................. 109
Figure 5.6 DC component in inrush current ................................................................ 109
Figure 5. 7 Digital filter used to compensate DC component ...................................... 110
Figure 5.8 Signal for compensation of DC component................................................. 110
Figure 5. 9 Inrush and fault current .............................................................................. 111
Figure A. 1 DC Component characterstic ..................................................................... 125
Figure A. 2 AC component characteristics .................................................................. 125
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List of Tables
Table 2.1 CT rating plate ................................................................................................ 29
Table 2.2 Amplitude of harmonics present during inrush [9] ........................................ 35
Table 4. 1: Summarizing the comparative results for harmonic analysis for three phases
without applying pre-fluxing .......................................................................................... 89
Table 4 2 Comparison of inrush current before and after mitigation ............................. 92
Table 4.3 Harmonics in different phases of an unloaded transformer after applying
filters and pre-fluxing device .......................................................................................... 93
Table 5. 1 RMS value of inrush currents for various switching instants (with and
without fault conditions) of one phase A ...................................................................... 111
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Chapter 1 Introduction
1.1 BACKGROUND AND SCOPE OF THE RESEARCH
Rapid growth in primary plant assets and the complexity involved in the power system
network has lead the operators and asset owners to focus on protecting these vital
equipments. Power system operators are emphasising on the reliability of protection
design. System engineers are striving towards improving the protection, by inventing
novel engineering techniques to keep power system healthy. Power system is severely
tested for reliability in the advent of a fault which could be due to the application of
nonlinear devices, switching operations, large interconnected grids and harmonics in the
system. Researchers are constantly upgrading existing methods and introducing novel
ones. With a competitive market environment in which power systems grid currently
operates, the need for reliable and robust protection of the costly assets like power
transformers, transmission lines, underground high voltage cable feeders, circuit
breakers, capacitor banks, reactor banks etc couldn't be overemphasised.
With the application of computer in the power systems, extensive design and research is
being carried out to protect system assets preventing damage due to short circuit or
other faults. System engineers are constantly working towards providing consumers
with a reliable power flow which is of high significance to the industry and utility
network operators. System engineers ensure that the network remains steady and power
flow remains smooth in the event of spurious positive spikes like inrush thereby
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preventing inadvertent relay operation. Further, protection engineers by applying
discriminative protection, isolate faulty equipments out of network speedily in mili
seconds while maintaining continuing power flow in the healthy section of the network.
In a typical case, the consequences of a faulty system could lead to one of the
following:-
1. May cause generators to go out of synchronization in a generating station,
thereby risking system wide instability
2. Risk of causing damage to men and material in the station (i.e. arc flash or
blow out)
3. Propagation of fire due to fault in a safe plant
In order to prevent faults affecting the network, system engineers are constantly
designing new relays with smarter logics. Today digital relays with smart algorithm are
easy to use and occupy less space in the control room. These digital relays enhance
system stability against faults and quickly isolate faulty section.
Failure of the system or network could occur due to :-
1. Incorrect setting of the protection relay
2. Mechanical failure of the equipment
3. Intrinsic design or component failure
4. Mal-operation of protection
5. Incorrect installation
6. Electrical interference
7. Mechanical vibrations
Given the cost associated with the primary plant assets, it is of vital interest to the asset
owner to ensure the equipments in the network are adequately protected from abnormal
transients to maintain a steady state supply. It is a difficult proposition to weigh the cost
associated in employing tiers of protection against the cost associated in having basic
protection compromising the system reliability and to spell out what is the optimum
amount to be invested in order to protect these assets. In a distribution system, speed of
fault clearance is relatively less important in comparison to a transmission system.
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Transmission system fault clearance is of much importance, as it forms backbone of the
network and outages have a significant impact on the number of the industrial and zone
customers affected. Among the electrical protections available, the most popular one
which reliably protects power transformer is differential protection.
Power transformer need protection against nuisance tripping and fault occurrence during
energization at the time of its switching. In this thesis, two methods have been proposed
to reliably mitigate inrush at starting and discriminate inrush from faults during initial
switching operation of an unloaded transformer.
1.2 OBJECTIVES
The main objective of this thesis is to mitigate inrush and identify inrush from faults in
an unloaded three phase power transformer located in a generating substation. The idea
of protection of the unloaded power transformer is based on pre-fluxing and second
harmonic ratio algorithm.
This thesis has been broadly divided into six parts with first part stating the motivation
to carry out the research, second part reviewing differential protection scheme and its
associated components e.g. current transformers, circuit breaker switching etc. The
thesis also gives an overview of inrush and short circuit generation and its effect on the
network. Further, it also gives an overview of the principles of modern digital relays
from differential relaying perspective and the reason for inclination towards
microprocessor based relays. Third part overviews the equations associated with digital
differential relay protection. Fourth part relates to the pre-fluxing method [1] and
applies a technique to mitigate inrush on a software model. Fifth part discusses
estimation and elimination of DC component and discrimination of inrush from short
circuit [2]. Sixth chapters conclude the thesis and emphasises the future work that could
be undertaken based on the given techniques on ultra high voltage power transformer.
Summarizing, the objective of the thesis which is divided into the following:-
(a) Power transformer protection and issues: This part discusses protection schemes
associated with emphasis on differential protection, current transformer errors and
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application to the protection, inrush and short circuit phenomenon and
fundamentals of digital differential protection using block diagram and the
algorithm applied.
(b) Pre-fluxing and harmonic analysis techniques: methodology of pre-fluxing and
harmonic analysis techniques employed in power transformer protection including
outlining of algorithmic models and data analysis interpreting the simulation carried
out using MATLAB. This part discusses the elimination of DC component and
recommends second harmonic technique (SHR) to compare and identify inrush and
fault current in an unloaded power transformer.
(c) Recommendation: Pre-fluxing and harmonic analysis methodology results
simulated in MATLAB are analysed. The generated results are interpreted for step
up transformers to show the benefits of the techniques.
(d) Future work: With the use of computer and application of digital based relays in the
modern power system, the reliability, speed and discrimination capability of the
relay has been significantly enhanced. However, there are number of challenges
which still lies unresolved due to parallel operation of power transformers, mal
operation of the relays due to tap change, different vector groups of transformers
connected to the bus in a generating and transmission substations, etc. Future work
shall motivate researchers to produce novel techniques which are not only reliable
and accurate but quick to act in isolating these assets during inrush and fault
condition, saving the operator costly outages and financial burden due to asset
replacement [3].
1.3 OUTLINE OF THE THESIS
This thesis is organised in six main chapters. Begining with the background and scope
of the research, the first chapter presents the objective and motivation leading to the
need for research on the improved method of protection during initial energization of an
unloaded transformer.
Chapter 2 revisits existing power transformer protection schemes and discusses
traditional electromechanical and solid state relays with respect to modern digital
differential relays. Further, it discusses the inrush and short circuits occurrences in the
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system and the impact of transients on the protection system. It also addresses the issues
of DC component during inrush and short circuit and examines the impact of DC
component on the protection system.
Chapter 3 presents modelling of power transformer protection schemes including
various mathematical models which goes into the relay logic. It also reviews some of
the popular algorithmic techniques used in the relay logic with special emphasis on least
square method (LSM) and second harmonic ratio (SHR) technique.
Chapter 4 elaborates on the need for pre-fluxing technique, saturation of current
transformer, controlled switching of the circuit breakers. A computer based model is
simulated on MATLAB applying pre-fluxing technique and the results obtained reflect
significant mitigation of inrush by inserting flux into the power transformer [4].
Chapter 5 outlines inrush and short circuit phenomenon. It also discusses the DC
Component issues and proposes a method of its elimination. A case study is undertaken
of an unloaded step up transformer wherein simulation during inrush and fault is carried
out on MATLAB. Comparing the results tabulated using SHR method which is based
on LCM technique, identification between inrush and fault currents is carried out. This
logic is incorporated into relay logic for protection purpose.
Chapter 6 deals with conclusions and future work on the methods exhibited based on
pre-fluxing and harmonic analysis techniques and gives a scope for the future research
to be undertaken on power transformer protection in the generating and transmission
substations.
1.4 CONTRIBUTIONS OF THE THESIS
The thesis has made two original contributions as described in the following:
(a) Pre-fluxing technique used in reducing inrush during energization of an unloaded
three phase power transformer. In this technique, a device having residual flux of
known polarity is inserted into an unloaded transformer. This device is simple in
construction and operates at a lower voltage. Further, this technique does not
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9
require prior knowledge of the transformer flux. Detailed discussion can be found
in chapter 4.
(b) Estimation and elimination of DC component and harmonic analysis of an unloaded
three phase transformer based on harmonic technique. In this method, identification
of inrush and fault current is carried out by comparing the ratios of second
harmonic to fundamental i.e. second harmonic ratio (SHR) which is compared to a
pre-set value and thus identifies inrush from faults, which could be used in the relay
and protection schemes. The detailed discussion and simulation on a step up power
transformer can be found in chapter 5.
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Chapter 2 Power Transformer
Protection and its issues
2.1 INTRODUCTION
Power transformer is integral primary plant equipment within a modern power system
network and plays an important role in transforming voltages from one level to another
for transmission and distribution purposes. However, due to short circuit, poor
workmanship, conduction of electric discharges in the suspended particles of an
insulating oil, poor welding or jointing techniques employed, displacement of winding
due to stress occurrence, failure of the insulation etc. are few of the causes in its failure.
It has been noted that the earth shields placed between primary and secondary windings
leads to stress at the edges causing failures in the long run [5]. Study indicates that 70%-
80% failure occur because of electromagnetic forces produced due short circuit stresses
on the power transformer windings. The other reasons of failures of power transformer
are due to sustained load, temperature rise due to poor cooling methods employed and
failure of protection relay to isolate the power transformer quickly in the event of an
external or internal short circuit. Hence, it is of great importance to the asset owners to
protect these costly apparatus within the substation environment with suitable and
reliable protection techniques.
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Researchers are constantly upgrading the protection system and employing new
techniques to check external and internal faults affecting power transformer from
damages. Damage may occur due to faults attributed to external factors like
overvoltage, overload, power system faults, excessive flux density or due to internal
causes like winding failure, inter turn failure, phase to phase faults, tank and accessory
faults, core faults etc. [3]
Transformers rated below 1 MVA are usually protected with fuses and simple
mechanical protection schemes due to economical considerations. However large power
transformers serving critical loads, need advanced protection schemes comprising of
phase failure, earth fault, over current, differential protection in the primary and
secondary side. For protection against lightning strikes and switching surges, design
engineers employ metal oxide surge arrestors on the primary side, using rod gaps etc.
Other techniques such as controlled switching of upstream circuit breakers using point-
on-wave (POW) reduces the chances of power transformer external faults and are a
useful practical method employed while energising transformer at no load. Power
transformer mechanical faults are usually protected using pressure relief devices,
Buchholz's relay, oil temperature and winding temperature sensors. However,
protection of power transformer against electrical faults require sensitive protection
relays which takes into consideration over current, earth fault and differential current
arising due to system unbalance, unequal loading, transients during switching etc. In
this thesis, differential protection has been discussed employing suitable algorithm to
discriminate inrush from short circuit.
Till date, differential scheme is the most popular method of protection employed by the
utilities and industries for the protection of all critical transformers in the network. In a
differential scheme, unequal or differential current arising due to phase and ground
faults within the zone of protection, helps in discriminating external and internal faults
affecting the transformer. Additionally, other faults such as switching-in voltage rise,
switching-in current rush, short circuit current rush which have a detrimental impact on
transformer winding, is also taken care by differential relay. The inrush phenomenon
occurring during transformer switching at no-load lasts several seconds and can cause
catastrophic damage to the power transformer winding. Protection engineers employ
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robust differential schemes to damp this high magnitude inrush and set the relay
operating parameters to restrain during an inrush and trip during a fault condition.
It is observed at the time of energization of a power transformer on no-load that, the
initial current waveform is rich in harmonics and consists of fundamental, second and
fifth harmonics. For the matter of protection, these lower order harmonics are employed
in the relay algorithms to discriminate inrush from short circuit while higher order of
harmonics beyond fifth order are neglected due to its non existence. Protection
specialists have found magnitude of second harmonic current to be one of the main
indicators of the presence of inrush current which often results in mal-operation of the
protection relay. These harmonic current signals, when fed to a differential protection
module equipped with complex algorithms, discriminates transient inrush from faults
[6]. Other reasons of inrush occurrences could be due to transformer core saturation or
current transformer (CT) saturation, largely due to magnetic core materials used and
flux produced. CTs at primary and secondary end of a transformer convert high
magnitude current signal into smaller secondary current for protection purpose at a
certain ratio depending on primary to secondary turns. In a normal condition, current
entering the transformer and exiting at the secondary remains steady. However, during
an abnormal condition like inrush or fault in one or more phases of the transformer
circuit, this balance condition is disturbed resulting in CT secondary current to sharply
rise. This necessitates relay to either restrain during an inrush or trip the upstream
circuit breaker in case of a fault and thus avoiding damage to the transformer. Usually,
all differential relays are fitted with a bias features. This bias enables the relay to
restrain for few seconds at the time of initial energization to prevent mal-operation. In
order to build a bias feature into a differential scheme, relay designers take into account
phase shift between different phase currents, tap changing in the transformer winding
and CT turns ratio etc. Differential relay is heavily dependent on the secondary input of
CT's located on primary and secondary of transformer. Improper input due to errors in
the CT ratio could severely limit the protection scheme.
CT saturation is an important phenomenon and has been discussed in the context of
differential protection scheme in this chapter. All CTs including modern optical based
CTs have magnetic cores. The magnitude of current required to magnetise the core and
maintain its accuracy with minimum loss during the transformer operation is a
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challenging task, as the CT saturation could lead to the mal-operation of differential
relay. In the next few sections of this chapter, CT errors and its effect on differential
relaying has been elaborated. Correct selection of CT ratios and working within the
specified errors, is of importance to the operators and protection engineers which
otherwise could lead to unnecessary tripping of the transformer during its energization.
2.2 EQUIVALENT CIRCUIT AND PHASOR DIAGRAMS OF CT
Appearance of transients at the time of transformer energization is a common
phenomenon and it not unusual to find CT with errors resulting out of these
disturbances. CT errors could seriously compromise the protection or cause spurious
operation, fed via the secondary leads to the differential relay. Hence, the location of
CTs on either side of the transformer has a significant relevance from differential
protection scheme perspective and cannot be ignored [7].
Fig 2.1 indicate a two winding CT where the current in the secondary side of a CT Is
core produces a magnetic field which counter balances the primary current Ip [8].
Almost all CTs works with the principle that magnetic field of primary and secondary
current balance out each other and there is a direct relationship with respect to the ratio
of primary to secondary turns which is almost close but not identical. The magnetic core
of CT produces two opposite fluxes in the primary and secondary winding, which
oppose each other. These opposing fluxes balance out each other and maintain a
relationship between primary Np to secondary Ns turns.
It must be noted, CT secondary should never be kept open as the secondary current Is
with a normally connected burden Zb will circulate the current in a loop. However,
when the secondary terminal is accidentally left open with CT energized will encounter
cable and source impedance. Further, this voltage appearing at the open circuit end of
the secondary terminal, will acquire a disproportionate magnitude which could be up to
the tens of kilovolts. This is a risky situation from safety point of view for the operator
and insulation of the component.
______________________________________________________________________
14
Ψp Ψs
Secondary Circuit
Zb
Is
NP NS
IP
Magnetic
Core
Secondary
WindingPrimary
Winding
.
.
Figure 2.1 Current transformer and impedance burden [8]
where,
- Polarity marking
Np - Number of primary windings NS - Number of secondary windings
IP - Current primary windings Is - Current in secondary windings
Ψp - Flux in primary Ψs - Flux in secondary
Zb - Secondary burden
Fig 2.2 exhibits an equivalent circuit of a simplified two winding CT model which
replicates an actual CT of Fig 2.1. Current flowing into the primary IP circuit and out of
the secondary Is are denoted by marking dots on the winding NP and Ns respectively. Imp
represents the primary current which sets up flux in the transformer core and cause
hysteresis and eddy current losses in the CT.
Representing the CT shown in Fig 2.1 with an equivalent circuit in Fig 2.2, Leakage
resistance and reactance on the primary side is denoted by Rp and Xp while on
secondary side are given by Rs and Xs respectively. Magnetising current fluxes are
______________________________________________________________________
15
produced due to Imp on the primary side and the common flux, which links both these
fluxes, is called mutual flux. This mutual flux is responsible for electromagnetic
coupling between the two windings. Losses in the CT i.e. magnetic and hysteresis are
caused due to Imp.
Rp
Ip
jXp
Iep
Imp
RcpXmp
Np
RsjXs
Is
Zb VsVp
Icp
Ns
. .
Figure 2.2 Equivalent circuit referred to primary [8]
where:
Rp – Primary winding resistance
Xp – Primary winding leakage reactance
Rcp – Resistance of core losses
Xmp – Magnetising reactance
Rs – Secondary winding resistance
Xs – Secondary winding leakage reactance
Zb – Secondary burden impedance
• - Polarity marking
Fig. 2.3 shows the equivalent circuit model referred to the CT secondary. The value of
Rs and Xs represents the total of actual resistance and leakage reactance on the
secondary side of the CT. It also represents a primary when referred to the secondary as
the primary side resistance (R) and reactance (X) being very low, can be neglected. On
the secondary side in Fig 2.3, a core loss component (Rc) and magnetisation reactance
(Xm) branch of the CT are shown through which core losses of CT dissipated. This
______________________________________________________________________
16
equivalent circuit model of the CT replicates an actual CT in the high voltage
transmission network.
Study of equivalent circuit referred to secondary of the CT is of interest because
secondary current in the CT is usually not greatly affected by the change in burden
ratings and it helps to gain knowledge of the CT errors such as ratio and phase angle
errors which can be determined by knowing the CT magnetization characteristics.
