High Voltage Technology and Asset Management
The Effect of Temperature Cycling and
Transients on the Dielectric Properties of
Transformer Impregnated Insulation
Master of Science Thesis
J.W.B. Kers, BSc.
Author: J.W.B. Kers
Student number: 1304542
E-mail address: j.w.b.kers@student.tudelft.nl or bartkers@gmail.com
Copyright © 2011 by J.W.B. Kers and the Delft University of Technology
Abstract
This master’s thesis project is a part of the Sinergie project (sponsored by Agentschap NL, 2007-2012)
which is dedicated to analyze the functionality of the grid of the future. The European Union has
advanced plans to decarbonize the power sector onwards the year 2050 and therefore the use of
renewable energy sources is expected to increase. The distributed energy generation from, for
example, wind turbines and solar cells are not constant during a day as the wind speeds and
incoming solar radiation vary. Therefore an increase in power transport between different regions
throughout Europe is expected.
During operation, transformers heat up or cool down depending on the varying loads. These
variations in load depend mostly on the time of the day, as consumers require more power at
specific times of the day. The high electric field strengths, which are a result of peaking power
transport, combined with these thermal cycles have their impact on transformer insulation. The grid
of the future will still be partly composed of today’s components and asset management strategies
will be used to replace components, such as transformers, just before their end of life. The
aforementioned renewable energy sources are often connected to the grid via power electronic
converters. These convertors introduce transient spikes in the grid. Therefore the effect of both
temperature cycling and transients on transformer insulation are investigated in this research.
Chapter 2 includes a literature study on transformers. Transformers are essential parts of the electric
grid. They can be found at the generation, transmission and distribution level. During operation,
degradation factors influence the state of the transformer insulation. The insulation experiences
environmental ageing factors such as pyrolysis, oxidation and hydrolysis.
Chapter 3 shows the measurements which have been performed. Three series of experiments have
been performed on transformer paper samples with a thickness of 0.060mm. These series consist of
AC breakdown tests, time to breakdown tests and tangents delta measurements. The breakdown
voltage increases from 3.11kV to 3.59kV (11V/˚C) when the temperature is increased from 16.6˚C to
60˚C. Up to 80˚C, the breakdown voltage decreases to 3.12kV (23.5V/˚C) when temperature is
increased to 80˚C. The time to breakdown is determined at 2.91kV and the time 63.2% of the
samples fail increases from 48.4 to 82.1 and 147 hours when temperature is increased from 40˚C to
60˚C and 80˚C, respectively. In the third series, transient spikes of 1kV superimposed on a 2.22kV AC
waveform and samples are stressed for 22 hours. The transients are applied in a range from 1kHz up
to 10kHz and it can be observed that the tangents delta increases with 6.4% compared to stressing
with 2.22kV AC only.
The results of the main experiments are interpreted in Chapter 4. Based on this interpretation, a
model is made that can be used to calculate the accelerated ageing factors of the insulation and to
incorporate the interaction between oil and paper. Measurement data should be used to calculate
the loss of life due to daily loading cycles. Two loading scenarios are compared and it is shown that
when renewable energy sources increase transport and introduce transients in the grid, ageing of
transformers is accelerated.
Contents
1
Introduction ..................................................................................................................................... 1
1.1
What is a transformer?............................................................................................................ 1
1.2
Introduction on transformer paper impregnated insulation .................................................. 2
1.3
Goal of the master’s thesis ...................................................................................................... 3
1.3.1
Background information.................................................................................................. 3
1.3.2
Research objectives ......................................................................................................... 3
1.3.3
Thesis approach ............................................................................................................... 4
1.4
2
Literature study ............................................................................................................................... 5
2.1
Applications of transformers ................................................................................................... 5
2.2
Parts in a transformer ............................................................................................................. 6
2.2.1
Core ................................................................................................................................. 6
2.2.2
Windings .......................................................................................................................... 6
2.2.3
Tap changer ..................................................................................................................... 6
2.2.4
Paper................................................................................................................................ 7
2.2.5
Oil .................................................................................................................................... 7
2.3
Ageing processes in a transformer .......................................................................................... 7
2.3.1
Environmental factors ..................................................................................................... 7
2.3.2
Degradation effects on the oil ......................................................................................... 8
2.3.3
Degradation effects on the paper ................................................................................. 11
2.3.4
Diagnostic techniques ................................................................................................... 14
2.4
3
Thesis outline........................................................................................................................... 4
Conclusions............................................................................................................................ 16
Experiments and results ................................................................................................................ 17
3.1
Experiment 1: AC breakdown ................................................................................................ 17
3.1.1
Initial results .................................................................................................................. 17
3.1.2
Goal................................................................................................................................ 17
3.1.3
Temperature.................................................................................................................. 17
3.1.4
Procedure ...................................................................................................................... 18
3.1.5
Hypothesis ..................................................................................................................... 20
3.1.6
Test setup ...................................................................................................................... 20
3.1.7
Results ........................................................................................................................... 22
3.1.8
Analysis .......................................................................................................................... 25
3.1.9
Summary........................................................................................................................ 29
3.2
3.2.1
Goal................................................................................................................................ 30
3.2.2
Temperature.................................................................................................................. 30
3.2.3
Procedure ...................................................................................................................... 30
3.2.4
Hypothesis ..................................................................................................................... 30
3.2.5
Test setup ...................................................................................................................... 30
3.2.6
Results ........................................................................................................................... 31
3.2.7
Analysis .......................................................................................................................... 32
3.2.8
Summary........................................................................................................................ 33
3.3
Goal................................................................................................................................ 34
3.3.2
Temperature.................................................................................................................. 34
3.3.3
Voltage........................................................................................................................... 34
3.3.4
Procedure ...................................................................................................................... 35
3.3.5
Hypothesis ..................................................................................................................... 35
3.3.6
Test setup ...................................................................................................................... 35
3.3.7
Results ........................................................................................................................... 36
3.3.8
Analysis .......................................................................................................................... 41
3.3.9
Summary........................................................................................................................ 42
Conclusions............................................................................................................................ 43
Results interpretation and modeling ............................................................................................ 45
4.1
Interpretation of measurement results ................................................................................ 45
4.1.1
AC breakdown tests....................................................................................................... 45
4.1.2
Time to breakdown tests ............................................................................................... 45
4.1.3
Tangents delta tests ...................................................................................................... 45
4.2
5
Experiment 3: Tangents delta ............................................................................................... 34
3.3.1
3.4
4
Experiment 2: Time to breakdown ........................................................................................ 30
The ageing model .................................................................................................................. 46
4.2.1
The general form of the model ..................................................................................... 46
4.2.2
Model parameters ......................................................................................................... 46
4.2.3
Measurement data ........................................................................................................ 48
4.2.4
Processed data .............................................................................................................. 49
4.2.5
Asset strategy ................................................................................................................ 52
Conclusion ..................................................................................................................................... 57
5.1
Conclusions............................................................................................................................ 57
5.2
Recommendations................................................................................................................. 57
Appendix A: Raw measurement data .................................................................................................... 59
Initial results AC breakdown tests ..................................................................................................... 59
Final results AC breakdown test ........................................................................................................ 61
Appendix B: Weibull plots ..................................................................................................................... 63
Analysis AC breakdown tests............................................................................................................. 63
Analysis time to breakdown tests ..................................................................................................... 70
Weibull parameter calculations .................................................................................................... 70
Weibull plots.................................................................................................................................. 72
Extra measurements with transients ............................................................................................ 74
Analysis tangents delta tests ............................................................................................................. 75
Appendix C: Extra measurement setup information............................................................................ 77
Measurement setup AC breakdown tests ......................................................................................... 77
Measurement setup time to breakdown tests ................................................................................. 78
Measurement setup tangents delta tests ......................................................................................... 79
Appendix D: Characterization of the paper ........................................................................................... 81
Dielectric spectrograph tests............................................................................................................. 81
Appendix E: Model calculations ............................................................................................................ 85
Bibliography........................................................................................................................................... 87
Acknowledgements ............................................................................................................................... 91
1 Introduction
In the future, the use of renewable energy sources will increase as the European Union has advanced
plans to decarbonize the power sector onwards the year 2050 [1]. These energy sources do not
deliver constant power like today’s coal- and gas-fired power plants. The distributed energy
generation from, for example, wind turbines and solar cells are not constant during a day. The wind
speeds and incoming solar radiation vary, causing power transport between different regions
throughout Europe to increase. The grid of the future will still be partly composed of today’s
components as neither the money nor the manpower is available to replace all components. To
overcome reliability problems, in-depth knowledge about the grid’s assets will be used to replace
components just before their end of life. Therefore, current components, like paper-oil
transformers, will be further stressed.
In a transformer, the insulation is the most critical parameter for it cannot be replaced (e.g. like
contaminated oil) and insulation failures are severe in both number and in cost [2]. When more
power is transported through these transformers, higher average- and peak-temperatures are
reached during the daily temperature cycle. Therefore, faster ageing of the various parts in a
transformer can be expected.
As mentioned before, more power is coming from renewable sources. Consequently, transients can
be expected as well. Transients are steep waveforms superimposed on the normal AC waveform and
are caused by fast switching of the power electronic converters. These converters are involved in
converting the power from, for example, wind turbines and solar panels to an AC waveform. This
thesis therefore focuses on the effect of both temperature and transients on transformer paper
insulation.
This chapter starts with a brief explanation of the transformer in section 1.1. Section 1.2 will discuss
the impregnated paper insulation used in transformers. Section 1.3 contains the goal of the thesis
and background information which puts it in context. The thesis outline is displayed in final section
1.4.
1.1 What is a transformer?
The first transformer was made by Faraday in the year 1831 [3]. A transformer is a device that
transforms voltage and current to a level required by the next application. In the electric grid, many
stages are required to let companies and consumers use electric power in a safe and efficient way.
Transformers are one of the main components required to meet this goal.
The operating principle of a transformer is based on magnetomotive force. An alternating voltage is
put on the primary winding causing a current flow. The alternating current sets up a magnetomotive
force hence an alternating flux in the core. This alternating flux induces an electromotive force in the
secondary windings [4]. If a load is connected to the secondary windings, a current will flow to the
load.
