remnant life estimation of power transformers based on chemical diagnostic parameters using
TRANSCRIPT
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Faculty of Science and Engineering
Department of Electrical and Computer Engineering
Remnant Life Estimation of Power Transformers Based on
Chemical Diagnostic Parameters Using Adaptive Neuro-
Fuzzy Inference System
Mohammadsaleh Forouhari
This thesis is presented for the Degree of
Master of Philosophy
of
Curtin University
January 2017
Declaration
To the best of my knowledge and belief this thesis contains no material previously
published by any other person except where due acknowledgment has been made.
This thesis contains no material which has been accepted for the award of any other
degree or diploma in any university.
Signature:
Date: 26/01/2017
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Abstract
Power transformer plays a critical role in the reliability of the electrical networks.
Failure of power transformers may lead to catastrophic consequences. Thus,
continuous monitoring of power transformers is of great importance to utilities across
the world. As the age of numerous power transformers operating worldwide are close
to or have even surpassed their designed life expectation, utilities have recently been
accentuating on the transformer condition-based maintenance so as to elongate
transformers’ operational lifetime. In addition, establishing life estimation and asset
management decision models which is able to estimate the extent of criticality and age
of a power transformer is a great contribution to utilities to best formulate an asset
management strategy.
Among several contributing factors to the failure of a power transformer, pre-mature
ageing of the transformer insulation system is one of the major causes which mostly
stem from the accumulated impact of three processes of pyrolysis, hydrolysis as well
as oxidation. The extent of criticality and ageing of a power transformer can be
determined by using several parameters which are of diagnostic importance in the
condition monitoring field of power transformers. Thus far, several attempts in
developing life estimation and asset management decision models have been made.
However, the common feature of all these investigations is using inference systems
which are based on static rules. In order to eradicate this constraint, this research study
aims at developing an integrated life estimation and asset management decision model
based on adaptive neuro fuzzy inference system, ANFIS. Diagnostic indicators which
are utilized in the proposed model, such as interfacial tension of the oil, moisture
content of the paper insulation and 2-FAL content of the oil show a strong correlation
with ageing of power transformers insulation system. Implementation of this ANFIS
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methodology is expected to project patterns existing in the practical measurements
history of power transformers by adaptive and real-time updating of the inference
system’s rules and to provide utilities with a more reliable asset management and
condition monitoring tool.
Keywords – power transformer; adaptive neuro fuzzy inference system; life
estimation; asset management; dissolved gas analysis; moisture content; 2-FAL
content; IFT number; acidity.
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Acknowledgments
I would like to first thank my wife for her great support during my studying at Curtin
University.
Special thanks to my supervisor, Associate Professor Ahmed Abu-Siada, for being
always approachable, supportive and inspiring as well as my co-supervisor, professor
Syed M. Islam for his undeniable help. Also, sincere gratitude must be expressed
towards all the electrical and computer engineering department staff for providing
endless technical and administrative support to students and their efforts in building
an environment in which students can have the most out of their potential. At the end,
I am so grateful of Dr Zahra Jabiri, Kerry Williams and Emmanuel Santos at Western
Power Corporation in Western Australia for their guidance and support over the course
of this research study.
VI
Publications
Over the course of this research study, the outcome has been published as follows:
1. Saleh Forouhari, A. Abu-Siada, “Integrated Life Estimation and Asset
Management Decision Model for Power Transformers Using ANFIS”,
Submitted to IEEE Transaction on Dielectrics and Electrical Insulation
Society.
2. Saleh Forouhari, A. Abu-Siada, “Remnant Life Estimation of Power
Transformer Based on IFT and Acidity Number of Transformer Oil”,
International Conference on the Properties and Applications of Dielectric
Materials (ICPADM), Australia, 2015.
VII
Table of Contents
1 Introduction ...................................................................................................... 1
1.1 Background ............................................................................................... 1
1.2 Scope of Work ........................................................................................... 4
1.3 Research Methodology .............................................................................. 5
1.4 Thesis Outline ............................................................................................ 5
2 Power Transformer Diagnostic Indicators ......................................................... 6
2.1 Dissolved Gas Analysis (DGA).................................................................. 6
2.2 DGA Measurement Methods...................................................................... 7
2.3 DGA Interpretation Methods: ...................................................................10
2.3.1 Key Gas Method (KGM): ..................................................................10
2.3.2 Doernenburg Ratio Method (DRM): ..................................................10
2.3.3 Rogers Ratio Method (RRM) .............................................................11
2.3.4 Duval Triangle Method (DTM): .........................................................13
2.4 Transformer Cellulose Insulation: .............................................................16
2.4.1 Cellulose Insulation Degradation: ......................................................20
2.4.2 Insulation Life Plots ...........................................................................24
2.5 Furan Compounds .....................................................................................27
2.5.1 Formation of Furan Compounds ........................................................28
2.5.2 Furan Compounds Stability................................................................28
2.5.3 Correlation between Paper Insulation DP and Furan Content of the Oil
30
VIII
2.5.4 Effective Factors on the Furan Production Rate .................................32
2.6 Moisture in Oil-Paper Insulation System of Power Transformers ..............35
2.7 Acid in Power Transformer Insulation System ..........................................40
2.8 Interfacial Tension Number of the Insulting Oil ........................................42
3 Fundamentals of Fuzzy and Adaptive Neuro Fuzzy Inference Systems ............46
3.1 The Architecture of ANFIS .......................................................................49
4 ANFIS Modelling ............................................................................................57
4.1 Life Estimation Model ..............................................................................57
4.2 Integrated Life Estimation and Asset Management Decision Model ..........70
4.2.1 Oil Criticality Sub-model ...................................................................70
4.2.2 Paper Criticality Sub-model ...............................................................71
4.2.3 Electrical Criticality Sub-model .........................................................72
4.2.4 Asset Management Decision Sub-model ............................................73
5 Conclusion and Future Work ...........................................................................82
5.1 Conclusion ................................................................................................82
5.2 Future Work .............................................................................................83
6 References .......................................................................................................85
7 Appendix .........................................................................................................97
7.1 Oil Criticality Sub-Model .........................................................................97
7.2 Heating Criticality Sub-model ...................................................................98
7.3 Paper Degradation Criticality ....................................................................99
7.4 Thermal Criticality Sub-model ................................................................ 100
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7.5 Paper Criticality Sub-model .................................................................... 101
7.6 Partial Discharge Criticality Sub-model .................................................. 102
7.7 Arcing Criticality Sub-model .................................................................. 103
7.8 Electrical Criticality Sub-model .............................................................. 104
7.9 Overall Criticality Sub-model ................................................................. 105
7.10 Asset Management Decision Sub-model ................................................. 106
7.11 Case Studies ........................................................................................... 107
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List of Figures
Figure 1.1. Power transformer structure ................................................................... 2
Figure 2.1. A basic setup of gas chromatograph [12] ................................................ 8
Figure 2.2. Duval triangle with fault zones and associated coordinates [12].............13
Figure 2.3. Complementary Duval triangle 4 [16] ...................................................14
Figure 2.4. Complementary Duval triangle 5 [12] ...................................................14
Figure 2.5. Different transformer parts formed from pressboard [24].......................17
Figure 2.6. Power transformer HV coil wrapped by paper [24] ................................17
Figure 2.7. Cellulose polymer [24] ..........................................................................18
Figure 2.8. Hydrolytic degradation reaction of cellulose [29] ..................................21
Figure 2.9. An instance of oxidative cellulose degradation [31] ...............................21
Figure 2.10. Cellulose degradation mechanisms [4].................................................23
Figure 2.11. The relation between mechanical properties of crepe kraft paper and
ageing [4]................................................................................................................24
Figure 2.12. Different Arrhenius life plots for different types of cellulose insulation
[4] ...........................................................................................................................26
Figure 2.13. Chemical structure of furan compounds [44] .......................................29
Figure 2.14. The relation between DP of the kraft paper samples and 2FAL content
of the oil obtained from an accelerated ageing test conducetd at different
temperatures [7] ......................................................................................................31
Figure 2.15. The relation between DP and 2-FAL content of the oil [4] ...................33
Figure 2.16. Moisture content of paper insulation as a function of temperature and
percentage of relative humidity [52] ........................................................................36
Figure 2.17. Piper charts for lower paper insulation moisture contents [4] ...............38
Figure 2.18. Moisture equilibrium curves [4] ..........................................................39
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Figure 2.19. Transformer insulating oil oxidation [30] ............................................40
Figure 2.20. Acid hydrolysis paper degradation [30] ...............................................43
Figure 2.21. Interfacial tensiometer [70]..................................................................44
Figure 2.22. Relation between acidity, IFT number of the oil and in-service years of a
transformer [71] ......................................................................................................44
Figure 3.1. Qualitative classification of transformer diagnostic indicators [72] ........46
Figure 3.2. Fuzzy inference system decision-making structure [76] .........................48
Figure 3.3. Type-3 fuzzy inference and corresponding equivalent ANFIS structure
[77] .........................................................................................................................50
Figure 3.4. Physical effect of the bell-shaped membership function parameters [77]
...............................................................................................................................51
Figure 3.5. A 2-input ANFIS network with nine rules and how it relates to fuzzy
subspaces [77] ........................................................................................................54
Figure 3.6. A generic example of how ANFIS training results in more precise
membership functions [77] ......................................................................................55
Figure 3.7. Flowchart of ANFIS learning [81] .........................................................56
Figure 4.1. Membership functions of 2-Furfural content..........................................58
Figure 4.2. Membership functions of cellulose insulation moisture content .............58
Figure 4.3. Membership functions of IFT number of the oil ....................................58
Figure 4.4. Fuzzy rules of the proposed FIS-based model ........................................60
Figure 4.5. Three-dimensional display of the proposed FIS-based mapping.............61
Figure 4.6. ANFIS training error .............................................................................62
Figure 4.7. ANFIS-based model network ................................................................63
Figure 4.8. Adjusted membership functions of 2-FAL content in oil........................65
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Figure 4.9. Adjusted membership functions of the paper insulation moisture content
...............................................................................................................................65
Figure 4.10. Adjusted membership functions of interfacial tension number of the oil
...............................................................................................................................65
Figure 4.11. Generated rules of the proposed ANFIS-based model ..........................66
Figure 4.12. The ANFIS-based model validation against testing data ......................67
Figure 4.13. Integrated life estimation and asset management decision model of
power transformer ...................................................................................................78
Figure 7.1. Adjusted membership functions of interfacial tension number ...............97
Figure 7.2. Adjusted membership functions of acidity .............................................97
Figure 7.3. Adjusted membership functions of paper insulation moisture content ....98
Figure 7.4. Adjusted membership functions of ethane concentration .......................98
Figure 7.5. Adjusted membership functions of ethylene concentration ....................98
Figure 7.6. Adjusted membership functions of carbon-monoxide concentration ......99
Figure 7.7. Adjusted membership functions of carbon-dioxide concentration ..........99
Figure 7.8. Adjusted membership functions of carbon-oxides ratio (CO2/CO) ...... 100
Figure 7.9. Adjusted membership functions of paper degradation criticality .......... 100
Figure 7.10. Adjusted membership functions of heating criticality ........................ 100
Figure 7.11. Adjusted membership functions of thermal criticality ........................ 101
Figure 7.12. Adjusted membership functions of 2-FAL content of the oil .............. 101
Figure 7.13. Adjusted membership functions of hydrogen concentration ............... 102
Figure 7.14. Adjusted membership functions of methane concentration ................ 102
Figure 7.15. Adjusted membership functions of hydrogen concentration ............... 103
Figure 7.16. Adjusted membership functions of acetylene concentration ............... 103
Figure 7.17. Adjusted membership functions of partial discharge criticality .......... 104
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Figure 7.18. Adjusted membership functions of arcing criticality .......................... 104
Figure 7.19. Adjusted membership functions of oil criticality................................ 105
Figure 7.20. Adjusted membership functions of paper criticality ........................... 105
Figure 7.21. Adjusted membership functions of electrical criticality...................... 106
Figure 7.22. Adjusted membership functions of overall criticality ......................... 106
Figure 7.23. Adjusted membership functions of life estimation ............................. 106
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List of Tables
Table 1.1. Typical sources of power transformers failure [1] .................................... 1
Table 2.1. Comparison between gas chromatography (GC), hydrogen on-line monitor
and photo-acoustic spectroscopy (PAS) techniques [12] ........................................... 9
Table 2.2. L1 Concentrations of Doernenburg ratio method [11] .............................11
Table 2.3. Associated faults with fault-gas concentrations ratios in Doernenburg
method [12] ............................................................................................................12
Table 2.4. Suggested diagnoses by Rogers ratio method [2, 3] ................................12
Table 2.5. Comparison between DGA interpretation methods [12] ..........................15
Table 2.6. Typical paper and pressboard specifications [24] ....................................19
Table 2.7. Significance of paper degree of polymerisation and 2-FAL content of the
oil in paper insulation ageing interpretation [51] .....................................................33
Table 2.8. Diagnostic significance of paper insulation moisture content and
interfacial tension of the oil [42, 72] ........................................................................45
Table 4.1. Membership functions parameters of the ANFIS-based model ................64
Table 4.2. Comparison between FIS- and ANFIS-based models life estimation .......68
Table 4.3. Management decisions as per the output of the proposed integrated model
...............................................................................................................................73
Table 4.4. Comparison between actual and estimated asset management decision
numbers ..................................................................................................................79
Table 7.1. Adapted parameters of oil criticality membership functions ....................97
Table 7.2. Adapted parameters of heating criticality membership functions.............98
Table 7.3. Adapted parameters for paper degradation criticality membership
functions .................................................................................................................99
Table 7.4. Adapted parameters of thermal criticality membership functions .......... 100
XV
Table 7.5. Adapted parameters of paper criticality membership functions ............. 101
Table 7.6. Adapted parameters of partial discharge membership functions ............ 102
Table 7.7. Adapted parameters of arcing criticality membership functions ............ 103
Table 7.8. Adapted parameters of electrical criticality membership functions ........ 104
Table 7.9. Adapted parameters of overall criticality membership functions ........... 105
Table 7.10. Adapted parameters of asset management decision membership functions
............................................................................................................................. 106
Table 7.11. Case Studies ....................................................................................... 107
1
1 Introduction
1.1 Background
Power transformers are crucial assets and play a crucial role in the continuity and
reliability of electric power systems. Rising demand of energy as well as increase in
the number of operating transformers which either are close or have already exceeded
their expected technical life have resulted in a high failure rate of power transformers
in service [1]. A survey conducted by the IEEE organisation points out that during a
period of 16 years, a fleet of oil-immersed power transformers is expected to have a
significant failure rate of 10% [2]. As failure of in-service transformers has
catastrophic consequences on the electric power network in terms of economical and
operational aspects, regular condition monitoring of power transformers to detect
incipient faults is necessary. This fact has encouraged transformer operators, including
utilities across the world to employ more efficient condition-based asset management
and monitoring strategies [3]. Table 1.1 [1] summarises typical sources of power
transformers failure and Figure 1.1 shows a typical structure of a power transformer.
Table 1.1. Typical sources of power transformers failure [1]
Internal Causes External Causes
Insulation degradation Lightning strikes
Overheating Switching operations in power system
Oxygen and moisture Overloading of transformers
Solid contamination in transformer oil Faults occurrence in power system, e.g.
short circuit
Partial discharge activity
Design problems
Winding clamping loss and deformation
of windings
Resonance of windings
2
Figure 1.1. Power transformer structure
A noticeable part of failures in power transformers originate from their insulation
system. Therefore, in order to define effective maintenance schemes, it is essential to
obtain a thorough understanding of transformer insulation system ageing process and
determine the insulation integrity extent. The cumulative effect of oxygen,
temperature, and moisture along with mechanical and electrical stresses which a
transformer undergoes over its operational course are contributing parameters to the
ageing of the insulation system [4]. Although insulation system normal ageing is an
expected event once a power transformer is put into service, accelerated ageing of the
insulation system is what should be avoided to elongate transformer operational
lifetime. Restricted financial resources call for the utilization of uncomplicated,
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economical and reliable life estimation and asset management decision models based
on minimum number of condition monitoring parameters. In line with this necessity,
some models have been suggested by IEEE [5] and IEC [6], which give an estimation
of transformer remnant life by considering merely the effect of operating temperature
of power transformers. Even though transformer operators are now more equipped to
sense power transformer temperature data due to recent technological innovations in
the field of condition monitoring of power transformers, there is still an uncertainty
regarding temperature distribution within a transformer [7]. Another criticism which
can be directed towards these efforts is that models which are established based on
only operating temperature of transformers do not account for the impact of the other
ageing factors, such as moisture and oxygen. An age estimation and condition
monitoring model for power transformers developed based on fuzzy logic inference
system was proposed in the literature [8]. Although this model takes into consideration
almost all diagnostic parameters of power transformers, there are some limitations on
regular application of this model. Firstly, this model includes some parameters which
are not measured at routine transformer testing intervals. Secondly, for measurement
of some parameters used in this model, such as sweep frequency response, a
transformer needs to be off-line. Additionally, so far, all suggested models concerning
life estimation and management decision of power transformers have been based on
fuzzy logic inference system or fixed artificial neural network, ANN, methodologies
in which corresponding rules cannot be automatically adapted based on future
measurements and feedbacks. In order to tackle these issues, a life estimation model
of power transformers is proposed, which is based on adaptive neuro fuzzy inference
system (ANFIS). One of the advantages this model brings into practice is utilizing
parameters which are frequently measured during transformer routine maintenance.