Np
R jX
Is
Zb
Ns
jXmp
SecondaryPrimary
Ips
Ic
Ip
Vi
Rc VS
Ie
Im
Figure 2.3 Equivalent circuit as refrerred to Secondary [8]
where,
Rc - Resistance of core loss
Xm - Magnetization reactance
R - Total winding resistance referred to secondary
Zb - Secondary burden impedance
X - Leakage reactance referred to secondary
Ips - Primary current referred to secondary
The relationship between primary and secondary current in a CT is best described by a
phasor diagram given in Fig 2.4. Taking the secondary current Is as the reference, Vs
leads Is at angle Øs where the value of this angle depends on burden Zb. Secondary
resistance R is in phase with Is and voltage drop across X is shown to be perpendicular
______________________________________________________________________
17
to Is in the phasor diagram. Further, the internal CT secondary voltage Vi is the phasor
sum of voltage drop across shunt branch combination of Rc and Xm and Vs as shown in
the equivalent circuit diagram in Fig 2.3.
Assuming the CT reactance is less than the resistance, the voltage drop RIs is normally
greater than the inductive circuit XIs which is reflected in the phasor diagram in Fig 2.4.
The excitation current Ie is the vector sum of Ic and Im which represents core loss and
magnetisation component of the CT. The internal CT voltage drop Vi and Ic are in phase
while Vi lags Im by 90°. Phasor diagram in Fig 2.4 is constructed referring to the
secondary side of the equivalent circuit shown in Fig 2.3, with the horizontal axis
current Is as the reference and secondary voltage Vs subtending angle Øs with Is.
Voltage drop referred to secondary is denoted by RIs and XIs. The phasor sum of Ie and
Im gives rise to Ips, which is the total current referred to secondary transformed from
primary. Ic is the component which causes core loss and is in phase with Vi and
perpendicular to Im. Vector summation of magnetising current Im and core loss
component Ic gives rise to the excitation current Ie. The relationship between Ip and Ips
is strictly based on Np, turn ratio on primary and Ns, turns ratio on secondary.
Ic
Im
Ie
Is
Vi
Vs
XIs
RIs
Φs
Is
Figure 2.4 Phasor diagram of a CT referred to the secondary [8]
______________________________________________________________________
18
Fig 2.5 shows the phasor diagram of a CT which exhibits the relationship between
primary and secondary current when there is an inductive burden. Phasor Ic and Im gives
the magnitude and phase error in the CT and is directly depends on the phase
displacement between secondary current Is and secondary voltage Vs [8]. Ips which
represents the total current of primary transformed to secondary and is the phasor sum
of Is and Ie, where Ie represents the excitation current and is vector sum of Im and Ic. In
the vector diagram of Fig 2.5, the component Ic is in phase with Vi and is responsible
for the core loss. Ip and Is have are linked by the primary turns ratio Np and secondary
turns ratio Ns and is given by (2.1)
øs
Is
Ips
Ie
Ic
Vi
VsR Is
X Is
Im
Figure 2.5 Phasor diagram of CT having inductive burden [8]
Fig 2.5 shows the phasor diagram of a CT which exhibits the relationship between
primary and secondary current when there is an inductive burden. Phasor Ic and Im gives
the magnitude and phase error of the CT and is directly proportional to the phase
displacement between Is and Vs [8].
Assuming a large inductive burden in the secondary side of CT in Fig 2.2, it is useful to
study the effects of secondary burden on the transformation errors in Fig 2.5. In this
______________________________________________________________________
19
phasor diagram Ips is almost in phase with Is. Voltage drop RIs being greater than XIs in
magnitude in the phasor diagram Fig 2.5 and Ips being almost in phase with Is, it is
observed that phase angle errors reduces as the power factor of the burden becomes low.
Alternatively, higher power factor and higher inductive burden (with less X/R ratio in
the secondary circuit) causes more phase angle errors. CT errors vary directly with the
burden and operate better at low power factor giving rise to lesser phase angle errors. To
reduce magnitude errors in the CT, turns compensation is introduced as an alternative
and is accomplished by reducing few turns in the secondary. The relationship of number
of turns on primary side with respect to secondary is given by (2.1)
psspp ININ (2.1)
where,
Np- Number of turns in the primary side of CT
Ip - Current in the primary side of CT
Ns - Number of turns referred to secondary side of CT
Ips - Total current transformed from primary to secondary of a CT
Errors in transformation occur when there is a mis-match in turns ratio with the current
ratio and it is called transformation errors. However, in an ideal situation CT primary
side current should replicate secondary side without any errors but in a practical case
with CT's on either side of the transformer, this is not possible and many other errors
occur e.g. ratio, phase, composite, transformation errors etc. All these errors cause mal-
operations of the protection relay and saturation of the CT cores. Therefore, it is of
interest to revisit various errors affecting the CT's which has been outlined in section
2.2.1 to 2.2.4.
2.2.1 Transformation Errors
In a CT, when the current is transformed from primary to secondary, it must preserve all
its current characteristics of the primary and reflect it on the secondary side for metering
and protection but usually that is not the case. However, in a practical set up, these
errors occur due to burden and phase angle displacement between secondary voltage
and secondary current of the CT and largely depend upon the rating of the burden.
______________________________________________________________________
20
Higher impedance of the burden cause greater transformation errors due to magnitude
and phase shift between secondary voltage and current. Transformation errors are
directly related to the power factor (P.F). Lower the power-factor (i.e. the more
inductive the burden) better is the CT operation with respect to transformation errors.
The method to resolve the transformation errors caused due to magnitude and phase
shift is by reducing the number of turns in the secondary side known as turns
compensation.
2.2.2 Current Error (Ratio Error)
CT is said to be having current error when there is a difference between Ip and Is as the
primary current Ip is not a replica on the secondary side Is, when multiplied by the turns
ratio. This is caused by the core excitation current and as given in (2.2)
Current error % = 100'
'''
p
ppn
I
IIK (2.2)
where,
I's – RMS value of the supply frequency component
I'p – RMS value of the supply frequency component of the primary current
Kn – Rated transformation ratio of the CT
KnI's - Turns ratio
Expressing current transformation ratio in another form [8]
Current error % = 100'
)/''(
np
nps
KI
KII (2.3)
where,
np KI /' in (2.3) is denoted as nominal secondary current
Usually the current error is determined to be negative as the value of I'p is greater than
'
sn IK in (2.2). However, in an ideal lossless CT with zero magnetising current
requirements, the available current output is less than the ideal case which is normally
not the situation. Current or ratio error is important from relaying point of view during
______________________________________________________________________
21
short circuit condition and the percentage increase in the error is directly proportional to
the increase in primary current.
2.2.3 Phase Error
Secondary current can lead or lag the primary current depending upon the power factor.
Most CTs have voltage leading the actual current by a small amount leading to phase
angle error. Phase error represents values indicating the phasor position of secondary
with respect to primary. When Is leads Ip, phase error is stated to be positive and when it
is behind it rated negative and the method to compensate this phase error is by reducing
one or two secondary turns [7]. Assuming leakage reactance of the burden to be
negligible, the maximum error that could occur is limited to +.70% when the burden is
very low. The range of values in a practical situation for the measured errors varies
between 0.2 to 6 degrees for CT. Phase angle errors at a low power factor below .7 or
less and has a significant impact on protection system and measuring instruments
connected in the network when errors are below .7 power factor (PF).
Manufacturers of CT's are improving windings materials and fine tuning to obtain zero
phase angle error by improving the CT accuracy at lower PFs.
2.2.4 Composite Error
The excitation component Ie as seen in the equivalent circuit Fig 2.3 produces
harmonics and increases as CT progresses towards saturation. This excitation current
causes waveform distortion and introduces composite errors in the CT. The error occurs
when there is a difference of an instantaneous value of primary Ip and secondary current
Is integrated over one complete cycle of operation at supply frequency as shown in (2.4)
and (2.5) [8]
When expressed as the RMS value, composite error is expressed as
dt (t) i- (t)iK1100
T
0
2
psn'
TI p
(2.4)
______________________________________________________________________
22
Alternative expression for composite error is given by (2.5)
dt (t)/K i- (t) i1
/
100T
0
2
nss' TKI np
(2.5)
Where,
ε - Composite error
T - Time period over one complete cycle over the supply frequency
s i - Instantaneous secondary current
pi - Instantaneous primary current
If harmonics during power transformer energization are considered, composite errors
assume a positive value but if harmonics in the system are discounted, the expression of
composite error becomes (2.6)
np
e
KI
I
100 (2.6)
Where,
Ie - supply frequency excitation current phasor
Is and IP - supply frequency phasor
Equation (2.6) has errors resulting due to phase angle and magnitude of eI and pI in
steady state operations taking the harmonics into consideration. Hence, it is called
composite errors.
As mentioned earlier, ideal CT's are expected to be free from errors but that not being
the case, the minimum expectation of a measuring or protection CT functionality, is to
keep the errors within specified limits and perform its function within its characteristics
as enumerated in section 2.3. In order to keep CT errors in check, manufacturers use the
following materials and techniques:
Construct high permeability and low hysteresis materials
Keep rated burden close to the actual burden
Reduce flux path and increasing cross sectional area of CT core
Minimizing the joints in the core
Decreasing the secondary internal impedance
______________________________________________________________________
23
2.3 TYPICAL CHARACTERSTICS OF AN IDEAL CT
During CT energization, with primary kept open and if voltage is measured across
secondary, a characteristic curve results and this typical excitation characteristics is
given in Fig 2.6. This characteristic is divided into four regions namely:
1. From origin to ankle point
2. From ankle point to knee
3. Knee point region
4. Saturation region
Fig (2.6) shows typical CT excitation characteristics in which a non linear response in
the graphical form is shown.
Where,
Vk -Knee point open circuit voltage
Ik -Knee point excitation currents
Open-Circuit
Voltage
1.1 Vk
Vk
10% increase in Open-circuit Voltage
50% increase in excitation
current
1.5 IkIk
Figure 2.6 CT open circuit excitation characteristics [8]
Vk i.e. knee point voltage of the CT is said to have attained, when 10% increase in the
open circuit voltage gives rise to 50% increase in the excitation current. Any further
______________________________________________________________________
24
increase in the open circuit voltage of CT would not increase the excitation current at
the secondary and CT is said to be driven towards saturation. This saturation exists as
long as primary transient current is not reduced. An ideal protection CT is expected to
perform above ankle and below knee point region while a measuring type CT is
expected to perform below ankle point. Beyond the knee point region occurs the
saturation of CT.
In a short circuit condition, CT saturation is a common phenomenon and has an impact
on the protection relaying operations by its slow response, reduced output etc. CT is
determined to have entered a saturation zone when the current signals on the secondary
side is found to be distorted and has a great impact on the protection system particularly
in a differential scheme for the protection of a power transformer. In differential relay,
short circuit could drive CT to saturate fast causing disturbance in balance, speed,
operation of the relay. To keep the CT in balance state and minimise the effect of
saturation, CT burden connected to the secondary terminal should be chosen accurately
which plays an important role in relay restrain and operation.
2.4 CT BURDEN EXPLAINED
The load side of the CT consists of secondary cables, relays or the meters which has
resistance and reactance. The voltage and current across these components constitute as
burden and is exhibited in Fig 2.7 which shows a typical burden on the secondary side
of a single core CT circuit which are in the form of coils or electronics of a relay.
Designers determine the CT secondary cable parameters and relay reactance while
sizing the CTs Determination of CT burden is an important aspect while configuring
protection settings [8].
______________________________________________________________________
25
CTConnecting
Leads Protection Relay
Ip
Vi
Rs
Vs
Is
Bay in
Substation Switchyard Relay Room
VR
RR
RL
RL
Figure 2.7 Burden connected to a secondary circuit of a CT [8]
Where,
Rs - Secondary winding resistance
RL- Lead resistance for one conductor from switchyard to the protection relay
unit
RR - Relay Resistance
Is - Secondary current
VR - Voltage drop across the relay winding
In Fig 2.7 the resistance of the lead wire is considered while reactance of the wire is
neglected because the secondary cable from switchyard to relay control room is not too
long. Burden is directly related to the secondary current and assumes an important role
during CT current transformation ratio. CT must always be procured based on burdens
connected on the CT secondary i.e. relays, lead cables. If the burden calculated is larger
than CT rating, CT size will become large and uneconomical.
2.5 CT CHARACTERSTICS AND ITS EFFECT ON PROTECTION RELAY
When the knee-point on the CT characteristics is exceeded, saturation takes place and
results in waveform distortion. This has a pronounced effect on relay and may cause
mal-operation of the relay particularly in the differential protection wherein two or more
CTs are required to balance each other out in normal condition. However during a fault
~
!~ r I' --;~
-'--
r:- r:-
______________________________________________________________________
26
this equilibrium is disturbed resulting in an out of balance and instability in the
protection [8].
Further, due to CT saturation the balance between primary and secondary CT is greatly
disturbed resulting in mal-operation of differential relay. However, it is observed that
CT saturation has less effect on over current and distance protection. Hence it is of
interest to the author to analyze the differential protection scheme with respect to CT
saturation and its effect on it.
2.6 DIFFERENTIAL PROTECTION
Differential protection is the most comprehensive unit protection that isolates the power
transformer from external and internal faults. In this method of protection the input
signals at the primary end of the transformer is compared with the secondary side. The
CT ratio at the primary and secondary side of the transformer have a linked relationship
which is disturbed in a fault condition as the magnitude of the fault current in the CT
secondary shoots up during a fault resulting in a large difference in phase and
magnitude of the primary and secondary current. If these current increases beyond a
pre-determined value, the relay will trip the circuit breaker associated with the
transformer at the primary side preventing permanent damage. However, when the
transformer is energized without load, there is a sudden rush of the current to saturate
the core. This phenomenon is termed as inrush and could last for several seconds
characterised by high magnitude and rich in harmonic. As this is a transient
phenomenon which decays slowly, it is expected of the differential protection to restrain
itself during an inrush condition. By incorporating a biased feature in the differential
scheme, the relay restrains itself during an inrush and thereby enhancing the stability of
the power transformer during initial energization.
CT saturation has a great effect on the differential protection in terms of distortion, loss
of accuracy, secondary current zero shift and loss of secondary peaks. In order to
eliminate these issues, CT in a bias differential scheme is installed as shown in Fig 2.9.
This diagram exhibits a differential protection wherein for an external fault, the fault
current flows either from left to right or from right to left side of the plant depending
______________________________________________________________________
27
upon the fault location. However, during an internal fault, the flow of the current is in
opposite direction to the normal current flow.
A
B
c
1600/1
CT
Main Transformer Protected 200/1
Interposing
CT Ratio
1.21/1
Biased Differential
Protection
30 MVA11kV 132kV
Figure 2.8 Biased differential relay with interposing CT [8]
Sum of Ip/Kp + Is/Ks for through faults while it is the difference of quantity i.e. Ip/Kp -
Is/Ks for internal faults.
Where;
Ip - Primary current
Is - Secondary current
Kp and Ks are transformation ratio referred to primary and secondary side of the
power transformer.
Biased differential protection relay operates on the principle that when operating current
exceeds the restraining current, the relay trips. Further, biased differential relay provides
stability during an external fault while tripping during an internal fault. However, it is
observed that during a through fault, stability of the biased differential protection is
much lower compared to an unbiased differential protection and hence there is a
necessity of introducing interposing CT (ICT) in the relay scheme, particularly for
electromechanical type of relays. Also, ICT help the biased differential relay to measure
the rated current, when the full load current flows in the protected circuit. By
r'-'-'-'-'-'-'-'-'-' ---;~~--~.~~ ~+'------F¥~
______________________________________________________________________
28
introducing ICT it is possible to correct this error. Details of differential protection has
been elaborated further in chapter 3, section 3.2
2.7 FUNCTION OF INTERPOSING CT (ICT)
The function of ICT is to maintain high through fault stability in the differential relay
and are connected between output of the secondary side of a CT and differential relay.
ICT oppose the phase shift of protection signal due to winding connections of the
transformer protected, which otherwise would been the function of the main CT.
A typical connection of the interposing CT is given in Fig 2.8. It is observed that the
primary side of the ICT is star connected while the secondary side of the ICT is delta
connected because of the need to block the zero-sequence current arising out of delta
connection of the transformer primary. With the advancement in technology, numeric
differential protection schemes these days has replaced ICTs as it can counter zero-
sequence currents by incorporating suitable algorithms in the software of the relay.
ICT exhibited in Fig 2.8 may be arranged in the same panel as the differential relay.
This electrical proximity by being located in the same panel greatly enhances ICT's
output and ensures speed of operation of differential relay during internal fault
conditions of a transformer.
CT sizing and selection as applicable to different vector group of transformers are of
importance as a wrong selection or use of a non standard size could compromise the
protection significantly. International electrotechnical commission (IEC) and Australian
standards (AS) specify the standard burden, rating and percentage errors of the various
CTs to be manufactured for measurement and protection relaying.
2.8 CT SELECTION AND APPLICATION OF STANDARDS
As mentioned in previous section CTs play an important role during measurement and
protection of the power transformer. Correct CT sizing is of importance to engineers
and designers as improper CT connected to the primary and secondary side of power
______________________________________________________________________
29
transformer causes mal-operation of the relay. Hence, standards associations around the
world have laid strict guidelines while selecting CTs.
CTs supplied by the manufacturer has been standardised by various countries for
protection, measurement, accuracy and errors etc. As per Australian Standard (AS), the
standard associated with CT selection and sizing is AS 1675-1986 which guides the user
to specify the key element of CTs such as:-
1. Definition for CT errors, accuracy, performance, ratings, service conditions and
terminal markings
2. CT tests : Type tests, routine tests and special tests
3. Classification of CTs : Class P, PL, PS etc
4. Application of CTs
5. Summary of service condition i.e. ambient temperature, local atmospheric and
climatic condition
IEC 60044.1 defines CTs on
1. General application, rating, application, tests
2. Definition, accuracy, tests for accuracy, name plate rating
3. Measurement of CTs
4. Protection of CTs
As per AS 6044.1 designation of a typical Class P, CT may be read as [8]
Table 2.1 CT rating plate
Item in
Designation
1
2
3
4
5
6
7
Example of
Entries
AS 1675
1986
10
P
100
F
20
Meaning of different items in Table 2.1 and CT specification is given by:-
Item 1: Australian standard to which CT complies
Item 2: Year of publication of the standard
______________________________________________________________________
30
Item 3: Rated composite error in percent at the accuracy limit current
Item 4: CT class
Item 5: Rated secondary reference voltage
Item 6: Rated accuracy limiting factor
Item 7: Value of the accuracy limit factor
For CTs to be identified for protection or measurement it is important to know the knee-
point voltage and accuracy class parameters.