As can be seen in Figure 1-1, there are windings at the each leg of the core. The voltage induced is
proportional to the windings ratio. The general equation is:
1
Figure 1-1 Simple scheme of a three phase transformer. An alternating voltage on the windings
eventually causes, through physics, an alternating flux in the core. This flux induces an
electromotive force in the other windings [39]
1.2 Introduction on transformer paper impregnated insulation
Transformers consist of copper windings in coil alike shape. The windings are not allowed to touch
each other and are isolated using impregnated paper which is shown in Figure 1-2. Impregnated
means that the paper insulation is first dried in a vacuum and then saturated with an impregnating
medium such as mineral oil [5]. After isolating the wires, the windings are put in a transformer tank
and the tank is filled with mineral oil.
Figure 1-2 The copper wires are insulated by using transformer paper. This solid transformer insulation is manufactured
at Smit Transformatoren B.V.
2
1.3 Goal of the master’s thesis
1.3.1 Background information
This master’s thesis project is a part of the Sinergie project (sponsored by Agentschap NL, 20072012). This project is dedicated to analyze the functionality of the grid of the future. The grid of the
future will have many tasks such as: facilitating bidirectional electricity flow from customers to the
grid, providing energy from renewable sources and maintaining a reliable supply of electricity. One
way in which this can be achieved is to monitor the ageing of certain components in the grid, such as
e.g. transformers, cables and circuit breakers. To monitor the state of these components, sets of
limits and acceptable boundaries are determined so the measured values from the field can be
compared with them and inputted into an ageing model. This ageing model needs to give an accurate
state of the component and also predict the remaining lifetime of this component so that
appropriate maintenance and/or replacement can be scheduled.
The aforementioned increase in loading is pushed mainly by an increase in power demand. In order
to meet these demands, the power grid operators will have to adapt either by installing new
components, which is difficult to perform in a timely measure due to complex company policy, or by
stressing the current system further, the most probable solution. The extra stressing of components
can be further pushed by new developments such as HVDC, new materials and super conducting
cables. The aforementioned factors make increasing transport an efficient and more likely to be
applied solution.
During operation, transformers heat up or cool down depending on the varying loads. These
variations in load depend mostly on the time of the day, as consumers require more power (heating,
lighting etc.) at specific times of the day.
The high field strengths, which are a result of peaking power transport, combined with these thermal
cycles have their impact on transformer insulation. Presence of moisture and bubble formation, both
related to high temperatures, are just a few examples of factors that increase ageing of transformer
insulation [6].
1.3.2 Research objectives
The goal of the master thesis project is to create an aging model that quantifies the effect of
temperature and transients on the dielectric properties of transformer paper impregnated insulation.
To accomplish this goal, the following research questions are proposed:




Which factors determine the dielectric properties of transformer paper insulation?
What is the effect of temperature on the AC breakdown voltage of transformer paper
impregnated insulation?
What is the effect of temperature on the time to breakdown of transformer paper
impregnated insulation?
What is the effect of temperature and transients on the time to breakdown of transformer
paper impregnated insulation?
Based on the answers to the aforementioned questions, a complement to the model in IEEE Std.
C57.91-1995 ‘Guide for Loading Mineral-Oil-Immersed Transformers’ will be proposed that quantifies
the effect of transients.
3
1.3.3 Thesis approach
The initial step is to perform a literature study on the work carried out so far and identify the most
relevant parameters for the evaluation of the insulation. The physical processes in a transformer will
also be investigated to build general hypotheses on the behavior of the insulation.
To be able to make an aging model, ageing tests have to be performed. These ageing tests have to
indicate if and how much a transformer ages when it is operated at higher loads. If, for example, it
turns out that when a transformer is loaded 20% more it ages 10% faster, one could consider – also
from an economic perspective – to stress today’s transformers further.
To verify such loading strategies, paper samples will be investigated qualitatively after they have
been exposed to thermal and electrical stresses. During the aforementioned ageing tests, it is
important to apply the correct field strength. Therefore, in the first set of experiments, AC
breakdown tests will be performed in a wide temperature range. This will provide useful information
for calibrating the ageing tests and it might also provide interesting information on the relationship
between temperature and AC breakdown voltage.
The second set of experiments consists of ‘time to breakdown’ tests performed at a voltage level just
below breakdown level. The relation between applied field strength and lifetime can then be
quantified.
The final set of experiments is a series of tangents delta measurements. Prior to measuring, samples
will be stressed with an AC voltage. An extra waveform will be added to investigate the effect of
transients introduced by renewable sources.
The final step is to construct a model that quantifies the effect of temperature and transients on the
dielectric properties of paper impregnated insulation.
1.4 Thesis outline
This document is written to represent the steps taken in the master’s thesis project. The chapters
chronologically represent the process.
Chapter 2 includes a literature study on transformers. It will explain the main functions of the
components inside and indicate which factors are responsible for ageing of the insulation. Based on
these factors, relevant measurement techniques can be selected to assess the quality of the
insulation.
Chapter 3 shows the results of three series of experiments. A series of AC breakdown tests, time to
breakdown tests and tangents delta measurements have been performed. This chapter also contains
an analysis of the measurement results.
The results of the main experiments are interpreted in chapter 4. Based on the interpretation, a
model will be made. This model quantifies the effect of temperature and transients on the dielectric
properties of paper impregnated insulation.
The fifth and final chapter is a reflection on the research objectives. It presents the conclusions that
can be made based on the data obtained from the experiments. Recommendations will be given for
further research on loading mineral-oil-immersed transformers.
4
2 Literature study
2.1 Applications of transformers
Transformers are used in many stages of the electric grid as can be seen in Figure 2-1.
Three main stages can be distinguished:
1. Generation. The voltage at the generation level is typically 10-25kV. Transformers are used to
increase the voltage after generation.
2. Transmission. The transmission level voltage is in the range 110-420kV. At this stage, power is
transported to cities and industrial areas over relatively large distances.
3. Distribution. The final conversion stage is to a distribution voltage level of 10kV-72.5kV [7]. At the
distribution level, electricity from small combined heat and power (CHP) stations and solar energy
can be fed in. For end-use by businesses or residential customers, a final conversion stage is required
to convert the voltage level to, in Europe, a three phase 400V or two phase 230V.
Figure 2-1 An electric grid overview with generation, transmission and distribution levels. Transformers are used to
convert to the voltage level each stage requires [8]
It is clear that the transformer, whether at transmission or distribution level, is an essential part of
the grid. As a transmission medium, an engineer can choose between overhead lines or a high
voltage cable. It is, however, not possible to choose a different apparatus for transforming the
voltage up or down.
5
2.2 Parts in a transformer
2.2.1 Core
The core of a transformer is most often made of iron or steel. These materials have a high relative
permeability and can therefore carry more magnetic flux compared to normal air. The relative
permeability of modern steel can be in the order of 1500 compared with 1.0 for air [9].
The iron or steel is laminated in order to reduce heating of the core caused by eddy currents. Eddy
currents are induced by the changing magnetic fields at power frequencies [4].
2.2.2 Windings
The windings of a transformer are made of copper because of its high conduction compared to other
metals. It is important to know is that the windings (Figure 2-2) will heat up during transformer
operation. There are three main causes for heating of the core framework:



Resistive losses
Stray losses
Eddy current losses
Resistive losses are caused by current going through an resistive material, the so called
-losses.
Stray losses for example cause eddy currents to be induced as leakage flux crosses the windings and
induces a voltage [4].
Figure 2-2 Windings are aligned and wound around a core. Oil will be able to flow through the spaces in between the
windings. The heat caused by losses in the windings and core can then be removed by the oil - Smit Transformatoren B.V.
2.2.3 Tap changer
A tap changer is a part of the transformer that changes the voltage ratio on the high voltage side.
This is achieved by increasing or reducing the number of windings. A tap changer is necessary as the
6
high voltage side of the transformer will usually experience fluctuations in voltage level due to e.g.
variations in (renewable) generation power or switching loads on and off. An adjustment can be
made on-load so that the output voltage of the transformer remains constant over time [4].
2.2.4 Paper
The solid insulation in a transformer is simply called ‘paper’ or ‘kraft paper’. It consists mainly of
cellulose molecules which can be seen in Figure 2-3 with other components being 10-20%
hemicelluloses and 2-6% lignin. This paper is designed for is 98˚C, 110˚C for thermally upgraded
paper [10].
Figure 2-3 Cellulose molecules are the main component of transformer paper (Cigré, 2007, p. 7). Transformer paper is
used as it can withstand high field strengths at high temperatures
The focus of this research is on paper insulation as insulation failure is the leading cause of
transformer failure, as was explained in the introduction of Chapter 1 [2]. When a transformer would
be overloaded in the future, it is likely that insulation remains the most critical failure factor. The
insulation strength can be quantified by looking at the dielectric properties of the paper. A detailed
study on these properties follows in section 2.3.3.
2.2.5 Oil
Oil is used as a coolant and an isolator. It is a coolant because it conducts the heat from the windings
and the transformer core [4]. Transformer oil also acts as an isolator because its relative permittivity
(ϵ) is higher than that of air [11]. It is known that for oil ϵ = 2.2 and for oil-impregnated paper ϵ = 3.5.
In high epsilon material, the electric field strength will be higher than in the low epsilon material.
Paper impregnated insulation uses this property very well. Since oil is more homogeneous than
paper, this property prevents local field enhancement thus preventing breakdown.
2.3 Ageing processes in a transformer
2.3.1 Environmental factors
In a transformer, many ageing processes take place. The transformer components age due to both
electrical and environmental factors. The focus in this thesis is on the insulation of the transformer.
In Figure 2-4, it can be seen that insulation suffers mainly from processes caused by environmental
factors such as pyrolysis (thermal degradation), oxidation (oxygen in the oil) and hydrolysis (moisture
in the oil).
7
Environmental
E
l
e
c
t
r
i
c
a
l
Moisture
Air
Temperature
Hydrolysis
Oxidation
Pyrolysis
Transformer Components
VFT
Lightning/
Light
Surges
Insulation
•Bubble
formation
•Particle
formation
•Dielectric and
tensile losses
Core
•Vibration
•Noise
•Core’s insulation
failure
Tap Changer
•Corrosion
•Sparking
•Sticking
•Jamming of
Windings
•High inter-disk
stress
contacts
Figure 2-4 Electrical and environmental factors affect the ageing of multiple transformers components. The main
components affected are the insulation, core, tap changer and windings. When focusing on the insulation, it can be seen that
hydrolysis, oxidation and pyrolysis are responsible for its degradation [6]
Moisture can eventually get in the transformer tank due to leakages, poor condition of the built-in oil
dryer or decomposition reactions of cellulose [12]. Under normal operating conditions, (temperature
<140˚C) pyrolysis does not take place in a transformer [10]. Bubble formation is the direct result of
moisture and gas content (for example oxygen) in the oil [13].