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Also, using the ANFIS technique enables this model to enhance its precision with
deploying repeated self-assessments based on the newly measured parameters and the
model’s output.
1.2 Scope of Work
This thesis is aimed at achieving following objectives:
Acquiring comprehensive knowledge of transformer’s insulation system
ageing factors and corresponding diagnostic indicators used in the integrated
age estimation and asset management decision model for power transformers.
Developing a model based on fuzzy logic for estimating the age of power
transformers. Although fuzzy logic inference system has already been applied
in other research works in the literature for life estimation and asset
management of power transformers, the purpose of using such a technique in
this thesis is only to compare its performance with the ANFIS model proposed
in this thesis and highlighting the advantages of the applications of neuro fuzzy
logic inference system in this field.
Introducing an integrated neuro fuzzy logic-based model for life estimation and
asset management decision of power transformers, which is the main
contribution of this research work in this area.
The outcome of this thesis is expected to help transformer operators monitoring the
condition of their power transformers fleet more regularly with less cost over the
operational course of power transformers. Also, it can have a remarkable contribution
to life cycle management of transformers.
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1.3 Research Methodology
To verify the above-mentioned objectives, this study covers a thorough investigation
on the contributing factors to the ageing of power transformers’ insulation system.
Therefore, it examines ageing mechanism of the insulation system and all the
diagnostic indicators showing a correlation with ageing of power transformers.
Adaptive neuro fuzzy logic inference system is implemented to develop an integrated
life estimation and asset management decision model of power transformers.
1.4 Thesis Outline
Following chapters are organised as below:
Chapter 2 covers the knowledge required for understanding power
transformers insulation system ageing mechanism along with diagnostic
parameters used in determining power transformers condition and management
decision.
Chapter 3 brings a short summary of fuzzy logic, only giving an idea to the
readers on the principles of fuzzy inference system. Then, it covers adaptive
neuro fuzzy inference method as used in this thesis.
Chapter 4 explains the details of integrated life estimation and asset
management decision model proposed in this thesis along with case studies,
and obtained results from the model.
Chapter 5 draws the main conclusions form this research and presents some
recommendations for future work on this subject.
6
2 Power Transformer Diagnostic Indicators
Oil-immersed transformers are indispensable assets in the power generation,
transmission and distribution networks. The major function of a transformer is to
increase or decrease the level of voltage throughout the electric network. After electric
energy is generated in a power plant, by means of a step up generation power
transformer, the voltage level elevates in order to diminish the amount of loss of the
transmitted electric energy for long distances. On the other hand, when electric energy
reaches distribution network where it should be delivered to the end consumers, the
voltage needs to be reduced to different levels. At this stage, a step down transformer
is utilized for this purpose. Power transformers which in majority are present in the
generation and transmission networks are one of the most expensive assets of electric
utility companies, playing a crucial role in continuity of the electric energy delivery to
consumers. A great deal of money is annually spent on the operation, maintenance and
repairing of these transformers. Continuity and reliability of power transformers
operation are key factors affecting the profitability of the electric energy networks.
Due to limited financial resources and considering the immense cost of power
transformers replacement, avoiding power transformers failure is number one priority
for all the utility companies throughout the world. The following section presents the
main condition monitoring tests for power transformers.
2.1 Dissolved Gas Analysis (DGA)
Owing to oil and paper insulation decomposition in an oil-immersed power
transformer, fault-gases are produced inside transformer tank, which are dissolved in
the oil and decrease dielectric strength of the oil [9]. Dissolved gas analysis, DGA, is
used as a reliable method to detect incipient and/or active faults in transformers based
on the concentrations of the fault gases dissolved in the oil [10]. Basically,
7
transformers experience thermal and electrical faults over the course of their
operational lifetime. The thermal energy originated from these stresses result in the
generation of five major gases, including hydrogen (H2), methane (CH4), ethane
(C2H6), ethylene (C2H4), and acetylene (C2H2), related to the oil decomposition, and
carbon-monoxide (CO) and carbon-dioxide (CO2), due to the cellulose
degradation[11]. The type and criticality extent of each fault, such as partial discharge,
thermal faults of different temperatures or high intensity electrical discharge, sustained
arcing, can be detected based on the fault-gas concentrations by deploying DGA
measurement and interpretation techniques, which assist in condition monitoring of
power transformers [12]. Dissolved gas analysis is now regarded as one of the regular
measurements performed by utilities on the insulating oil of in-service power
transformers as part of preventive maintenance schemes [3]. Data collated form the
analysis of dissolved gases in the oil over a period of time can be used for the purpose
of not only identifying existing faults, but also determining the progress of the faults
by considering fault-gas generating rates, which facilitates asset management decision
of power transformer [11].
2.2 DGA Measurement Methods
Different techniques are currently used in the analysis of gases dissolved in
transformer oil. Gas chromatography (GC) is one of these methods, which need to be
conducted in the laboratory environment as it requires sophisticated equipment. Whilst
gas chromatography is unanimously identified as the most reliable technique in
analyzing dissolved gases in the oil, it is deployed annually due to being time-
consuming and relatively higher costs incurred. If the analysis detects noticeable
concentration of the gases, it is however necessary to consider this analysis with a
higher frequency as per the recommendations of the IEEE standard C57.104-2008
8
[11]. It is worth mentioning that GC method can also be utilized to quantify the content
of free gases existing in for instance, gas blanket of transformers. Figure 2.1 [12]
illustrates a basic setup of a gas chromatograph which is used in the laboratory to
measure the concentration of the gases dissolved in the oil.
Figure 2.1. A basic setup of gas chromatograph [12]
As another solution to monitor fault-gas concentrations dissolved in the oil, online
hydrogen monitoring device has first been designed and proposed by Syprotec [12].
The ideology behind using this device to monitor condition of power transformers is
that it is agreed that most of the faults occurring in the electrical apparatus which use
oil as insulating medium result in the generation of hydrogen [10]. Therefore,
deploying hydrogen online monitoring device may detect faults, especially hot spots,
partial discharges and arcing at an early stage. Furthermore, photo-acoustic
spectroscopy (PAS) is a relatively new technique in determining the concentration of
fault-gases in the oil [13].
9
Table 2.1. Comparison between gas chromatography (GC), hydrogen on-line monitor and photo-
acoustic spectroscopy (PAS) techniques [12]
Method Advantage Disadvantage
GC
Can detect and analyse
each gas dissolved in
transformer oil
Has the highest accuracy
and repeatability
Results can be utilized to
identify the fault type
Can be conducted only in the
laboratory because of the
sophistication of the equipment
Time-consuming
Expensive
A trained person is required to
perform the test and interpret the
results
Hydrogen
on-line
monitor
Rugged, relatively
cheaper, and continual
on-line monitoring
Detects imminent faults
Only detects H2, CO, C2H2, and
C2H4
Provides the most accurate
concentration only within the
monitor temperature range of 20
to 40 degrees centigrade
Results are not usable to
determine the type of fault
PAS
Continuous on-line
monitoring
Can measure a broad
range of fault gases
content
Results can be used to
identify the fault type
Sensitive results to the wave
number range of the optical
filters and their absorption
characteristics
Concentration accuracy
influenced by the external
temperature and pressure, and by
vibration
Still undergoing development
In this method, pressure waves are produced after the conversion of infrared light
energy of different wavelengths which are absorbed by fault gases into kinetic energy.
These pressure waves are detected through a microphone and consequently the
10
concertation of fault-gases can be identified based on the intensity of these waves [14].
Table 2.1 [12] compares the positives and negatives of the three mentioned techniques
in analysing concentration of fault gases dissolved in the oil samples extracted from in
service power transformers.
2.3 DGA Interpretation Methods:
So far, several methods have been put forward to interpret dissolved gas analysis
results of samples extracted from oil-immersed electrical apparatus. The common
feature of all of them is utilizing absolute or ratios of the main hydrocarbon gases
generated by degradation of the oil/paper as mentioned earlier. For instance, 2-gas
ratios are proposed in IEEE [11] and IEC [15], 3-gas ratios in Duval Triangles 1 to 7
[16] and recently proposed 5-gas ratios in Duval Pentagon [17] as a complementary
tool to the Duval Triangles. Some of these interpretations commonly used by asset
management expert teams so as to determine the condition of power transformers are
explained below.
2.3.1 Key Gas Method (KGM):
Once an electrical or thermal fault happens inside the transformer tank, chemical bonds
of the insulating oil break, resulting in the production of fault gases. Key gas method,
KGM, uses the concentrations of six fault gases of carbon-monoxide (CO), hydrogen
(H2), methane (CH4), Ethane (C2H6), Ethylene (C2H4), and Acetylene (C2H2) to
identify four different faults based on the percentage concentrations of the mentioned
gases, which are obtained from practical experience [18].
2.3.2 Doernenburg Ratio Method (DRM):
DRM is one of the DGA interpretation methods which deploys the ratios of fault-gas
concentrations in order to determine the type of faults [11]. In this method, faults are
11
distinguished according to pre-defined limits for the gas concentrations ratios of
CH4/H2, C2H2/C2H4, C2H2/CH4 and C2H6/C2H2 as shown in Table 2.2 [11]. To use this
interpretation method, two criteria must be met. Firstly, the content of at least one of
the key fault gases of H2, C2H4, CH4, and C2H2 must be more than two times of the
corresponding L1 limit and secondly, the content of at least one of the gases used in
each ratio must exceed related L1 limit. Table 2.3 [12] contains associated faults with
the quantity of the four gas ratios utilized in this method.
Table 2.2. L1 Concentrations of Doernenburg ratio method [11]
Key Gas L1 Concentration (ppm)
Hydrogen (H2) 100
Methane (CH4) 120
Carbon Monoxide (CO) 350
Acetylene (C2H2) 35
Ethylene (C2H4) 50
Ethane (C2H6) 65
2.3.3 Rogers Ratio Method (RRM)
In contrast to Doernenburg ratio method, it is not needed to have remarkable
concentrations of fault-gases to apply Rogers ratio method, RRM so as to identify fault
types. Once fault-gas concentrations surpass the L1 limits suggested in Table 2.2, the
requirement has been addressed and this method is applicable. Although Rogers ratio
method first included four fault-gas concentrations of C2H6/CH4, C2H2/C2H4, CH4/H2,
and C2H4/C2H6, the ratio of C2H6/CH4 was then disregarded due to having less
diagnostic value [19]. Currently, 5 different fault types together with normal condition
may be identified using the proposed fault-gas ratios ranges in
12
Table 2.4 [2, 3].
Table 2.3. Associated faults with fault-gas concentrations ratios in Doernenburg method [12]
Faults
CH4/H2 C2H2/C2H4 C2H2/CH4 C2H6/C2H2
Oil
Gas
Space
Oil
Gas
Space
Oil
Gas
Space
Oil
Gas
Space
Thermal
Fault
>1 >0.1 <0.75 <1 <0.3 <0.1 >0.4 >0.2
PD <0.1 <0.01 Not significant <0.3 <0.1 >0.4 >0.2
Arcing
>0.1
to <1
>0.01 to
<0.1
>0.75 >1 >0.3 >0.1 <0.4 <0.2
Table 2.4. Suggested diagnoses by Rogers ratio method [2, 3]
Case C2H2/C2H4 CH4/H2 C2H4/C2H6 Fault Diagnoses
0 <0.1
>0.1 to
<1
<1 Normal
1 <0.1 <0.1 <1
Partial discharge of low energy
density
2 0.1 to 3 0.1 to 1 >3 Arcing
3 <0.1
>0.1 to
<1
1 to 3
Thermal fault of low temperature (T
< 300 °C)
4 <0.1 >1 1 to 3
Thermal fault of medium
temperature (300 °C < T < 700 °C)
5 <0.1 >1 >3
Thermal fault of high temperature
(T > 700 °C)
13
2.3.4 Duval Triangle Method (DTM):
This method was established using IEC 60599 ratio method and IEC TC10 databases
[16]. It is represented by a triangle using the concentrations of CH4, C2H2, C2H4 shown
on the sides of this triangle [11]. This method facilitates the identification of seven
different faults, including partial electrical discharge (PD), electrical discharges of low
energy (D1) as well as high energy (D2), thermal faults at varying temperatures (T1,
T2, T3), and a combination of thermal faults and electrical discharges (DT) as
displayed in seven different zones on the triangle in Figure 2.2 [12]. As a disadvantage
of this method, Duval triangle cannot recognize the conditions in which power
transformers have a normal operation, leading to inability of this method to identify
incipient faults. Furthermore, Duval has also put forward some other triangles using
the same principles and methodology, such as DTM 2 [16], which is developed for the
detection of faults in oil-filled load tap changers, DTM 3 [16] for electrical apparatus
utilizing non-mineral insulating oils and DTM 4 together with DTM 5 [16], which are
used in order to have a particular attention to cases when the occurrence of partial
discharge (PD), thermal fault of T1 and thermal fault of T2 are detected using the
original Duval triangle.
Figure 2.2. Duval triangle with fault zones and associated coordinates [12]
14
In addition, Duval pentagon [17] has recently been introduced as a new
complementary technique for the interpretation of dissolved gas analysis in power
transformers. The triangles of DTM 4, and DTM 5 are displayed in Figure 2.3 [16] and
Figure 2.4 [12] respectively.
Figure 2.3. Complementary Duval triangle 4 [16]
Figure 2.4. Complementary Duval triangle 5 [12]
Table 2.5 [12] compares the key gas method (KGM) with all well-known ratio methods
for the interpretation of DGA results.
15
Table 2.5. Comparison between DGA interpretation methods [12]
Type Method Fault Types Gases
Involved
KGM
Deploys individual gas
contents, convenient to apply,
very conservative
PD, arcing, overheated oil,
overheated cellulose
CO, CO2,
H2, CH4,
C2H2,
C2H4, and
C2H6
DRM
Utilizes four gas concentration
ratios (CH4/H2, C2H2/C2H4,
C2H2/CH4, and C2H6/C2H2) to
distinguish three different fault
types, deploys specified
concertation limits to identify
faults
Thermal decomposition,
PD, arcing
H2, CH4,
C2H2,
C2H4, and
C2H6
RRM
Utilizes three gas
concentration ratios
(C2H2/C2H4, CH4/H2, and
C2H4/C2H6) to distinguish five
different fault types, deploys
specified concentration limits
to identify faults
PD, arcing, low
temperature thermal fault,
thermal fault <700 ◦C,
thermal fault >700 ◦C
H2, CH4,
C2H2,
C2H4, and
C2H6
IRM
Analogous to RRM, however
excluding the C2H6/CH4 ratio,
identifies six fault types,
deploys specified
concentration limits to identify
faults
PD, low energy electrical
discharge, high energy
electrical discharge,
thermal faults <300 ◦C,
between 300 and 700 ◦C,
and greater than 700 ◦C
H2, CH4,
C2H2,
C2H4, and
C2H6
16
DTM
Deploys triangles to identify
six faults, not able to detect the
normal condition of a power
transformer
PD, low energy discharge,
high energy discharge,
thermal faults <300 ◦C,
between 300 and 700 ◦C,
and greater than 700 ◦C
CH4, C2H2,
and C2H4
As stated above, several interpretation techniques of DGA results have so far been
established. However, some inconsistency in the application of these methods to
recognize fault types have been reported [20]. In order to address this issue, researchers
have suggested AI methods, such as fuzzy logic [20] and neural network [21, 22],
yielding a higher precision in transformer diagnoses.