2.8.1 Accuracy Class
In electromagnetic CTs, the protection scheme suffers from phase angle and ratio errors.
Hence, it is important to limit these errors by applying standards to define the lower and
upper limit of the CT accuracy within specific tolerances for different applications [9].
Following symbols are usually marked while specifying the accuracy class of a CT:
Class P : CT is for general purpose application where transient response is not so
important (Example: for slow speed over current and earth fault relay)
Class PL : Applicable to relay requiring good transient response (Example: High
speed over current, distance and differential)
Class PS : Anything that does not fall within P and PS and is different from the
above application
2.9 FACTORS DETRMINING CT RATIO AND SELECTION
Ratio of the CT is affected by:-
Continuous primary current
Nominated continuous secondary current
Specific application in protection
The most commonly used secondary ratings are 5A, 2A, 1A.
______________________________________________________________________
31
The ratio of CT =currentondaryContinuous
currentprimaryContinuous
sec (2.7)
Following factors are considered while specifying the relevant CT selection:-
CTs are selected based on the most conservative through fault condition
CT saturation is taken into account while determining protection response to
internal faults
Typical burdens connected to CTs are given below :
lead (phase and neutral together) 1.2 Ω
over current relay on 5A tap .055 Ω
earth-leakage relay on 1 A tap .78 Ω
instantaneous Relay .002 Ω
2.10 NEW TRENDS IN CT MANUFACTURE
There has been new trend in the manufacture of the CT in terms of materials used and
design. One such innovation is optical CTs. Optical CTs [7] are finding application in
the industries and utilities these days due to its compactness and small foot print. The
insulator structure is considerably reduced due to use of composite light weight
materials. Reduction of weight causes savings in civil foundations and structural
supports for the outdoor CTs installed in a air insulated high voltage substation. Use of
fibre optic cables on the secondary side also has economic benefit to the cutomer.
Further, the electromagnetic interference and conventional secondary wiring is
considerably minimized using these instrument transformers as the sensor and optical
fibre could carry out the task of a copper cable with higher efficiency and lesser human
effort for the installation. In recent years hybrid technology is gaining popularity.
Hybrid optical CT's combine the design of a conventional CT in conjunction with
passive optical sensing medium. The sensors used in a optical CTs are less immune to
saturation and electromagnetic interference and hence provide greater protection
features to differential protection.
______________________________________________________________________
32
The use of optical CTs is expected to bring technical changes in the differential
protection. However, future works need to be expanded on these novel instruments to
fully understand its behaviour during transients.
2.11 TRANSIENTS AND ITS EFFECT ON PROTECTION SYSTEMS
When a power transformer is energized, there is an abrupt change in its status due to
sudden rush of current in saturating the core winding before decaying in few cycles to
stabilize and this transient inrush phenomenon could be influenced due to one or
combination of reasons like [10]:-
1. Removal of a short circuit
2. Sympathetic inrush due to transformers in parallel
3. Synchronization of multiple transformers in a generating station
The transient phenomenon causes CTs to be driven into saturation causing differential
relay to mal-function as the relay tends to misinterpret this transient phenomenon as a
short circuit thereby commanding the relay to trip. Inrush due to transients lasts few
seconds and its magnitude is typically 5-7 times the rated current of a power
transformer.
In the last decade, protection engineers had relied on blocking resistors to check this
unwanted relay operation due to inrush by pre-inserting resistors in the circuit and by
performing harmonic blocking etc. Few other methods of mitigating transients are:-
1. Removal of residual flux
2. Adjustment of phase angle voltage
3. Insertion of resistance, PWM inverters etc.
It is observed that to mitigate inrush of a single phase transformer easier than a three
phase power transformer, because it is not easy to remove the magnetic flux in a three
phase power transformer. Also, in a three phase system different phase angles do not
switch-on at the same time and it is usually due to the timing of the three phase circuit
______________________________________________________________________
33
breaker which doesn't closes and opens at the same time. There is always a lead or lag
of the closing mechanism by few mili seconds of the three poles in a circuit breaker.
Large inrush current reflects a pattern similar to that which occurs during a short circuit
and this abnormal electromagnetic force stresses the winding of the transformer. If the
stress becomes a regular occurrence, it could affect the entire power transformer
winding. Elimination of inrush is of great interest to the protection engineer and can be
achieved by proper control of switching angle of the circuit breaker at the primary side
of the transformer and by elimination of residual magnetisation [11].
Based on above discussion, it is essential from power system prospective to formulate
an algorithm which is accurate and identifies short circuit from inrush taking into
consideration of the following:-
Inductance of the power transformer core
Impedance of the power transformer including the HV cable connected
Vector configuration of the power transformer i.e. Star-Star , Star-Delta etc
Fig 2.9 exhibits a typical inrush phenomenon due to incorrect switching angle of the
circuit breaker [4, 12]. In this diagram is shown an inrush current magnitude is
dependent on residual flux and the angle of energization of circuit breaker is not carried
during AC current passage through point zero resulting in an inrush.
Fig 2.10 shows no inrush occurrence, as the circuit breaker has been closed when the
current passes through zero instance which is usually an ideal case [13]. The waveforms
shown in Fig 2.9 and Fig 2.10 are system voltages in solid lines. Flux of the transformer
is shown in Y axis and Time in X axis. The combination of prospective flux and
residual flux in the transformer during energization gives rise to worst peak as shown in
Fig 2.10. The magnitude of inrush diminishes gradually [14] after short time.
Beside inrush phenomenon caused by switching of circuit breaker, harmonics also play
a role towards the unwanted operation of protection relay described in the subsequent
section.
______________________________________________________________________
34
Flux
Flux Symmetry
0Residual
Flux
Time
Voltage
Time
Current
Flux
Figure 2.9 Incorrect switching time leads to inrush [12]
Flux
Flux Symmetry
0 Time
Voltage
Time
Current
Flux
Figure 2.10 No inrush occurrence due to correct switching time [12]
2.12 EFFECT OF HARMONICS ON POWER TRANSFORMER
In early 1960's application of electronics in industries grew rapidly leading to use of
non-linear devices which produced harmonics. Harmonics are impure or distorted
sinusoidal waves caused due to introduction of rectifiers, diodes, converters etc. termed
t I I
\ I \ ---+!,L.---\-T-7
t I I
\
T
\ I \ ~4:;zC.--VT-:7 \
i
!
\
\
______________________________________________________________________
35
as non-linear devices. Embedded within harmonic waveforms is inrush current which
carry fundamental, second, third and higher order of harmonics but it is the second
harmonic which is most pronounced. Hence, second harmonic detection is deemed as
the one of the preferred method in identifying inrush and discriminating it from fault
currents. Percentage of second harmonic to fundamental is shown in Table 2.2.
Modern digital relays are equipped with reliable algorithms incorporated into the
software which enables differential relay to restrain during an inrush, while operating on
a faulty condition to trip.
Table 2.2 tabulates the results of the amplitude percentage of different harmonic
components present in the current waveform during initial energization of a typical
three phase power transformer [9]. It is inferred from the given table that it is of high
importance to investigate second and third harmonics by virtue of its large percentage
presence in the input signal to the transformer.
Table 2.2 Amplitude of harmonics present during inrush [9]
Harmonic component in
magnetising current
Amplitude as % of
fundamental
Second 63.0
Third 26.8
Fourth 5.1
Fifth 4.1
Sixth 3.7
Seventh 2.4
When a transformer is energised, the inductance being high compared to resistance in
the circuit, large inrush of current occurs which 5 to 7 times the rated transformer
normal current. This inrush lasts several cycle after switching instance and could be due
to one or multiple causes as enumerated below:-
Size of the transformer
Type of the magnetic material of the transformer core
Presence of residual flux in the transformer core
______________________________________________________________________
36
Switching angle of energization are different for each phases
Configuration of transformer i.e. line voltages appearing in delta connected
transformer winding is different to that of star connected one
Saturation occurs only in some of the limbs of the transformer
The effects of harmonics on power transformers are:-
Increase in copper loss
Increase in resistance to the current flow and thereby giving rise to temperature
rise and creating hotspots in the power transformers
Increased iron loss
Reduction in transformer life
Malfunctioning of protection relays
Decreased power factor
For the protection schemes to be reliable and robust, it needs to be equipped with
suitable algorithms to face inrush and short circuit. Hence, the next chapter in this thesis
overviews some of important algorithms and its principles applicable to differential
relays based on digital technology as conventional electromagnetic technology is fading
out.
2.13 PRINCIPLE OF DIGITAL RELAYS
With the arrival of microprocessor and digital technology, protection of power
transformer has undergone tremendous changes in the recent time. Protection of
transformer has been improved to an extent that engineers and system operators expect
it to be fast acting & sensitive to discriminate inrush from fault conditions in mili
seconds without unduly causing network instability which otherwise could cause [15]:-
1. Loss of synchronization in generating station
2. Mechanical stress, fire and explosion in generators or transformer
3. Damage to other healthy plant within substation and power network
4. Injury to technical staffs within the generating substation
______________________________________________________________________
37
Researchers have analyzed that power system network is usually thrown out of step due
to mal-operation of protection system by 30% and due to internal faults of power
transformer by 50%. Protection of large power transformers which is one of the costliest
electrical asset in the network, remains till date, a challenging problem for the relay
designers as they have to consider complex problems like mitigating magnetizing inrush
during energization of power transformer under no-load besides controlling over
excitation due to over-voltage, tap changing, CT saturation, ground faults, internal and
external faults etc. In the recent years, protection relay engineers have manufactured
relays which are compact and light in weight based on microprocessor and digital
technology. These protection relays are found to be more reliable and sensitive than its
previous ones i.e. numerical and mechanical operated relays due to its fast acting
algorithm and compact dimensions.
Algorithms used in digital protection system play a critical role in the relay operations.
It is expected to have better performance in withstanding mal-operations in power
transformer during magnetizing inrush and saturation of CT's during energization.
These modern digital relays are equipped with complex algorithms which analyses
initial current signals including DC offset, harmonics and overexcited conditions. It
restrains from mal-operations during inrush while tripping the relay at fault conditions.
Fig 2.12 gives the basic model of a current digital differential relay [7]. Usually current
imbalance takes place during an inrush condition which predominantly carries a second
harmonics component of the initial signal and is dominant during circuit breaker
switching. By applying suitable algorithms in the relay logic, it is possible to design a
robust and sensitive digital differential relay.
Some of the popular algorithms used in the protection of the power transformer by the
researchers [15] are listed below :-
Least squares method
Finite impulse response filters
Walsh functions
Harr functions
Rectangular functions
Kalman filtering technique.
______________________________________________________________________
38
The problems associated with these algorithms are, either these are practically not
applicable in the protection of various vector groups transformer vector groups (i.e.
Star-Delta, Delta-Delta, Delta-Star, parallel operation of Transformer etc) or the
accuracy and response to isolate during a fault are found to be inconsistent across all
kinds of bus configuration i.e. single bus, double bus, breaker and half, ring type etc.
In order to mitigate such issues, this thesis relies on the combination of algorithmic and
MATLAB simulink models to analyses voltage and current data, the details of which
are explained in chapter 4 and 5 with the pre-fluxing technique and harmonic analysis
method as improved techniques respectively.
In the following section, an insight into the design of a current digital differential relay
using a functional block diagram has been described by exhibiting a hardware model in
Fig 2.11. New digital protection of power transformer so designed exhibits,
dependability (no missing operations), security (no spurious tripping) and fast
operations (short fault clearing time).
Digital relay architecture is divided into three parts [15] as shown in Fig 2.11 :-
1. Signal conditioning subsystem
2. Conversion subsystem
3. Digital processing relay subsystem
Signal conditioning subsystem has transducers in the form of CTs and VTs. CT
transducers scale down the primary current to much lower value which could be
measured, analyzed and applied to the filters before subjecting the signals to protection
relay system. Similarly VT transducers reduce high voltages to 110 volt alternating
current, which forms input signal to the digital relays. Saturation of the CT is a matter
of concern but it is adequately compensated using suitable algorithm and by considering
physical parameters of cables and power transformer impedances into the digital
protection relay logic. These digital relays compare the analogue signals against many
parameters such as switching of the circuit breaker, analogue inputs, timing etc. Digital
relays have scope for up gradation i.e. in case of any change of algorithms these
microprocessors within the digital relay system can accept the new algorithm without
______________________________________________________________________
39
any change of its part or physical component. With digital ports available on the relay,
it is user friendly in communicating data to central control room via supervisory control
data acquisition system (SCADA). Digital relay acts as a source of information as it can
accurately record details of the faults or inrush occurrence with accurate time stamping.
Digital relays are protected from switching and lightning surges. Surge protection
devices located in the relay circuit which are in the form of capacitors and zener diodes.
These are connected to CTs and VTs via capacitors and zener diodes which protect the
electronic circuits against switching and lightning surges. Careful screening techniques
during the installation of surge arrestors, filters out large amplitude of surges by passing
it through filter circuit and further transmitting these signals to the processing hardware.
______________________________________________________________________
40
transducer
surge protective circuit
LP filter
analogue multiplexer
sample hold circuit
A/D converter
digital multiplexer
D/O D/I memory CPU
SIGNAL
CONDITIONIN
G SUBSYTEM
DIGITAL
PROCESSING
RELAY
SYSTEM
LP = Low pass
A/D =analogue to digital
D/A = digital to analogue
CPU = central processor
unit
D/I = data input
D/O = data input
DIGITAL RELAY
COMPONENT LAYOUT
D/A
Trip Signal(s) Remote location data
Figure 2.11 Block diagram of a typical digital relay [15]
r I I L...
r---------,
..... _-- -----~ r--- -----, I I I I I I I I I I I I I I I I ---- ----_.
-t---r--------1-I I I I I I
-~------- -----
I -l
I I
_ .J
______________________________________________________________________
41
Surges in power system appear due to instantaneous switching of lightning strikes and it
is characterized by sudden rise and slow decay in the waveform pattern. In Fig 2.12 is
shown a surge protection circuit where unwanted high frequency component of the
current and voltage signals originating from CTs and VTs and are screened out using a
low pass filter which is nothing but a combination of capacitor and isolating
transformer. Depending upon the digital relays data requirement, the sampling is carried
out as per Fig 2.13 (a) and (b). With low pass filter, the rise time, overshoot and settling
time is exhibited for a given output signal with clarity. Further, analogue signal
component from main CT is attenuated to avoid errors in subsequent digital processing.
Analogue low pass filters perform "anti-aliasing" function as shown in Fig 2.13 (a)
which has an ideal low pass filter characteristics.
To Filters
From main CT
and VT
a
b
c
d
Surge Capacitor Isolating
transformer
Figure 2.12 Surge protection circuit [15]
______________________________________________________________________
42
Figure 2.13 (b) indicate a practical low pass filter which has transition between pass and
stop bands and which in practice is difficult to achieve. Understanding the dynamics of
the low pass filter and steady state characteristics is important as it gives insight into
digital relay a feature with its dynamic response like :-
Rise time
Overshoot
Settling time
Output Voltage /
Input Voltage
1
f
1
1/√2
fcf
(a)
(b)
fc
Figure 2.13 Characteristics of an (a) ideal filter response (b) practical filter response of a
low pass filter [15]
______________________________________________________________________
43
The signals originating as an out of A/D converter as seen from the block diagram in
Fig 2.11 is next sent to output channels which is more like a rotary switch which obtains
a single input signal and converts many signals to digital processing systems.
In the final stage of processing of the signal it enters into a digital relay subsystem
which comprises of hardware and software modules like central processing units (CPU)
memory, data input (I/O) etc. The software of this digital sub system is greatly
influenced by the algorithm used, the sampling frequency and harmonics present in the
signal which is usually eliminated by applying suitable filters.
2.14 POWER TRANSFORMER PROTECTION
Traditionally tripping of power transformer was prevented by switching off power
transformer protection relay during initial energization condition [11]. With the advent
of modern technology, restraining of the differential relay has been carried out using
harmonic analysis, wave form analysis, fuzzy logic method etc.
Restraining the relay by inserting resistors and switching off the power transformer is
no longer deemed reliable for the inrush protection of large power transformers which
could seriously compromise the safety of the asset.
High voltage (HV) three phase power transformers with a rating of 10 MVA and above
normally have online tap changers. During an external fault, the ratio of primary to
secondary could be hugely affected variation of the tap changers turns ratio. Further,
mismatch between primary and secondary side of the transformer could occur due to
saturation or CT ratio error. One method of overcoming such malfunction is to restrain
the relay using harmonic retrained method. In this method, the second harmonic being
the largest harmonic component is detected in the inrush and compared to a
fundamental component thereby restraining the protection to operate.
______________________________________________________________________
44
2.15 SHORT CIRCUIT CURRENTS AND ITS EFFECT ON POWER
TRANSFORMER
Reliable operation, maintenance and economical power system network requires a safe
and a robust system which can withstand, discriminate and clear faults quickly in the
form of short circuit. In order to achieve this, proper planning in the design,
construction and commissioning of the electrical apparatus are required [16].
Short circuit may occur due to lightning strikes on phase conductors of overhead lines
or damages to cables due to internal faults i.e. aging of insulation. Design engineers try
to mitigate short circuit by introducing switchgears and fuses that isolate the circuit in
the event of short circuit within mili-seconds. Short circuit current not only pose a risk
to electrical apparatus in which it occur, but also forms hazard to the general public who
may be unaware of the induction effect of the short circuit that may induce impressible
voltage in the neighbouring metallic pipeline, communication and power circuit. It also
simulates oscillation in generators which can have cascading effect on banks of
generators in operation and lead to instability in the network that could further escalate
to a system blackout.
Figure 2.14 exhibits a typical time course characteristics of a current wave pattern. u
and i are the RMS value of the voltage and current and ω is the angular frequency фu
and фi are the phase angle of voltage and current. The time course has been shown on a
real axis on the right hand side of the Fig 2.16 with an emphasis on following four
parameters which has been discussed in chapter 3.