2.3.2
Degradation effects on the oil
Equilibrium between moisture in oil and paper
There is a balance between the moisture in the paper and the moisture in the oil. Moisture can
dissolve better in hot oil than in cold oil. Combined with the hot conductors in a transformer (due to
high loads), this will drain the moisture out of the paper into the oil. When the transformer cools
down again, the moisture will go back from the oil into the paper as can be seen in Figure 2-5. This is
in fact a temperature dependent equilibrium reaction. The reversed process of getting moisture out
of the paper, i.e. absorption of moisture, does not occur in an equal measure [9]. Consequently, [14]
describes the moisture absorption of paper by a concentration dependent diffusion coefficient. The
concentration gradient of moisture will be higher when the moisture exits the paper compared to
the moment where the moisture enters the paper. The moisture will then be diffused in the oil, a
large volume, thus lowering the concentration gradient. When multiple temperatures are reached
during a day, the paper will not have absorbed its maximum moisture content and it will remain in a
dried out state.
8
Figure 2-5 The Oomen Curve shows the equilibrium between moisture in the oil and the moisture in the paper [10]. This
equilibrium is temperature dependent. For example the higher the temperature, the more moisture will move from the
paper in the oil.
The second chemical reaction is the equilibrium between moisture in the air and moisture in the oil
(in case of open air transformers). Because of these two reactions, and depending on the thickness of
the paper, it can take up to three weeks (after disturbance of the moisture level) to get a stable
moisture level in the paper and the oil [10].
A higher moisture content in the oil increases the electric conductivity of the oil [15]. A higher
conductivity will increase leakage current and cause even higher temperatures in the transformer.
That is the reason why the moisture content can be related to the remnant lifetime of the
transformer.
Transformer insulation has losses which are quantified by the measure ‘tangents delta’. A short
explanation of this definition will follow.
Short explanation: Tangents delta
An insulation material such as paper is not a perfect isolator and still has small losses. An
isolator can be modeled using a circuit of a capacitor and a resistor. When the isolator is
excited with a voltage, the angle with the current is 90° if the isolator is lossless. Any
deviating angle δ indicates losses and can be used for quantification of the papers dielectric
qualities, which is shown in Figure 2-6.
9
Figure 2-6 Insulation materials such as paper are not lossless. The figure shows the voltage over a component
with a loss current at an angle [16]
This dielectric dissipation factor is called tangents delta. The definition for tangents delta is
shown in the formula below [16].
Effect of moisture on oil
As can be seen in Figure 2-7, the tangents delta of mineral oil increases as relative humidity
increases. The dielectric constant barely changes and stays around ε = 2.2 according to [17].
Figure 2-7 Tangents delta and ε of mineral oil as a function of relative humidity [17]
The breakdown strength of oil decreases when the relative humidity increases (Figure 2-8). This
situation can occur when a specific amount of moisture (e.g. the amount of water molecules
enclosed in a transformer tank) dissolves in heated transformer oil. As will be elaborated later, in the
practice, this effect will be counteracted by an increase in the moisture level of oil due to movement
of moisture out of the paper (as shown in Figure 2-5).
10
Figure 2-8 The 50Hz breakdown strength of low-viscosity mineral oil [5]. The breakdown strength of the oil decreases
when the relative humidity increases.
Effects of temperature on Oil
When the oil temperature changes, several other parameters change as well. For example, if
temperature increases, there is an increasing number of water molecules that can dissolve in the oil
before saturation occurs (Figure 2-5). Besides that, the viscosity decreases and the conductivity of
transformer oil increases. Table 2-1 shows some values for these parameters that can be found in
literature.
Table 2-1 The water solubility, viscosity and conductivity of oil change when increasing the temperature
Temperature
increase
20°C to 90°C
Parameter
Literature value
Water solubility
0°C to 100°C
Viscosity
35°C to 70°C
Conductivity
55ppm to 648ppm
[18] [12]
62.3cSt to 2.31cSt
[19] cf. [20]
0.7pS/m to 7.2pS/m
[18]
2.3.3 Degradation effects on the paper
The degradation of transformer paper has, besides electrical stressing, many other causes. Other
degradation factors are temperature, water, oxygen, acids and contaminants [10]. Due to these
factors, the state of the paper changes. This change can be quantified by measuring several
properties of the paper. As will be explained in the following section, the tangents delta, degree of
polymerization and breakdown strength can be measured at AC voltages. At DC voltages, the
insulation resistance is measured instead of tangents delta.
In transformer insulation, moisture exists in the capillaries of cellulose. The conductivity of paper
changes as the moisture content increases. This change in conductivity subsequently increases its
tangents delta. Unlike oil samples (Figure 2-7), the of paper is very sensitive to changes in
moisture content [17].
11
Figure 2-9 Tangents delta and ε_r of paper as a function of moisture content [17]
Insulation resistance
In high voltage cables, impregnated paper insulation has the same application as in transformers. In
literature information can be found on these cables with impregnated paper insulation, as listed in
Table 2-2.
Table 2-2 Electrical and dielectric properties of paper-insulated high voltage cables [5]. A decrease in insulation
resistance and impulse voltage strength – both DC related parameters – can be found with increasing temperature
Property
Dielectric dissipation factor tan δ
Relative permittivity
Specific insulation resistance ρ
Specific insulation resistance ρ
Impulse voltage strength
Impulse voltage strength
Average short term dielectric strength
Average long-term dielectric strength
Test conditions
20°C- 50 Hz
20°C- 50 Hz
20°C - 1 min
90°C - 1 min
20°C - 1/50µs to 5/50µs
90°C - 1/50µs to 5/50µs
20°C – 50Hz
20°C – 50Hz
Value
3.5 to 3.8
100 to 130 kV/mm
70 to 100 kV/mm
45 to 70 kV/mm
25 to 50 kV/mm
When testing at DC, it is found that the breakdown strength as well as the insulation resistance will
decrease with increasing temperature. Figure 2-10 also confirms that the resistance will decrease
with increasing temperature.
12
Figure 2-10 DC breakdown voltage of Oil vs. Oil-impregnated paper [21]. The figure shows that the resistivity of both oil
and paper decreases with increasing temperature.
Degree of polymerization
In Figure 2-11, it can be seen that as a transformer ages, the moisture content in the oil – at the
beginning of the lifetime – determines the degree of polymerization [22]. The degree of
polymerization (DP) is “the average number (n) of glycosidic rings in a cellulose macromolecule” [10]
and it is a measure of the strength and quality of the cellulose transformer paper.
13
Figure 2-11 The degree of polymerization (DP) as a function of time and moisture content [22]. The DP value decreases
towards the end of life and is linked to the moisture level at the begin of life
When a sample of paper is taken out of a transformer, the DP-value can be measured. By using
standard rules, the lifetime of the insulation can be determined.
2.3.4 Diagnostic techniques
There are many techniques available for diagnosing the state of the insulation and these are shown
in Table 2-3. The important question is: which measurement techniques are useful for evaluating the
state of paper impregnated insulation samples?
Table 2-3 An overview of often used measurement/diagnostics techniques [23]
Method
Dissolved Gas Analysis
(DGA)
Tests what?
Ageing of oil and paper,
appearance of hot spots
and arcing or PD
Degree of
polymerization (DP)
Ageing of the insulating
paper
Furfural
Ageing of paper
insulation
Return Voltage
Measurement (RVM)
Water content and
ageing of the paper
insulation
Accumulation of
polarizable material at
insulation interfaces
Dielectric losses in the
insulation system
Insulation resistance
and polarization index
Tangents delta (tan δ)
Status
Widely used, much
research goes into
refining the linking of
gases and causes
Relation of polymer
chain length and
dielectric/mechanic
strength is known
Under research, first
applications in the field.
There are still unknowns
in the behavior of
furfural in a transformer
Under research, some
utilities use it on a
regular basis
Known
Known, portable
instruments have been
developed, an online
system that measures
14
Who uses it?
Many utilities, many
laboratories
Mainly research
laboratories as second
opinion. Not many
utilities use it
Utilities, laboratories
Some utilities,
laboratories
Mainly utilities. Can be
used off line, on site for
periodic check
Some utilities, and most
transformer producers,
as a quality control
Frequency dependent
tangents delta (f)
Dielectric frequency
response, ageing of
paper, accumulation of
polarizable material in
the insulation system
Partial discharge
Deterioration of the
insulation system, able to
detect some localized
defects
relative tangents delta
for bushings of a
transformer is in use in
Australia
Instruments
commercially available,
but much research is
being done on the
interpretation of the
results
Well known, research is
being done on noise
suppression, data
interpretation and online
use.
Some utilities,
laboratories
Many utilities use it in
laboratories. PD level
measurement is part of
the commissioning test
for power transformers.
Some companies
specialize in on-site or
online measurements
using various methods:
Filtering, VHF, UHF,
acoustical detection
Dissolved Gas Analysis (DGA)
As [23] explained, gas concentrations will be produced in the oil due to breakdown and degradation
effects. Gas production will start around 140-150˚C [24]. This temperature will not be met in a
transformer under normal loading conditions. For example Tennet TSO, the Dutch grid operator,
works with secure margins (normal transformer operation at 40˚C) and will not accept the failure
risks involved when operating their transformers at high temperatures.
Degree of Polymerisation (DP)
It is not available at the test site, the High Voltage Laboratory of the Delft University of Technology
[25].
Furfural
Due to thermal ageing, furfural can be formed in the paper insulation [23]. It is, however, hard to
reliably relate these levels to ageing [10]. Moreover, it is a technique which is not available in the
High Voltage Laboratory of the Delft University of Technology [25].
Return voltage measurement (RVM)
This is used for the determination of the water content and thermal ageing. With this information, it
is possible to compare the effect of moisture and different temperatures on the samples.
Insulation resistance and polarization index
This could be interesting in order to estimate the quality of the cellulose material which would be
non-polar and have a large resistance.
Tangents delta and Tangents delta (f)
A tangents delta measurement quantifies the dielectric loss factor of the insulation. This is an
important failure risk factor because a high tangents delta means that the insulation will heat up,
making partial discharge or even breakdown likely to occur.
15
Tangents delta (f) is a frequency dependent tangents delta measurement technique. It is not relevant
as this research focuses on the dielectric properties at power frequencies.
Partial discharge
This measurement technique is suitable for finding defects. Partial discharge detection is not
necessary as this is not the goal of this research.
2.4 Conclusions
Transformers are essential parts of the electric grid. They can be found at the generation,
transmission and distribution level. During operation, degradation factors influence the state of the
transformer insulation. The insulation experiences environmental ageing factors such as pyrolysis,
oxidation and hydrolysis.