2.4 Transformer Cellulose Insulation:
Due to the abundance of cellulose in nature, which can be obtained from soft wood, it
has been the first option to be used as solid insulation in power transformers. Cellulose
is consumed as an insulating medium not only in transformers, but also in condenser
bushings, HV power cables and power capacitors [23]. It is reported that the quantity
of cellulose consumption in electrical equipment in the year 1939 in the United States
was 18 million kilograms the majority of which was used in manufacturing power
transformers and HV power cables [24]. However, cellulose insulation shows a great
affinity for moisture, identified as the main disadvantage of the utilization of cellulose
in high voltage electric apparatus, especially power transformers. In power
transformers, it is strongly recommended to dry out cellulose insulation as it improves
dielectric properties of cellulose although drying-out process is time-consuming and
sophisticated [25]. Generally, cellulose insulation is considered in oil-filled power
transformers ranging from small ones, such as pole-mounted transformers to large ones
in substations with 40,000 to 100,0000 litres of oil. Cellulose insulation in power
17
transformers comprise the HV and LV windings insulation together with support
structures, spacers etc. as illustrated in Figure 2.5 [24]. Figure 2.6 [24] also shows the
high voltage, HV, coil of a power transformer wrapped by paper tapes [24].
Figure 2.5. Different transformer parts formed from pressboard [24]
Figure 2.6. Power transformer HV coil wrapped by paper [24]
18
The majority of paper and pressboard which are specifically manufactured for
electrical purposes are made up of processed wood pulp by a chemical process
identified as kraft process [24]. Kraft is a German word meaning strong. The main part
of paper and pressboard in power transformers is cellulose. Cellulose consists of
repeated glucose units connected to each other as displayed in Figure 2.7 [24] and can
be represented by the chemical symbol of [C5H10O5]n in which n is recognised as the
degree of polymerisation (DP) of the cellulose. New kraft paper and pressboard have
a DP ranging between 1100 and 1200.
Figure 2.7. Cellulose polymer [24]
A few decades after inventing power transformers in 1885 by Austrian engineers [26],
it was unanimously accepted that a combination of paper insulation with insulating oil
was vital to address all the issues with boundary areas in power transformers, such as
angels and corners, which were raised due to increasing voltage levels. The usage of
insulating oil in power transformers began in 1892 by GE company [24]. Impregnating
paper with resin which was used prior to this time to improve insulating characteristics
of the paper insulation ceased by the introduction of the insulating oil. By increasing
the operating temperature of power transformers due to the elevation in transformers
rating, the use of thermally upgraded paper insulation in transformers was considered.
It is evident that thermally upgraded paper increases insulation life and extends the life
of transformers by at least the factor of three [24]. In order to compare the function of
thermally upgraded papers with respect to ageing, long-term ageing studies were
19
performed in the 1960s on different types of these papers each of which was upgraded
deploying different upgrading agents [24]. Morrison’s studies indicated considerable
difference in the lifetime of these papers among which the best ones endured 10 times
more than regular kraft papers [27]. Generally, it is believed that thermally upgraded
paper designed for up to 65◦C rise in insulating oil has at least 12 ◦C improvement in
thermal performance as compared with regular kraft papers [24]. As another
improvement, some synthetic materials are being used to produce paper and
pressboard insulation for power transformers. The advantage of using them is
improved thermal capability, 220 ◦C, while it is 105 ◦C for paper insulation made of
cellulose [24]. Moreover, synthetic paper insulation has remarkably lower
hygroscopicity, adsorbing considerably less moisture [24]. As a result, hybrid solid
insulation comprised of both cellulosic and synthetic paper insulation is now
commercially utilized in small power transformers to benefit from these advantages.
However, it is still not economically viable to use them in medium and large power
transformers due to the high cost of synthetic paper insulation. For each transformer,
there is a list of all the specifications of the material used for producing paper and
pressboard. Table 2.6 [24] contains typical specifications indicating the properties of
paper and pressboard insulation.
Table 2.6. Typical paper and pressboard specifications [24]
Physical and Mechanical Electrical Properties
Thickness Dielectric breakdown strength at 60 Hz
Apparent density Impulse strength
Tensile strength Hold strength at 60 Hz for pressboard
Edge tear strength for paper Hold strength of impulse for pressboard
Shrinkage for pressboard Dissipation factor at 25 ◦C
Stretch capacity when subject to tension
Resistance to air (porosity)
20
2.4.1 Cellulose Insulation Degradation:
Generally, it is accepted that the condition of power transformer paper insulation
determines whether a power transformer is operable. Hence, preserving cellulose
insulation integrity and life is necessary. In order to fulfil this goal, it is essential to
have a comprehensive understanding of the ageing mechanisms of the cellulose
insulation.
Contributing factors to cellulose insulation ageing used in power transformers are
temperature, water, oxygen and acids formed in mineral oil. They are generally
classified into three processes of hydrolysis related to water, oxidation related to
oxygen and pyrolysis related to heating [28]. For instance, through hydrolysis which
is a reaction involving water and acids, cleavage of cellulosic polymer chain occurs,
generating free glucose molecules [7]. Further degradation of these glucose molecules
results in the formation of furans which will be elaborated later. It is worth mentioning
that the water molecules formed as a by-product of the hydrolysis reaction will
contribute to more degradation of the cellulose insulation. This is one the situations in
which contributing factors to the ageing of cellulose insulation act in a synergistic way.
Degradation rate of the cellulose insulation increases if no remedial actions are
performed to recover the condition of cellulose insulation. Figure 2.8 [29] depicts
hydrolytic degradation reaction of cellulose. Moreover, there are a number of oxidative
reactions which engage cellulose, breaking its polymeric chain and leading to the
production of water molecules [30]. Concurrently, this moisture causes more
hydrolytic cellulose decomposition. Figure 2.9 [31] demonstrates one of the oxidative
reactions contributing to the degradation of cellulose structure.
21
Figure 2.8. Hydrolytic degradation reaction of cellulose [29]
Several studies have been conducted to examine the effect of oxygen, moisture and
temperature on the ageing rate of paper insulation [23, 24, 25] with different
conclusions. For example, Lundgaard et al [32] identified that cellulose in oil with
excessive oxygen content has 2 to 3 times faster degradation rate compared to vacuum
conditions.
Figure 2.9. An instance of oxidative cellulose degradation [31]
22
The ageing of power transformers has been a continuing concern since the first day of
transformer operation due to the significant replacement cost. As mentioned earlier,
cellulose insulation consists of long chains of glucose monomers, which breaks when
cellulose is exposed to thermal and electrical stresses within a power transformer.
Degree of polymerisation (DP) which is a reliable indicator to the extent to which
paper insulation has been degraded is a reflective of the average number of the glucose
monomers in these chains [33]. For a new paper, DP is expected to be in the range of
1100 to 1600 although it reduces as the paper insulation depolymerises under the
influence of the ageing factors of temperature, oxygen and moisture. Figure 2.10 [4]
shows paper degradation mechanisms and the final products of each ageing process.
Carbon-monoxide (CO), carbon-dioxide (CO2) and moisture are the ultimate by-
products of cellulose insulation degradation. As a result, CO and CO2 concentrations
dissolved in the insulating oil together with their generating rates may be considered
as diagnostic indicators for paper insulation degradation in condition monitoring of
power transformers [3, 28]. As paper ages, its mechanical properties, such as tensile
and burst strength diminishes due to reduction in the length of cellulose polymeric
chains.
Figure 2.11 [4] depicts how mechanical properties of thermally crepe kraft paper, a
type of kraft paper with more elongation capacity [24], changes as the paper
decomposition occurs over time. Identical curves have been also established for non-
crepe kraft paper [34]. As DP values of the paper insulation reach between 250 and
300, mechanical strength of the paper considerably decreases, so any induced forces
originating from lightning or short-circuit currents could cause catastrophic failures to
the transformer. DP value of 200 is considered as the end of practical life of paper
insulation. Alongside paper insulation degradation due to thermal stresses, electrical
23
faults, such as partial discharge and sustained arcing could also have detrimental
impact on the paper insulation and cause further paper decomposition [35].
Additionally, metallic sharp points in the vicinity of paper insulation and wet paper
contribute to the occurrence and development of partial discharge affecting cellulose
insulation [36]. Paper insulation remarkably degrades in the case of general
overheating happens inside a power transformer, mainly due to operating transformers
at close or even higher than their nominal power rating. The ratio of carbon-oxide
concentrations is one of the diagnostic tools in detection of paper insulation
overheating [37]. Typically, the ratio of carbon-oxides, CO2/CO, is in the range of 7
to 10 when paper decomposes normally [11]. Any acceleration in degradation of the
paper insulation could result in ratios less than 3 or more than 11 [37], identified as
excessive cellulose decomposition which is caused by oxidation or burning of paper
in the presence of significance oxygen. In addition, carbon-oxide content of more than
30% of the overall carbon-oxides concentration is a certain reflection of cellulose
overheating [4].
Figure 2.10. Cellulose degradation mechanisms [4]
24
2.4.2 Insulation Life Plots
The assessment of cellulose insulation life commenced in 1930s by conducting
accelerated ageing tests in laboratories on regular kraft paper [4]. In 1960s when
thermally upgraded and creped cellulose insulation were introduced, they regained
their popularity. In the beginning, tensile strength retention property was chosen as the
criterion for determining cellulose insulation end of life.
However, it has recently changed to degree of polymerisation (DP) in the IEEE
standard C57.91 as a majority of transformers can live longer even though the tensile
strength retention of their paper insulation is less than 50 % [5]. DP of 200 is now
deemed as the end of paper insulation life in the IEEE standard C57.91 [5]. Initial
paper insulation life plots that were developed based on the tensile strength of 50 %
end-of-life criterion showed an exponential relationship between cellulose age and the
temperature it was exposed to [4].
Figure 2.11. The relation between mechanical properties of crepe kraft paper and ageing [4]
25
In addition, a research [38] performed in 1948 in the Westinghouse Electric
Corporation in the USA indicated that thermal deterioration of cellulose comply with
Arrhenius relationship, resulting in (1) [38].
𝑡 = 𝐴𝑒𝑥𝑝−𝐸 𝑅𝑇⁄ (1)
In this equation, t represents the time spent until a cellulose property diminishes to a
certain level, T is the absolute temperature in degrees Kelvin (◦K) to which paper is
subjected, A is a constant, R is the gas constant and E is the activation energy. Because
of some discrepancies in the results obtained from the life equations established by
considering cellulose tensile strength as the critical property, DP has been introduced
by the IEEE standard C57.91 [5] for the investigation on paper life equations. As
mentioned earlier, once DP of 200 is considered as the end-of-life criterion, life
equations for thermally upgraded paper insulation, 65 ◦C rise units, is as displayed in
(2) [4].
𝐿𝑜𝑔10 𝐿𝑖𝑓𝑒 (𝐻𝑜𝑢𝑟𝑠) = (6514.42 𝑇⁄ ) − 11.754 (2)
Figure 2.12 [4] illustrates different Arrhenius life plots for cellulosic insulation. In this
figure, D-65 stands for distribution transformers having thermally upgraded paper
insulation, PD-65 for power and distribution transformers with thermally upgraded
paper, P-65 for power transformers with thermally upgraded cellulose insulation, D-
55 for distribution transformers with non-upgraded paper and P-55 refers to power
transformers which have non-upgraded cellulose insulation. For instance, for
thermally upgraded paper insulation in both power and distribution transformers, the
expected life at the reference hot-spot temperature of 110 ◦C is estimated to be 180,000
hours which is approximately 20 years. It is evident form the Arrhenius life plots which
temperature has significantly detrimental impact on the cellulose insulation life. For
26
instance, Arrhenius relationships indicate that for every 6 to 7 ◦C increase in
temperature, cellulose life may halve when the hot spot temperature ranges between
80 ◦C and 100 ◦C. As a result, in order to elongate transformer lifetime, all the proper
precautions, such as proper cooling of transformers to stay within the temperature rise
limit should be taken into consideration so as to maintain the operating temperature of
power transformers at the lowest possible level. During the intervals when
transformers are overloaded, the life aging of cellulose is more than normal situations
and loss of life can be estimated deploying Arrhenius equations [5]. Using thermally
upgraded papers in warmer climates in which hot spot temperature is normally higher
than regions with cold weather could be a solution to prolong the life of cellulose
insulation.
Figure 2.12. Different Arrhenius life plots for different types of cellulose insulation [4]
27
However, despite the fact that thermally upgrading agents used in the structure of
cellulose can rise thermal stability and tolerance of the paper insulation, the amount of
these agents plays a great role in their performance and must be properly balanced. As
extending the life of transformers is of significant importance to transformer operators,
efficient maintenance programs together with regular condition monitoring of the
suspected units should be formulated.
2.5 Furan Compounds
Furan compounds are one of the by-products of cellulose insulation degradation.
Therefore, furan testing has obtained a remarkable importance in assessing the
condition of paper insulation over the operational course of power transformers. Furan
compounds which are dissolved in the insulating oil of transformers are tested as part
of routine transformer oil sampling in order to monitor the condition of transformers.
It is reported that thermal decomposition of cellulose yields five furan compounds of
2-furaldehyde (2FAL), 5-hydroxymethyl-2-furaldehyde (5H2F), 2-acetyl furan
(2ACF), 5-methyl-2-furaldehyde (5M2F), and 2-furfurol (2FOL) [39]. After furan
compounds generate through thermal degradation process, they dissolve in oil and the
content of furans in the oil can be measured using high performance liquid
chromatography (HPLC) [40]. There are two main reasons why furan analysis has
gained a lot of popularity in transformers condition monitoring filed. Firstly, furan
compounds originate merely from paper insulation degradation [41], so they are direct
reflection of the extent of paper insulation degradation, while other diagnostic
indicators of paper degradation, such as carbon-oxide concentrations in oil not only
come from cellulose thermal decomposition, but also they may come from oil
oxidation process. Secondly, in contrast to measuring degree of polymerisation of the
paper insulation, furans testing is not an intrusive procedure, i.e., once oil sample form
28
transformers is extracted from the sampling point located outside transformers, it can
be tested for furans deploying HPLC test method.
2.5.1 Formation of Furan Compounds
Kraft paper insulation is generally produced by the kraft process in which wood pulp
delignification is conducted. The major component of paper insulation is cellulose,
being a natural polymer of glucose units as displayed in Figure 2.7 earlier. It is
commonly accepted that paper insulation decomposition is dependent on the
conditions paper experiences. Basically, there are four factors affecting paper
insulation life including temperature, oxygen, moisture and acids. Exposure of paper
insulation to increased operating temperature of transformers, the presence of acids in
the oil and paper [30] and excess moisture in cellulose [42] lead to the paper insulation
depolymerisation, which generates free glucose molecules. These glucose molecules
degrade further under the impact of the ageing factors and form furan compounds
along with moisture and some gases [43]. The chemical structure of the five commonly
known furan compounds are displayed in Figure 2.13[7]. Among these five furan
compounds, 2FAL is deemed as the most dominant one and mainly used in the
interpretation of furan test results for determining the extent of paper insulation
degradation [44].
2.5.2 Furan Compounds Stability
It is of great importance to understand whether furan compounds are stable under the
operating conditions in a transformer so as to use furan results in the most efficient
way. There have been several studies to probe the stability of these compounds so far.
Some laboratory experiments conducted on the furan compounds in the oil for this
purpose without the presence of oxygen indicate that at temperatures lower than 100
◦C, all above-mentioned furan compounds do not show a noticeable decline [7].
29
Figure 2.13. Chemical structure of furan compounds [44]
However, 2FOL remarkably degrades as the oil temperature exceeds 100 ◦C and up to
160 ◦C [45]. Therefore, it can be concluded that all the furan compounds in the
transformer oil are quite stable because as per the IEEE C57.91 standard for loading
of transformers [5], top oil temperature which is considered as the hottest oil should
always be maintained lower than 110 ◦C and it scarcely surpasses 100 ◦C. In contrast,
it is revealed that in the presence of excessive oxygen, such as in free breathing
transformers, furan compounds, especially 2FOL and 5H2F exhibit an unstable
behaviour with regards to oxidative stability in the temperature range of 70 ◦C to 110
◦C [7]. As a result, diagnostic importance of these two furan compounds is lower than
the other three ones of 2FAL, 5M2F, and 2ACF when interpreting furan analysis
results of an oil sample which has a high oxygen level, normally in the range between
30
16500 ppm to 25000 ppm [31]. In general, the stability of 2ACF is quite the same as
5M2F compound and having lower stability than these two, the other three compounds
come in the order of 2FAL> 5H2F > 2FOL [45].