1. Total time duration
2. Peak short circuit current
3. RMS value
4. Short circuit breaking current
______________________________________________________________________
45
Figure 2.14 Time course of AC voltage [16]
2.16 EFFECTS OF SHORT CIRCUIT ON POWER SYSTEM AND OTHER
MECHANICAL APPARATUS
There are several damaging effects of short circuit currents on the power system
apparatus if not mitigated instantly at the inception and could lead to thermal and
insulation failures of the transformer.
Three phase and double phase short circuits without earth connection can cause highest
mechanical force and the duration of this short circuit effect depends on the time until it
lasts. Also, short circuit has a mechanical effect on rigid and flexible conductors
creating a dynamic force and bending stress on the conductor tubes. Particularly in air
insulated substations, this could cause disaster as a large section of HV outdoor
switchyard comprises of tubular and flexible bus conductors. IEC 60865-1 gives the
mechanical effects of the short circuit current and gives practical calculation methods
for various short circuit currents. Short circuit effect also leads to interference problems
in mechanical apparatus in the vicinity of overhead lines and cables. Interference of
short circuit causes inductive, ohmic and capacitive coupling of the short circuited path
and the circuit affected.
IT lI (r); i(r) ,". u (t) U ---T ' HI) -, / f\\ (;
"1''>" ., • ', - 2HI • I • \ 2 .:' o
, I " - ' , , "I \ I I , I 2
\ \' / ",I
-, " '. / J ., ~, -
______________________________________________________________________
46
Permissible values of voltages induced in mechanical pipelines are governed by
standards in place by various countries. Germany allows touch voltages to be 200V to
1500V for fault duration of .5s. Brazil and Australia allow a maximum permissible
1700V and 1500V respectively. As an example, if the most severe restriction is applied
on a 50Kg body weight with fault duration being 150ms, the maximum touch voltage
shall not be greater than 350V.
2.17 CONCLUSION
This chapter gives the background transformer protection including discussions on
sizing and selection of CTs. It gives an overview of traditional differential protection
and use of ICTs in a differential scheme with explanation of various CT errors and its
limits. It discusses the use of optical CTs and its effect on differential relay. Further, it
explains the phenomenon of harmonics, inrush and short circuit in the system and
methods of mitigation. It discusses the issues related to harmonics and transients and
how it reduces the life of transformer and also causes mal-operation of the relay. It gives
various mechanical and electrical protection commonly used like, pressure relief valve,
oil, winding temperature sensors, surge arrestors, controlling the switching angle etc
which has been employed currently for the transformer protection. While there are
protections schemes like over current, restricted earth fault available and currently being
used, but this chapter focuses on large power transformer in a generating station
stepping the voltage using differential relay as the primary and back up protection.
This chapter outlines few important algorithms used in digital protection systems while
giving a broad overview of the basic digital protection relay block diagram used in a
digital protection scheme.
Further, the chapter discusses the cause and effect of inrush and short circuit on power
transformers, substation primary plants and a recommendation for its mitigation, which
is one of the key interest area of this thesis and has been dealt in chapter 4 and 5 with
novel techniques.
______________________________________________________________________
47
Chapter 3 Algorithms for the
Protection of a Power Transformer
3.1 INTRODUCTION
In chapter two, the background of transformer protection has been discussed and the
importance of discrimination between inrush and short circuit has been emphasised.
Practically, this is achieved by restraining the relay, preventing CT saturation and
incorporating a reliable algorithm into the relay logic etc. Modern digital relays usually
have microprocessor in its hardware equipped with algorithms which performs complex
iterations and commands circuit breaker to trip in milliseconds. These algorithms
respond to inrush and fault conditions faster than the electro mechanical relays and are
finding its usefulness in the modern power system protection in light of its weight,
compactness and real estate occupied in the control room cubicles.
In the previous chapter, it has been emphasised regarding the effects of harmonics on
the transformer leading to degradation of winding insulation and CT saturation. Further,
inrush component, which is a derivative of the harmonics deteriorates the power quality
significantly. Together with decaying DC component and higher order of harmonics,
inrush causes heating, noise, short life of the transformer.
______________________________________________________________________
48
Present chapter enumerates few mathematical models used in current based relay
protection. It highlights the limitations of a traditional differential method and suggests
improved techniques to mitigate DC component and harmonics arising out of inrush and
short circuit. Mitigation of inrush is of importance which otherwise would make relay
vulnerable to tap changing, point-of-wave switching, fluxes in the magnetising core etc.
Basic unit protection of a power transformer along with reliable algorithms, discussed in
this chapter, gives an insight in to inrush control and fault isolation.
3.2 OVERVIEW OF THE UNIT PROTECTION SCHEME
Over current scheme employed to protect transformer do not always meet the
requirement due to unsatisfactory grading and reliability in protecting the transformer in
a complex power system network. This is overcome by unit protection wherein a
section of the power system network is protected. A unit protection which is also known
as differential protection is a reliable form of protection in comparison to protection
employing fuses for over current. The fundamental principle on which unit protection
works is by comparing protection signals derived from the input and output side of the
primary plant CT and feeding them to the relay. During a healthy operational condition,
current signals on primary and secondary side of the transformer are in balanced state.
However, during a fault within the protected zone, the relay trips the circuit breaker in
the upstream. Thereby, isolating the transformer from an imminent danger of damage to
its windings. Such a differential protection forms a unit protection wherein the
boundaries of protection are defined.
Fig 3.1 shows a unit protection scheme wherein two CTs, on each side of the
transformer are shown feeding signals to a high impedance differential relay (Id>) and
defining the boundary of the protection zone [7]. These CTs are connected on to the
primary and secondary side of the power transformer forming a circulating current loop
system. The phase and ratio errors of these CTs are compensated by connecting star-
delta CT's on a delta-star connected power transformer is shown in Fig 3.2.
On a normal operating condition, current flowing into the primary side of the
transformer and the secondary current on the load side are in a balanced state. However
______________________________________________________________________
49
during a fault, current imbalance occurs between primary and secondary side of the CTs
which feeds signal to the relay (Id) causing the relay to operate.
Id >High impedance relay
Delta-Star power transformer
Primary side CT Secondary side CT
Δ Y
Figure 3.1 Basic unit protection scheme of a transformer [7]
A certain degree of biasness is provided in the unit protection to prevent spurious
tripping as a result of through fault current due to tap changing operation in the
transformer. In additions to the problems encountered due to tap changing operation,
biasness is also required in the unit protection scheme due to the following reasons [7] :-
Phase shift across the transformer windings
Effects of earthing and winding arrangements
Detection of unbalance signals
Effects of inrush during energization
However, the major concern of a protection engineer has been to calculate accurately
the relay bias setting due to tap changing operations, particularly for the large power
transformer wherein, the on load tap changer (OLTC) attempts to maintain a regulated
output in the event of an unsteady source voltage. This unsteady voltage frequently
occurs due to voltage fluctuation on the source side of the transformer. OLTC is usually
located on the primary side of a transformer in order to give a regulated output, as it
easier to handle smaller current on the high voltage side. An off nominal tap position is
______________________________________________________________________
50
deemed to be an internal fault and in which case unit protection trips the upstream
circuit breaker but in a practical situation, the protection relay should maintain stability
against an off nominal tap position. System engineers achieve this by resorting to a
relay setting with minimum bias adjustment which is greater than the sum of the
maximum tap of transformer and possible CT errors.
Fig 3.2 shows that CT on either side of the primary plant i.e. transformer, play a major
role in defining the unit protection. However, correct operation of the relay within the
unit protection scheme depends on the following [3] :-
1. Phase correction - primary and secondary of the voltages of the transformers
measured by the differential relay are in phase irrespective of vector
relationship.
2. Ratio correction - mismatch due to ratio of primary to secondary
transformation during tap-changing operation could result in tripping. In
electromechanical relay installation days, it was carried out by using interposing
CTs but these days all digital differential relays are equipped with suitable
algorithm to deal with this situation.
3. Zero-phase sequence current filter - applying this filter, it is easy to
discriminate external earth fault from a in zone earth fault.
4. Magnetizing inrush sensitivity during energization.
In Fig 3.2 is shown a digital unit protection scheme of a delta-star transformer, wherein
the phase compensation ratio correction of CTs and filtering of zero sequence currents
are achieved by incorporating suitable algorithms into the differential relay software.
Use of the software eliminates the requirement of ICT making it compact. Most of the
power transformer electrical faults can be taken care by differential relay using unit
protection scheme such as [3] :-
Primary winding phase fault
Primary winding phase earth fault
Secondary winding phase-phase fault
Secondary winding phase-earth fault
Inter-turn fault
Core fault
______________________________________________________________________
51
R
Y
B
Delta Star
Id>Id>Id>
Primary CT Secondary CT
Step up power transformer
Differential relay with
bias set
Figure 3.2 Three phase delta-star transformer with bias set on the differential relay [7]
Fig 3.3 shows two section dual slope bias characteristics. The first section has a slope
which represents transformer magnetising current and prevents spurious tripping due to
inrush. In the second section, 30% slope prevents mal-operation of the relay due to off
nominal setting. Third slope is kept at 70% or higher to ensure that the relay operates
only on heavy through faults. Applying these bias settings on the differential relay, it is
possible to operate or restrain during an internal fault or inrush.
70% slope
30% slope
Operate
Restrain
1 2 3 4
1
5 6 7
1
8 9
1
2
3
4Diff Current
(Id)
Effective bias (x In)
Setting Range (0.1-
0.5 Id)
Figure 3.3 Typical dual slope bias characteristics of a differential relay [7]
~.-.-.-.-.-.-'
·1 ..
______________________________________________________________________
52
It is observed that traditional protection schemes are not so reliable during a
combination of inrush and fault current at the time of transformer energization. The
traditional electromechanical scheme doesn't guarantee restrain in an over excitation
situation. One such traditional scheme developed by Sharp and Glassburn [17] used
harmonic blocking instead of restraining. However their method suffered from certain
limitation as it was unable to detect low harmonic content present in the operating
current which lead to further research and development [18]. Traditional relays behave
correctly when the CT's replicate the primary current in the correct ratio on the
secondary side but such ideal situation don't occur normally due to CT mismatch,
saturation and errors. In addition to the problems of CTs, traditional differential relays
suffers from inaccuracy in estimation of inrush and over excitation, inability to detect
low harmonics during over excitation, blocking of relay even while higher order
harmonics are present and taking full one cycle to analyse the inrush current. Reliable
algorithms when applied on to a microprocessor digital relay give a robust protection.
3.3 APPLICATION OF ALGORITHMS IN DIGITAL DIFFERENTIAL RELAYS
In order to mitigate the disadvantages explained in 3.1 in terms of speed, reliability,
flexibility, cost/benefit consideration, operational performance and accuracy,
microprocessor based digital differential relay processors using algorithms described in
section 3.4 considerably improves the performance over traditional protection relay
[15]. These algorithms are constantly being improved by researchers to increase the
efficiency. A basic digital differential relay block diagram has been explained with
hardware and software components involved in the section in Fig 2.13. These
algorithms have many advantages over conventional relay such as economy, reliability,
compactness in the relay size and improved performance etc. Some of the commonly
used algorithms used in the digital differential relays are [15]:-
1. Finite duration impulse response filter method
2. Fourier series method
3. Flux restrained current differential method
4. Least Square Method (LCM)
______________________________________________________________________
53
3.3.1 Finite duration impulse response filter method (FIR)
In this digital signal processing technique, magnitude of fundamental and second
harmonics are estimated using four filters, two each for fundamental and second
harmonic shown in (3.1) to (3.2). Finite filters used in this technique play an important
role in the estimation of the second harmonic ratio. Using this technique the magnitude
of second harmonic ratio (SHR) to fundamental is calculated and if the ratio is
determined to be greater than the threshold value it is assumed to be inrush condition
[15].
The four filters used in these algorithms represent the harmonics for a period of one
cycle (T). The system frequency responses are given in the form of sine and cosine
function from (3.1) to (3.2) to the four filters. The input currents are in the form of
samples with values ranging from +1 to -1.
2/01
2/1)(
1
Tt
TtTtS (3.1)
TtTTt
TtTtC
4/3,4/01
4/34/1)(
1 (3.2)
The impulse response of fundamental harmonic is given by (3.1) and (3.2) while second
harmonic components are represented by (3.3) and (3.4).
4/32/,4/01
4/3,2/4/1)(
2
TtTTt
TtTTtTtS (3.3)
TtTTtTTt
TtTTtTtC
8/7,8/58/3,8/01
8/78/5,8/38/1)(
2
(3.4)
The system frequency response of the above four filters is given in sine and cosine form
from (3.5) to (3.6)
1
2cos
2/2)(
1
TTje
jF
s
(3.5)
______________________________________________________________________
54
4
sin22
cos
2/2)(
1
TTTj
ejc
F
(3.6)
1
4sin2
2cos
2/2)(
2
TTTje
jF
s
(3.7)
8sin2
8sin2
2sin
2/2)(
2
TTTTje
jF
c
(3.8)
Where,
T = 2 π /ω is for period when system frequency f0
Fs1 and Fs2 are the frequency response using cosine filters of fundamental
component
Fc1 and Fc2 are the frequency response of cosine and sine parts of second
harmonics
Equation (3.1) to (3.4) are further used to extract the current inputs of the fundamental
and the second harmonic by computing the impulse response of the transformer current
and evaluating at t=T. These outputs from four filter are summed up for a period of one
cycle as shown from (3.9) to (3.12). Mathematically, four equations (3.5) to (3.8) are
expressed with N samples per cycle of current i(t) and is chosen as multiple of eight.
2/
1 2/(t)S
1
N
k Nki
ki
(3.9)
4/
1 4/32/4/(t)C
1
N
k Nki
Nki
Nki
ki (3.10)
4/
14/32/4/
(t)S2
N
kNk
iNk
iNk
ik
i (3.11)
______________________________________________________________________
55
8/
1
8/74/38/5
2/8/34/8/(t)C
2
N
k
Nki
Nki
Nki
Nki
Nki
Nki
Nki
ki
(3.12)
Where,
N - Number of sample cycles in multiples of eight
∆t - Time between successive samples i.e. ∆t = 2 π / N ω0 and
i k = i (tk ) is the k th sample at any time t= k ∆t
S1(t), S2(t) , C1(t) and C2(t) - impulse responses of the four filters used i.e two for
fundamentals and two for second harmonics
During a fault within the transformer, there is a high value of fundamental component
and a low value in the second harmonic component. Alternatively, for an inrush
condition, the second harmonic component's magnitude is higher and fault is
characterized by smaller magnitude with respect to the threshold.
Typical values for inrush lies within the range:
0 ≤ ε ≤ 0.146 for X/R =5
0 ≤ ε ≤ 0.093 for X/R =10
0 ≤ ε ≤ 0.146 for X/R=20
Where, X/R is the system reactance resistance ratio.
Typical values of ε = .125. Any value greater than .125 is regarded as inrush and shall
render the relay inoperative.
Fig 3.4 exhibits a typical impulse response of the fundamental and second harmonic
filters whose output responses have a value ranging from -1 to +1 depending upon the
responses of four filters to the transformer input current.
The simplicity of digital FIR algorithm is best appreciated when the multiplication
process required for convolution is a simple sign change from +1 to -1 as shown in
Fig.3.4
______________________________________________________________________
56
T
S1(t)
1
-1
0T/4
T/2
3T/4
a
0
C1(t)
T/4
T/2 Tt
T
t3T/4
T/2
T/4
0
C2(t)
-1
d
c
b
T/4
T/2
3T/4
T
t
t
3T/4
S2 (t)
Figure 3.4 Impulse responses of FIR filters [15]
In Fig 3.5 the amplitude of the ratio ω/ω0 is plotted (X axis) against frequency response
(Y-axis) which is obtained by solving (3.1) to (3.4) for one period (T) and the typical
frequency responses of fundamental and second harmonic are exhibited for the four
filters in the Fig 3.5.
______________________________________________________________________
57
.5
1 3 52 4
ω / ω0
1 2 3 4 5 6
.5
1 2 3 4 5 6
.5
1 2 3 4 5 6ω / ω0
ω / ω0
ω / ω0
6
|Fs1 (ω)|
|Fc1 (ω)|
|Fs2 (ω)|
|Fc2 (ω)|
a
b
c
d
Figure 3 5 Magnitude of the frequency response of filters [15]
The main advantages of this algorithm is finite impulse response (FIR) filters :
Require no feedback
Inherently stable
Can be designed to be linear phase (used in phase sensitive applications)
______________________________________________________________________
58
However, FIT suffers from the following disadvantages:
Filter requiring more time in computation
Low frequency harmonics may not get filtered
3.3.2 Fourier analysis method
This method is based on the assumption that the fault generates a waveform within
certain period of time say (t0) to (T+t0) containing fundamental, second and fifth
harmonic waveforms. Expanding a periodic function f(t) and applying Fourier series
after digitally extracting the harmonics [19] from equation (3.10)
1sin
1cos
200
0
ntnωb
ntnωa
af(t) nn (3.13)
where,
)(tf - Periodic function which varies with time
0
a , n
a , n
b - Coefficients of the periodic function
0
n - nth
order of angular frequency
0
- Angular fundamental frequency = 2πf0
Coefficients can be determined from (3.14), (3.15) and (3.16)
Tt
t dttfT
a 1
10 )(2
(3.14)
Tt
t dttntfT
an1
1 0cos)(2
(3.15)
Tt
t dttntfT
bn1
1 0sin)(2
(3.16)
The main advantages in the Fourier analysis method is that it makes no assumptions of
the faulted waveform having both voltage and current signals and can be migrated to the
frequency domain. Using the data obtained from voltage and current the impedance is
calculated of the fault.
______________________________________________________________________
59
Fourier series suffers from the following limitations:
Boundary conditions need to be defined and discontinuity of the waveform
periodicity may arise if not defined clearly.
Odd and even harmonics are difficult to extract.
Specification of odd and even harmonics around the boundary conditions is
difficult to predict at times.
3.3.3 Flux based algorithm
In this method restraint function is obtained by flux-current relation of power
transformer and requires less computation than Fourier analysis. If the flux is estimated
correctly then over excitation and magnetising inrush could be dealt easily.