An increasing temperature greatly influences the properties of the insulation and the oil surrounding
it. Heating up the oil will have consequences for multiple parameters:




Moisture goes from the paper to the oil
Increasing solubility
Increasing conductivity
Decreasing viscosity
Paper on the other hand will experience an improvement of breakdown strength under a constant
moisture level. Due to the heating, the decreasing moisture level of the paper and the increasing
moisture level of the oil causes:



Increasing tangents delta of oil
Decreasing breakdown strength of the oil
Increasing breakdown strength of the paper
These effects will oppose each other and it is expected that the breakdown voltage will first increase
and then decrease again.
Several diagnostic techniques are available for diagnosing the state of the paper insulation. Usable
techniques for this research are insulation resistance and polarization index, return voltage
measurements and tangents delta measurement.
16
3 Experiments and results
This chapter covers the performed experiments with their results. As discussed in the previous
chapter, the breakdown voltage and tangents delta of paper and oil will change as a result of
temperature increase. The goal of the experiments is to quantify the effect of temperature on the
dielectric properties of impregnated paper. Section 3.1 shows the first set of experiments which
consisted of AC breakdown tests. These tests were performed to find the right loading conditions for
the consequent experiments. Secondly, in section 3.2, experiments were performed to assess the
time to breakdown. In the final experiments in section 3.3, the tangents delta of the paper was
determined. Each sections contains a subsection goal, temperatures, hypothesis, test setup and
results. A subsection concludes with a short analysis and a summary.
3.1 Experiment 1: AC breakdown
3.1.1 Initial results
Prior to the AC breakdown tests, some initial experiments were performed. This was done to get a
better understanding of the behavior of the transformer paper. The results of this experiment can be
found in Table 3-1.
Table 3-1 Results of initial experiments. It can be seen that placing a sample in oil 60 hours prior to testing decreases the
breakdown voltage. The breakdown voltage is also dependent on the rate at which the voltage is increased
Condition
Placing a sample 60 hours in oil prior to testing
Slowly increasing the voltage
Increasing the voltage at a higher rate
Breakdown voltage [kV]
1.94 kV (40˚C)
2.68 kV, 2.88 kV (43˚C)
3.61 kV (43˚C)
The first paper sample stressed was taken from a sealed jar and placed in oil for about 60 hours prior
to testing. The breakdown voltage of this sample was found by slowly increasing the voltage until
breakdown occurred at 1.94kV (40˚C). The second paper sample had been imaginarily split up in
three areas and this sample has been tested less than an hour after it had been placed in oil. Slowly
increasing the voltage led to a breakdown at 2.68kV and 2.88kV (both at 43˚C). The third area of the
second sample was stressed by increasing the voltage at a higher rate. In this case, a breakdown
occurred at 3.61kV. These results will be interpreted in section 3.1.4 to design a procedure.
3.1.2 Goal
The breakdown voltage of the paper will be determined to find the suitable loading conditions for
the ageing tests, which will be performed hereafter.
3.1.3 Temperature
The temperatures at which the breakdown will be determined are 40˚C, 50˚C, 60˚C and 80˚C. These
are picked as 60˚C and 80˚C are approximately the top and bottom of the peaks in Figure 3-1. This
figure shows the hot spot temperature in a transformer over a 24 hours period. The aforementioned
top and bottom of the temperature peaks are indicated with arrows. The temperatures of 40˚C and
50˚C will be tested because with these temperatures breakdown data is gathered on the operating
temperature of the rest i.e. non-hot spots of the transformer [26].
17
Figure 3-1 The hot spot temperatures are shown which a transformer experiences over a 24 hour period according to the
model in [27]. The deviation line indicates the error of the model proposed in this paper.
For each temperature, a new paper sample will be used. The paper is then imaginarily split up into
areas in such a way that at least five data points are gathered [28]. Each time a breakdown has
occurred, the electrode will be moved to the next area.
3.1.4 Procedure
To find the AC breakdown voltage, a procedure was designed. Prior to designing the AC breakdown
procedure, some interesting initial results were found as shown in section 3.1.1. The difference in the
breakdown voltage of the first and second sample is likely due to the time the sample spent in the
oil. Due to the fact that the oil is in contact with air, moisture will slowly dissolve causing a lower
breakdown voltage [29]. The scatter in the second paper sample is likely to be the result of the speed
at which the voltage is increased. A procedure for the testing had to be designed to avoid wide
scatter in the determination of AC breakdown voltages.
This procedure is about increasing the voltage at the right speed. When going too slow, the
breakdown voltage decreases and when going too fast, the breakdown voltage will be much higher
(3.61kV versus 2.78kV). A commonly observed phenomenon, shown in Figure 3-2, is that high
voltage components can be overstressed for a short period. The figure shows that when a cable is
stressed at rated voltage , its lifetime will be 50 years. When it is stressed with for example
,
the lifetime decreases to 1 day.
When increasing the voltage at a high rate, the scatter will be higher because apparently small
variations in executing the procedure cause a relatively large error (e.g. staying at a voltage level just
0.5 sec too long if a voltage step takes just 5 seconds). The goal of the procedure is that it gives a
reliable estimate of the average breakdown voltage in order to find the right loading conditions for
the experiments to come. The ageing experiments will run multiple hours, therefore the loading
conditions can be based on a voltage lower than the intrinsic breakdown voltage. Therefore, to give
the operator an error margin, the breakdown data is based on a relatively slow increase of the
voltage.
18
Figure 3-2 Lifeline of high voltage components [16]. The time a high voltage component can withstand the applied
voltage level decreases logarithmically with time when the voltage level is increased
The voltage will be increased using the so-called step-by-step-test. The breakdown voltage is
estimated to be at least 2kV and the voltage steps are chosen in such a way to keep the total
breakdown time between 120 and 720 seconds in about 4-10 steps. This way, sufficient accuracy is
maintained (this is defined by a maximum deviation from median of 15%). If the breakdown voltage
turns out to be much higher (exceeding 12 voltage steps or 720 seconds until breakdown) or lower
(less than 4 voltage steps or 120 seconds until breakdown) the table can be adapted especially for
that experiment in order to meet the IEC 243-1 standard [30].
The voltage applied to the test setup originates from a high voltage transformer connected to a
variable autotransformer (or variac). The winding ratio of the high voltage transformer is
:1
This means that when the variac is turned to “10”, the output voltage of the high voltage transformer
will be
V
In Table 3-2, the values given in the second column are the values that should be set on the variac
during the time stated in the third column.
19
Table 3-2 Reference table for increasing the voltage. The table shows the name of the step, the applied voltage according
to the value on the variac and the waiting time after each voltage step
Step
A
B
C
D
E
Primary variac position
Slowly to 25
30, 35
40, 45, 47.5
50 to 59
60 to 64
Voltage [kV]
Slowly to 1.44
1.73, 2.02
2.31, 2.60, 2.74
2.89 to 3.41
3.46 to 3.70
Waiting time (sec)
30
(2x) 20
(3x) 20
(10x) 20
(5x) 20
The paper sample is placed in the oil 10 minutes prior to testing. It was found that this so-called
standing time resulted in measurement data with a relatively high accuracy (i.e. no more than 15%
deviation from median). This high accuracy is a result of the standing time as this allows tiny bubbles
(which enter the oil when a sample is placed) to dissolve.
3.1.5 Hypothesis
The breakdown voltage of the paper and oil is expected to be higher as the temperature increases.
The viscosity of the oil decreases, with increasing temperature, which increases the ability of the oil
to fill up the spaces between the cellulose molecules. The conductivity of the oil will increase at
higher temperatures which will increase leakage current and cause even higher temperatures in the
transformer. During these experiments, dried paper is used so that the paper will not dry out any
further. As discussed before, in that case, the breakdown voltage of paper will decrease as the
temperature increases. All these effects oppose each other and will eventually level out. It is
expected that the breakdown voltage will first increase and then remain constant.
3.1.6 Test setup
The voltage is applied by a high voltage transformer which can be controlled by a variac outside an
earthed cage. The electrical schematic of the setup is drawn in Figure 3-3. The sample is placed in a
deep fryer which has been modified so that it can be used for scientific testing, which is shown in
Appendix C. A perspex lid prevents dust and other particles from entering the oil. It is, however, not
air tight meaning that moisture and oxygen are in contact with the oil. A schematic drawing is shown
in Figure 3-4.
Figure 3-3 Schematic drawing of the test setup. The variac is fed by a 230V AC source and connected to a high voltage
transformer. The sample is placed at the high voltage side and can be modeled as a capacitor.
20
Figure 3-4 Schematic drawing of the test setup. The base electrode has a diameter of 120mm and is connected to earth
via an earthed copper plate. The top electrode has a diameter of 25mm and is connected to high voltage via a metal bar.
The deep fryer is used for heating the oil. Inside the basket, there is an earthed copper plate. On top
of the copper plate, a base electrode with a diameter of 120mm and a top electrode with a diameter
of 25mm are located. The actual setup is shown in Figure 3-5 in which, for clarification, there is no
sample present.
Figure 3-5 The deep fryer with the top electrode connected to high voltage via a metal bar. For clarification, no sample is
present in this setup. Normally, it would be situated between the two electrodes thus completely covering the bottom
electrode.
21
The tests are performed on paper samples with a size of 150x150x0.060mm. The sample is placed
between the bottom and top electrode. The paper is moved after a breakdown so that a new area
can be used. While moving the paper, the operator should not take an area which is close to the
edge of the paper or previously stressed spots.
Figure 3-6 One of the impregnated paper samples. The size is 150x 150x 0.060mm
These spots are relatively simple to locate because the location of all previous breakdowns are
clearly visible. In Figure 3-7, three black spots with carbon traces can be found.
Figure 3-7 Three black spots consisting of carbon traces. This is a confirmation of a breakdown for the operator of the
test setup
3.1.7
Results
First results
The first results were gathered from measurements performed on impregnated paper that was taken
from a closed jar. The results in Figure 3-8 and Table 3-3 show that some samples deviate from
average in the range of approximately 4-7%. In this table, error is defined as the maximum deviation
from the average. When the definition ‘corrected data’ is used it means that one or two outliers have
been removed from the data and this is indicated with a star.