2.5.3 Correlation between Paper Insulation DP and Furan
Content of the Oil
As degree of polymerisation of cellulosic paper insulation is considered as the most
reliable indicator which shows the extent of paper insulation deterioration in a power
transformer, there has been much effort in establishing a correlation between DP and
furan content of the oil based on laboratory results [39] as well as statistical analysis
of field data [46]. Developing this correlation eliminates the need for intrusive
measures to extract paper samples from transformers and cellulose insulation
degradation level can be determined by only testing oil samples taken from
transformers.
Degree of polymerisation of cellulosic paper can be measured according to ASTM
D4243-99 (2009) [47] standard test method. IEC standard 60450 is a similar test for
this purpose as well [48]. Through these test methods, a solution of a small amount of
fluffed oil-removed cellulosic paper or board dissolved in cu-priethylenediamine is
used for determining the viscosity of the solution. The viscosity of the solution is
related to the molecular weight of the cellulose paper at a low concentration.
Deploying an experimentally developed equation, the DP of the cellulose can be
calculated [47]. Viscometric degree of polymerisation is indicative of the glucose units
on average in each cellulose chain. As paper insulation ageing diminishes the number
of glucose units, DP has been utilized as the reliable reflection of the paper insulation
deterioration. For a new paper insulation after drying out of the transformer through
manufacturing process, DP is expected to be between 1000 and 1200 [41]. Generally,
31
as paper insulation DP reaches about 200, this stage is regarded as the end of paper
insulation practical life when paper cannot tolerate further mechanical stresses
happening during normal operation of a power transformer [49]. However, as some
transformers can still be operated even if paper insulation DP is lower than 200,
determining end of life criterion with respect to degree of polymerisation remains as
an engineering judgment. In order to establish the correlation between furan content
in the insulating oil and DP of the kraft paper, accelerated ageing on the paper samples
was conducted in several laboratories [41, 44] together with using data gathered from
field sample testing [39]. Investigating the test data from accelerated ageing studies, it
is proposed that there is an approximately linear relation between the logarithm of the
2-FAL content in the oil and the degree of polymerisation of standard kraft paper
samples. Figure 2.14 [7] displays one instance of the relation between DP of the kraft
paper samples and 2-FAL content in the oil obtained from an accelerated ageing test
which was conducted at different temperatures.
Figure 2.14. The relation between DP of the kraft paper samples and 2-FAL content of the oil
obtained from an accelerated ageing test conducetd at different temperatures [7]
32
Several proposed correlations between cellulose insulation DP and 2-FAL content of
the oil are illustrated in Figure 2.15 [4] and their corresponding mathematical
equations are listed below [4]:
𝐷𝑃 = 1.51−log10 𝐹
0.0035 (Chendong) (3)
𝐷𝑃 =1.17−log10 𝐹
0.00288 (Scholnik et al.) (4)
𝐷𝑃 =800
(0.186×𝐹)+1 (Pahlavanpour) (5)
𝐷𝑃 =7100
8.88+𝐹 (Depablo) (6)
In these equations F denotes 2-FAL content of the oil in parts per million (ppm).
In spite of a great deal of effort to establish correlation between DP and 2-FAL content
of the oil, there is still some uncertainty in determination of paper insulation DP using
2-FAL content in the oil as there are some discrepancies and variations in the results
of the proposed equations [7]. Table 2.7 [51] shows the significance of paper degree
of polymerisation and furan content of the oil in the interpretation of paper insulation
ageing extent.
2.5.4 Effective Factors on the Furan Production Rate
Although there have been several studies on developing the correlation between furan
content of the oil and degree of polymerisation of the paper insulation as mentioned
above, there are some technical restrictions which confine the applicability of the
proposed outcomes to power transformers under actual operational conditions as well
as statistical investigations on furan data gathered from transformers in service [7].
33
The first factor which has to be taken into consideration in interpreting furan test
results is the typical hot-spot temperature of each specific transformer together with
its loading profile.
Figure 2.15. The relation between DP and 2-FAL content of the oil [4]
Table 2.7. Significance of paper degree of polymerisation and 2-FAL content of the oil in paper
insulation ageing interpretation [51]
DP Value 2-FAL (ppm) Significance
1200-700 0-0.1 healthy insulation
700-450 0.1-1.0 moderate deterioration
450-250 1-10 extensive deterioration
<250 >10 end of life
An explanation to this is that the hot spot has the highest temperature across winding
insulation, which is regarded as the most important location for paper insulation
thermal ageing and consequently, furan production. The second parameter affecting
the production of furans in power transformers is differences in transformer design.
Most often, two transformers of different make and design with the same operational
34
conditions show different behaviour with respect to their thermal features. For
example, different specifications in the design of transformers may lead to distinct
temperature gradients across windings. As a result, it is obvious that this may have
different contribution to the production of furans. Also, it is worth considering in the
comparative study of furan production in power transformers that the type of materials
used for insulating transformer windings has a great impact on the furan production
[7]. This accentuates design dependency problem in examining furan test data
collected from actual operating transformers. The temperature of the environment in
which a power transformer operates also plays an effective role in the furan production
in power transformers. It is expected for transformers functioning in hot climates that
furan production rate is higher than that for transformers in cold environments. Along
with the effect of operating and ambient temperatures on the furan generation rate, the
ageing level of paper insulation is also effective as proved by some laboratory
examinations [45]. These studies indicated that when the DP of paper insulation is
lower than 500, furan generation rate increases and at DP of 200, production rate starts
decreasing. There are some other parameters influencing furan production rate in
power transformers to be listed, namely, insulation type to be either standard kraft
paper or thermally upgraded paper, moisture concentration within paper insulation,
acids and other contaminants in insulating oil, oxygen content in vicinity of paper
insulation, furan partition between oil and paper, insulating oil maintenance
procedures, such as degassing, drying out and reclamation of the oil. In order to have
a justifiable assessment of furan test results, all these factors should be examined. In
addition, measuring furan content baseline in new transformers is of diagnostic
importance as this baseline is essential in the future assessment of furan testing results.
However, a reliable diagnosis of a power transformer should deem not only furan
35
content of the oil and production rate of furan compounds, but also the trending of oil
quality test and DGA results [7].
2.6 Moisture in Oil-Paper Insulation System of Power
Transformers
The presence of moisture is an important factor when considering operational
reliability of power transformers. Moisture contributes to degrading transformers’
insulation system by compromising its electrical and mechanical properties. It is
believed that the life of regular kraft paper in regards to mechanical properties halves
when moisture content within insulation system doubles [52]. Furthermore, cellulose
insulation degradation rate is highly dependent on paper insulation moisture content
[53] and it is also believed that moisture is a contributing factor to partial discharge
occurrence within transformers as well as bubble formation in transformer oil [52].
Therefore, understanding behaviour of moisture in the oil-paper insulation system of
a power transformer is of a great importance.
Although insulating oil in power transformers show a low affinity for moisture,
moisture solubility in insulating oil normally rises with the increase in oil temperature
[54]. Generally, moisture can be found in insulating oil in three situations. It is either
dissolved in the oil or firmly connected to oil molecules which is more likely in
degraded oil. Also, it can be found in the form of free drops or in suspension when the
moisture content of the oil is higher than its saturation level. The content of moisture
in the oil is quantified in parts per million (ppm), which is the weight of moisture to
the weight of oil (µg/g) [55]. Relative humidity is another technical term used in the
context of moisture in transformer insulation system. Relative humidity of the oil can
be defined as the ratio of moisture content dissolved in the oil to the maximum
concentration of moisture which can be dissolved in oil before it reaches its saturation
36
level [56, 58]. It is accepted that relative saturation of the oil is a better reflection of
the operational changes in power transformers than moisture content of the oil which
is measured in ppm [52]. Considering paper insulation in transformers, moisture can
be detected in several situations, such as absorbed water to paper insulation surface or
vapour. Paper insulation in a power transformer holds approximately all the moisture
in a transformer and insulating oil contains a relatively very minor portion of the
existing moisture. Moisture content of paper insulation is typically calculated in
%M/DW, which is the ratio of the weight of moisture to the weight of dry oil-free bulk
cellulose insulation in a transformer expressed in percentage. Furthermore, as it is
evident from Figure 2.16 [52], cellulose insulation has significant affinity for moisture.
For instance, in the room temperature range of 20 to 25 °C, paper insulation can
contain 4 to 8 % moisture when the relative humidity ranges from 30 to 70 %.
Figure 2.16. Moisture content of paper insulation as a function of temperature and percentage of
relative humidity [52]
37
As transformer life is adversely affected by the presence of moisture in insulation
system of a power transformer, especially solid insulation, it is essential to conduct
drying out process of power transformer insulation system in a fastidious way over the
course of transformer manufacturing [27]. For example, as paper insulation typically
experiences a relative humidity of 30 to 70% through manufacturing process during
hot and cold seasons, in a temperature range of 20 to 25 °C, it is expected to absorb 4
to 8% moisture, %M/DW, and it must therefore be dried out to about 0.5%, which is
the acceptable level of moisture in a new transformer prior to commissioning [4]. In
addition, transformer units in operation with high level of moisture content needs to
be dried out [25]. Similar to drying out process performed in the factory, the acceptable
limit of moisture after field drying out is 0.5%. The drying out methods conducted on
power transformers have the same principals originating from Piper charts which is
illustrated in Figure 2.17 [4]. These functions express the relation between logarithm
of vapour pressure and temperature in degrees centigrade. For the lower moisture
contents of the paper insulation, this function can be approximately formulated by (7)
[52]. In this formula, PV represents the atmospheric vapour pressure, C is the paper
insulation moisture content in percentage and T is the temperature in degree Kelvin.
𝑃𝑉 = 9.2683 × 109 × 𝐶1.4959 × 𝑒(−7069 𝑇⁄ ) (7)
As discussed before, paper insulation degradation yields moisture as one of the by-
products of this deterioration process. As moisture accelerates paper insulation
degradation rate [23], it is necessary for transformer users to routinely assess moisture
presents in transformer insulation system. Moisture migrates between paper and oil
with changes in transformer operating temperature. For example, once operating
temperature of a transformer decreases due to load reduction, moisture migrates from
the insulating oil to paper insulation [52].
38
Figure 2.17. Piper charts for lower paper insulation moisture contents [4]
In order to have an estimation of the paper insulation moisture content, equilibrium
curves established based on moisture absorption data of paper and oil [57] are used as
depicted in Figure 2.18 [4]. In this figure, equilibrium curves at different temperatures
correlate moisture content in the oil measured in ppm with paper insulation moisture
content. As a power transformer experiences different temperatures across its cellulose
insulation, moisture content of the paper insulation is not necessarily the same in all
the locations. In addition, moisture equilibrium curves can be used in order to estimate
the average moisture content of the bulk cellulose insulation. Hence, in order to have
a better evaluation of the water content in hot spots which are the most vulnerable
regions with respect to thermal degradation due to having highest temperatures, some
39
modifications in theses curves are needed. Generally, it is expected for hot-spot regions
to have lower moisture content than the bulk cellulose insulation as higher temperature
causes them to be drier. For example, if water content of the bulk cellulose is estimated
to be 2% in an equilibrium situation between oil and paper once the oil temperature is
on average at 50 °C and its moisture content is 20 ppm, for a hot spot region in the
paper insulation with temperature of 70 °C, moisture content is approximately 1%,
%M/DW [4]. Nevertheless, there is more limitation on utilizing moisture equilibrium
curves at lower oil temperatures as equilibrium status between oil and paper is hardly
achievable due to slow transition of moisture between oil and paper. This also reveals
the issue that wet oil does not always mean high level of moisture in paper insulation.
The reason behind this is that when transformer oil temperature reduces, it takes a
relatively long time until moisture migrates back to the paper insulation [56, 60].
Figure 2.18. Moisture equilibrium curves [4]
In order to assess moisture content existing in the insulation system of power
transformers in a more reliable way, some alternative methods, such as dielectric
spectroscopy [59] for which it is not necessary to have the equilibrium status between
40
paper and oil and recovery voltage method have been proposed [50, 61, 52]. In
addition, a recent study has proposed a method for measuring moisture content of the
paper insulation in non-equilibrium conditions [62].
2.7 Acid in Power Transformer Insulation System
To extend life of power transformers, it is vital to identify all the factors affecting
insulation system ageing. Acids are another by-product of transformer insulation
system degradation process, which accelerate ageing of power transformers whose life
is dominantly dependent on their paper insulation condition. It is shown that paper
insulation deterioration is caused by heat along with the aid of oxygen, moisture and
acids in the insulating oil of transformers [55].
Acids form as a result of reactions involving insulating oil as well as paper insulation
[30]. Mineral insulating oil is basically made up of three different hydrocarbon
molecules, including paraffins, naphthenes, and aromatics [64]. Over the course of oil
oxidation process, dissolved oxygen in the oil reacts with these molecules, generating
carboxylic acids as displayed in Figure 2.19 [30].
Figure 2.19. Transformer insulating oil oxidation [30]
Using chemical titration method, neutralisation number of transformer oil samples is
quantified, which is indicative of the amount of potassium hydroxide, in mg KOH/g
oil, needed to neutralize acidic content of the oil samples [65]. Nonetheless, it is proved
that neutralization number cannot differentiate between types of acids in oil and their
strengths [63]. This necessitates the need for more investigation to establish a more
41
reliable correlation between oil acidity and paper insulation ageing rate. The extent to
which a specific type of acid is effective on the paper insulation degradation rate
through acid hydrolysis reactions depends on its solubility in insulating oil as more
soluble acids in insulating oil of power transformers have a less impact on cellulose
deterioration [30]. In addition, some researches on acids in transformer insulating oil
with respect to their molecular weight suggest that low-molecular-weight acids are
more hydrophilic, having a higher affinity for paper insulation and water, while high-
molecular-weight acids show a lower tendency to paper insulation, having a lower
impact on paper insulation degradation [30]. Over time, aggregation of acids formed
by the oxidation process results in the formation of some insoluble materials in oil,
called sludge [3]. The presence of sludge can contribute to the thermal degradation of
paper insulation when it deposits on paper or internal parts of transformer, such as
radiator pipes and reducing transformer cooling [67]. In order to hinder oxidation
process in the oil, oxidation inhibitor, such as 2,6-ditertiary-butyl para-cresol is added
to the oil. Oxidation inhibitor is consumed while reacting with oxygen dissolved in the
oil, slowing down acid formation and elongating transformer operational life. Once
oxidation inhibitor in the oil is consumed, oil oxidation accelerates, resulting in rapid
formation of acids until acidity reaches a saturation level [30].
As shown in Figure 2.20 [30], acids degrade paper insulation through acid hydrolysis
reactions [32]. The reactions indicate that transformer cellulose paper degradation rate
is dependent on the moisture content of the paper and H+ cations stemming from acids
dissociation [30]. In addition to acids originating from oil oxidation, acid hydrolysis
of paper insulation in power transformers also lead to the formation of several types
of acids, such as levulinic, formic and acetic acid. These acids remain in the paper
insulation and show a high willingness to dissociate, leading to an increase in cellulose
42
degradation rate [66]. It is also suggested that acid content of the paper is of more
importance than acidic content of the oil as the majority of low-molecular acids which
mainly aid in paper insulation degradation exist in cellulose insulation [68]. Some
methods have been suggested on how to estimate paper acidic content of transformers
in service [69], which depend on several factors, including temperature and condition
of the paper insulation.
2.8 Interfacial Tension Number of the Insulting Oil
Interfacial tension, IFT number, of the insulating oil in power transformers indicates
the extent of soluble polar contaminants and oil degradation by-products present in the
oil solution. It can also be affected by dissolved moisture in the oil as water consists
of polar molecules [3]. Standard ASTM D971 – 12 [70] is the test method used by
laboratories to measure interfacial tension between oil and water. Through this method
which is conducted at the room temperature of 25 °C, oil sample extracted from an
operating transformer is added to distilled water. As oil gravity is less than water’s, it
tends to float at the top of the solution, so a noticeable border between oil and water is
formed. The IFT number is indicative of the amount of force required to pull up a small
planar ring for a distance of 1 cm through the border area between the oil and water
[71]. Figure 2.21 [70] displays equipment deployed for the interfacial tension
measurement. IFT number which is measured in dynes/cm or mN/m shows a strong
correlation with oil acidity and the number of years a transformer has been operating
as shown in Figure 2.22 [71]. Interfacial tension number of new oil is expected to be
around 50 mN/m, while significantly degraded oil has the interfacial number of about
14 mN/m or lower [72].