Fig 3.5 gives a simple two winding transformer where primary is linked to the
secondary by flux ψ. Assuming the resistance of the winding to be negligible the
relationship establishing between primary voltage and the mutual flux linkage ψ is
given by
)()()(
tvdt
td
dt
tdiL p
p
p
(3.17)
Applying trapezoidal rule after rearranging and integrating (3.14)
)]()([)]()([2
1)()(
12121212
titiLtvtvttttppppp
(3.18)
Where,
p
v - Primary applied voltage on the power transformer
p
i - Primary applied current on the power transformer
ψ - Mutual flux linkage of on the power transformer
Expressing (3.15) as the kth
sample of voltage and current waveform and calculating the
mutual flux linkage of a transformer
______________________________________________________________________
60
)()(2
11,,1,,1 kpkppkpkpkk iiLvvt (3.19)
Where,
p
L
- Leakage inductance of the primary winding
kp
i,
- kth
samples of primary current
1, kpi - kth
samples of primary voltage
Equation 3.19 is normally used to calculate the mutual flux linkage ψ of the transformer
At time tk, the differential current of a power transformer is given by (3.17)
kskpkd
iii,,,
(3.20)
Where,
ks
i,
- kth
sample of the secondary current
kd
i,
- Represents the differential current in the transformer
Equation 3.20 represents the differential current of a transformer which is equal to
magnetisation current of a transformer. If kd
i,
and k
are plotted, it will be observed that
the resulting curve aligns with the open circuit magnetisation of the transformer. Using
this flux restrained method, the first step is to detect the faults within the transformer at
every sampling interval. In second phase, a check is carried out on the location of the
points kd
i,
andk
. If the sampling points lie outside the open circuit magnetising curve,
then a trip signal is issued with an assumption that an internal fault within the
transformer has occurred.
In Fig 3.6, the relationship between current and flux is shown for a two winding
transformer. The accuracy of this method depends on the correct estimation of
magnetisation fluxk
, which would discriminate inrush from fault condition, depending
on its value.
______________________________________________________________________
61
vs (t)
Ip(t) Is(t)
ψ
Vp (t)
Figure 3.6 Two winding Transformer [15]
When the residual flux is close to zero, the above technique works fine, but practically
the case is different as d
i and k
characteristics varies as shown in Figure 3.7 (b) when
computed in equation (3.20). This is because estimated value is subject to an error to the
residual flux linkages value.
Equation (3.18) shows the way to mitigate the problem by using flux restrain method
which is determined by the slope di
drather than using flux ψ itself
p
kpkp
kpkp
kk
kk Lii
VVt
iidi
d
1,,
1,,
1
1
2
1 (3.21)
where,
p
L - Leakage inductance
kp
V,
- kth
sample of the primary voltage
Figure 3.7 designates a region containing fault and non-fault zones within which the
inrush current alternates in the dψ/di - id plane. Fig 3.7 (a) shows the fault within a
saturated part, while 3.7 (b) operates in an unsaturated part.
During power transformer internal fault, current samples dψ/di remains continuously in
region 1. However during inrush, they oscillate between the two regions. This
______________________________________________________________________
62
phenomenon is generally used to create an index of restraint k whenever it falls in
region 1. Index is decreased whenever sample pair enters region 2
Fault
id
ψ
No fault
Fault
No Fault
(a)
Id
ψ
(b)
Figure 3.7 Transformer magnetising curve [15]
(a) Fault and non fault region
(b) effect of remanent flux
Fig 3.7 (b) exhibits the typical characteristics of an id and ψ plane with the effect of
remanent flux. It is observed practically residual core flux doesn't work close to zero.
______________________________________________________________________
63
Fig 3.8 shows a dt
dplane which shows the fault and non-fault region. In the non-fault
region, flux is located in an unsaturated part i.e. region 1. However, during inrush
condition, the flux oscillates between region 1 and region 2
Region 2 : no fault region
Region 1 : Fault region
l
dψ/dt
Figure 3.8 Fault and non fault regions in dψ/di- i plane [15]
In Fig 3.8 a trip condition results when the pair
kk dt
di |, is in region 1, where
r
k is
regarded as the restraint index. The value of this index increases in region 1, while it
decreases in region 2. It is noted that, the value kr never reaches the threshold for all non
fault conditions. Threshold value actually depends upon the sampling rate and hence kr
must be determined experimentally.
The above algorithm has an advantage when the residual flux circulates in the
transformer core close to zero. Practically this difficult and identification of faulted
region is difficult to determine.
3.3.4 Least Square Method
In this method, fundamental and higher order harmonic contents are extracted from
current signals by data sampling and plotting a curve as shown in Figure 3.9. The plot is
, ,
..
______________________________________________________________________
64
established by extracting voltage and current waveform coordinates. Least square curve
fitting method (LSC) differentiates inrush from internal faults by comparing current
based signals with a set threshold value [15, 20].
In Fig 3. (X1,y1), (X2,y2),.....(Xn,yn) are a set of N coordinates where X represents
current and it is an independent variable taken at the ith
measurement, y represents
voltage variable and it is a dependent variable. Using many X, y coordinates, a curve is
plotted and the function of y is derived using Taylor series expansion in equation (3.22).
Unknown polynomials are solved using matrix for equation (3.23)
Least square polynomial curve (u)
Vertical displacement from
Least square polynomial curve
X1,y1
X2,y2
Y
x
X X
XX
X
X
X
X X
XX
X
X
X
X
X
X
X
Figure 3.9 Least square curve fitting method [15]
Fundamental component of current is expressed in phasor form equation (3.19) and is
given as [20]
)](sin5
1[)(
00 mmtm
mI
teIti
(3.22)
where,
τ - Time constant of any decaying DC component
m - Harmonic order
m
I - Harmonic current samples (up to 5th
order)
0
- Angular frequency
0
I - Decaying DC current
______________________________________________________________________
65
Assuming that the inrush current consists of fundamental to fifth harmonic only and re-
writing (3.22) to solve for aTaylor series expansion expression (3.23)
5
1 0
5
1 000)(cossin)(sincos)(
1
m mmm mm
tmItmIt
eIIti (3.23)
The unknowns in (3.23) are0
I , teI
0
, mm
I cos , mm
I sin (where, m=1,...,5) which
can be written in matrix form
)(
.
.
.
)(
)(
cos
.
sin
cos
5cos...5sin.....1
......
......
......
5cos5sin,...cossin1
5cos5sin,...cossin1
2
1
55
11
11
00
202020202
101010101
0
0
NNNn
ti
ti
ti
I
I
I
teI
I
ttt
ttttt
ttttt
(3.24)
Rewriting matrix operation in (3.24), in general form,
1212111122111.....
xaxaxaxaa (3.25)
011
1 Ixa
/022 Ixta k
5,....,1cos
sin
05
02
ntna
tna
k
k
n
n
5....,,1cos
sin
5
2
nIx
Ix
nnn
nnn
(3.26)
To solve for unknown elements of xn (n=1,.....5), m equations can be constructed from
N current samples in a matrix form having 12 samples as shown in (3.23) in simplified
form.
______________________________________________________________________
66
NmNmNN
N
N
i
i
i
i
x
x
x
X
aaa
aaa
aaa
A
.
.
.
.
.
.
...
......
......
......
...
...
2
1
2
1
21
22221
11211
(3.27)
Matrix (3.27) is solved by further simplification
A X = i
(Nx12) (12x1) (N x1)
Or X = (B) * (i) (3.28)
where,
B = A T. A)
-1 (3.29)
and A is pseudo inverse of A and AT
is the transpose of matrix A
Solving for real and imaginary parts of the fundamental and second harmonic,
N
nn
inbxI1
311
),3(cos (3.30)
N
nn
inbxI1
811
),8(sin (3.31)
N
nn
inbxI1
411
),4(cos (3.32)
N
nn
inbxI1
311
),9(sin (3.33)
where , k
x is the kth
element of vector X and b (k, n) is the kth
row and nth column of
matrix B
______________________________________________________________________
67
Amplitude of fundamental and the second harmonic is calculated by
2,1)sin()cos(22
nwhereIIInnnnn
(3.34)
For 5th
harmonic, above technique may also be applied in a similar manner but it has
been neglected for higher order as it does not carry significant inrush component.
Discrimination is obtained when we compare second harmonic component 2
I with
fundamental component 1
I in 3.34. Determination of magnitude of the current is done
by 3.34 and calculated by Second Harmonic Ratio (SHR)
2
1
I
ISHR (3.35)
If the SHR is greater than a set value then inrush is assumed otherwise, if it is less is
regarded as internal fault.
Fig 3.10 gives the four filters which represent the digital filters and which has the real
part (x3 and x4) and imaginary parts ( x8 and x9). It shows the graphical output of the
filters where unwanted harmonics are filtered out.
∑B(4,n)in
∑B(9,n)in
∑B(3,n)in
∑B(8,n)in
I2
I1
In
X4
X9
X3
x8
÷SHR
2
9
2
4
xx
2
8
2
3
xx
Figure 3.10 Block diagram for determining the Second Harmonic Ratio (SHR) [15]
______________________________________________________________________
68
In the LCM determination of sampling frequency and filtration of noise using digital
filtration is an important aspect. Sampling frequency must be greater than two times the
highest system frequency and it is not realistic to have lower sampling frequency below
600Hz and incorrect curve may occur if taken. Sampling frequency must be taken more
than 10 samples to get a correct result between 600Hz to 1300Hz. Higher order
harmonics i.e. 5th, 6th, 7th,...9th harmonics don't have major impact in the calculation
using LCM technique and can be eliminated.
3.4 REVIEW OF DIGITAL DIFFERENTIAL PROTECTION ALGORITHM
In view of the benefits which digital algorithms provide over conventional relaying, it is
of interest to review the best method to be used in the differential protection. However
no single algorithm is chosen as the best one because application of the algorithm
depends on the transformer connection, tap changing mechanism i.e. delta-star, star-
star, on-load and off load tap changing etc.[21]
Rockefeller, in 1969 was the first to propose the differential protection algorithm for
transformer by wave shape analysis with the simulation carried out on a sampling rate
of 2000Hz and having response time of 10 mili seconds (ms). Larson, Schweitzer and
Flechsig proposed Finite impulse response filters (FIR) for inrush detection having a
sampling rate of 480 Hz with a response time of 16 ms using Fortran language. He
simulated the test on a single phase transformer. Thorp and Phadke used discrete
Fourier transformer (DFT) model for simulation in 1982. They successfully simulated
in the differentially relay for a sampling window of 720Hz in a full cycle and obtained
the relay response time within 16 ms. Degens is credited with the LCM method in 1982
using least square curve fitting method to protect the transformer with a 600Hz
sampling window on a full cycle having a response time of the relay being less than
30ms, but his test was carried out on a single phase transformer in the laboratory on a
smaller rated transformer. Thorp and Phadke in 1983 are credited with establishing flux
restraint method with a sampling window of 720Hz and relay response time being
12ms.
The specific requirement of an algorithm depends on the excitation current and
harmonics produced during initial energization of the transformer. For a harmonic based
______________________________________________________________________
69
algorithm, the requirement is transformer input and output currents while flux and
voltage based restrained method the requirement is more complex having not only the
requirement of transformer input and output voltage and current but also the scaling and
isolation signals, low pass filters and A/D filters. Details of the common methods for
determining inrush and faults in a three phase transformer are elaborated in the next
section.
3.5 COMMON METHODS FOR DETRMINING INRUSH AND FAULTS
When an unloaded transformer is energized it draws a non symmetrical magnetising
current known as inrush which spuriously trips protection relay [14]. The main cause of
inrush is transformers core saturation. Inrush if not checked, could cause transformer
winding to be stressed and hot spots to occur and ultimately leading to insulation
failure. Hence it is very important to mitigate the inrush right at its onset at the time of
switching. Traditionally, tripping of transformer was prevented by switching off the
transformer protection during energization. With the advancement in numerical and
digital relaying technology, restraining during inrush and tripping on fault has
undergone changes. In today's world, complex algorithms using harmonic analysis,
wave form analysis, fuzzy logic method etc. are being used to restrain the digital relay.
These algorithms are incorporated into the relay, certain boundary conditions to trip.
Restraining the relay by inserting resistors and switching off the transformer are no
longer considered reliable to control spurious tripping during inrush protection of a
large transformer. Subsection 3.4.1 to 3.3.3 describes methods commonly used for
protection against inrush and operation during faults [13].
3.5.1 Harmonic restraint method
Voltage waveform when distorted in its sinusoidal form is regarded as harmonics.
Harmonics generate inrush current which causes heating, stress on transformer
insulation ultimately leading to transformer failure. As this causes nuisance tripping of
relay, few methods have been developed to restrain at the time of inrush and harmonic
restraint is one of them. There could be multiple reasons for inrush occurrence during
the transformer energization beside transformer core saturation. Inrush currents are
______________________________________________________________________
70
typically characterised by high harmonics due to several factors like presence of non-
linear devices in the circuit, switching the transformer at a non zero switching angle etc.
Presence of second order harmonics is one of the significant characteristics of inrush
and the protection relays are designed to restrain during inrush condition. However, the
same protection system shall act due to the presence of lower order harmonics i.e.
fundamental harmonics which could be laced with fault signals. Some of the methods
developed by the manufacturers are per phase method, cross blocking method,
percentage average blocking method and summing-type harmonic sharing method [22].
However, the most popular method used by relay manufacturers are second harmonic
restrain method wherein the SHR is compared to a set value. The relay logic restrains if
SHR is greater than the set value and trips if SHR is below the set value. However
harmonic restraint method suffers from few shortcomings as given below:
1. Accurate estimation of second harmonic is difficult
2. Amount of higher harmonics may drop below 10% and second harmonics could
be well below 7%. and inaccurate estimation chances are high
3. Second harmonics ratio could be well below safe 20% due to transients
4. Voltage drop across network reactance due to harmonics
3.5.2 Waveform based restraint method
As described previously, inrush currents have high peak waves and slow decays. This
high magnitude peaks and its decaying part are analysed for detecting and restraining
the relays by waveform based restraint methods. The two fundamental wave form based
methods of restraints are given in two approaches [13]:
Approach 1: Pays attention to the periods of low and flat values in the inrush current
known as dwell time. Magnetising inrush is ruled out as it does not show up every cycle
lasting atleast for 1/4th
Cycle in which the shape of the waveform is both flat and close
to zero.
Weaknesses of this method are:
Internal fault vs magnetisation takes one full cycle which is regarded slow
CT saturation may cause false tripping
______________________________________________________________________
71
During CT saturation, secondary currents may show periods of low and flat
values which may cause relay to miss an operation
Approach 2: It has its peaks displaced by half cycles and does not have two
consecutives peaks of the same polarity
Weaknesses of this method are:
Not easy to detect peak values
Timing between two successive peaks may be checked
Difficulty in checking the peaking timings between two consecutive peaks
At any given period shall have all three phases inrush in uni-polar waveform and
likely to fail the operation of the relay
However approach 2 is preferred over approach 1 due to its robustness in tolerating CT
saturation.
3.5.3 Flux restraint method
In this approach the internal faults are discriminated from over excitation and inrush
based on the flux in the transformer core. Flux recognization is one of the preferred
methods and a technique to mitigate inrush using this method has been dealt in chapter
4 of this thesis as the pre-fluxing method of mitigating inrush. In this technique
saturation of the transformer core is used to detect current imbalance and the relay
commands the circuit breaker to restrain due to presence of high flux.
3.6 ANALYTICAL EXPRESSION FOR INRUSH CURRENT
Transient performance is best understood by modelling the equivalent circuit of a two
winding transformer and applying the basic equations. Consider the equivalent circuit of
power transformer given in Fig 3.11 having dual slope saturation characteristics shown
in Fig 3.12 [23].
______________________________________________________________________
72
rplp lsp
rsp
Lm
Rn
Primary Secondary
i
vn
Vp Vs
is
Figure 3.11 Transformer Equivalent Circuit [23]
LS
Lm
ImIS
λ
Figure 3.12 Simplified two slope saturation curve [23]
where,
p
r - Primary resistance
p
l - Leakage reactance
m
L (i) - Non linear inductance of iron core
sp
r - Primary resistance referred to secondary
p
l - Primary side leakage reactance
p
v - Primary ground terminal voltages
p
v - Secondary ground terminal voltages
______________________________________________________________________
73
During transformer energization the equation governing the saturated transformer core
is as given in (3.36)
dt
d
dt
diitiRrtv
pnpp
)(.)( (3.36)
Using the relationship between the flux linkages with magnetising current and rewriting
the equation (3.36)
dt
diL
dt
diitiRrtv
corepnpp
.)(.)( (3.37)
The solution to (3.37) is found by introducing non linear inductor as a linear inductor in
unsaturated “Lm” and saturated “Ls” modes of operation. During transformer
energization initial flux λ0 shall go below saturation level λs until the cores are
saturated. There is no effect of hystersis on ts i.e. saturation time.
0
0
sin. dttv
ts
ms (3.38)
)](1[cos1
)( 01
0
n
s
s
t
(3.39)
Where,
n
- Nominal peak flux linkages
0
- Initial flux
s
- Saturation flux
ω - Angular frequency
m
v - Nominal peak supply voltage
Upon reaching saturation the current equation of the transformer and its parameters
shall be written as:
s
t
ttwheretBeAti
11
/
1
sin)(
(3.40)
s
t
s
ttwheretBeAiti
22
/
2
sin).()(
(3.41)
______________________________________________________________________
74
Where,
1
A ,2
A - Magnitude of decaying DC offset of fundamental and second harmonic
τ - Decaying DC time constant
1
B , 2
B - Amplitude of the fundamental an second harmonic
1
, 2
- Phase angle of fundamental and second harmonic
- Angular frequency
To determine the parameters A1, B1 A2, B2 , θ1 , θ2 ,is ,τ1, τ2 followings expressions are
used.