22
2,0
1,8
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
Breakdown voltage [kV]
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
-
45.3°C 65.4°C 65.4°C
-
-
-
-
-
45.3°C
-
4 days
-
-
-
-
-
3 days
1 day
2 days
Error in breakdown voltage [kV]
4,0
16.6°C 16.6°C 16.6°C 16.7°C 40±2°C 40±1°C 50±2°C 60±2°C 80±2°C 80±2°C
Condition [Oven temperature, oven time, testing temperature]
Raw data average
Corrected data average
Raw data error
Corrected data error
Figure 3-8 First results of the AC breakdown tests. It can be seen that removing one or two outliers decreases the error
(i.e. deviation from average) but does not change the average. Preparing samples in the oven did not cause any
significant improvement of the average breakdown voltage or the error
Table 3-3 Measurement results on the average breakdown voltage at different temperatures. The results with a star are
calculated with corrected data in which the most off-average data points were removed
T [°C]
16.6
16.6
16.6
16.7
40±2
40±1
50±2
60±2
80±2
80±2
Treated in
oven?
4 days
1 day
2 days
3 days
Oven T
[°C]
45.3
65.4
65.4
45.3
Number of
samples
8
8
8
8
5
8
5
5
5
8
Error to
AVG [kV]
0,45
0,43
0,40
0,59
0,27
0,39
0,62
0,24
0,32
0,52
Error* to
AVG [kV]
0,14
0,07
0,21
0,28
0,20
0,25
0,19
0,14
0,12
0,20
Average
[kV]
3,11
3,12
3,19
3,38
2,76
3,05
2,62
3,02
3,15
3,26
Average *
[kV]
3,22
3,05
3,21
3,36
2,69
3,07
2,46
3,08
3,23
3,28
Some samples were placed into a vacuum oven prior to the measurements. This was done to remove
the moisture that could have gone into the jar if it had been in contact with air for a long period of
time. Moreover, it was tested whether the paper was impregnated with a different kind of oil. At the
start of the experiments, it was clear that the samples were impregnated with mineral oil, but it was
unclear whether this was Shell Diala B transformer oil (i.e. the oil used in the test setup) or not. This
might have caused the scatter due to (partial) diffusion of two types of oil during the experiment in
the deep fryer. To make sure that this was not the case, a few paper samples were “dried in a
vacuum and then saturated with impregnating medium” [5]. It turned out that the results were not
positively affected by this act.
23
Firstly, the temperature of the oven was 45˚C in order not to age the paper. The results slightly
improved when a sample remained in the oven for 3-4 days. The samples were pre-impregnated with
the same oil (Shell Diala B) in which the experiments were conducted.
The better the vacuum (the lower the pressure) and the higher the temperature of the oven, “the
quicker and more effectively the drying and degassing process” [5]. Therefore, it was attempted to
place the samples in the vacuum oven at 65˚C. This, however, as can be seen in Appendix A, did not
prevent scatter and it could be concluded that moisture in the paper – at least at the beginning of
the experiment – was not a cause of error.
The standard IEC 60243-1 [28] states that if five samples do not give enough accuracy, ten samples
should be taken. According to the standard, sufficient accuracy is accomplished when measurement
results deviate less than 15% from the median. Because it is not possible to get ten samples out of
one paper sheet, a tradeoff was made between the number of samples and the distance between
the stressed parts of the paper. The experiments at the temperatures shown in Table 3-3 were
repeated, the remaining temperatures from section 3.1.3 were added and eight breakdown tests
were performed on one paper sample. Because the base electrode began to erode, it was replaced
by an electrode that was simpler to maintain by polishing. Polishing is important as it removes the
small pits from aged electrodes which can cause local field enhancement (see Appendix C, page 76).
Figure 3-9 Earthed copper plate (previously used as bottom electrode) with polished bottom electrode and top electrode
A newly polished electrode sometimes causes breakdown voltage to drop during the first few tests.
This can be the result of impurities on the atomic scale caused by the polishing process. Therefore,
the electrode was conditioned by performing three breakdown tests prior to use.
24
Final results
The final results are summarized in Table 3-4.
Table 3-4 Measurement results on average breakdown voltage of paper. The results with a star are calculated with
corrected data in which the most off-average data points were removed
Test
temperature *˚C+
16,6
40
50
60
70
80
90
Samples
8
8
8
8
8
17
8
Error to
AVG [kV]
0,45
0,29
0,48
0,29
0,50
0,81
0,45
Error* to
AVG [kV]
0,26
0,24
0,32
0,11
0,23
Average
[kV]
3,11
3,41
3,49
3,59
3,26
3,12
3,40
Average*
[kV]
3,11
3,51
3,24
3,23
3,42
These results are shown graphically in Figure 3-10. A linear increase of the breakdown voltage can be
seen. Up to 60˚C the breakdown voltage increases with 11V every degree Celsius.
Vbd [kV]
Breakdown voltage
4,00
3,80
3,60
3,40
3,20
3,00
2,80
2,60
2,40
2,20
10
20
30
40
50
60
70
80
90
Temperature [˚C]
Figure 3-10 Average breakdown voltage at different temperatures on a linearized scale. It can be seen that up to 60˚C,
the breakdown voltage increases with increasing temperature with approximately 11 V/˚C
3.1.8 Analysis
Scatter can be found in the results. The average, however, is not affected by the scatter as can be
seen from removing the outlying samples (see Appendix A). Thus, these errors can be considered
random errors and not structural errors.
The graphs in the previous section only show the average breakdown voltage. To perform a more indepth analysis, Figure 3-11 shows a box plot of the breakdown voltage. The green and red areas
show the 1st and 3rd percentile, meaning that 50% of the data is in this area. The boundary between
the 1st and 3rd percentile is the median, which is the number that separates the upper and the lower
50% of the results. The error bars show again the results that were most off-average (or off-median
in this case).
25
Breakdown voltage
4,0
3,8
3,6
Vbd [kV]
3,4
3,2
3,0
1st percentile
2,8
3rd percentile
2,6
2,4
2,2
2,0
16.6˚C
40˚C
50˚C
60˚C
70˚C
80˚C
90˚C
Temperature *˚C+
Figure 3-11 Box plot of the breakdown voltages. It can be seen that the data of the 40˚C and 60˚C measurement is
bundled i.e. the box containing 50% of the data and the error bars are close together
Statistically, the best results are the 40˚C and the 60˚C measurement as the spread in the data is
small. The higher and lower quartiles are narrow and still close to the median. The measurement
data at 80˚C shows a lot of scatter. It can be concluded that the data showing the increase in the
breakdown voltage is more concentrated around the 1st and 3rd percentile and therefore more
reliable than the subsequent decline at 70˚C and 80˚C.
An alternative to removing the worst data is plotting 10th and 90th percentile boundaries of the
measurement data. In Figure 3-12, it can be seen that the area between the 10th to 90th percentile
lines evolves smooth, except for the trajectory around 80°C.
Breakdown voltage
4,00
Vbd [kV]
3,50
90% boundary
3,00
Median
2,50
10% boundary
2,00
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Temperature [˚C]
Figure 3-12 The temperature dependent median breakdown voltage. The 10% and 90% boundaries indicate the
remaining scatter in the results when the most off-median samples are removed
26
Weibull distribution
Most failure processes in electrical phenomena can be modeled with the Weibull distribution.
Especially for breakdown data for solid insulation, the most common distribution is the Weibull
distribution [31].
The cumulative distribution function of a three-parameter Weibull distribution is:
( )
{ (
) } with
t is the breakdown voltage
F(t) is the probability of failure at a voltage less than or equal to t.
is the scale parameter (positive), it represents the voltage at which the failure probability is
is the shape parameter (positive), it represents the range of the breakdown voltages: the larger ,
the smaller the range of breakdown voltages
is the location parameter, the probability of breakdown is zero for
[31]
In Appendix B, the Weibull plots can be found for every temperature at which a measurement has
been performed. Table 3-5 shows the Weibull parameters. The data is fitted to a 2-parameter
Weibull distribution. A 3-parameter Weibull distribution can be calculated to determine the 0%
failure boundary, but this is shown in Appendix B.
Table 3-5 The 2- parameter Weibull distributions that fit the data best
16.6°C
40°C
50°C
60°C
70°C
80°C
80°C*
90°C
13,4273
18,0299
13,0639
19,9103
13,6664
10,1281
36,6444
15,1619
3,2188
3,5048
3,6202
3,6783
3,3719
3,2659
3,3172
3,5144
0,9885
0,9059
0,9781
0,9512
0,9463
0,9039
0,9395
0,9740
The 80°C* shows the Weibull parameters after three outliers (see Appendix B Figure ) have been
deleted. Parameter ρ is an indication of the goodness of fit: the better the fit, the higher the value of
ρ. The three-parameter Weibull distribution for 40°C, 50°C and 70°C provides a better fit than the
two-parameter version. The elimination of three samples at 80°C improved the fit, shown by the
increase in ρ.
By using Figure 3-13, the minimal ‘goodness-of-fit’ before a particular fit can be considered good can
be determined. The number of test samples was eight for all temperatures except for 80°C, which
was seventeen and fourteen for 80°C*. For eight samples
is good and for fourteen and
seventeen samples approximately
is good. All fits can be regarded as good except for the
two-parameter Weibull distribution of 40°C and 80°C which is the reason why alternatives (threeparameter and eliminating data points) have been found.
27
Figure 3-13 Plot to check the goodness-of-fit of a 2p-Weibull distribution [31]. The number of samples and the calculated
correlation coefficient ρ are used to assess the quality of the fit
When all (2p) parameters are plotted in a contour plot, the and values can be compared. A
contour plot shows what the actual value can be with 90% likelihood or confidence. According to
[16], when multiple Weibull distributions are compared, the actual distribution and confidence
intervals should not overlap. Figure 3-14 shows a large overlap which confirms that it is not possible
to draw strong conclusions for all distributions. The areas of 16.6°C and 60°C do not overlap at all. In
that case, differences can be validly distinguished and conclusions can be drawn. Therefore, it can be
concluded that the breakdown voltage improves. The 60°C and 80°C areas do not overlap and it can
also be concluded that the breakdown voltage has decreased in this temperature step.
28
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
50,000
Contour
16.6\Data 1
Weibull-2P
RRX SRM ME...
F=8/S=0
90%
41,000
40\Data 1
Weibull-2P
RRX SRM ME...
F=8/S=0
90%
50\Data 1
Weibull-2P
RRX SRM ME...
F=8/S=0
32,000
B eta
90%
60\Data 1
Weibull-2P
RRX SRM ME...
F=8/S=0
90%
70\Data 1
Weibull-2P
RRX SRM ME...
F=8/S=0
23,000
90%
80\Data 1.1
Weibull-2P
RRX SRM ME...