43
Once transformer insulation system deteriorates, oil and paper degradation by-
products contaminant insulating oil, diminishing interfacial tension number over time.
Hence, acidity and IFT number of the oil are considered as diagnostic indicators to
identify when remedial actions are required to be performed on oil to avoid formation
of sludge. It is recommended to reclaim transformer oil when the IFT number is about
25 mN/m as the sludge formation starts at IFT number of 22 mN/m [71].
Figure 2.20. Acid hydrolysis paper degradation [30]
44
Figure 2.21. Interfacial tensiometer [70]
Once transformer insulation system deteriorates, oil and paper degradation by-
products contaminant insulating oil, diminishing interfacial tension number over time.
Hence, acidity and IFT number of the oil are considered as diagnostic indicators to
identify when remedial actions are required to be performed on oil to avoid formation
of sludge. It is recommended to reclaim transformer oil when the IFT number is about
25 mN/m as the sludge formation starts at IFT number of 22 mN/m [71].
Figure 2.22. Relation between acidity, IFT number of the oil and in-service years of a transformer
[71]
45
Table 2.8 [42, 72] displays diagnostic significance of moisture content of the paper
insulation and interfacial tension of the oil.
Table 2.8. Diagnostic significance of paper insulation moisture content and interfacial tension of the
oil [42, 72]
Paper Insulation
Moisture Content
(%M/DW)
Interfacial Tension
Number (mN/m) Significance
0.5% - 1.5% >27 healthy insulation
1.5%-2.5% 24-27 entering medium risk zone
2.5%-4% 18-23 entering in high risk zone
>4% <18 entering imminent failure zone
46
3 Fundamentals of Fuzzy and Adaptive Neuro Fuzzy Inference
Systems
Ageing of a power transformer is a sophisticated process in which contributing agents
act simultaneously and synergistically. Owing to this sophistication, developing
analytical equations to precisely calculate ageing dynamics of a power transformer is
quite impossible. As a result, available guidelines for power transformer diagnostics
are classified in a qualitative way similar to the example shown in Figure 3.1 [72].
Figure 3.1. Qualitative classification of transformer diagnostic indicators [72]
An effective modelling tool in addressing such situations is fuzzy logic inference
system [73]. Fuzzy logic inference modelling is defined as a soft-computing technique,
which is capable of yielding a certain output from ill-defined input data. The variables
deployed in the fuzzy logic inference method are in the form of words, which are
mapped form input to output variables by fuzzy rules in the form of conditional if-then
statements. Using the effectiveness of fuzzy logic inference system in modelling
complex systems, many research works have been conducted for different power
47
transformer condition monitoring purposes, including DGA interpretation techniques
consistency analysis, determining transformer criticality, asset management decision
of power transformers, etc. [2, 35, 74, 75].
Accessing enough data of input and output variables, fuzzy logic inference system can
be utilized for mapping input variables to output ones. As illustrated by the flowchart
in Figure 3.2 [76], fuzzy decision-making procedure is composed of five distinct
components as elaborated below:
Fuzzification: it is the process of assigning each input variable to its
corresponding membership function representing a fuzzy set, and subsequently
determining the membership degree of that input variable in the designated
membership function.
Membership functions: characterizing fuzzy sets and are used in both
fuzzification and defuzzification stages. They can be in different shapes, such
as bell or Gaussian functions, depending on the features of input and output
data.
Fuzzy Rules: fuzzy rules are developed through the relationship between input
and output data, having a conditional form of “IF-THEN” or “IF-AND / OR-
THEN”.
Fuzzy Inference Engine: at this step, the conversion of fuzzy inputs to fuzzy
outputs with the use of fuzzy rules takes place
Deffuzification: using deffuzification methods, such as centre of gravity or
bisector, fuzzy inference modelling output is quantified from the associated
output membership functions.
48
Figure 3.2. Fuzzy inference system decision-making structure [76]
The basic structure of a model relying on the fuzzy inference system comprises a
procedure which includes mapping of input variables characteristics to their
corresponding membership functions, input membership functions to fuzzy rules,
fuzzy rules to output variables characteristics, output characteristics to their
corresponding membership functions, and output membership functions to an outcome
in the form of a value or a pertaining decision. In such modelling scenarios, fuzzy
inference system rules are developed by the user’s understanding to the characteristics
of the available data of the modelled system. In addition, mathematical parameters
defining each membership function included in the intended model are determined
randomly without taking into consideration the features of the system data. Therefore,
to increase model’s accuracy, it is essential to employ techniques which consider all
the changes and features of the input and output data of a system.
Adaptive neuro fuzzy inference system (ANFIS) is an artificial intelligence, AI,
technique in the framework of adaptive networks which can satisfy this necessity.
What is noted as the advantage of ANFIS-based models over models established based
on fuzzy inference system, FIS, is that with using ANFIS method, one can customize
49
the membership functions parameters and model rules as per the patterns and attributes
of the system data. Basically, membership functions are determined by some
geometrical parameters defining the shape of each membership function and their
covering range. Applying ANFIS method to map input variables to output ones
facilitates the adjustment of membership functions parameters to the variations in the
input data in an optimal way. Therefore, in establishing estimating model for power
transformer remnant life and asset management decision based on insulating oil
diagnostic parameters, ANFIS modelling has the advantageous of considering the
changes in transformers data, loading profile, environmental and operational factors
and design of transformers.
3.1 The Architecture of ANFIS
Different equivalent ANFIS structures have so far been proposed with respect to
adaptive networks application to different types of fuzzy logic inference and reasoning
systems [77]. This section elaborates on the architecture of adaptive neuro fuzzy
inference system, which is embedded into the Takagi and Sugeno type [78] fuzzy
inference system as used in the model developed in this thesis.
In order to provide a simple explanation of how the adaptive neuro fuzzy inference
system functions, it is assumed that fuzzy inference system under study has two inputs,
x and y and one output, z. provided that this FIS is based on two fuzzy if-then rules of
the Takagi and Sugeno type, these rules are expressed as follows:
Rule 1: if 𝑥 is 𝐴1 and 𝑦 is 𝐵1, then 𝑓1 = 𝑝1𝑥 + 𝑞1𝑦 + 𝑟1
Rule 2: if 𝑥 is 𝐴2 and 𝑦 is 𝐵2, then 𝑓2 = 𝑝2𝑥 + 𝑞2𝑦 + 𝑟2
50
Type 3 fuzzy inference system and its associated ANFIS structure is depicted in Figure
3.3 [77]. In this ANFIS structure, the nodes in each layer represents functions of the
same family as explained below:
1. In layer 1, each node is expressed by (8) [77] in which 𝑥 shows the input of
node 𝑖 and 𝐴𝑖 serves as the related linguistic variable to this node function.
Therefore, it can be concluded that 𝑂𝑖1 represents the associate membership
function with 𝐴𝑖, which determines the membership degree of the input 𝑥.
𝑂𝑖1 = 𝜇𝐴𝑖
(𝑥) (8)
In the model presented in this research work, bell-shaped membership
functions are utilized which are mathematically presented by (9) [79] and
depicted in Figure 3.4. Evidently, characteristics of this type of membership
functions are dependent on the parameters 𝑎𝑖, 𝑏𝑖 and 𝑐𝑖 named as premise
parameters. Once any change in the quantity of these parameters occurs, the
shape of membership functions varies, representing distinct features.
Figure 3.3. Type-3 fuzzy inference and corresponding equivalent ANFIS structure [77]
51
𝜇𝐴𝑖(𝑥) =
1
1+|𝑥−𝑐𝑖
𝑎𝑖|2𝑏𝑖
(9)
Figure 3.4. Physical effect of the bell-shaped membership function parameters [77]
2. In layer 2, function of each node is to multiply input signals by a weighting
factor wi and to send the outcome to the next layer. For example, 𝑤𝑖 of each
node can be calculated as below [77]:
𝑤𝑖 = 𝜇𝐴𝑖(𝑥) × 𝜇𝐵𝑖
(𝑦) 𝑖 = 1, 2. (10)
Principally, the outcome of every node in this layer determines the weight of rules
and any other generalized AND operator in the content of fuzzy logic can also be
utilized as the function of nodes in this step.
3. In the third layer, the output of each node, �̅�𝑖, is the proportion of the weight
of associated rule with the node to the summation of all the rules’ weights as
defined by (11) [77]. The outputs of this layer is also identified as normalized
weights.
�̅�𝑖 =𝑤𝑖
𝑤1+ 𝑤2 𝑖 = 1, 2. (11)
4. In layer 4, each node’s function is defined as (12) [77] in which �̅�𝑖 is the
normalized weight of the corresponding rule with the node, which is the output
52
of the previous layer and 𝑝𝑖 , 𝑞𝑖 , and 𝑟𝑖 are this layer’s parameters recognized as
consequent parameters.
𝑂𝑖4 = �̅�𝑖𝑓𝑖 = �̅�𝑖(𝑝𝑖𝑥 + 𝑞𝑖𝑦 + 𝑟𝑖) (12)
5. Layer 5 as the final layer includes only one node whose function is the
summation of all the inputs coming from layer 4 as below [77].
𝑂15 = 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 = ∑ �̅�𝑖𝑓𝑖 =
∑ 𝑤𝑖𝑓𝑖𝑖
∑ 𝑤𝑖𝑖𝑖 (13)
As depicted in Figure 3.3, the proposed adaptive network is a multilayer feedforward
structure whose node functions have a particular performance on their inputs and
associated parameters. Basically, in the adaptive networks, nodes are distinguished as
circle or square nodes. Circle nodes present those nodes without any parameters, which
are identified as fixed nodes, whereas square nodes indicate nodes with parameters,
which are known as adaptive nodes. To obtain an acceptable mapping from input data
to output data, the parameters of these adaptive nodes need to be optimized based on
available training data. There are several optimisation algorithms, such as back
propagation learning algorithm [80], hybrid learning algorithm [77], etc. For the
purpose of developing ANFIS model proposed in this thesis, backpropagation
algorithm is deployed. It is important to mention that the backbone of all these
optimisation procedures is the gradient descent method [77] which is described below.
Provided that an adaptive network includes 𝐿 layers and the 𝑘th layer of this structure
has 𝑘 nodes, the 𝑖th node of the 𝑘th layer can be denoted as (𝑘, 𝑖) and its pertaining
function as 𝑂𝑖𝑘 . If we present a training data set of 𝑃 entries, the error function of the
𝑝th entry of this data set, 1 < 𝑝 < 𝑃, can be defined as the summation of squared
errors by (14) [77] in which 𝑇𝑚,𝑝 is the 𝑚th element of 𝑝th expected output vector and
𝑂𝑚,𝑝𝐿 is the 𝑚th element of 𝑝th actual output vector.
53
𝐸𝑝 = ∑ (𝑇𝑚,𝑝 − 𝑂𝑚,𝑝𝐿 )2𝐿
𝑚=1 (14)
Therefore, the overall error function can be defined as in (15) [77].
𝐸 = ∑ 𝐸𝑝𝑃𝑝=1 (15)
In order to establish an optimum procedure for the parameters of an adaptive network
using gradient descent method, it is required to quantify the rate of error, 𝜕𝐸𝑝
𝜕𝑂, for 𝑝th
training data and every node output denoted as 𝑂. The rate of error for the output of a
node in the 𝑖th position of the 𝐿th layer can be calculated as in (16) [77].
𝜕𝐸𝑝
𝜕𝑂𝑖,𝑝𝐿 = −2 × (𝑇𝑖,𝑝 − 𝑂𝑖,𝑝
𝐿 ) (16)
Using the chain rule, for instance, for an internal node in the 𝑖th position of the 𝑘th
layer, the rate of error is defined as below [77]:
𝜕𝐸𝑝
𝜕𝑂𝑖,𝑝𝑘 = ∑
𝜕𝐸𝑝
𝜕𝑂𝑚,𝑝𝑘+1 ×
𝜕𝑂𝑚,𝑝𝑘+1
𝜕𝑂𝑖,𝑝𝑘 1 ≤ 𝑘 ≤ 𝐿 − 1𝑘+1
𝑚=1 (17)
As a result, if 𝛼 is a parameter pertaining to a node in the adaptive network, the rate of
error depending on 𝛼 can be defined as below [77]:
𝜕𝐸𝑝
𝜕𝛼= ∑
𝜕𝐸𝑝
𝜕𝑂∗𝑂∗ ∈ 𝑆 ×𝜕𝑂∗
𝜕𝛼 (18)
In the above equation, S refers to the set of nodes whose outcomes are dependent on
𝛼. Therefore, the overall error rate regarding 𝛼 is defined as (19) [77].
𝜕𝐸
𝜕𝛼= ∑
𝜕𝐸𝑝
𝜕𝛼𝑃𝑝=1 (19)
According to the above overall error rate equation, the generic formula for updating
node parameters can then be expressed as in (20) [77] in which 𝜌 is recognised as the
54
rate of learning and can be defined as in (21) [77]. In this equation, k determines the
size of each gradient transition step when parameters are being updated, on which the
learning algorithm convergence speed is dependent.
∆𝛼 = −𝜌𝜕𝐸
𝜕𝛼 (20)
𝜌 =𝑘
√∑ (𝜕𝐸
𝜕𝛼)2
𝛼
(21)
Figure 3.5. A 2-input ANFIS network with nine rules and how it relates to fuzzy subspaces [77]
Adaptive networks can be trained in two ways. The first is off-line learning functions
in which each parameter of the network is updated after the entire training data has
been given to the network. In other words, just following every epoch, the update of
network parameters takes place. The second is on-line or pattern learning through
which parameters of the network are updated exactly following the presentation of
Premise Parameters Consequent Parameters
55
each input-output data pair. Figure 3.5 displays how a 2-input ANFIS network with
nine rules corresponds with fuzzy subspaces. As three membership functions pertain
to each input in this structure, fuzzy input space consists of nine fuzzy subspaces and
each of the nine fuzzy rules which are in the form of if-then statements determines
how their associated subspace changes. Figure 3.6 [77] shows a generic instance of
how ANFIS learning procedure leads to adjusted membership functions of the input
variables x and y. Parts a and b depict membership functions prior to the
implementation of the learning algorithm and parts c and d illustrate membership
functions once desired minimum error between actual data and model output has been
achieved.
Figure 3.6. A generic example of how ANFIS training results in more precise membership functions
[77]
56
Figure 3.7 [81] shows a generic flowchart of ANFIS learning procedure.
start
generating initial parameters
of neuro fuzzy model
presenting input training
data set
calculating the output of neuro
fuzzy model
calculating the quantity of
error
(difference between desired
output and model output)
is error less
than the
expected value?
saving adjusted
values of
parameters of
neuro fuzzy
system
correcting
the value of
neuro fuzzy
model
parameters
end
YesNo
Figure 3.7. Flowchart of ANFIS learning [81]
57
4 ANFIS Modelling
4.1 Life Estimation Model
Degradation of the insulation system of a transformer is a sophisticated process. This
complexity originates from synergistic and retrospective participation of factors
affecting the ageing process of a transformer. Hence, as mentioned earlier, finding a
mathematical equation for transformer ageing process is quite impossible. As a
solution, this work implements ANFIS modelling to establish life estimation model
for power transformers based on diagnostic indicators which are regularly measured
at routine maintenance intervals of a transformer. Applying ANFIS modelling
technique accounts for all the variations in the operational and environmental
parameters playing a significant role over the course of transformer ageing and results
in a higher precision in the model output.
This chapter describes the proposed model and highlighting the advantage of using
ANFIS method in modelling complex systems over fuzzy inference system, FIS,
which has already been used in other research works. Therefore, FIS-based life
estimation model of power transformers is firstly presented. Secondly, the ANFIS-
based model as the main contribution of this thesis is elaborated. Results of these two
models are compared in order to give a better understanding of how the ANFIS method
improves the accuracy of modelling. Finally, an integrated asset management decision
model developed based on the ANFIS learning technique is put forward.