221 )]([)(
pmnp
m
lLRr
vB
(3.42)
222 )]([)(
pSnp
m
lLRr
vB
(3.43)
111
sin. BA (3.44)
)(sin.222 s
tBA (3.45)
])(
[tan1
1
np
pm
Rr
ll
(3.46)
])(
[tan1
2
np
ps
Rr
ll
(3.47)
sss
ii
/1.|0
00
(3.48)
np
pm
Rr
lL
1
(3.49)
np
ps
Rr
lL
2
(3.50)
Equation 3.40 and 3.41 are simplified further to determine the peak inrush per phase
and is given by equation
2/].[2
nnpeak
RRt (3.49)
Simplifying and rearranging (3.49)
______________________________________________________________________
75
n
npeak
RRt 2
2/ (3.50)
Expressing the equation for inrush in general form
2
2/)(
2.)( BeARI
stpeakt
npeak
(3.51)
3.7 CONCLUSION
Digital protection is gaining ground over conventional relays by employing algorithms
described in this chapter and due to its compactness and reliability in protecting the
primary plant assets within the utility network. With the application of these algorithm
digital differential protection has become more economical, flexible and has improved
the performance considerably over traditional relays. It is observed in table 2.2 that
inrush current contains high percentage of second harmonic component. Hence, it is of
great interest to engineers and relay manufacturers to utilise SHR to discriminate inrush
from faults. Modern relay uses the some of the algorithms described in this chapter like
fundamental and second harmonics to discriminate inrush from short circuit current.
Four commonly used algorithms on harmonic determination, flux evaluation and least
square curve fitting method has been described in this chapter such as FIR, Fourier
analysis, Flux restrain method and LCM. These algorithms are used in digital protection
with due consideration given to the signal processing for relaying purpose.
Removal of DC component has been a challenging task and usually takes complex
calculations to remove the DC offset in a real time application. Estimation of DC
decaying component using simple and numerically efficient method has been proposed
in this chapter based on simplified equation and its elimination of DC components is
given in chapter 4. Presence of DC components tends to make the relay operation slow
and cause large errors. A real time solution and mitigation of inrush and fault current
has been proposed in further chapters using Fourier filters in a MATLAB model. The
performance of two of these algorithms for the protection of an unloaded three phase
power transformer has been explained with a case study, in chapter 4 and 5.
______________________________________________________________________
76
Chapter 4 Mitigation of Inrush
Current in a Three phase Power
Transformer using Pre-Fluxing
Technique
4.1 INTRODUCTION
At the time of transformer energization under no-load, a high current is drawn due to
its core saturation known as transient inrush current. This transient inrush could rise
up to seven to eight times the nominal full load current of the transformer and this
phenomenon may last for tens of seconds. Further, these transients could produce
mechanical stress on the power transformer assembly and could lead to mal-function
of protection system. Inrush current often affects the power system quality and may
disrupt the operation of sensitive electrical loads connected to the system. The
method of mitigation of transient currents has become an important concern to the
protection specialists, as it contains rich harmonics laced with DC components [24].
Decaying DC components are produced due to inrush and faults which introduces
errors up to 15% in the protection system. Conventionally, the method to counter
these transients was to de-sensitise the relay or increase the size of the fuses or
______________________________________________________________________
77
control the switching angle of the circuit breaker or perform a point on wave
switching, but it is observed that these methods require the knowledge of residual
flux of the transformer prior to energization and time constant τ of the system. This
is a challenging task for the relay manufacturers as the values of these parameters
depends on the system configuration, circuit breaker switching angle and fault
location. Few other known methods of transient mitigation include, placing
capacitors at the secondary side of the transformer, using distributed line on the
secondary side of a low pass filter. However, these techniques cannot guarantee the
desired outcome due to different vector groups of transformers and tap changers
operation.
As the security and stability of transformers is of great interest to the system
operations, in which three-phase transformer is a key component, it is important to
protect the primary plant reliably. The large transient current of transformer due to
flux saturation in the core, which is called inrush current, often causes the mal-function
of the protective relaying system. This transient current affects outage time of
transformer as the engineers have to examine closely the transformer and the
protective system, to check for faults. The large transient current causes serious
electromagnetic stress impact and shortens the life of transformer. It is very important
to solve the effects of inrush current [25]. Uncontrolled energization of transformer
produces high inrush currents, which can reduce the transformer life and can also lead
to the unexpected operation of protective relays and power quality reduction. This
current depends upon various operating conditions, such as the magnitude of the
voltage, the switching-on angle, the residual flux, the hysteresis-characteristics of the
core, the resistance in the primary circuit, and many other parameters which has been
described in [26]. There are three negative side-effects of inrush currents. First, the
protective devices for overloads and internal faults may falsely operate and disconnect
the transformer from the power system spuriously In order to prevent this occurrence,
number of methods has been incorporated in the relay logic to distinguish between
faults and inrush currents which could reduce these undesirable trips. Second, the
windings are exposed to mechanical stresses that can damage the transformer and third,
power-quality problems may arise like high resonant harmonic over voltages and
voltage sags [27].
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In the recent years, many digital differential protective systems for transformer have
been developed. Different techniques based on complex circuits or microcomputers
have been proposed to distinguish inrush current from fault current. However, the
protected transformer must still withstand large electromagnetic stress impact caused by
the inrush current without unduly causing the mal-operation. Further, transformer being
a sensitive component and being exposed to power system transients, must have a
robust and fast acting protection system to prevent any damage to its core as a
consequence of harmonics. It is noted that non-sinusoidal harmonics are generated from
different nonlinear sources within the power system. These harmonics flow through
transformers and have a detrimental effect on the equipment in the network. The main
factors affecting the magnetizing inrush current are point on-wave voltage at the instant
of energization, magnitude and polarity of the remnant flux. Additionally, total
resistance of the primary winding, power source inductance, air-core inductance, the
geometry of transformer core and the maximum flux carrying capability of the core
material are also affected by inrush current [27, 28]. In light of this discussion, it is of
interest to mitigate inrush while isolating the three phase transformer from further
damage due to fault.
Hence, this chapter proposes a technique to mitigate inrush current in a three phase
transformers by injecting predefined value of DC flux in the primary of the
transformer applying a process known as pre-fluxing. Using this pre-fluxing
technique, the transformer is energized by a conventional controlled switching. A
sample case is considered in which a three phase transformer is connected to a
supply source, a MATLAB simulation model is designed and developed by
considering this case and verifying the effectiveness of the proposed pre-fluxing
method. The results derived are validated using this model for its efficient inrush
current control. This chapter proposes this novel technique to mitigate inrush current of
three phase power transformer called pre-fluxing in which pre-fixed value of DC flux is
injected in primary of transformer before energization.
4.2 NATURE OF INRUSH TRANSIENTS
The saturation of the magnetic core of a transformer is the main cause of an inrush
current transient. The saturation of the core occurs due to an abrupt change in the
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system voltage which could be caused due to switching transients, out-of-phase
synchronization of a generator, external faults and faults restoration. The energization of
a transformer yields most severe case of inrush current and the flux in the core could
reach a maximum theoretical value of two to three times the rated value of peak flux.
Inrush during transformer energization causes operational problems to the power
system. It affects the transmission lines being energized after an outage or line being
loaded suddenly. Inrush characteristics are usually unidirectional which rises sharply
and decays slowly. The maximum rise of inrush current occurs after the first half cycle.
The magnitude and duration depends mainly on four factors [29] :
1. Point on the voltage wave at the time of transformer energization
2. Impedance of the circuit
3. Residual flux linkage
4. Non-linear magnetic saturation of transformer core
The first two factors, depends on the vector group and connection of the power
transformer while the second two factors, depends on the flux in the magnetic circuit
which again is dependent on the material and steel used in the transformer core. Details
of magnetic circuits are difficult to obtain, as manufacturers do not submit detailed
composition of the core materials used. Additionally, there is no direct evidence that the
energization of a transformer can cause an immediate failure due to high inrush
currents. However, insulation failures in power transformers which are frequently
energized under no load condition support the suspicion that inrush currents have a
disastrous effect. A more typical problem caused by the energization of transformers is
due to harmonics interaction with other system components that develops over-voltages
and resonant phenomenon. The study of the energization of a transformer installed in an
industrial facility carried out to address problems due to harmonics, over-voltages and
resonances. In few international conferences [30], the authors have discussed how the
harmonic distortions caused by switching on of lightly loaded or unloaded transformers
may be amplified during a power system restoration process, creating high harmonic
over-voltages. During the process of energization of large MVA transformers in EHV
substations at the end of long transmission line is observed to cause significant
temporary disturbances when harmonic resonances are reached. This phenomenon
particularly occurs, when there are transformers which are already connected to the bus
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and the disturbances caused by the energization of one more transformer have greater
duration and intensity. In [31], it is discussed how transformer inrush current can excite
resonance frequencies in inter-connected grid system.
4.3 PRE-FLUXING TECHNIQUE
In the past few years, controlled switching has been deemed as a popular technique to
mitigate inrush current. However, the key aspect of this method is to gain the
knowledge of residual flux in the transformer. Earlier, several techniques had been
suggested to obtain residual flux at the instance of transformer switch off, but it is a
lugubrious and time consuming process. In order to make a simplistic model having
minimum application of residual flux, this chapter proposes a new technique to set the
initial fluxes of transformer to a desired value, which is known as pre-fluxing [1].
The innovation behind the pre-fluxing inrush current reduction strategy lies in the pre-
fluxing device itself. The pre-fluxing device (capacitor) is charged to a user specified
voltage and then discharged into the transformer during which the circuit breaker switch
is closed. For the pre-fluxing device, it is necessary not only to set the residual flux of a
transformer as high as possible to minimize the inrush current, but also doing it
efficiently. The pre-fluxing reduction strategy is a two part process. First, the
transformer residual flux is set as close as possible to its maximum achievable residual
flux when the transformer is de-energized. The second part of process controls the
circuit breakers (CBs) to energize the transformer. There are three controlled strategies
for the control of circuit breaker switching, first is rapid closing, second is delayed
closing and third is simultaneous closing [24]. In the rapid closing method, CB closes
one phase first and the remaining two phases within a quarter cycle. Knowledge of the
residual flux prerequisite and required for all three-phases, independent pole breaker
type control, and a model of the transformers transient performance. In a delayed
closing method, first pole closes instantly and the remaining two phases after 2 − 3
cycles. However, this needs knowledge of the residual flux in one phase only of the
independent pole breaker control, but does not require any transformer parameters. In
simultaneous closing method, all three phases closes together at an optimum point of
the residual flux pattern. It does not require independent pole breaker control, but
requires knowledge of the residual flux in all three phases and the residual flux
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magnitudes in two phases which are high and follow the most traditional residual flux
pattern [27, 28]. These closing times of the circuit breaker (CB) are chosen as a part of
an inrush current reduction strategy for the three phase transformer that enable the use
of the three pole CBs.
The pre-fluxing device shown in Fig.4.1 is equipped with a capacitor, a diode, and a
switch. A charging circuit not given in this Fig 4.1 provides the initial voltage across the
capacitor. The device is used across the primary winding of the transformer but not
when the transformer is connected to the network. The reason for using high voltage
winding is to reduce the magnetizing current on this winding. However, it is to be noted
that this pre-fluxing device is used only when the transformer is isolated state and
operated at a very low voltage. The advantage lies in using relatively inexpensive
isolator switches which can connect the pre-fluxing device to the transformer.
Figure 4.1 Pre-fluxing device
The pre-fluxing device is sized to operate around the transformer’s magnetizing
current level, so the capacitor, diode and switch can be sized for a fraction of the
transformer rated current [1].
4.4 MITIGATION OF INRUSH CURRENT IN TRANSFORMERS USING PRE-
FLUXING
This section describes mitigation of inrush current in two steps. The inrush current is
mitigated using pre-fluxing device as shown in Fig.4.2
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Figure 4.2. Connection of pre-fluxing device in a three phase power transformer
4.4.1 Step-1: Pre-fluxing device
The pre-fluxing device is connected to the primary winding of an unloaded three phase
transformer. The device should be connected to the three phase transformer only during
its isolation state, because it can back feed DC flux to the core before energization of
the transformer.
During the transformer energization, it is observed that the pre-fluxing device will be
bypassed using an independent switch at the same instant[32]. Further, this pre-fluxing
device sets a known residual flux in the primary of transformer. Applying point on
wave switching [1], the transformer will be energized according to the residual flux.
The capacitor will be charged to the maximum value of the transformer voltage. Pre-
fluxing device injects DC flux till the transformer is energized. The simulation of this
model has been designed and developed using MATLAB and filters have been applied
to limit the harmonics.
4.4.2 Step II: Controlled Switching
The controlled switching of the three phase transformer has been used to mitigate
inrush current after applying the pre-fluxing device. The switching operation is
controlled by circuit breakers. Three circuit breakers (CB) are connected on each
phase which is normally open. When CBs are open, transformer is isolated from the
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system and at that instant, the pre-fluxing device is allowed to get connected to the
transformer via switch [1]. As the CB closes and power is given to the transformer,
the pre-fluxing device will be disconnected through isolator. Disconnection of pre-
fluxing device occurs instantaneously as soon as the transformer is energized. The
controlled switching is applied after the pre-fluxing. It has three strategies, described
in Section III. In this chapter, simultaneous closing strategy has been used for
controlled switching [24, 33]. Fig.4.3 shows the simultaneous closing in three phase
transformer, which uses the basic concept of controlled switching. A three-phase AC
voltage consisting of three voltage waves U, V, and W is shown in Fig. 4.3a.
Figure 4.3 Three - phase simultaneous controlled switching with phase voltage.
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The magnitudes of the residual magnetic fluxes, which depend on the phase angle at
which the circuit breaker opened, are plotted in Fig. 4.3b. In this example, the
maximum residual magnetic flux is in magnetic phase U. The sum of the residual
magnetic fluxes in the three iron cores in a three-phase transformer with delta
windings is zero. Consequently, when the residual magnetic flux is a maximum in a
certain core, the residual magnetic fluxes in the other two cores have the reverse
polarity and smaller absolute values. The magnetic flux magnitudes that would be
induced by the voltage waves, as functions of the phase angle at which the voltages
are applied is plotted in Fig. 4.3b.
4.5 MODELLING OF TRANSFORMER FOR INRUSH CURRENT STUDY
A 3-phase, unloaded, step up power transformer, having a rating of 250 MVA, 25
kV/400 kV, star-star, 50 Hz, is connected to a 3-phase 25 kV source is shown in Fig.4.4.
The core magnetizing resistance and inductance is 450Ω and 1.4325 H of three phase
transformer respectively. Using the reference model formed by [1] where the magnetic
modelling of core is carried out and transformed into an electric model, which is
developed in MATLAB for simulation study.
Figure 4.4 MATLAB model to determine inrush current in an unloaded transformer
The transformer is energized with appropriate initial flux and saturated core in each
phase to get the value of inrush current. When the transformer is energized, the flux of
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all three-phase increases until it reaches its maximum value. After attaining the
maximum value, this flux will become saturated and draw more current from the source,
which will be 7 to 8 times greater than rated current. The main reason of saturation of
flux is residual flux is certain amount of flux which remains in the transformer core at
the time of switching off of the transformer. Residual flux depends on the rating of
transformer and de-energization instant. It will have different values for different ratings
of transformer [32]
4.6 SIMULATION RESULTS
4.6.1 Inrush current in power transformer without using pre-fluxing device
The results of the model explained in Section 4.3, the inrush current in each phase is
determined without pr-fluxing device. Fig 4.4a,4.4b,4.4c shows the inrush current in
phase A, B and C and Fig. 4.5(d) show the fluxes in all three phases. The value of
current in phase A, Fig 4.5 (a) is 1650 A and reaches a steady state condition in 8000
ms (8 s)
(a) Inrush current in phase A
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(b) Inrush current in phase B
(c) Inrush current in phase C
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87
(d) Fluxes in all three phases.
Figure 4.5 Inrush current and fluxes in individual phase and collectively
In Fig 4.5 (b) the value of this inrush current is found to be 670 A and it reaches in
steady state condition in 7500 ms (7.5 s) in phase B which is less compare to phase A
current. Fig. 4.5(c) shows the inrush current in phase C where the value of the inrush
current is 630 A and it goes in to steady state condition in 7400 ms (7.4s). The inrush
current in phase C is lowest current compared to other two phase currents. Fig. 4.5(d)
describes the variation of flux in each phase. The maximum flux in phase A is 1300
Wb, in phase B is 1200 Wb and in phase C is 1200 Wb.
4.6.2 Harmonic analysis without filters
In section 4.1 of this chapter, it is seen that inrush current is a harmonic rich current and
hence the results support that the total harmonic distortion (THD) in each phase are
much high. Harmonic analysis of inrush currents with residual flux in phases A, B and
C is shown in Fig 4.6. Now in Fig. 4.6 (a) THD is 70.22%. The DC component in this
phase is 58% and second harmonics is 62 %. In Fig 4.6 (b) THD indicates to be
106.16% and the DC component in this phase is 52% which is slightly less in
comparison to phase A and second harmonic is greater than phase A which is 78%. Fig.
4.6(c) shows harmonics in phase C. Highest THD generated in this phase which is
107.51%. The DC component in this phase is 50% which is lesser compared to phase A
and phase B. Second harmonic is 79% which is highest among all three phases.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-1500
-1000
-500
0
500
1000
1500
Time (s)
Flu
x (
wb)
Flux in three phase without Pre-flux device
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(a). Harmonics in phase A
(b). Harmonics in phase B
(c). Harmonics in phase C
Figure 4.6 Magnitude of harmonics without filters
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Summarizing the results in a tabular format:
Table 4. 1: Summarizing the comparative results for harmonic analysis for three phases
without applying pre-fluxing
Parameters Phase A Phase B Phase C
THD (%) 70.22 106.16 107.51
DC Component (%) 58 52 49
Second Harmonic (%) 62 78 79
4.6.3 Inrush current in transformer using pre-fluxing
Now, using a pre-fluxing device by connecting it to a three phase power transformer
having the parameters given in section 4.5 and MATLAB model in Fig 4.4 and injecting
some amount of DC flux in the primary side by removing it at the instant when a power
transformer is energized results in a wave pattern as shown in Fig.4.7 with inrush
current in phase A, B and C. Fig. 4.8 shows fluxes of all three phases. Fig. 4.7(a) shows
the inrush current in phase A in power transformer currents using pre-fluxing technique,
the magnitude of current is 19A. On comparing with Fig. 4.5(a), the inrush current is
mitigated from 1600A to 19A.