F=14/S=0
14,000
90%
90\Data 1
Weibull-2P
RRX SRM ME...
F=8/S=0
90%
5,000
2,000
2,400
2,800
3,200
3,600
4,000
Eta
16.6\Data 1:                
40\Data 1:                
50\Data 1:                
60\Data 1:                
70\Data 1:                
80\Data 1.1:                
90\Data 1:                
Figure 3-14 In this contour plot the η and β values of the 2-parameter Weibull distribution at different temperatures are
shown. A contour appears instead of a point as the confidence intervals are taken into account as well. When these
intervals do not overlap, it can be concluded that the parameters describe a different process. Such conclusions can be
drawn for 16.6˚C (red) v. 60˚C (blue) and 60˚C v. 80˚C (green) as their confidence intervals do not overlap
3.1.9 Summary
The breakdown voltage increases with 11V per degree when the temperature is increased from room
temperature to 60°C. However, when the temperature is further increased to 80°C, then the
breakdown voltage decreases again. What happens in between these two temperatures is
statistically more uncertain and it seems that the breakdown voltage starts to increase from 80°C
onwards.
29
3.2 Experiment 2: Time to breakdown
3.2.1 Goal
The goal of the time to breakdown test is to gather parameters at multiple temperatures which can
later be used to draw conclusions on the dielectric properties of the paper.
The temperature of 40°C occurs in practice during operating conditions in the Netherlands and, going
back to the goal of the entire research, these measurements should indicate what the consequences
for the time to breakdown of the insulation would be when in the future a transformer is heated up
to for example. 60˚C or 80˚C.
3.2.2 Temperature
In this experiment, the time to breakdown will be determined for the same temperature range as the
AC breakdown tests (section 3.1). Due to the time consuming nature of these experiments, it was not
possible to determine the time to breakdown for all previously measured temperatures in the
available time frame.
From the results of the AC breakdown measurements, it can be seen that the properties of the paper
and the oil change considerably in the measured temperature range. Therefore, the temperatures of
40°C, 60°C and 80°C were chosen to perform measurements at.
3.2.3 Procedure
The oil will be heated to a temperature mentioned in the previous section. It takes about 90 to 120
minutes to get a stable temperature. The applied voltage is 2.91kV as it is approximately 10% below
the lowest average breakdown level in the 40°C-60°C-80°C temperature trajectory thus preventing
immediate breakdown. This voltage also makes the outcome of the experiments comparable with
previously performed experiments [32]. Four samples will be placed in a setup for each temperature
and this experiment will be performed twice. During the experiment, the time to breakdown is
monitored.
3.2.4 Hypothesis
It is expected that the time to breakdown will be around 120 hours for the 40°C sample based on
previous research [32]. The breakdown strength of the sample is expected to improve at 60°C, like it
did at the AC breakdown tests, causing a larger time to breakdown. Analogous to the previous, the
time to breakdown probably decreases again at 80°C.
3.2.5 Test setup
The test setup consists of a hotplate with a ±2% accurate temperature control. A cup glass filled with
750ml of transformer oil is put on top of the hotplate (see Figure 3-15). The paper sample is
squeezed between a top electrode of 25mm diameter (20mm flat surface) and a bottom electrode of
120mm (100mm flat surface) diameter. The bottom electrode is connected to earth and the high
voltage is connected to the top electrodes.
30
Figure 3-15 Front view of the time to breakdown test setup. The base electrode has a diameter of 120mm and is
connected to earth via an earthed copper plate. The four top electrodes have a diameter of 25mm and are all connected
to high voltage via metal bars (only 3 present here). It is possible to easily disconnect a sample after breakdown has
occurred
To pipeline the experiment, it is possible to disconnect one of the high voltage leads. After a
breakdown has occurred, visually confirmed by a bubble, the voltage source immediately shuts
down. The sample that broke down has to be disconnected and the high voltage can be turned on
again. In total, four samples can be put on this electrode, each contact area spaced about 20mm
apart. More details about this setup can be found in Appendix C.
3.2.6 Results
When performing the experiment, about 30% early breakdowns occurred within 30 minutes. These
breakdowns were regarded as infant mortality and were eliminated from the final results stated in
Table 3-6. This time, the samples were taken from a new jar. It was noted that some of these samples
had a more irregular surface than the samples used before (although they are supposed to be the
same). The thickness was measured with a micrometer for verification, but no abnormalities were
found (thickness between 60 and 62μm).
31
Table 3-6 The time to breakdown for samples stressed with 2.91kV at three different temperatures. The F represents a
failure at the time stated in the table. When a sample survives the test, an S is filled in.
Sample
1
2
3
4
5
6
7
40°C
25,12
44,54
18,07
42,12
44,74
39,74
State
S
F
F
F
S
F
60°C
15,02
67,78
2,42
41,87
46,24
State
F
S
F
F
S
80°C
31,72
3,49
99,64
99,64
98,19
98,19
98,19
State
F
F
S
S
S
S
S
Censored data
In this experiment, besides failure data, so called censored data was recorded. This means that
besides the failed samples, samples that survive are taken into account as well. Use is taken of the
fact that if a sample survives a certain amount of time, this contains information about its life
distribution as well. When it is known that a sample survived up to a certain time and is then
withdrawn from observation, it is called a suspension [33]. This is exactly what is happening in this
experiment.
The reason that suspended data is used is that for fire safety, the hot plate in the test setup was not
allowed to be active during the weekend. Practically, this means that when a sample is alive at Friday
late in the afternoon, it will be removed from the test setup. If the measurement would be continued
after the weekend, it is not known what the effect of the cooling down and heating up would be on
the time to breakdown of the sample. In a closed container this should not be a problem. However,
when the contact with air is considered, the equilibrium reactions described in section 2.3.2 will
influence the dielectric properties of the paper.
The Weibull parameters are calculated differently when censored data is used. An example on how
this is calculated is given in Appendix B (page 70).
3.2.7 Analysis
When the failure data is fitted with the Weibull++ software, Table 3-7 can be made. In this table, it
can be seen that for the 60°C and 80°C measurement this resulted in low values of . This means that
63.2% of the samples at 60°C break down after 22.8 hours versus 22.2 hours for the 80°C samples.
Table 3-7 The 2- parameter Weibull distributions that fit the failure data
40°C
60°C
80°C
2,6426
0,6697
0,8969
40,8215
22,8076
22,1688
0,8969
0,9970
1,000
When the suspended data in Table 3-6 is taken into account, these values should increase as
suspended data records surviving samples up to 67.8 hours for the 60°C samples and up to 99.6
hours for the 80°C samples. When these suspended data points are taken into account, new
parameters are calculated as shown in Table 3-8. As predicted, an increase in the η parameter for
32
60°C and 80°C can be observed. For the 80°C measurement, the suspended data points have only
been taken into account once to avoid that these data points are overweighted in the calculation.
Table 3-8 The 2-parameter Weibull distributions that fit the data best. Both failure and suspended data are included in
the calculation
40°C
60°C
80°C
2,4904 48,4473
0,5628 82,1275
0,4685 147,1338
0,9223
0,9998
1,000
3.2.8 Summary
In this experiment, an increase in time to breakdown is observed when temperature is increased
from 40°C to 80°C. The breakdown time for 63.2% of the samples is 48.4, 82.1 and 147 hours for
40°C, 60°C and 80°C respectively. The value for β is decreasing with increasing temperature meaning
that the expected failures are spread out over a larger time interval.
33
3.3 Experiment 3: Tangents delta
3.3.1 Goal
The goal of this series of experiments is to quantify the effect of thermal and electrical stresses on
the tangents delta of transformer insulation. The results of these experiments will be compared to
the previous experiments.
3.3.2 Temperature
The thermal stresses will be the same as applied in the time-to-breakdown experiment; therefore
comparisons between the measured parameters can be reliably made. The measurements will be
performed with samples that are electrically stressed while being heated to 40°C, 60°C and 80°C.
3.3.3 Voltage
The samples are electrically stressed by applying different waveforms. The AC waveform will consist
of a sinusoidal wave with an RMS value of 2.22kV. A DC source simulates the transient behavior of
the grid and this signal will be superimposed on the aforementioned AC waveform. The DC waveform
consists of small spikes with a rate of rise of 1kV/μs and a repetition frequency between 1kHz and
10kHz as used in [34]. The waveform for 2.22kV + 5kHz transients is shown in Figure 3-16.
The 2.22kV AC waveform has a lower amplitude compared to the 2.91kV of the ‘time to breakdown’
experiment. By stressing the samples with this lower voltage, a margin is built in because the samples
are neither allowed to break down during the stressing nor in the measurement apparatus.
Measurements will be performed on samples stressed with 2.22kV, 2.22kV + 1kHz, 2.22kV + 5kHz
and 2.22kV + 10kHz waveforms. This will be repeated for the three aforementioned temperatures,
namely 40°C, 60°C and 80°C. The tangents delta for a new, non-stressed, sample will be measured as
a reference.
5
4
3
voltage [kV]
2
1
0
-1
-2
-3
-4
-5
0
0.002
0.004
0.006
0.008
0.01
time [s]
0.012
0.014
0.016
0.018
0.02
Figure 3-16 A 2.22kV 50Hz AC waveform with a 1kV 5kHz DC signal superimposed. The DC signal contains small spikes
which have a rise time of 1kV/μs.
34
3.3.4 Procedure
The samples are stressed for 22 hours while heated and stressed with the aforementioned
temperatures and waveforms. The samples are aged for this specific period as it will age the samples
without initiating breakdowns. A sample that breaks down during the stressing cannot be used for a
tangents delta measurement. Additionally, the samples should not be at the end of their lifetime
because a breakdown while performing the tangents delta measurement is detrimental to the
tangents delta measurement setup.
3.3.5 Hypothesis
The dielectric properties of the paper are expected to improve with increasing temperature as there
will be less moisture in the paper due to absorption by the hot oil. As discussed in the literature study
in section 2.3.3, the tangents delta of paper decreases with decreasing moisture content. The
tangents delta of oil remains constant up to 50% relative humidity as could be seen in Figure 2-7
(page 10). It is expected that this level of moisture in the oil is not reached as Table 2-1 (page 11)
shows that a temperature increase from 20°C to 90°C allows 12 times more moisture to dissolve.
So any change of the tangents delta measured is a change in the properties of the paper
(
) hence the tangents delta is expected to decrease with increasing
temperature.
In the case that transients are added to the waveform, these transients are expected to increase the
tangents delta. The transients form an extra stress on the fibers of the paper (consisting of cellulose
molecules) as the transients cause the polar molecules to vibrate more than they would do solely in
the presence of an electric field of the AC waveform.