The FIS-based model is established by utilizing fuzzy logic toolbox graphical user
interface in MATLAB software to map the input variables of 2-FAL content, in mg/kg
oil, oil interfacial tension number, in mN/m, and the water content within paper
insulation, in %M/DW, to the percentage of transformer remnant life as the output
variable. These diagnostic indicators show a strong correlation with ageing of power
58
transformers. Membership functions of these variables chosen are displayed in Figure
4.1, Figure 4.2 and Figure 4.3. These membership functions were defined using
qualitative information in Table 2.7, Table 2.8, and Figure 3.1 and according to the
user’s perception of available data.
Figure 4.1. Membership functions of 2-Furfural content
Figure 4.2. Membership functions of cellulose insulation moisture content
Figure 4.3. Membership functions of IFT number of the oil
59
One of the negative points being effective on the accuracy of this FIS-based model is
that the parameters determining the physical characteristics of these bell-shaped
membership functions are selected randomly. As a result, these membership functions
will not reflect all the characteristics and patterns existing between the input and output
data. This deficiency can be mitigated to a satisfactory extent by deploying adjusted
membership functions through optimised ANFIS technique.
Required number of fuzzy rules for this model is 125 as each input variable involves
five membership functions. Each of these rules represents a probability in the relation
between input variables and output one, being in the form of “If-And-Then”
statements. The graphical illustration of these rules that shape the relation between
interfacial tension number, 2-FAL content of the oil, and water content in the paper
insulation with the remanent age of a power transformer is shown in Figure 4.4. As an
example, for 2-FAL content of 4.3 mg/kg oil or ppm, moisture content within paper
insulation of 3.5%, %M/DW and oil interfacial tension number of 22 mN/m, the
proposed model yields a percentage of transformer remnant life of 32.2%, based on an
average operational life of 40 years. Another disadvantage of using fuzzy logic
inference system is that fuzzy rules are defined according to the user’s understanding
and experience to the investigated problem, which makes it inconsistent; moreover,
these rules are static and cannot be dynamically adapted. In contrary with FIS, ANFIS
modelling facilitates dynamic change of rules based on the changes in the system data
[82]. The mathematical representation of the centre of gravity method is as in (22) [8]
where Z0 is the defuzzified output, µc (z) are the output membership functions
associated with the input data and fuzzy rules and z is the fuzzy system output variable.
Figure 4.5 displays one of the three-dimensional plots of the suggested FIS model,
60
showing how 2-FAL content of the oil and cellulose moisture content correlate with
the percentage of transformer remnant life.
Figure 4.4. Fuzzy rules of the proposed FIS-based model
𝑍0 =∫ 𝑧.𝜇𝑐(𝑧)𝑑𝑧
∫ 𝜇𝑐(𝑧)𝑑𝑧 (22)
Due to the above-mentioned disadvantages which fuzzy logic inference system has in
modelling complex systems and in order to improve the accuracy of the model
representing the behavior of the system under study, this research study deploys
adaptive neuro fuzzy inference system method to develop an integrated life estimation
and asset management decision model as elaborated below. ANFIS learning method
61
enables membership functions and rules to be tailored to the features and any changes
in the input and corresponding output data.
Figure 4.5. Three-dimensional display of the proposed FIS-based mapping
ANFIS modelling contributes to better projecting all the features of transformers,
sourced by distinctions in the loading profile, environmental factors affecting the
operation of a transformer, and design of transformers into the membership functions
of the input and output variables and defined rules in the model.
The underlying principles of the adaptive neuro fuzzy inference system are identical
to the fundamentals of artificial neural networks, ANN. Due to successful
implementation of the ANN methods for addressing complex problems and in self-
learning algorithms, these principles have gained a significant popularity in
establishing algorithms for recognising patterns, predicting trends, etc. [77]. In order
to develop ANFIS-based life estimation model of power transformers, diagnostic
indicators of interfacial tension number, 2-furafural content of the oil and water
content of the cellulose insulation, which are reliable indictors of the ageing of power
transformers as described in chapter 2 are used as the input variables. The studied
62
transformers are from a wide range of age, design, rating and operational condition. In
order to apply ANFIS method, ‘anfis’ function accessible in the fuzzy logic toolbox of
MATLAB software is used. The collated data is separated into two batches of data for
training and testing purposes. Training batch includes 60 and testing one contains 40
sets of data. Through training process of the adaptive neuro fuzzy inference system,
back propagation algorithm [80] is utilized so as to optimise membership functions
parameters and the rules of the proposed model. Backpropagation optimising
procedure employs input and output data history in order to adjust the parameters of
the membership functions. It computes and adapts random weights as the learning
procedure goes forward until the difference between the actual and desired output,
model error, meets the specified criterion [83]. The error of model training during the
application of ANFIS method to the collected data is illustrated in Figure 4.6.
Figure 4.6. ANFIS training error
This error expressed in years, which is the difference between actual age of the studied
transformers, determined as per their commissioning date, and their estimated age by
the model diminishes as training is in progress until it reaches the value of 1 year at
the epoch of 2000. The typical structure of the adaptive neural fuzzy networks for the
63
proposed model is depicted in Figure 4.7. In this architecture input variables, namely
2-FAL content of the oil, paper insulation moisture content and oil interfacial tension
number together with the estimated age of power transformers as the single output are
displayed. It also shows how multiple layers and nodes of the proposed ANFIS
network collaborate with each other. As shown in this structure, input variables are
mapped through representative nodes of the input membership functions, and then
through the representative nodes of rules and output membership functions into the
output variable.
Figure 4.7. ANFIS-based model network
Following finalization of the training procedure, the proposed model optimised
through ANFIS learning algorithm and the adjusted membership functions are the
outcome of this learning procedure. The proposed life estimation model in this work
uses four generalized bell-shaped curves as the membership functions of each input
variable. The equation of this type of function is as in (23). Considering the equation,
physical characteristics of this function which define the shape and interval they cover
64
are dependent on the parameters of a, b and c. Over the course of ANFIS learning,
these parameters are changed until the error of the model reaches a satisfactory level.
𝑓(𝑥; 𝑎, 𝑏, 𝑐) = 1
1+│𝑥−𝑐
𝑎│2𝑏
(23)
The parameters of the adapted membership functions are shown in Table 4.1. Figure
4.8, Figure 4.9 and Figure 4.10 also display the membership functions of the input
variables of the suggested model.
Table 4.1. Membership functions parameters of the ANFIS-based model
Optimisation of these parameters occurs on the basis of a gradient vector which is
basically a mathematical function indicative of the accuracy of the model which maps
the presented input data to output data for a specific set of parameters as explained
earlier. Once the gradient vector is achieved, optimization methods can be performed
on this function so as to minimize the output error of the ANFIS-based model. It is
worth mentioning that the ANFIS graphical user interface of MATLAB software also
provides the possibility of using an integration of the back propagation algorithm and
the least squares estimation as an alternative optimization method for the adjustment
of the parameters of the membership functions. Generally speaking, one of the ways
Membership
Function
Paper Insulation
Moisture Content
(a,b,c)
2-FAL Content
(a,b,c)
Interfacial
Tension Number
(a,b,c)
Good (0.47,2.12,0.30) (0.86, 1.74, -0.23) (4.76, 2.08, 43.05)
Marginal (0.61,2.15,1.39) (0.55, 2.15, 0.98) (6.21, 1.31, 32.25)
Poor (1.34 2.21 3.13) (0.55, 2.69, 2.86) (5.68, 2.46, 23.28)
Critical (0.99, 2.02, 4.96) (0.52, 3.20, 4.96) (6.38, 1.89,15.44)
65
to improve the performance and reduce the estimation error of this proposed ANFIS-
based model is to utilize more accurate optimising algorithms which can determine
membership functions parameters and model rules in a more precise way.
Figure 4.8. Adjusted membership functions of 2-FAL content in oil
Figure 4.9. Adjusted membership functions of the paper insulation moisture content
Figure 4.10. Adjusted membership functions of interfacial tension number of the oil
66
In the above figures, the range of input variables membership functions is selected
through the ANFIS training as per the given input data. However, the calculated
parameters of each membership function defines the interval they cover. In contrast
with FIS-based models which are static, ANFIS training facilitates continuous
enhancement of the ANFIS-based models because the parameters of membership
functions are updated every time a new set of data is presented to them. Figure 4.11
depicts corresponding rules with the suggested model, which are automatically
generated through ANFIS learning algorithm.
Figure 4.11. Generated rules of the proposed ANFIS-based model
In order to assess the accuracy of the proposed model, testing data consists of 40 sets
of the input and output data, which are extracted from different transformers
67
information are used. Figure 4.12 documents the testing data shown in blue circles
which are the actual age of transformers investigated for the purpose of testing, and
the output of the trained ANFIS-based model which represent the age of these
transformers by estimated the developed model.
Figure 4.12. The ANFIS-based model validation against testing data
Evidently, validation process yields a satisfactory result, confirming the effectiveness
of ANFIS training algorithm in modelling complex and non-linear systems. In order
to compare the performance of the proposed ANFIS-based model with FIS-based
model in estimating the remnant life of power transformers, another group of 20 sets
which are collected from several in-service transformers of different ratings, designs,
operating conditions and lifespans are utilized as the presented data into the established
models.
Table 4.2 shows the values of the input variables, actual age of the transformers in
years, determined based on their commissioning date, estimated age of transformers
in years by fuzzy inference system, and estimated age of transformers in years by
68
adaptive neuro fuzzy inference system as well as the error of estimation of each model
calculated as below.
% 𝐸𝑟𝑟𝑜𝑟 = |𝐴𝑐𝑡𝑢𝑎𝑙 𝐴𝑔𝑒−𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝐴𝑔𝑒
𝐴𝑐𝑡𝑢𝑎𝑙 𝐴𝑔𝑒| × 100 (24)
Table 4.2. Comparison between FIS- and ANFIS-based models life estimation
Categ
ory
2-F
AL
Con
tent
(mg/k
g O
il)
Pap
er
Moistu
re
Con
tent
(%M
/DW
)
IFT
Nu
mb
er
(mN
/m)
Actu
al A
ge
FIS
-
Estim
ated
Age
AN
FIS
Erro
r (%)
AN
FIS
-
Estim
ated
Age
FIS
Erro
r
(%)
En
d-l
ife
5.3 4.6 15 39 36.6 6.2 38 2.6
5.6 4.6 17 36 36.9 2.5 37 2.8
5.4 4.2 17 35 36.8 5.1 35.5 1.4
4.9 4 18 34 32.7 3.8 33.7 0.9
5 3.3 19 32 34.8 8.8 31.3 2.2
4.3 3.5 17 31 27.9 10 30.8 0.65
Nea
r-en
d-l
ife
4 3.2 18 29 27.9 3.8 27.7 4.5
3.6 3.1 19 27 27.5 1.85 26.9 0.4
4.1 3.3 18 27 27.9 3.3 27.7 2.6
2.3 2.9 20 24 20.1 16.3 24.9 3.8
3 2.7 22 22 24 9.1 23.8 8.2
Mid
dle
-age
1.2 2.4 25 19 15.5 18.4 17.9 5.8
0.9 2.1 22 17 15.1 11.2 16.4 3.5
1.7 2.3 25 17 19.1 12.4 16.9 0.6
1.6 2 26 15 17.6 17.3 13.4 10.7
1.3 1.9 26 12 15.1 25.8 12.1 0.8
Hea
lth
y
1 1.8 28 10 13.2 32 10.3 3
0.4 0.8 34 8 9.2 15 8.2 2.5
0.05 0.9 40 7 6.1 12.9 7.45 6.4
0.03 0.5 43 3 3.7 23.3 3.02 6.7
69
Comparison of the outcome of both models shows a noticeable improvement in
ANFIS-based model compared to fuzzy inference system mapping. The trained model
by ANFIS is able to estimate the age of selected transformers with a higher degree of
precision. Generally, ANFIS modelling functions very well and best optimizes the
parameters of the membership functions if the presented data for training
comprehensively includes all the features of the system, which is aimed to be
modelled. In the table provided above, examined transformers are classified into four
categories based on their actual age, which is calculated based on their commissioning
date and by assuming an average operational life of 40 years [1]. Accordingly,
transformers with the actual age between 30 and 40 years are categorized as “End-
life”, transformes between 20 and 30 years of age as “Near-end-life”, between 10 and
20 years of age as “Middle-age” transformers and those with the age between 0 and 10
years as “New” transformers. As an instance, one of these studied power transformers
having an actual age of 34 years, 2-FAL content of 4.9 mg/kg, cellulose insulation
water content of 4%, %M/DW, and interfacial tension number of 18 mN/m is
estimated to have 32.7 years of age by the FIS-based model with estimation error of
3.8 %. For the same set of input parameters, ANFIS-based model estimation is 33.7
years with estimation error of 0.9 %. The reason behind this higher precision is that
parameters of the membership functions and the model rules are adapted by
implementation of ANFIS method, while the user in the FIS-oriented model selects
these parameters haphazardly and according to their perception.
70
4.2 Integrated Life Estimation and Asset Management Decision
Model
Due to successful application of ANFIS for estimating power transformers age, the
methodology of ANFIS training is expanded to establish an integrated life estimation
and asset management decision model. The model deploys the same parameters of 2-
FAL content, interfacial tension number of the oil and moisture content of the cellulose
insulation as well as some other parameters such as dissolved gas concentrations in the
oil, which are vital elements in determining transformers condition and are included
in the routine maintenance program of transformers. For this purpose, these parameters
are collated by investigating several in-service power transformers, which are
represented in case studies in Table 7.11. Figure 4.13 shows the proposed integrated
life estimation and asset management decision model of power transformers. This
model incorporates several sub-models which are trained by the same ANFIS learning
method elaborated earlier in this work. The proposed model integrates the outputs of
the oil, paper and electrical criticality sub-models with the estimated age of the
transformer to provide an asset management decision code. This code is
corresponding to appropriate action should be taken to maintain the reliability and
operability of the transformer. The significance of each diagnostic parameter used in
this model and the reason why they should be taken into consideration in asset
management decision of power transformers is covered in chapter two of this thesis
and will be briefly explained below.
4.2.1 Oil Criticality Sub-model
This sub-model is developed to indicate the extent of danger which the quality of the
insulating oil poses to the general health of a power transformer. The sub-model
includes parameters of interfacial tension number, acidity of the oil, and moisture
71
content of the paper insulation. Interfacial tension number and acidity of the oil have
a strong correlation with the number of years a transformer has been in service and
they are reliable indicators for the quality of the insulating oil in a power transformer.
They should be considered in the asset management of power transformers as acids
formed during oxidation process settle on the paper insulation of a power transformer
and damage it over time. Also, the presence of sludge which can be determined
according to the interfacial tension number contributes to the reduction of transformer
cooling. Consequently, higher temperature inside a power transformer leads to a faster
degradation of the cellulose. Moisture content of the paper insulation can be estimated
from the relative saturation of the insulating oil by using equilibrium curves. Moisture
content of the paper has the most destructive effect on its integrity by accelerating
degradation rate of the cellulose insulation. By considering these parameters in the
sub-model, both individual and synergistic contribution of them to the insulation
degradation rate are accounted using the pattern existing in the presented data. It
should be noted that by deploying moisture content of the paper insulation, the role of
temperature is also considered to some extent as the estimation of the bulk cellulose
moisture content using equilibrium curves is dependent on the insulating oil
temperature, so this parameter can act as a reflection of the transformer operating
temperature as well.
4.2.2 Paper Criticality Sub-model
This sub-model employs two input variables of 2-FAL content of the oil, and the
output of thermal criticality sub-model to estimate the general condition of the
cellulose insulation. As the other input variable of the paper criticality sub-model,
thermal criticality sub-model output determines the criticality of paper insulation
72
ageing rate. It is a decision made based on the outputs of two other sub-models of
heating and paper degradation criticalities.
Paper degradation criticality sub-model uses carbon-monoxide, CO, carbon-dioxide,
CO2, as well as the ratio of these two carbon-oxides, CO2/CO, as the input variables.
Carbon-oxides are the by-products of the reactions involved in the cellulose
deterioration under electrical and thermal stresses in a power transformer. This sub-
model also deploys the ratio of the carbon-oxides as it is recommended to be a more
reliable indicator of the excessiveness of cellulose degradation. However, it should be
noted that this ratio is applicable for this purpose once it is more than 11 or less than 3
[11]. Heating sub-model uses concentrations of Ethane and Methane gases, which are
identified as the heating gases in the context of dissolved gas analysis, DGA. The
reason for assigning this sub-model is to reflect whether heating inside a power
transformer has been effective on the rate of paper insulation degradation. Therefore,
the concentrations of heating gases are included in conjunction with carbon-oxide
concentrations to determine the thermal criticality of a power transformer.