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(a) Mitigated current in phase A
(b) Mitigated current in phase B
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91
(c) Mitigated current in phase C
(d) Fluxes in all three phases
Figure 4.7 (a), (b) and (c) Inrush current in Phase A, B and C,
(d) Fluxes in all three phases
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Fig.4.7 (b) shows the inrush current in phase B of the power transformer using pre-
fluxing. The magnitude of current is 17A. There is momentary shoot up to 150A at
100ms but later it decays to 17A for phase B and same for phase C. Comparing with
Fig.4.5 (b), the inrush current is mitigated from 650A to 17A. Fig. 4.7 (c) showed the
inrush current in phase C in power transformer using pre-fluxing. The magnitude of
current in this phase is reduced to 16A from 630A. Fig. 4.8 shows the fluxes in each
phase. The maximum flux in phase A is 1200Wb, in phase B is 1000Wb and in phase C
is 990Wb. Summarizing the above in a tabular form in Table 4.2 and tabulating:-
Table 4 2 Comparison of inrush current before and after mitigation
Phases Inrush current before mitigation (A) Inrush current after mitigation (A)
A 1651 19
B 651 17
C 629 16
4.6.4 Inrush current using pre-fluxing in transformer with filter
It is observed that when filter is connected to the 3 phase power transformer, the
percentage of DC component and THD will decrease drastically in magnitude which
is shown in Fig.4.8. After connecting filters, THD in phase A is 2.05%. The and DC
component is 14 % in Fig. 4.8(a). In phase B, THD is 4.98 % and DC component in
this phase is 11%. In phase C, THD is 5.38 % and DC component in this phase is 6%.
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(a) Harmonic in phase A
(b) Harmonic in phase B
(c) Harmonics in phase C
Figure 4. 8 (a), (b), (c) Harmonics in different phases with pre-fluxing
Table 4.3 Harmonics in different phases of an unloaded transformer after applying
filters and pre-fluxing device
Phases DC component (%) THD (%)
A 14 2.05
B 11 4.98
C 6 5.38
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4.7 CONCLUSION
Inrush phenomenon has been regarded as an unwanted activity during transformer
energization which is characterized by high magnitude and harmonic-rich currents.
Harmonic currents cause saturation of the transformer core leading to mal-operation of
the protection scheme, reduced power quality, reduced life of the transformer.
This chapter details a technique to mitigate inrush current by setting the residual flux of
a three-phase power transformer of a large magnitude and with a specific polarity using
a method known as pre-fluxing. The tested three phase power transformer is energized
at a specified system voltage angle based on the flux polarity. Among the three strategy
described to mitigate the inrush in this chapter, the preferred method of pre-fluxing
applying simultaneous closing of individual breakers, where all three poles of the
circuit breaker are energised at an optimum flux pattern is regarded most suitable. The
advantage with simultaneous method is it doesn't require the knowledge of independent
breaker control of its poles.
Further, this strategy using pre-fluxing has an advantage over some of the presently
suggested reduction strategies on three phase transformers, including the need of
residual flux measurement during transformer de-energization. The pre-fluxing device
that sets the flux of the transformer is in simple form and flexible to apply to higher
rating of transformer sizes. In addition, the device can operate at low-voltage levels,
such as the substation AC or DC supply, regardless of the voltage rating of the power
transformer.
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Chapter 5 Elimination of DC
Component and Discrimination of
Inrush and Fault based on Harmonic
Analysis method
5.1 INTRODUCTION
In the previous chapter, inrush phenomenon has been discussed extensively and a pre-
fluxing technique has been proposed for three phase power transformer. Beside inrush,
we have few other issues during energization of a three phase power transformers like
appearance of DC component and harmonics. Inrush current contains decaying DC
component and dominant second harmonic components which may cause undesirable
effects like poor power quality and reduced mean lifetime of the transformer. Adding to
this complexity during power transformer energization is, if a fault occurs during initial
start up when the transformer is un-loaded, the protection system fails to discriminate
between inrush and the fault. This chapter provides a method to eliminate this
undesirable DC component and discriminate inrush from fault condition for the purpose
of three phase power transformer protection. Exponentially decaying DC component
causes large errors and mal-operation of the relay due to its effect on the algorithm
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embedded in the software of digital differential relay.
The proposed algorithm based on least square method (LSM) in this chapter, not only
handles the undesired decaying DC component but also discriminates fault from inrush
which is provided by a MATLAB platform. Earlier research studies based on wavelet,
Kalman filtering and discrete Fourier algorithm has successfully eliminated the DC
component but these algorithms suffered from complexity and difficulty in practical
utilization related to all vector groups of power transformers as original signals require
more calculation time, power system bus configuration, fault resistance and fault
location [2]. Further, DC component if not eliminated, could cause undesirable
oscillation and abnormal operation in the differential digital relaying system.
In this chapter, applying LSM technique, estimation of DC component has been
achieved and the effect of the unwanted DC component is eliminated to a large extent.
This model when tested, produces accurate results with minimal time delay as compared
to other conventional algorithms based on Fourier, finite, flux based algorithms. The
present chapter gives a technique involving estimation of DC component time constant,
magnitude of DC component, Taylor series expansion for inrush current and subjecting
the DC components to suitable filters in a MATLAB environment. Once the DC
components have been mitigated, inrush is discriminated versus fault and decision is
taken. As second harmonic component is dominant in the inrush current, discrimination
is carried out by comparing SHR to a pre-set value. The decision to trip or restrain the
differential relay is based on whether the SHR is greater than this pre-set value or not.
5.2 BACKGROUND OF DC COMPONENT
When a circuit breaker is switched on in an AC circuit consisting of resistance and
inductance, it results in an input signal which is regarded as a noise. This noise must be
rejected at all cost otherwise it shall have detrimental effect on the DC component and
AC component of the current as shown Fig 5.1. The magnitude of this DC component
current depends on the voltage at the instant of switching. DC component is zero when
the voltage is maximum and vice versa as shown in Fig 5.1 (a) and (b) [9]. These
decaying DC components are generated during transient inrush and fault conditions and
depend upon the X/R ratios (inductive reactance to resistance ratio) of the system. The
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bigger is the ratio, slower is the decay which has an effect on the algorithm and relay
operation. Benmouyal [34] has predicted that the error of decaying DC component
could reach up to 15.1% in the phasor estimation. Hence it is preferable to eliminate at
the time of occurrence. Further, it is observed the presence of DC component will
postpone the speed of the relay and reduce its accuracy and response time in the relay
algorithm [35] and is generally pronounced in current signals than in the voltage
signals. The motivation to eliminate the DC component is significant as it affects high
performance relay due to its unpredictable nature and random factors linked such as
fault resistance, fault location and fault inception angle.
A doubling effect is said to have occurred when the DC component is maximum [9].
DC component depends on the switching instance of the breaker and it occurs during
transient condition like inrush or short circuit. The transient recovery voltage which
appears across circuit breaker poles at the instant of closing and during arc interruptions
gives rise to AC and DC component and is used for specifying the circuit breaker at the
time of design and application. In Fig 5.1 (a) AA' envelopes the current wave. Due to
transients, the DC component (Idc) deviates from axis CC' when circuit breaker contact
separates and its at maximum during voltage zero. The RMS value of AC component is
denoted Iac. RMS value of AC component is always denoted in kilo Amperes (kA) and
manufacturers usually rate the materials used in transformers and circuit breakers
according to peak short circuit breaking and making capacity. The RMS value of AC
component is given by expression Iac/√2 while, DC component (Idc) is given at the
instant of contact separation as Idc x100/ Iac in percentage
DC component estimation cannot be made as a parameter of equipment. It is usually
deemed as a noise which is best estimated by deterministic and probabilistic methods.
In this chapter we have chosen LSM method and its performance during a transient
condition is simulated on a software platform applying filters. The filters are designed
such that it closely suits the properties of input signals. The algorithm presented in this
chapter considers the time constant (τ) and magnitude of the transient current (I0) at the
instant of breaker closing [36] and eliminates its effect before impressing the signal to
discriminate inrush from short circuit.
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98
DC Component
T in mS
a) DC Component is maximum at the instance of voltage zero
Current waveform
T in mS
b) DC Component is zero at the instance of voltage maximum
Current waveform
0
Idc
Iac
A
A’
C
C’
B
B’
E
E’
Figure 5.1 Status of DC component during closing of an inductive circuit[36]
5.3 DISCRIMINATION OF INRUSH FROM SHORT CIRCUIT AND
ELIMINATION OF DC COMPONENT
Three phase power transformer is one of the costliest equipments in the power system
network which needs to be isolated quickly in the event of a fault. Network operators
have a responsibility towards the consumers, in providing reliable and continuous
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power without causing extensive blackouts in the network. Hence, it is of paramount
interest to protect the power transformer from being subjected to inrush and faults
during initial energization and short circuit. Differential protection is one of the most
preferred schemes used for the protection of power transformers. However, the main
problem encountered while using differential protection is its limited ability to
discriminate between inrush and fault current. While it is observed that magnetizing
current of transformer may be only 1-2 percent of rated current at steady state operation,
it could reach 10-20 percent of rated current during energization of transformer [37].
This causes not only spurious tripping of differential protective relay but also leads to
mal-operation of other associated protective schemes. Researchers and engineers are
constantly developing new methods in the past decades to discriminate between inrush
and fault current like the second harmonic restraint [38], dead-angle restraint [39],
voltage restraint [40] and the flux-based inrush restraint [41].
As the inrush current has dominant second harmonic component as compared to fault
current, second harmonic restraint (SHR) using LSM algorithm method is one of the
popular technique widely used in practice till date. In this paper, the proposed strategy
for discriminating the inrush current from fault current is based on the SHR method and
phasor equations. Furthermore, as the inrush and fault current contains decaying DC as
well as harmonic components it is of great importance to increase the accuracy and
precision of the protection relay while discriminating the inrush from fault current.
Hence, using fundamental algorithm and applying filters in a MATLAB model
decaying DC component is eliminated. The reason for eliminating DC component is of
high importance as it is observed that it is a non-periodic signal which contains odd and
even harmonics, causing an increased reactive power absorption. This further results in
increased power loss and consequently overheating and stressing of the power
transformer insulation [42]. Thus, it has become necessary to establish methods to
eliminate the DC component from inrush current. Several algorithms to eliminate the
decaying DC component have been developed [34, 38, 43, 44] and some of the most
commonly used methods are least error square (LES) algorithm, digital mimic filter
[34], Kalman filter [44] and Fourier filter algorithm [38]. In this chapter a strategy
encompassing the fundamentals of fourier filter algorithm to remove the decaying DC
components from inrush current is proposed [2].
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5.4 MODELLING OF THE INRUSH CURRENT
In general, when a power transformer is energized, a transient current which is much
larger than the rated transformer current in magnitude than the nominal current flows
for several cycles. This is caused due to the residual magnetism of the power
transformer. When the power transformer is re-energized, the incoming flux will add to
the already existing residual flux which will cause the power transformer to peak into
saturation and produce transient current [37]. The effect of this inrush current on the
differential relay is a false tripping of the power transformer without having
encountered any actual fault. According to the principle of operation of the differential
protection scheme, the relay compares the currents coming from both sides i.e. primary
and secondary side of the power transformer during a healthy operation and maintains a
balance. However in an inrush condition, the current flows in the primary side of the
power transformer, giving rise to significant differential current. The protection system
now has to restrain itself and prohibit spurious mis-operation. The relay algorithm
proposed in this chapter recognizes that this inrush current is a normal phenomenon and
the relay must not trip due to this abnormal rise in current. Furthermore, the inrush
current is not only rich with DC offset component but also carries higher order
harmonics which lessens the life of transformer. It is noted, DC offset current has a
significant effect on the signals which contain large errors [42] and is observed that the
calculated value of the DC offset amplitude could vary by up to 10-15 percent from the
actual value, which causes increased power loss and consequently overheating of
windings [2].
5.4.1 Estimation of DC component from inrush current
For the consideration of the given signal model the equation for magnetizing inrush
current up to 5th harmonic is given in (5.1). Higher order harmonics are treated
negligible beyond fifth harmonic.
)sin()( 0
5
1
/0 m
m
mt tmieiti
(5.1)
Magnitude of the intial value of DC component i0e-t/τ
in (5.1) is maximum at the time
of closing of switch or voltage maximum.
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101
Where,
)(ti - Instantaneous differential sampling current at time‘t’
m - Harmonic order i.e fundamental to fifth harmonic
mi - Maximum component of the mth
harmonic differential current
0i - Magnitude of dc decaying component current
τ - Decaying time constant of dc offset component
m - Initial angle of the mth
harmonic component
/te - DC decaying component
ω - Frequency of fundamental component
To extract only DC component from the inrush current, integrating (5.1) on both side
for period (T)
t
Tt
m
m
m
t
t
Tt
dttmidteidtti )sin()(0
5
1
/
0
(5.2)
Simplifying (5.2) further,
)()1(.)( //
0tZeeidtti tt
t
Tt
(5.3)
Where,
Z(t) represents integral of DC component for one period at time (t) and
Z (t+ΔT) is the integral of DC component after a small time step
By integrating (5.3) in one period (T) with small step of t
)1(.)( //)(0
Ttt eeittZ (5.4)
Rearranging and substituting the value of Z(t) from (5.3)
/).()( tetZttZ (5.5)
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102
From (5.5) determining the faults currents for one period and use it to calculate time
constant (τ) and magnitude (i0) in (5.6) and (5.7) for the decaying DC component
/
)(
)( tetZ
ttZ
(5.6)
Magnitude of τ can be determined by solving (5.7)
)(
)(ln
tZ
ttZ
t
(5.7)
Magnitude of i0 can be determined by solving (5.4)
)1(.
)(//0 Tt ee
tZi
(5.8)
DC component is extracted from inrush current using (5.7) and (5.8)
5.4.2 Estimation of DC component from fault current
The voltage supplied by generator in a power system network as shown in Fig.5.2 is
given by ,
No Load CB
Transformer
E
Generator
Figure 5.2 Single line diagram of the network simulated
)sin( tVE m (5.9)
where,
E- AC source voltage
Vm - maximum value of the voltage having an amplitude
______________________________________________________________________
103
When the circuit breaker (CB) is closed expression (5.9) results,
)sin()(
)( tVdt
tLditRi m (5.10)
)sincoscos(sin)(
)( ttVdt
tdiLtRi
m
(5.11)
Where, R- Resistance of the transformer winding
L - Inductance of the transformer winding
By taking Laplace transform on both sides of (5.11)
(5.12)
Further, taking Laplace inverse of (5.12) and substituting the value of R/L = α
(5.13)
Where, = R
L1tan
Fault current cannot achieve its steady state value instantaneously due to presence of
inductance in the circuit and presence of exponential component in (5.13) which shows
that fault current consists of DC decaying component as well as AC component.
DC Component (5.14)
AC Component (5.15)
2222
sincos)0()()(
s
s
sVmLIsLsisRi
tm e
LR
V
)sin(
)( 21
222
)sin(
)( 21
222
t
LR
Vm
)sin()sin()(222
teLR
Vmti t
/
/
/
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104
Thus, DC component can be extracted from fault current by using (5.14). A detailed
calculation to obtain (5.14) and (5.15) has been exhibited in Appendix A.
5.4.3 Discrimination between inrush and fault current
Transformer differential protection scheme is based on the comparison of the balanced
currents flowing into an energizing winding with those flowing through loads. During
normal condition, there is an ampere turns balance, which results in differential current
is insufficient to cause a trip [45]. However, unbalance currents are produced in the case
of transformer inrush condition as it is flowing only in primary side of transformer.
There is significant probability that the differential relay could mistake this as fault
current and thereby isolating the transformer. To avoid this problem, differential
protection technique needs to be improved in order to detect transformer inrush current
and prevent spurious tripping. In this paper, proposed algorithm is based on the Taylor
series expansion of inrush current.
By using Taylor series equation in (5.1)
kmm
m
kmm
mkk
tmi
tmitiiti
0
5
1
0
5
100
cos)sin(
sin)cos()/()(
(5.16)
Where,
i0 -(i0/τ) tk - First two terms in decaying DC current
tk - Time at which current sample i(tk ) is measured
Writing the sampling current i(tk ) (5.16) in a matrix form,
______________________________________________________________________
105
22221111
sincossincos iiii
)(
.
.
.
)(
)(
cos
.
sin
cos
/
5cos5sin..1
..
..
......
5cos5sincossin1
5cos5sin..cossin1
0
20
10
55
11
11
0
0
00
202020202
101010101
NNNN ti
ti
ti
ti
i
i
i
i
ttt
ttttt
ttttt
(5.17)
A X i
(Nx12) (12x1) (N x 1)
Unknowns in (5.17) are
)5,...1(sin,cos),/(, 0000 kiiii kk
To solve the unknowns Xn (n=1,.....,12), m equations are constructed from N samples
X=B*i (5.18)
Where,
B = AT A
-1 (5.19)
and is the pseudo inverse of A and AT is the transpose of matrix A
There are 12 unknown elements in X matrix and as a result, at least 12 current samples
are required, hence, vector X can be solved if N≥12. Further, for calculation of SHR, the
four important unknowns to calculate the fundamental and second harmonic component
are:
Xunknown=
(5.20)
Above unknowns can be calculated by segregating real and imaginary part of
fundamental and second harmonic. In general, magnitude of current is given as
22 )sin()cos( nnnnn iiI Where, n= 1, 2, 3.. (5.21)
~----~.-------- L-,--J L-,--J
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106
Solving (5.20) for I1 and I2 , SHR can be found by
SHR (Second Harmonic Ratio) = 2I / 1I (5.22)
If SHR is greater than the set value, then it is considered to be inrush condition occurs
while, below the set value is assumed to be a fault condition.
5.5 SIMULATION RESULTS
5.5.1 Case I : Discrimination between inrush and fault current
The inrush current phenomenon and its discrimination from fault current is tested for a
three phase step up power transformer rated 22kV/220kV, 250 MVA, star-star
connected using MATLAB as shown in Fig 5.3.