3.3.6 Test setup
The test setup is the same as described in section 3.2.5. This time, only one top electrode is placed
and connected to the high voltage. The stressed area has a diameter of 20mm. After 22 hours of
stressing, the sample will be put in a Tettex 2840 tangents delta measurement device (shown in
Figure 3-17). This device has a built-in Schering bridge with automatic tuning. The measurement
electrode has a diameter of 40mm. When measuring the sample, the measured tangents delta value
is partially based on a non-stressed area. However, the leakage current will be highest in the stressed
area and any ageing effects in this area (thus any change in applied stress) will be dominant for the
measured value.
35
Figure 3-17 The tangents delta measurement device. A sample is placed between two measurement electrodes
measuring applied voltage and leakage current. The analyzer then calculates the tangents delta
3.3.7
Results
Characterization of the paper
To better understand the properties of the paper when performing tangents delta measurements,
the paper has been investigated using a dielectric spectroscope. Details about this measurement can
be found in
36
Appendix D: Characterization of the paper. The chosen range of applied voltage of the forthcoming
measurements is explained in this appendix as well.
Results of varying temperature for tangents delta
The behavior of tangents delta as a function of temperature can be investigated by comparing the
measurement results for every type of electrical stress. When the sample is stressed with a 2.22kV
AC waveform (no transients), the graph in Figure 3-18 can be made. The lowest values for tangents
delta are observed for the 80˚C measurement.
At every temperature, two measurements are performed and the average of these measurements is
plotted. The plots of the individual measurements can be found in Appendix C, Figure B-17.
2.22kV AC waveform
0,0046
Tangents delta
0,0045
0,0044
0,0043
0,0042
40C
0,0041
60C
0,0040
80C
0,0039
0,0038
0
50
100
150
200
250
300
350
400
Vapplied [V]
Figure 3-18 Tangents delta measurement for a sample stressed for 22 hours with a 2.22kV AC waveform. At 80˚C, the
lowest values for tangents delta can be observed
Tests are performed with samples stressed with a 2.22kV with superimposed transients of 1kHz, 5kHz
and 10kHz. The results are shown in Figure 3-19, Figure 3-20 and Figure 3-21 respectively.
37
2.22kV AC + 1kHz transients
0,0046
Tangents delta
0,0045
0,0044
0,0043
0,0042
40C
0,0041
60C
0,0040
80C
0,0039
0,0038
0
50
100
150
200
250
300
350
400
Vapplied [V]
Figure 3-19 Tangents delta measurement for a sample stressed for 22 hours with a 2.22kV AC waveform with 1kHz
transients superimposed
2.22kV + 5kHz transients
0,0046
Tangents delta
0,0045
0,0044
0,0043
0,0042
40C AVG
0,0041
60C AVG
0,0040
80C
0,0039
0,0038
0
100
200
300
400
Vapplied [V]
Figure 3-20 Tangents delta measurement for a sample stressed for 22 hours with a 2.22kV AC waveform with 5kHz
transients superimposed
38
2.22kV + 10kHz transients
0,0047
0,0046
Tangents delta
0,0045
0,0044
0,0043
40C
0,0042
60C
0,0041
80C
0,0040
0,0039
0,0038
0
50
100
150
200
250
300
350
400
Vapplied [V]
Figure 3-21 Tangents delta measurement for a sample stressed for 22 hours with a 2.22kV AC waveform with 10kHz
transients superimposed
At 1kHz, 5kHz and 10kHz, the lowest values for tangents delta is measured at 80˚C and the highest
values for tangents delta is measured at 40˚C.
Results of varying transient frequencies for tangents delta
The effect of the frequency of the superimposed transients is investigated by comparing the
measurement results for every temperature. The results for the 40˚C measurements can be found in
Figure 3-22. The lowest value for tangents delta is measured when stressing with an AC waveform
only. The highest value for tangents delta is measured at 10kHz. The abbreviation ‘AVG’ in the graph
means that the shown graphs indicate the average of two measurements. After all measurements
were performed, it was decided to add extra measurements in order to confirm the course of the
graphs.
All 40˚C measurements
0,0048
0,0046
Tangents delta
0,0044
0,0042
0,0040
AC only AVG
0,0038
1kHz
0,0036
5kHz AVG
0,0034
10kHz
0,0032
0,0030
0
50
100
150
200
250
Vapplied [V]
39
300
350
400
Figure 3-22 All results from the measurements performed at 40˚C. It can be seen that the highest values for tangents
delta occur when the samples is stressed for 22 hours at 1kHz and 10kHz
The results for the 60˚C measurements are shown in Figure 3-23. The lowest losses occur when the
sample is stressed with an AC waveform only. The highest losses occur at 1kHz and 10kHz.
All 60°C measurements
0,0048
0,0046
Tangents delta
0,0044
0,0042
0,0040
AC only AVG
0,0038
1kHz
0,0036
5kHz AVG
0,0034
10kHz
0,0032
0,0030
0
50
100
150
200
250
300
350
400
Vapplied [V]
Figure 3-23 All results from the measurements performed at 60˚C. The highest value for tangents delta occurs at 1kHz
and 10kHz
Finally, the results for the 80˚C measurements are shown in Figure 3-24. The lowest losses are found
for the paper stressed with an AC waveform only. For the samples stressed with transients, it holds
that the higher the frequency, the higher the measured value for tangents delta.
40
All 80˚C measurements
0,0048
Tangents delta
0,0046
0,0044
0,0042
AC only AVG
0,0040
1kHz
5kHz
0,0038
10kHz
0,0036
0,0034
0
50
100
150
200
250
300
350
400
Vapplied [V]
Figure 3-24 All results from the measurements performed at 80˚C. The higher the frequency of the transients, the higher
the tangents delta
3.3.8 Analysis
The measured parameters can be compared by summarizing all results in a graph, as done in Figure
3-25. The average value for tangents delta is calculated over the applied voltage range from 50-350V.
When this is plotted, it can be seen that over the entire temperature range the highest losses occur
at 10kHz. The lowest losses occur when stressed with an AC waveform only. It is observed from the
40°C and 60°C graphs that the 5kHz measurement shows deviation from the hypothesis as its
trajectory was expected to lie between the 1kHz and 10kHz measurement.
Temperature vs. tangents delta
0,0047
0,0046
Tangents delta
0,0045
0,0044
0,0043
AC only
0,0042
1kHz
0,0041
5kHz
0,0040
10kHz
0,0039
0,0038
40
50
60
70
80
Temperature [°C]
Figure 3-25 Comparison of tangents delta values over the temperature range for differently stressed samples
41
The accuracy of the used equipment can be regarded high as it is
for tangents
delta [35]. Measurement errors can be caused by exposure to oxygen and moisture when the
operator keeps the sample in open air. This time was minimized during the expiring by putting the
cup glass with the oil sample next to the measurement device. This could have been a cause of
deviation for performed measurements at 5kHz as the error caused by moisture will be high relative
to the aforementioned accuracy. Another reason for error could be differences in the structure of the
samples, as this is an non-homogeneous organic material.
3.3.9 Summary
Firstly, the effect of temperature on the tangents delta was investigated. Samples were stressed for
22 hours with a 2.22kV waveform and with 1kHz, 5kHz and 10kHz transients. The lowest value for
tangents delta can then be observed at 80˚C for the AC only, 1kHz and 10kHz measurement. For the
AC waveform, the highest value for tangents delta can be observed at 60˚C. The overall highest value
for tangents delta is at 40˚C for the 1kHz and 10kHz measurement. The 5kHz measurement deviates
from this and at 60˚C and 40˚C the highest and lowest values for tangents delta are found.
The effect of frequency on the tangents delta is assessed when the results are compared at a single
temperature. At 40˚C, the lowest value for tangents delta is measured at AC only and at 5kHz. The
highest value can be found at 10kHz. At 60˚C, the lowest losses occur when the sample is stressed
with an AC waveform only. The highest tangents delta is measured at 5kHz and 10kHz. For 80˚C, the
lowest losses are found for the sample stressed with AC waveform only. For the samples stressed
with the superimposed transients, it holds that the higher the applied frequency, the higher the
measured value for tangents delta.
42
3.4 Conclusions
The first set of experiments was performed to measure the breakdown voltage of transformer
insulation. The breakdown voltage for one sheet of paper increases 11V per degree in the trajectory
from room temperature to 60°C. A temperature increase to 80°C makes the breakdown voltage
decrease again.
The second set of experiments is a time to breakdown experiment. Samples were stressed at 40˚C,
60˚C and 80 ˚C with a 2.91kV AC waveform. Breakdown times of 48.4, 82.1 and 147 hours were
calculated as failure times for 63.2% of the samples.
The final experiment is a tangents delta test. Samples are stressed for 22 hours with AC waveforms
and waveforms with 1kV 1kHz, 5kHz and 10kHz DC spikes (referred to as transients) superimposed.
The highest value for tangents delta can then be found for stressing with 10kHz transients. The
tangents delta is lower at 1kHz and for stressing with an AC waveform only. The results at 5kHz
deviate and it can be seen that this value are located between the results of AC stressing and 1khz
transients.
When the results are summarized, it is observed that when temperature is increased:




The AC breakdown voltage increases in the interval 16.6˚C to 60˚C and then decreases in the
interval 60˚C to 80˚C
The time to breakdown increases in the interval 40˚C to 80˚C
The tangents delta increases in the interval 40˚C to 60°C and then decreases in the interval
60˚C-80˚C when samples are stressed with an AC waveform
The tangents delta decreases in the interval 40˚C to 80˚C when a sample is stressed with
transients
An interpretation of these results can be found in the next chapter.
43
44
4 Results interpretation and modeling
In section 4.1 an interpretation of the measurement results will be made. A model and its
parameters will be derived in section 4.2. With this model, some transformer loading scenarios are
evaluated and an asset strategy will be proposed.
4.1 Interpretation of measurement results
4.1.1 AC breakdown tests
In the results of the AC breakdown tests, it can be observed that the breakdown voltage increases up
to 60˚C and then decreases up to 80˚C. A minor increase is then observed at 90˚C. Three reasons for
this behavior can be found.
1. Decreasing viscosity is dominant up to 60˚C, the intended operating temperature of the oil
[20]
2. Increasing conductivity starts to dominate around 80˚C
3. The deviation at 90˚C can be caused by the non-uniform heating of the deep-fryer
4.1.2 Time to breakdown tests
In the time to breakdown tests an increase in lifetime can be observed when the temperature was
increased from 40°C to 80°C. Multiple causes for this behavior can be distinguished.