4.2.3 Electrical Criticality Sub-model
Electrical criticality of a power transformer is determined by using the outputs of
partial discharge and arcing criticality sub-models. Partial electrical discharge and
sustained arcing are two common electrical faults in power transformers. In order to
monitor whether a power transformer is suffering from these faults, dissolved gas
analysis is regularly measured and based on the proposed interpretation techniques,
the existence of these faults are determined. Electrical faults in power transformers
should be avoided as they can have detrimental effects on power transformer insulation
system integrity.
73
Partial discharge criticality sub-model uses concentrations of hydrogen, H2, and
methane, CH4, as these two gases are mostly generated when a partial electrical
discharge activity exists inside a power transformer. In addition, arcing criticality sub-
model uses concentrations of hydrogen, H2, and acetylene, C2H2, as the two major
gases produced in case of a sustained arcing in a power transformer.
4.2.4 Asset Management Decision Sub-model
As the final step in the proposed integrated model for deciding on how to manage a
power transformer life cycle, asset management decision sub-model combines the
output of the life estimation sub-model with the output of the overall criticality sub-
model. The outcome is a number based on which a decision can be made when
managing the life of a power transformer. Table 4.3 lists several management decisions
based on %D, which is the output of the asset management decision model. In the table
provided below, %D ranges from 0% (indicative of transformers with normal
condition) to 100% (indicative of transformers at the risk of imminent failure).
Different ranges in this table were selected as per the practical utility data, showing
the condition of transformers under investigation.
Table 4.3. Management decisions as per the output of the proposed integrated model
Asset Management Decision Output
of ANFIS-based Model
Management Decision
0 % < %D < 25 %
Normal operation
Normal monitoring regime
25 % < %D < 50 %
Normal operation
Planning diagnostics
Specific monitoring
74
50 % < %D < 65%
Operation capacity reduction
(below 80% of nominal
capacity)
Strict overall monitoring scheme
More frequent sampling intervals
Planning specific diagnostics
Planning required remedial
actions
65% < %D < 75%
Operation capacity reduction
(below 60% of nominal
capacity)
Strict overall monitoring scheme
More frequent sampling intervals
Planning specific diagnostics
Planning required remedial
actions
75% < %D < 85%
Operation capacity reduction
(below 50% of nominal
capacity)
Strict overall monitoring scheme
More frequent sampling intervals
Planning specific diagnostics
75
Planning required remedial
actions
Deciding on relocation if
justified
85% < %D < 95%
Operation capacity reduction
(below 50% of nominal
capacity)
Strict online monitoring scheme
More frequent sampling intervals
Planning specific diagnostics
Planning required remedial
actions
Internal off-line detailed
inspection
Deciding on relocation or
retirement
95% < %D < 100%
Taking out of service
Specific diagnostics with internal
off-line detailed inspection
Deciding on retirement or
scrapping
76
Deciding on relocation,
retirement or scrap
In order to evaluate the accuracy of the proposed integrated model, the data gathered
from the investigated in-service transformers as shown in
Table 4.4 are employed and a comparison is made between the management decision
numbers obtained from the model and the asset management action decided by expert
asset management utility team. The error of estimation shown in this table is calculated
as below.
%𝐸𝑟𝑟𝑜𝑟 = |%𝐷(𝐸𝑠𝑡𝑖𝑚𝑎𝑒𝑡𝑑)−%𝐷(𝐴𝑐𝑡𝑢𝑎𝑙)
%𝐷(𝐴𝑐𝑡𝑢𝑎𝑙)| (25)
For example, the fifth case study in the table is estimated by the model to have oil
criticality of 96%, paper criticality of 87%, and electrical criticality of 60%. These
criticalities yield overall criticality of 96% and subsequently, with considering the life
estimation of 97%, the estimated asset management decision number of 98.4% with
an error of 0.4% in comparison with the actual asset management decision number
determined by an expert utility asset management team is estimated by the model. To
explain more, very high oil criticality of this transformer stems from high level of acids
in the oil and water content of paper insulation. Acids together with excessive moisture
within paper result in accelerated ageing of the cellulose insulation and the subsequent
pre-mature ageing of the transformer. Although DGA results for this transformer give
no indication of thermal fault within paper insulation, 2-FAL content in the oil is very
high, which means paper has degraded extensively and is close to its end of life.
Electrical criticality of 60% for this transformer originates from the detected partial
discharge activity according to the concentrations of hydrogen, H2, and methane, CH4.
77
As a result, the overall criticality of this transformer is estimated to be 96% which
categorizes this transformer in the critical group. In addition, the estimated life of this
transformer, based on the typical lifetime of 40 years for a power transformer, is 97%
which means this transformer is at the end of its operational lifetime. Eventually, as
per the estimated asset management decision number of 98.4% and Table 4.3, this
transformer needs to be taken out of service for a thorough internal inspection. Based
on the outcome, a decision can be made whether to retire or maintain this transformer.
78
Figure 4.13. Integrated life estimation and asset management decision model of power transformer
79
Table 4.4. Comparison between actual and estimated asset management decision numbers
Cate
gory
IFT
Acid
ity
%M
/DW
%O
il C
rit
icali
ty
CO
CO
2
CO
2/C
O
%P
ap
er D
egrad
ati
on
Cri
ticali
ty
C2H
6
C2H
4
%H
eati
ng C
riti
cali
ty
%T
herm
al
Cri
ticali
ty
2-F
AL
%P
ap
er C
rit
icali
ty
H2
CH
4
C2H
2
%P
D C
rit
icali
ty
%A
rci
ng C
rit
icali
ty
%E
lectr
ical
Cri
ticali
ty
%O
verall
Cri
ticali
ty
%L
ife E
stim
ati
on
%D
(E
stim
ate
d)
%D
(A
ctu
al)
%E
rror
Lo
w r
isk
30
0.0
1
0.3
3
21
421
20
1
6
4
1
1
0.0
6
1
12
2
1
12
2
12
12
3
11.7
12
2.5
40
0.0
1
0.9
11
54
52
6
9.7
7
26
16
7
7
0.0
8
7
42
25
1
7
13
13
14
11
14
.3
14
2.1
30
0.0
2
1.6
17
76
65
2
8.6
10
22
16
10
10
0.8
5
11
54
33
1
15
14
15
17
20
17
.1
17
0.6
40
0.0
2
0.9
12
96
12
10
12
.6
12
23
14
12
12
0.0
5
13
84
42
1
19
18
19
19
10
19
.3
19
1.6
34
0.0
2
0.8
9
11
4
22
10
19
.4
20
23
12
20
20
0.4
22
35
22
1
7
12
12
22
7
22
.3
22
1.4
40
0.0
1
1
13
21
2
12
56
5.9
19
27
17
19
19
0.1
20
87
42
1
19
19
20
23
12
23
.3
24
2.9
Med
ium
ris
k
27
0.0
5
1.8
30
86
1395
16.2
12
31
18
12
12
1.2
28
20
12
1
7
6
7
30
26
30.7
30
2.3
28
0.0
4
1.8
25
212
1120
5.3
19
21
16
19
19
1
30
32
22
1
6
12
12
32
25
32.4
32
1.3
29
0.0
2
2.1
27
12
4
12
83
10
.3
14
25
16
14
14
1.9
32
76
22
1
23
17
23
34
36
34
.3
34
0.9
80
26
0.0
5
2.4
37
64
860
13.4
10
3
1
10
10
1
25
16
5
1
10
4
10
37
44
37
37
0
29
0.0
2
0.6
7
135
1640
12.1
16
23
12
16
16
0.1
17
642
215
1
39
22
39
39
5
39
39
0
24
0.0
7
2.3
41
121
973
8
12
26
12
12
12
2
29
34
14
1
8
12
12
41
45
40.8
41
0.5
26
0.0
7
1.9
33
475
3280
6.9
49
4
1
49
49
1.3
49
16
22
1
5
4
5
49
27
48.8
49
0.4
Hig
h r
isk
42
0.0
1
1
13
10
2
1562
15
.3
14
41
28
14
14
0.8
15
87
8
45
3
1
53
23
53
53
13
52
.9
53
0.2
33
0.0
2
1.7
22
59
7
54
21
9.1
63
11
2
14
6
63
63
0.7
59
82
57
1
14
18
18
59
22
59
.4
59
0.7
22
0.1
2
2.1
51
12
5
98
0
7.8
12
10
8
12
12
0.9
14
15
20
34
0
1
63
24
63
63
37
62
.5
63
0.8
38
0.0
4
1.3
16
82
5
26
50
3.2
66
10
2
16
3
66
66
0.4
60
82
0
27
6
9
58
49
58
64
17
63
.5
64
0.8
25
0.0
8
1.8
37
34
5
32
21
9.3
57
84
66
57
57
1.2
73
14
6
12
4
3
28
33
37
73
26
73
.6
73
0.8
25
0.0
7
2.4
47
1350
10600
7.9
54
41
21
54
54
1.2
73
980
125
1
69
23
69
74
46
76.6
74
3.5
Imm
inen
t fa
ilu
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82
5 Conclusion and Future Work
5.1 Conclusion
Degradation process of power transformer insulation system is a sophisticated
procedure on the grounds that factors involved in this process affect the insulation
system ageing rate in a retroactive and synergistic way, resulting in the complexity of
establishing analytical equations which can comprehensively represent this dynamic
ageing mechanism. As a solution, this work deploys adaptive neuro fuzzy inference
system, ANFIS, to propose an integrated life estimation and asset management decision
model for power transformers. One of the main advantages this model brings into
practice is that it uses minimum diagnostic parameters of power transformers which are
measured and monitored routinely during regular maintenance intervals of power
transformers. In addition, deploying ANFIS learning algorithm for establishing this
model which estimates overall criticality, age and asset management decision number
for a transformer provides the possibility of having a reliable model for managing a
power transformer over its operational life time. Utilizing this model can facilitate
continuous condition monitoring of power transformers with the possibility of real time
enhancement of its performance through adaptive changing of rules and parameters of
the model in line with practical measurements and results obtained from the model.
This enables modification of the model in order to better reflect patterns existing in the
measured values of the diagnostic indicators and distinctions in the fleet of transformers
which are raised due to differences in their design, environmental conditions, etc. From
the economic point of view, utilization of this model can be a great contribution to
reducing financial costs when performing condition monitoring of power transformers
as this model is aimed at reducing the number of diagnostic parameters and employs
only those parameters, which are of significant monitoring and asset management
83
importance. Based on the results observed throughout this research work, the new
developed ANFIS modelling is able to model ageing mechanism of power transformers
with a higher accuracy in comparison with fuzzy logic-based models which have been
suggested in the literatures. On the basis of the same methodology used for estimating
the age of power transformers, it also provides satisfactory results in deciding on asset
management of power transformers.
To compare, ANFIS-based model shows a higher accuracy than FIS-based model in
estimating power transformer’s life. ANFIS-based model has a higher reliability
because membership functions and rules adapt to the exiting pattern in the presented
data and gives a better correlation between input and output data. On the contrary, as
FIS-based model relies on the perception of the user in defining membership functions
and rules, they may not represent the behaviour of system precisely. In terms of
computational requirements, both models can be developed using MATLAB software.
However, for establishing an ANFIS-based model, it is necessary that presented
training data reflects all the characteristics of the fleet of transformers under
investigation.
5.2 Future Work
Since ANFIS modelling uses optimising algorithms to map input data to output data,
the performance of the proposed model may be improved with the usage of more
powerful optimising algorithms which can adapt the model’s rules and parameters in a
more accurate way, resulting in more precise estimations. On the other side, the process
of collating case studies is of great importance and any variations in the values of the
parameters should be thoroughly investigated. For instance, if a transformer undergoes
insulating oil filtration and/or reclamation process which are common remedial actions
performed on power transformers in order to extend their lifetime and prevent their pre-
84
mature ageing occurring as a result of the accumulation of acids and water in the power
transformers, concentrations of dissolved gases in the oil, furan content and other
chemical indicators change which affects the trending of the measurements.
Moreover, considering the ANFIS training principals, by increasing the data presented
to the model for the purpose of training, one can improve the accuracy and performance
of the current model. What is also worth mentioning is that by providing data which
covers a broad range of in-service transformers of different type, make, and rating, the
generalization capacity of the model can be improved. Due to recent technological
advances providing utilities with reliable methods to supervise the condition of their
transformers online, such as recently introduced novel technique of the measurement
of interfacial tension number [83], obvious advantage which utilizing this technique
gives, is the possibility of designing an online feedback platform which can
automatically collect, process, self-train and make a timely decision.
85
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Every reasonable effort has been made to acknowledge the owners of copyright
material. I would be pleased to hear from any copyright owner who has been omitted
or incorrectly acknowledged.
97
7 Appendix
This part contains complementary information with respect to the proposed integrated
life estimation and asset management decision model in this work, namely generalized
bell-shaped membership functions of the employed sub-models, their adapted
parameters through ANFIS learning algorithm and all the case studies used for the
purpose of ANFIS learning of the integrated model.