______________________________________________________________________
107
Angleon time
of f time
pulse generatorDiscrete,
Ts = 5e-005 s.
powergui
A
B
C
Three-Phase Source
A
B
C
A
B
C
Three-Phase Fault
com
A
B
C
a
b
c
Three-Phase Breaker2
A
B
C
a
b
c
Three-PhaseV-I Measurement
A
B
C
a
b
c
Three-PhaseTransformer
(Two Windings)
Ia
Subsystem4
Ia
Subsystem3
Ic Out1
Subsystem2
Ib Out1
Subsystem1
Ia Out1
Subsystem
Ic2
Ic
Ib3
Ib2
Ib
Ia2
Ia
[C]
Goto2
[B]Goto1
[A]Goto
[A]
From4
[A]
From3
[C]
From2
[B]
From1
[A]
From
Display3
Display2
Display1
i+
-
Current Measurement2
i+
-
Current Measurement1
i+
-
Current Measurement
150
Continuous
RMS
CRMS2
Continuous
RMS
CRMS1
Continuous
RMS
CRMS
Figure 5.3 MATLAB model for harmonic analysis of inrush and fault current
As explained in Section 5.3, when an unloaded transformer is energized at zero degree,
the inrush current appears as shown in Fig 5.4. It is seen that, the peak value of inrush
current is very high as compared to normal magnetizing current and it is unsymmetrical
because of non linear magnetizing characteristic of transformer. In addition to this, the
magnetizing inrush current is found to rise up to 10-15 times of the steady state current
value, which flows only in one side of the transformer and tends to operate the
differential relay unless some form of restraint is not provided. The harmonic content of
the transformer inrush current with time has been calculated by Bronzeado et al. [46]. It
was shown that the peak value of any individual harmonic component during one cycle
is generally different from its peak during another cycle. Because of the non-
symmetrical wave shape, the transformer inrush current contains harmonics and DC
components. The harmonic content of the phase ‘A’ inrush current is calculated using a
discrete Fourier transform (DFT).
CJ
~:[J_2 ~.~~t;t!=====OO:
~,~ ~ D 'I
D-1 f--B
D-1 f--B
______________________________________________________________________
108
Figure 5.4 Magnitude of inrush current at zero degree energization
As shown in Fig 5.5, the most significant components are the fundamental, which is
initially 1.78 kA peak, and the second harmonic is initially 620 A peak.
In proposed strategy, second harmonic restraint is used to differentiate transformer
inrush and fault current. The fifth harmonic current reaches a peak value of
approximately 50 A peak, twelve times smaller than the second harmonic and 35 times
smaller than the fundamental component. Generally, the harmonic components decay as
the inrush current decays toward normal steady-state operating conditions. From Fig
5.5, it is also seen that harmonics of order three and above are discontinuous, with their
peak values decreasing to zero and then increasing again.
uto
"to 1410
.-3210 Q.
!,m ~ 860
" ~ C (lifO
'" :l1l ...
lt~ .
• ·'210 • '.1 '.l 004 '.So lUi '.7 '.8 ••• Time (sec)
______________________________________________________________________
109
Figure 5.5 Harmonic contents present in phase ‘A’ inrush current
Further, higher the harmonic order, smaller is the magnitude of corresponding current
component in the inrush current. The DC component present in inrush current is as
shown in Fig 5.6.
Figure 5.6 DC component in inrush current
In Fig 5.6, it is seen that DC component is exponentially decaying and non-periodic
signal, which affects the fundamental component of magnetizing current, therefore it
necessary to minimize with the help of filters. A digital filter whose parameters are
determined using equation (5.7) and (5.8) is used to filter out the DC components
present in the magnetizing inrush current. Further, in this method, Taylor series
1aOOr-~--r----'-----'-----'-----.-----'-----'-----'-----.----.
1600
1400
1200 .. ~ 1000 :t:: c ~ 800
:IE 600
400
- DC Component - fundamenlal Component - SKOnd Harmonic Componenl - Third Harmonic Componenl - Fifth HarmMlc Component - Seventh Harmonic Component
200~~~~~. 00 O.OS D.' 0.15 0.2 0.25 0.3 0.35 0.4 DA5 0.5
Time Isec)
5o0r-----,-----,-----,-----,-----,-----,-----,-----,------,----,
450
400
_350 a. ~ 300
.:: 250
" '" i200I
::IE 1S0r
tOOl
50
~~--~OL.',----~0~.2-,~~0~,'::::~O~,4=====O~,5~===O~,6~~=0~,~7 ====~O,~8 ====~O,~9----J1 Time (secl
______________________________________________________________________
110
expansion of inrush current is used to model the decaying DC component. The digital
filter whose output is shown in Fig 5.7, designed so that its output is exactly opposite to
that of DC component.
Figure 5.7 Digital filter used to compensate DC component
Figure 5.8 Signal for compensation of DC component
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111
5.5.2 Case II: Three phase power transformer under fault condition
Figure 5.9 Inrush and fault current
Fig 5.9 exhibits the inrush current when an external fault occurs, where L-G fault is
considered with terminating resistance 3.5 ohms, which occurs during 0.2 to 0.4 sec. It
is seen that significant increase in the primary current take place due to the occurrence
of fault. From Table 5.1 it can be seen that SHR is more for inrush current as compared
to fault current. Thus, SHR can be used to discriminate inrush from fault current such
that, if SHR is less than threshold value then that condition can be considered as fault
otherwise it is inrush condition. Table 5.1 shows the values of SHR for various
switching conditions of CB which is shown in Fig 5.1 in two different scenarios of fault
and without fault operating conditions.
Table 5.1 RMS value of inrush currents for various switching instants (with and without
fault conditions) of one phase A
Angle
(degree)
Without Fault With Fault
Inrush current
(RMS Value) SHR
Inrush current (RMS
Value) SHR
0 379.25 0.48 714.11 0.14
30 268.6 0.58 670.41 0.13
45 205.93 0.65 653.1 0.13
60 133.75 0.7 640.65 0.14
90 18.479 0.007 635.61 0.16
120 57.15 0.63 649 0.18
135 108.44 0.71 661.41 0.2
150 150.29 0.69 662.85 0.2
180 184.72 0.66 661.75 0.2
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112
5.6 CONCLUSION
From system security and transformer protection view, it is important to have a robust
and reliable protection system. However, during the transformer enerzization beside
inrush, if the transformer encounters a fault, it could spell disaster for the relay
operation due to presence of DC component embedded within inrush and fault wave.
DC component could cause 20% overshoot if appropriate algorithm is not used and
lead the protection engineer to set the relay value to a comparatively large setting.
This chapter presents a reliable algorithm for the estimation of DC component and
measurement of time constant as these are unwanted noise in the system which adversly
affect on the relaying application. Elimination of DC component signals is achieved by
passing it through smoothing filters in a software model. Further, these signals after
passing through filters are examined for its magnitude at various switching angles
during breaker closing for detection of inrush and fault. Results obtained are tabulated
and analysed applying SHR criterion to discriminate inrush and fault current for the
differential protection of a three phase power transformer based on harmonic analysis
and elimination of DC decaying component using digital filters.
To examine the robustness of the proposed algorithm, different scenarios are simulated
using MATLAB within one full cycle and results tabulated align with the theoretical
value. It is inferred from the results obtained that the proposed algorithm has better
convergence and accuracy as compared to DFT method in a static and dynamic model.
Detailed analysis of harmonic contents of the magnetizing inrush current has been
found to be important while designing the harmonic restraint and has been elaborated
in this chapter. The domination of second harmonic component in the inrush current is
an important factor for discrimination.
______________________________________________________________________
113
Chapter 6 Conclusions and Future
Work
6.1 CONCLUSIONS
In this thesis, the author presents a practical method to mitigate inrush current using pre-
fluxing technique as detailed in chapter 4 and discriminates inrush from fault current
after eliminating DC component in Chapter 5 of a three phase transformer. Applying
pre-fluxing technique, a residual flux in a transformer can be actively set-in which can
easily control the sudden inrush at the time of transformer energization. Inrush
occurrence is an undesirable phenomenon and occurs mainly due to:
Incorrect behavior of inrush during transformer saturation
Materials of the core used by the manufacturer does not accurately model
hysteresis and core loss component in the transformer
Amount of core flux present
Tap changing operation and parallel operation of large MVA three phase power
transformers
The block diagram on pre-fluxing circuit presented in Fig 4.1, chapter 4 is a simple
circuit consisting of capacitor and diode which when connected across primary side of a
______________________________________________________________________
114
three phase power transformer as shown in Fig 4.2, injects a DC flux which is set to a
maximum flux in the transformer. This pre-fluxing apparatus on the primary side of the
transformer controls the switching of the circuit breaker poles by rapid, delayed and
simultaneous closing of the circuit breaker. Designing of the components of pre-fluxing
apparatus like capacitor, diode and fuse is easy as these components carry fraction of
three phase power transformers rated current. Further, this pre-fluxing device proposed
in this thesis, does not require the knowledge of transformer flux or any additional
device to measure such flux within the transformer as this device shall set the
transformer to a desired flux. The second part of inrush reduction strategy highlighted
by the author is about controlling the switching of the circuit breaker by closing rapidly
or delayed or by simultaneously of the circuit breaker poles on the incomer side of the
three phase power transformer.
Results are validated using a computer model and the end results recorded shows
considerable reduction in inrush and effectiveness of pre-fluxing technique in mitigating
inrush of a three phase transformer during energization. Conditions of minimum inrush
current are shown graphically for all three phases in chapter 4 and results are
interpreted. Application of pre-fluxing device greatly helps in the smooth start of power
transformer and uses considerably lower voltages either in AC and DC regardless of
power rating of the three phase power transformer. Controlled switching of the circuit
breaker at the incomer side of three phase power transformer side prevents improper
operation of protection relays, reduction in power quality and mechanical damage to
three phase windings of these large power transformers. It also prevents failures of the
power transformers due to harmonic over voltages, sympathetic inrushes in the
neighboring power transformer. The inrush phenomenon mitigation method could find
useful application while switching on the transformer using circuit breaker.
In addition to inrush phenomenon and mitigation method proposed in thesis by applying
pre-fluxing method, the author also has proposed a technique to extract and eliminate
DC component which is an undesirable phenomenon during an inrush or short circuit.
The nature of DC components and issues related to have been dealt in chapter 5. DC
component have characteristics of exponentially decaying DC offset components having
unpredictable magnitudes and unknown time constants. DC components embedded in
inrush and fault could postpone the convergence speed of the relay algorithm, thereby
______________________________________________________________________
115
reducing the accuracy and operational time of the digital differential relay. It has been
observed that, presence of decaying DC component has been determined to cause
phasor estimation errors. Decaying DC components are usually non-periodic signals
which seriously affects the accuracy of digital filters like Fourier, Walsh, Cosine etc .
In light of the issues attributed to DC component, an investigation was carried out in
this thesis and the algorithm proposed, eliminated this unwanted noise i.e, DC
component which affected the protection system. The author, estimated DC components
which was not affected by system and fault conditions and the output signal did not
have the oscillatory signals in comparison to other algorithms. Applying this estimated
DC components to a series of digital filters within a MATLAB model these unwanted
DC components are filtered out discriminating inrush against short circuit using least
square method (LSM) and second harmonic ratio (SHR) algorithm. The performance of
time constant (τ) and DC decaying is found to be satisfactory within one cycle or
multiples of fundamentals frequency as outlined in chapter 5. The proposed algorithm
can be used in the estimation of DC component from inrush and fault for a range of time
constants (τ) is satisfactory in the midst of high frequency noises. The proposed method
of DC component extraction and elimination is characterized by its simplicity of phasor
algorithm formulation and computer simulation. Further, this technique of DC
component elimination after applying filters offer reasonable immunity in the event of
non-harmonic production and can be accomplished within one cycle. The principle of
this technique has practical utility and can be implemented in a digital microprocessor
based differential relays with immediate convergence being achievable.
6.2 FUTURE WORK
The author intends to progress his future research work on the following items listed as
under which will complement the existing thesis on inrush and fault current
identification and provide robust protection to transformer:-
1. Performance of DC component in light of heavy noise in the circuit needs further
study and future work related to suppression of noise in a dynamic environment needs
to be researched. DC component performance within half a cycle during energization of
multiple banks of transformers operated in parallel on a high voltage system at 220kV
______________________________________________________________________
116
or 330kV needs to be investigated and tested through comprehensive software
modelling platform.
2. Real power system network consists of different vector configuration of a three phase
power transformers. Energization of large MVA three phase power transformers in
parallel not only causes sympathetic inrush but significantly affects the relay
performance in the event of a fault. Mitigation of inrush and fault, if occurring
simultaneously, becomes a challenging task for the system engineers. Investigation of
fault elimination and inrush restraining method in light of a complex network
havingtransformer banks need more examination.
3. Investigation of phasor measurement of current in digital form require the application
of phasor measurement units (PMU) which may find application in the relay circuit and
tests may be carried out to validate its application on different magnetization condition
i.e. inrush, over excitation etc.
4. With the requirement of economy in some countries demanding ultra high voltage
(UHV) A.C network at 1200kV with parallel line transmission circuits cannot be
achieved by extrapolating high voltage results to UHV systems and a great deal of effort
in investigation and simulation needs to be carried out to unwanted DC component,
short circuit phenomenon and inrush restrain technology encompassing digital
protection relay in the circuit.
5. UHV AC to DC converter transformers in some countries, where UHV transmission
lines are operated in DC, provide additional challenges to mitigate transients, slow
frequency response and high resonance in transmission lines and power transformers.
Investigation and simulation needs to be carried out to mitigate transient issues during
its operation. [3]
______________________________________________________________________
117
______________________________________________________________________
118
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______________________________________________________________________
121
Appendix A: Determination of DC
and AC Components during
transients of an unloaded Transformer
A 1 Algorithm formulation for DC decaying component
The detailed algorithmic expression for the transients occurring in an unloaded
transformer takes place during its initial energization. Laplace transform has been used
to determine the mathematical expression .
In the given mathematical expression, is assumed that the source is having negligible
impedance compared to the load.
(A1)
where,
- Arbitrary phase angle which can be closed at any instant voltage cycle
R- Resistance of the Transformer
L - Inductance of the Transformer
)()(
)( tVmSindt
tdILtRI
______________________________________________________________________
122
In the expression (A1) current lags voltage by an angle ф and attains steady state after
few cycles but not instantaneously due to circuit inductance which requires current to
start at zero.
Rewriting (A1),
(A2)
On taking Laplace transforms on both sides of (A2)
(A3)
In (A3) the values of Sin and Cos are constant. Initial current at the time of closing
the circuit breaker is 0 i.e. when =0 , I(0)=0 as the current in an inductive circuit cannot
change to zero instantaneously.
(A4)
(A5)
Rearranging (A5),
(A6)
(A7)
If L
R= ,
(A8)
Taking partial fractions of (A8)
(A9)
SintCosCostSinVmdt
tdILtRI
)()(
2222)0()()(
s
Sins
s
CosVmLIsLsisRi
2222)()(
s
Sins
s
CosVmsLsisRi
2222)(
s
sSin
s
CosVmLsRsi
2222
1)(
s
sSin
s
CosVm
LsRsi
2222
)(
1)(
s
sSin
s
CosVm
L
RsL
si
))(())((
1)(
2222
ss
sSin
L
V
ssCos
L
Vsi mm
22222222
1
)(
1
))((
1
ss
s
sss
______________________________________________________________________
123
(A10)
(A11)
(A12)
On taking inverse Laplace of (A12)
(A13)
(A14)
(A15)
(A16)
22
2
222222 )(
1
))((
ss
s
sss
s
22
2
2222
222222
1
11)(
ss
s
sL
VmSin
ss
s
sL
CosVmsi
22
2
22222222
1
)()(
ss
s
sSin
ss
s
sCos
L
Vmsi
tSintCoseSin
tSintCoseCos
L
VmtI
t
t
)()(
22
tCosSinCos
tSinSinCos
eSinCos
L
VmtI
t
)(
)(
)(
)()(
22
tCosSinCos
tSinSinCos
eCosSin
L
VmtI
t
)(
)(
)(
)()(
22
tCosSinCos
tSinSinCos
eCosSin
L
Vm
t
)(
)(
)(
2222
2222
2222
22
______________________________________________________________________
124
If,
(A17)
(A18)
(A19)
(A20)
Substituting the value of = R/L, expression (A20) becomes
(A21)
Differentiating the DC and AC component from (A21),
Decaying DC Component (A22)
AC Component (A23)
tan and Sin ,
2222Cos
tCosSinCosCosSin
tSinSinSinCosCos
eCosSinSinCos
L
VmtI
t
)(
)(
)(
)(22
tCosSintSinCoseSinL
VmtI
t
)()()(()(22
)()(()(22
tSineSinL
VmtI
t
)()()(222
tSineSinLR
VmtI
t
tm eSin
LR
V
)()( 2
1222
)()( 2
1222
tSinLR
Vm
______________________________________________________________________
125
Expressing (A22) for DC component graphically in figure (A1).
Figure A.1 DC Component characteristics
Expressing (A23) for AC component graphically in figure (A2).
Figure A.2 AC component characteristics
t
I(t)dc= 1 pu
I(t)=1pu ac
ωt
______________________________________________________________________
126
Appendix:B Publications
1. S.Kumar , K.Kant, D.Tiwari, S.K.Bhil, and S.R.Wagh, "Pre-fluxing Technique to
Mitigate Inrush Current of Three-Phase Power Transformer", IEEE symposium,
APEMC-2013, Melbourne, Australia, April, 2013.
2. S.Kumar, V.Sreeram, "Elimination of DC Component of Identification of Inrush
Current using Harmonic Analysis for Power Transformer protection", IEEE
TENCON spring 2013 conference, Sydney, Australia, April,2013.
3. S.Kumar, S.R.Wagh and V.Sreeram, "Extraction of DC component and harmonic
analysis for protection of power transformer", 8th International conference on
Industrial Electronics and Applications , ICIEA , Melbourne, Australia, June, 2013.
4. S.S.Wamane, J.R.Baviskar , S.R.Wagh and S.Kumar, "Performance-based
comparison of UPQC compensating signal generation algorithms under
distorted supply and non-linear load conditions", 8th International conference on
Industrial Electronics and Applications, ICIEA, Melbourne, Australia, June, 2013.
5. S.Kumar, V.Sreeram, S.R.Wagh, "Differential Protection of a Power Transformer
using Harmonic Analysis Method." IEEE ECCE Asia Down Under, Melbourne,
Australia, June, 2013.