7.1 Oil Criticality Sub-Model
Table 7.1. Adapted parameters of oil criticality membership functions
Figure 7.1. Adjusted membership functions of interfacial tension number
Figure 7.2. Adjusted membership functions of acidity
Membership
Function
Paper Insulation
Moisture Content
(a, b, c)
Acidity Number
(a, b, c)
Interfacial
Tension Number
(a, b, c)
Good (0.76, 2, 0.2) (0.037, 2, 0.0065) (4.83, 2, 43)
Marginal (0.76, 2, 1.73) (0.039, 2, 0.086) (4.83, 2, 33.33)
Poor (0.76, 2, 3.26) (0.036, 2, 0.17) (4.83, 2, 23.67)
Critical (0.76, 2, 4.8) (0.056, 2, 0.24) (4.83, 2, 14)
98
Figure 7.3. Adjusted membership functions of paper insulation moisture content
7.2 Heating Criticality Sub-model
Table 7.2. Adapted parameters of heating criticality membership functions
Figure 7.4. Adjusted membership functions of ethane concentration
Figure 7.5. Adjusted membership functions of ethylene concentration
Membership Function Ethane
(a, b, c)
Ethylene
(a, b, c)
Good (805.5, 2, 1) (1998, 2, 1)
Marginal (805.5, 2, 1612) (1998, 2, 3997)
Poor (805.5, 2, 3223) (1998, 2, 7994)
Critical (805.5, 2, 4834) (1998, 2, 11990)
99
7.3 Paper Degradation Criticality
Table 7.3. Adapted parameters for paper degradation criticality membership functions
Membership Function Carbon-monoxide
(a, b, c)
Carbon-dioxide
(a, b, c)
Good (324.8, 2, 21) (2088, 2, 312)
Marginal (324.8, 2, 670.7) (2088, 2, 4488)
Poor (324.8, 2, 1320) (2088, 2, 8664)
Critical (324.8, 2, 1970) (2088, 2, 12840)
Membership Function CO2/CO Ratio
(a, b, c)
A (6.03, 2, 1.7)
B (6.03, 2, 13.77)
C (6.03, 2, 25.74)
D (6.03, 2, 37.9)
Figure 7.6. Adjusted membership functions of carbon-monoxide concentration
Figure 7.7. Adjusted membership functions of carbon-dioxide concentration
100
Figure 7.8. Adjusted membership functions of carbon-oxides ratio (CO2/CO)
7.4 Thermal Criticality Sub-model
Table 7.4. Adapted parameters of thermal criticality membership functions
Membership Function
Paper Degradation
Criticality
(a, b, c)
Heating Criticality
(a, b, c)
Good (16.5, 2, 1) (16.5, 2, 1)
Marginal (16.5, 2, 33.74) (16.5, 2, 34)
Poor (16.5, 2, 67) (16.5, 2, 67)
Critical (16.5, 2, 100) (16.5, 2, 100)
Figure 7.9. Adjusted membership functions of paper degradation criticality
Figure 7.10. Adjusted membership functions of heating criticality
101
7.5 Paper Criticality Sub-model
Table 7.5. Adapted parameters of paper criticality membership functions
Figure 7.11. Adjusted membership functions of thermal criticality
Figure 7.12. Adjusted membership functions of 2-FAL content of the oil
Membership Function
Thermal Criticality
(a, b, c)
2-FAL
(a, b, c)
Good (16.52, 2.04, 1.02) (0.86, 2.002, -0.044)
Marginal (16.46, 1.83, 33.97) (0.56, 1.99, 1.54)
Poor (16.54, 2.11, 66.96) (1.005, 2.08, 3.33)
Critical (16.51, 1.95, 100) (1.033, 2.042, 5.649)
102
7.6 Partial Discharge Criticality Sub-model
Table 7.6. Adapted parameters of partial discharge membership functions
Membership Function
Hydrogen
(a, b, c)
Methane
(a, b, c)
Good (269.8, 2, 1) (1463, 2, 1)
Marginal (269.8, 2, 540.7) (1463, 2, 2927)
Poor (269.8, 2, 1080) (1463, 2, 5876)
Critical (269.8, 2, 1620) (1463, 2, 8778)
Figure 7.13. Adjusted membership functions of hydrogen concentration
Figure 7.14. Adjusted membership functions of methane concentration
103
7.7 Arcing Criticality Sub-model
Table 7.7. Adapted parameters of arcing criticality membership functions
Membership Function
Hydrogen
(a, b, c)
Acetylene
Good (269.8, 1.998, 1) (186.7, 2, 1)
Marginal (269.8, 2, 540.7) (186.7, 2, 374.3)
Poor (269.8, 2, 1080) (186.7, 2, 747.7)
Critical (269.8, 2, 1620) (186.7, 2, 1121)
Figure 7.15. Adjusted membership functions of hydrogen concentration
Figure 7.16. Adjusted membership functions of acetylene concentration
104
7.8 Electrical Criticality Sub-model
Table 7.8. Adapted parameters of electrical criticality membership functions
Membership Function
Partial Discharge
Criticality
(a, b, c)
Arcing Criticality
(a, b, c)
Good (12.2, 1.817, 0.9928) (16.34, 1.18, 1.923)
Marginal (12.26, 1.842, 25.26) (16.41, 2.001, 34.67)
Poor (12.24, 1.771, 49.62) (16.38, 1.671, 67.31)
Critical (12.19, 1.932, 73.99) (16.33, 2.008, 100)
Figure 7.17. Adjusted membership functions of partial discharge criticality
Figure 7.18. Adjusted membership functions of arcing criticality
105
7.9 Overall Criticality Sub-model
Table 7.9. Adapted parameters of overall criticality membership functions
Membership
Function
Oil Criticality
(a, b, c)
Paper Criticality
(a, b, c)
Electrical
Criticality
(a, b, c)
Good (16.3, 1.9, 2) (16.5, 1.9, 0.9) (15.8, 2, 4.9)
Marginal (16.3, 1.8, 34.6) (16.5, 2, 34) (15.8, 2, 36.6)
Poor (16.3, 2, 67.3) (16.4, 1.9, 66.9) (15.8, 1.9, 68.3)
Critical (16.3, 1.9, 100) (16.5, 2, 99.9) (15.8, 1.9, 100)
Figure 7.19. Adjusted membership functions of oil criticality
Figure 7.20. Adjusted membership functions of paper criticality
106
Figure 7.21. Adjusted membership functions of electrical criticality
7.10 Asset Management Decision Sub-model
Table 7.10. Adapted parameters of asset management decision membership functions
Membership Function Overall Criticality
(a, b, c)
Life Estimation
(a, b, c)
Good (14.69, 1.88, 12.01) (16.35, 2.05, 2.02)
Marginal (14.66, 2.31, 41.37) (16.19, 1.49, 34.55)
Poor (14.59, 1.7, 70.67) (16.62, 2.48, 67.01)
Critical (14.69, 2.02, 99.97) (16.36, 2.20, 99.97)
Figure 7.22. Adjusted membership functions of overall criticality
Figure 7.23. Adjusted membership functions of life estimation
107
7.11 Case Studies
Table below contains the values of all the investigated transformers used in the ANFIS
learning algorithm for the integrated asset management decision model.
Table 7.11. Case Studies
Cate
gory
IFT
Acid
ity
%M
/DW
%O
il C
rit
icali
ty
CO
CO
2
CO
2/C
O
%P
ap
er D
egrad
ati
on
Cri
ticali
ty
C2H
6
C2H
4
%H
eati
ng C
riti
cali
ty
%T
herm
al
Cri
ticali
ty
2-F
AL
%P
ap
er C
rit
icali
ty
H2
CH
4
C2H
2
%P
D C
rit
icali
ty
%A
rci
ng C
rit
icali
ty
%E
lectr
ical
Cri
ticali
ty
%O
verall
Cri
ticali
ty
%L
ife E
stim
ati
on
%D
(A
ctu
al)
Healt
hy
30
0.0
1
0.3
3
21
42
1
20
.0
1
6
4
1
1
0.0
6
1
12
2
1
12
2
12
12
3
12
34
0.0
1
0.7
8
54
86
7
16
.1
8
12
8
8
8
0.8
9
36
21
1
7
12
12
13
14
13
40
0.0
1
0.9
11
54
52
6
9.7
7
26
16
7
7
0.0
8
7
42
25
1
7
13
13
14
11
14
43
0.0
1
0.5
5
14
0
14
20
10
.1
15
14
6
15
15
0.0
3
16
56
34
1
15
14
15
16
4
16
30
0.0
2
1.6
17
76
652
8.6
10
22
16
10
10
0.8
5
11
54
33
1
15
14
15
17
20
17
30
0.0
1
1.3
15
64
983
15.4
10
26
16
10
10
0.7
10
76
42
1
18
17
18
18
18
18
40
0.0
2
0.9
12
96
1210
12.6
12
23
14
12
12
0.0
5
13
84
42
1
19
18
19
19
10
19
108
28
0.0
2
1.6
17
230
1340
5.8
19
16
10
19
19
0.7
21
24
52
1
4
9
9
21
21
21
34
0.0
2
0.8
9
114
2210
19.4
20
23
12
20
20
0.4
22
35
22
1
7
12
12
22
7
22
43
0.0
1
0.6
6
140
2210
15.8
21
12
8
21
21
0.5
23
15
21
1
5
3
5
23
6
23
40
0.0
1
1
13
212
1256
5.9
19
27
17
19
19
0.1
20
87
42
1
19
19
20
23
12
24
Ma
rgin
al
27
0.0
5
1.8
30
86
1395
16
.2
12
31
18
12
12
1.2
28
20
12
1
7
6
7
30
26
30
28
0.0
3
1.6
18
50
54
6
10
.9
7
39
42
7
7
0.8
8
65
37
3
17
31
31
31
19
31
28
0.0
4
1.8
25
21
2
11
20
5.3
19
21
16
19
19
1
30
32
22
1
6
12
12
32
25
32
26
0.0
6
2
32
15
4
67
5
4.4
11
15
7
11
11
1.6
27
52
25
1
19
14
19
32
31
33
29
0.0
2
2.1
27
12
4
12
83
10
.3
14
25
16
14
14
1.9
32
76
22
1
23
17
23
34
36
34
26
0.0
6
2.1
35
86
563
6.5
9
10
4
9
9
1.6
26
26
14
1
7
10
10
35
34
35
26
0.0
5
2.4
37
64
860
13.4
10
3
1
10
10
1
25
16
5
1
10
4
10
37
44
37
25
0.0
7
2.1
38
12
6
23
40
18
.6
20
23
14
20
20
1.4
34
71
24
1
20
17
20
38
33
38
109
29
0.0
2
0.6
7
135
1640
12.1
16
23
12
16
16
0.1
17
642
215
1
39
22
39
39
5
39
26
0.0
6
2.3
40
94
1643
17.5
14
8
12
14
14
1.8
31
20
8
1
9
6
9
40
43
40
24
0.0
7
2.3
41
121
973
8.0
12
26
12
12
12
2
29
34
14
1
8
12
12
41
45
41
25
0.0
8
2.3
45
235
1450
6.2
23
10
2
23
23
1.7
35
35
15
1
8
12
12
45
42
45
26
0.0
7
1.9
33
47
5
3280
6.9
49
4
1
49
49
1.3
49
16
22
1
5
4
5
49
27
49
Po
or
26
0.0
6
2.2
36
45
2
31
20
6.9
49
31
18
49
49
1.8
49
62
31
1
19
15
19
51
39
51
42
0.0
1
1
13
10
2
15
62
15
.3
14
41
28
14
14
0.8
15
87
8
45
3
1
53
23
53
53
13
53
27
0.0
3
1.7
23
43
2
31
14
7.2
60
15
7
1
60
60
0.7
5
58
19
30
3
1
2
6
6
58
23
58
33
0.0
2
1.7
22
59
7
54
21
9.1
63
11
2
14
6
63
63
0.7
59
82
57
1
14
18
18
59
22
59
42
0.0
2
1.2
14
112
860
7.7
11
46
28
11
11
0.3
12
640
260
15
37
61
61
61
15
61
31
0.0
2
1.2
14
989
4979
5.0
67
121
435
67
67
0.5
61
190
410
1
26
21
26
62
16
62
22
0.1
2
2.1
51
12
5
98
0
7.8
12
10
8
12
12
0.9
14
15
20
34
0
1
63
24
63
63
37
63
110
38
0.0
4
1.3
16
825
2650
3.2
66
102
163
66
66
0.4
60
820
276
9
58
49
58
64
17
64
27
0.0
4
2.2
29
67
2120
31.6
19
26
12
19
19
1.3
33
760
180
12
62
56
68
68
38
68
25
0.0
8
1.8
37
345
3221
9.3
57
84
66
57
57
1.2
73
146
124
3
28
33
37
73
26
73
25
0.0
8
2.1
39
321
2894
9.0
56
87
63
56
56
1.6
74
112
78
2
29
26
33
74
34
74
25
0.0
7
2.4
47
1350
10
600
7.9
54
41
21
54
54
1.2
73
98
0
12
5
1
69
23
69
74
46
74
25
0.0
8
2.2
43
17
3
93
2
5.4
31
55
11
0
31
31
1.9
38
38
4
38
8
33
28
74
74
74
40
74
Crit
ical
24
0.0
8
2.1
39
12
00
78
52
6.5
53
23
11
53
53
1.2
73
11
20
45
2
4
56
37
56
75
32
75
26
0.0
6
2.1
35
37
4
26
20
7.0
58
96
92
8
58
58
1.8
74
56
28
6
7
3
44
44
75
35
75
32
0.0
3
0.8
10
72
0
67
50
9.4
51
62
26
51
51
0.7
57
86
0
80
22
71
70
78
78
9
78
40
0.0
3
0.8
10
521
1198
2.3
78
41
34
78
78
0.6
79
354
182
5
31
39
43
79
8
79
29
0.0
4
1.6
20
300
5130
17.1
83
8
100
83
83
0.8
79
1
8
6
1
41
41
79
19
79
34
0.0
2
0.8
9
47
0
10
25
2.2
92
28
5
16
4
92
92
0.6
80
84
29
1
20
18
20
80
8
80
111
41
0.0
1
0.2
2
562
1622
2.9
97
275
738
97
97
0.5
80
220
698
1
25
21
25
81
2
81
25
0.0
7
1.9
33
322
6421
19.9
77
43
29
77
77
1.6
81
83
67
1
14
18
18
82
29
82
24
0.0
8
2.4
49
416
1119
2.7
91
121
101
91
91
2.1
83
323
212
8
30
46
49
84
47
84
25
0.0
8
2.2
43
1140
9360
8.2
69
816
5450
69
69
2
75
1550
2740
184
50
88
88
88
41
85
22
0.1
2
2.7
54
28
6
2134
7.5
24
26
12
24
24
3
56
86
34
1
20
19
20
59
55
86
20
0.1
3
2.9
57
86
16
50
19
.2
13
21
14
13
13
2.3
51
34
28
1
6
12
12
57
56
86
21
0.1
6
2.7
60
32
1
23
40
7.3
35
84
73
35
35
2.2
39
21
18
1
6
7
7
60
52
86
21
0.1
4
3
65
15
2
16
93
11
.1
18
31
22
18
18
3.1
53
87
45
1
18
19
19
65
59
86
19
0.1
7
2.7
62
43
1
27
60
6.4
48
43
17
48
48
3
71
51
23
1
19
14
19
71
55
87
22
0.1
2
2.6
53
317
2959
9.3
61
4834
11990
61
61
2.9
76
12
8778
18
2
66
66
77
51
87
22
0.1
2
2.7
54
84
1102
13.1
30
86
353
30
30
2.3
68
78
161
10
4
52
52
71
53
87
18
0.1
9
2.7
64
21
1
16
40
7.8
22
58
12
22
22
2.6
54
98
0
73
1
74
23
74
74
54
87
112
21
0.1
6
2.8
63
145
3120
21.5
75
8
4
75
75
2.1
82
12
6
1
8
2
8
83
53
88
19
0.1
7
2.5
59
214
3459
16.2
76
24
16
76
76
2.9
85
63
34
1
18
15
18
85
50
88
17
0.2
2.9
75
821
1980
2.4
81
22
12
81
81
2.6
84
125
62
3
33
32
38
85
58
88
21
0.1
4
2.8
56
72
756
10.5
29
299
1810
29
29
3.1
67
290
966
57
25
84
84
84
57
88
22
0.1
1
2.9
55
84
1640
19
.5
13
34
14
13
13
3.4
52
18
12
1
7
5
7
55
61
89
20
0.1
5
3
66
16
5
24
20
14
.7
22
62
46
22
22
3.2
55
42
1
11
6
14
41
60
60
69
60
90
20
0.1
4
3.2
68
73
12
50
17
.1
12
27
18
12
12
4.1
64
85
64
1
14
19
19
69
68
90
19
0.1
7
2.9
67
12
0
76
0
6.3
11
25
15
11
11
4.3
63
70
52
1
14
17
17
69
64
90
25
0.0
7
3.4
52
42
1
32
10
7.6
49
16
12
49
49
4.2
72
22
18
1
6
8
8
72
70
91
21
0.1
5
3.1
69
238
2180
9.2
33
126
94
33
33
3.9
70
26
12
1
8
10
10
71
65
91
18
0.1
9
3.3
74
47
1280
27.2
12
21
18
12
12
4.1
64
32
17
1
7
12
12
74
69
91
19
0.1
6
3.3
72
69
79
8
11
.6
10
10
43
10
10
2.7
50
41
6
21
1
47
22
47
72
62
91
113
19
0.1
5
3.2
71
102
1840
18.0
27
98
127
27
27
4
69
240
157
1
30
21
30
72
67
91
20
0.1
3
3
58
660
3210
4.9
62
178
112
62
62
3.2
76
86
42
1
19
19
20
76
60
92
21
0.1
5
2.9
61
1120
11375
10.2
71
126
212
71
71
4
78
58
21
1
20
14
20
79
63
92
17
0.2
3.5
78
230
2430
10.6
23
52
21
23
23
4.3
66
1460
220
3
67
34
67
78
71
92
20
0.1
5
3.2
71
59
2
6210
10
.5
65
12
5
87
65
65
3.8
77
14
2
10
2
1
29
21
29
80
66
93
18
0.1
8
3.2
73
15
60
12
84
0
8.2
74
21
2
32
0
74
74
4
78
24
0
10
2
1
36
21
36
81
67
93
19
0.1
6
3.1
70
80
0
98
42
12
.3
80
10
6
80
80
3.6
86
29
12
1
8
11
11
86
64
93
17
0.2
3.7
79
91
11
20
12
.3
12
12
8
12
12
4.8
88
14
11
1
6
3
6
89
79
94
25
0.0
6
1.9
31
13
1
17
12
13
.1
28
89
61
28
28
1.4
37
10
9
49
34
5
34
94
94
94
28
94
18
0.1
9
3.8
80
98
312
3.2
9
11
3
9
9
4.2
62
15
4
1
11
3
11
80
78
94
19
0.1
6
3.3
72
1970
6230
3.2
73
140
86
73
73
5
96
64
21
1
22
15
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96
75
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18
0.1
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3.6
77
16
0
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20
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32
11
0
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32
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4.5
91
11
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5
36
59
78
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114
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0.1
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3.6
77
543
1243
2.3
95
164
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4.5
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3.6
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1.7
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4.7
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313
29
37
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19
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4.1
83
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15.6
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32
26
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4.4
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1
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16
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88
121
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10
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4.9
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