1. Decreasing viscosity of the oil (Table 2-1)
2. Increasing solubility of the oil (Table 2-1)
3. Less moisture in the paper causing an increasing breakdown strength (Figure 2-10)
It should be noted that the value for in the Weibull distribution is decreasing with increasing
temperature. This means that the expected failure times are spread out over a larger time interval.
This is an explanation for the increasing scatter at the 80˚C measurement of the AC breakdown test.
4.1.3 Tangents delta tests
When the sample is stressed for 22 hours with a 2.22kV AC waveform, the lowest value for tangents
delta is found at 80˚C. The tangents delta is the highest at 60˚C. When 1kHz, 5kHz and 10kHz
transients are superimposed on the AC waveform, it can be observed that the tangents delta
decreases with increasing temperature. Several explanations for this temperature dependent
behavior were found.


Low relative humidity at 80˚C due to increasing solubility of oil (Figure 2-7)
Decreasing moisture content of the paper, hence increasing dielectric properties (Figure 2-9)
The stressing period consumes different amounts of lifetime for each temperature. When using the
expected 63.2% failure times, it can be calculated which amount of lifetime are consumed for the
40°C, 60°C and 80°C measurements. Therefore, the increase in tangents delta compared to the
tangents delta value for a new sample is smaller when it is stressed at high temperatures.
Deviations in the trend, for example the low value for tangents delta at 60°C 5kHz, can be caused by
the difference in sample structure. Transformer paper is, after all, an organic material with a nonhomogenous structure.
45
When a sample is stressed with a 2.22kV AC waveform with transients superimposed, at 80 ˚C the
lowest value for tangents delta is found at the lowest frequency, 1kHz. When the frequency is
increased to 5kHz and 10kHz, the tangents delta increases. Reasons for this behavior at increasing
temperature are listed below.


Lower viscosity of the oil allows fibers to vibrate at transient frequency
Increasing ability of the fibers to vibrate causes faster ageing
At 40˚C and 60˚C, the experiments performed with 5kHz show lower tangents delta values than 1kHz.
This is probably the result of differences in the structure of the paper samples and is not expected to
have a fundamental cause. The ongoing research of T. Koltunowicz shows that for stressing with
transients at room temperature, it very likely holds that
.
4.2 The ageing model
4.2.1 The general form of the model
The model should represent the effect of temperature and transients. Therefore, formulas are used
and designed to quantify their effect on the ageing of the insulation. The measurement results are
used to show what an appropriate asset management strategy would be when using this type of
paper and oil. These measurement results incorporate lab results for the insulation and asset specific
parameters such as transformer history. Eventually, the lab results can be compared with
measurement results from transformers in the field. These field measurements are then used for an
ageing model resulting in an appropriate asset management strategy. Figure 4-1 shows the relation
between the model, measurement data and an asset strategy. It should be noted that different
parameters for the insulation can be inputted to increase accuracy of the model for other types of oil
and insulation.
Measurement
data
Asset
management
strategy
Model
parameters
Figure 4-1 An asset strategy can be made when measurement data is combined with an ageing model
4.2.2 Model parameters
The IEEE standard C57.91-1995 ‘Guide for Loading Mineral-Oil-Immersed Transformers’, mentioned
as research goal in section 1.3.2, is the basis for the model. Eventually, the transient behavior of the
transformer insulation should be added to the model.
The aforementioned standard mentions three important ageing factors.



Temperature
Moisture content
Oxygen content
46
With modern techniques, deterioration of the insulation due to moisture and oxygen can be
minimized. Therefore, the temperature is the most important parameter for calculating the useful
life of transformer insulation [36].
The standard describes that transformers, depending on their exact specification, can withstand a
55°C or a 65°C average winding temperature rise. This temperature can be added to the ambient
temperature. Often, an ambient temperature of 30°C is assumed and the rated nameplate
temperature is 85°C up to 95°C. Reasons for not increasing the temperature any further are, for
example, the loss of oil due to its expansion (at 105°C) or failure of the insulation due to expansion of
the conductors.
According to the experimental evidence in the standard, the speed of deterioration of transformer
insulation follows the rules of the Arrhenius reaction rate theory.
(
)
(4.1)
Per unit life is a measure that indicates how much longer a transformer operates compared to the
rated temperature. In Equation 4.1, A and B are constants and is the winding hottest local
temperature in degrees Celsius. The standard proposes
and
for
transformers with a designed temperature of 95°C [36]. Two main types of transformer paper can be
distinguished: thermally upgraded (110˚C [10]) and non-thermally upgraded (98˚C [10] or 95˚C [36]) .
The paper samples used in the experiments of this research is of the non-thermally upgraded type.
The aforementioned maximum specification of a transformer is in the range of 85°C – 95°C. For nonthermally upgraded paper is rated at 95°C, a maximum rated transformer temperature of 95°C is
used in the model.
Due to a temperature rise, the transformer ageing increases (or accelerates). The accelerated ageing
can be calculated using the formula:
(
)
(4.2)
When
= 95°C, a hot spot temperature of 95°C will result in a
equal to 1. This means that
the insulation will not age any faster than rated. When, at a lower temperature,
equals 0.5, this
means that it ages half as fast as it would be at the rated temperature of 95°C.
When the accelerated ageing due to higher temperatures is known, the equivalent life that would
have been consumed at the reference temperature can be calculated. One hour of operating at the
rated temperature of 95°C will consume 1 hour of the rated normal lifetime. One hour of operating
at the temperature where
=0.5, will consume only half an hour of the normal lifetime. This can be
used to calculate the percentage loss of life a certain loading costs.
∑
(4.3)
∑
(4.4)
47
where the normal insulation life can be chosen based on the criteria the asset manager wishes to
hold. When a 25% retained tensile strength is used, the normal insulation life is 135.000 hours. A
normal insulation life of 180.000 hours can be found when the criterion from C57.91-1981 for the
functional life is used. This is about 20.5 years and this is considered a realistic value to use in the
model.
4.2.3
Measurement data
Which properties should be taken into account for the model?
The measured quantities can be taken into account for the model. It is summarized which relevant
information is contained in the performed measurements.
Breakdown tests
 Instantaneous breakdown voltage level
The breakdown voltage is the start of the lifeline in Figure 3-2. It can be used as a measure
for ageing although the extrapolation is very sensitive for errors in the measured value. A 5%
measurement error at 5 minutes would cause a significant error when extrapolated to 30
years using the log-scale.
 Temperature effect measured
The effect of temperature on the breakdown voltage has been measured.
Time to breakdown test
 Ageing effects
The time to breakdown is a parameter advanced in time on the lifeline in Figure 3-2. This
means that, because the time the experiments took is larger, the measurement is performed
on a point of time which lies to the right compared with the AC breakdown tests. The results
of the time to breakdown tests can be extrapolated as a measure for long term behavior of
the insulation. This can be performed more accurately than with the breakdown voltage tests
data as the test took about 40-160 hours.
 Temperature effect measured
The temperature behavior of the time to breakdown has been measured.
Tangents delta test
 Quality measure
The tangents delta measurement is used by transformer manufacturers as a quality measure
(Table 2-3).
 Ageing effects
The ageing effects are incorporated as the measurement contains a 22 hour ageing period.
 Transient effect measured
The samples have been stressed with different waveforms containing transient frequencies.
 Temperature effect measured
The temperature has been changed for each type of waveform
48
4.2.4
Processed data
Lifeline
A lifeline is a line in a graph that plots the applied voltage level or applied field strength versus time
to quantify an ageing effect. The time a high voltage component can withstand an applied voltage
level decreases when the voltage level is increased [16].
To construct a lifeline like the one shown in Figure 3-2, the data from the AC breakdown tests and
the time to breakdown tests are most appropriate to use. As elaborated in the previous section, both
these tests contain information about voltage levels and time (i.e. ageing). The voltage from the AC
breakdown tests at which 63.2% of the samples break down is used to calculate the field strength at
the start of the lifeline. The total time the experiment took is used as time value. The applied field
strength during the time to breakdown tests is calculated and the Weibull parameter η for 63.2%
expected failures is used to calculate the lifetime. When the data from both test series is combined,
Figure 4-2 can be made. The crosses indicate the previously mentioned data points and the plotted
lines are the lifelines fitted through these data points.
80
40C
60C
70
80C
Applied field [kV/mm]
60
50
40
30
25
-2
10
0
10
2
4
10
10
6
10
Time [h]
Figure 4-2 The lifeline of the investigated transformer paper. A lifeline is fitted through the η-values of the breakdown
and time to breakdown tests. It can be seen that a transformer will have the longest lifetime at 80˚C when the same field
strenght is applied
An improvement in time to breakdown at 80˚C is concluded in section 4.1.2. This can be misleading
as it could easily be concluded that, in the practice, unlimited heating up of a transformer improves
lifetime. However, this is not a correct explanation. The actual cause of the elevated temperatures in
a transformer is an increasing loading of the transformer. An increased loading means that more
power is delivered by this transformer and this is responsible for higher applied field strengths. For
49
Figure 4-2 this would mean that when comparing lifetimes for e.g. the applied field at 40°C, the value
at 80°C can be located at the left and not at the right due to the increased field strength.
Arrhenius reaction rate
When the lifeline of 80°C is taken as a reference temperature, Equation 4.2 can be used. By stating
that
= 80°C, the accelerated ageing factor ( ) equals 1 for a 80°C hot spot temperature;
(
)
. In case it would have been assumed that
= 95˚C,
(
) would have been
(
)
equal to 1. If
= 95˚C is assumed,
(
)
but the ratio between
(
)
and
(
) would be the same. But by using
= 80°C, the accelerated ageing values are
already reweighted to live up to
(
) = 1. This is necessary as the ageing at 40˚C and 60˚C will
be compared to the data from the 80˚C measurements. A benchmark value of 15.000 [36] for is
chosen resulting in Equation 4.5.
(
(4.5)
)
The values for the accelerated ageing rate of the insulation are calculated in the second column of
Table 4-1. The lifetime is calculated in the third column by multiplying
with the normal
insulation life as explained in section 4.2.1.
Table 4-1 Accelerated ageing rate and expected lifetime for different temperatures for insulation when 80°C is taken as a
reference
Hot spot temperature θh
40°C
60°C
80°C
Accelerated ageing rate FAA
0.0044
0.0779
1.00
Expected insulation lifetime [yr]
4687
263.6
20.53
The per unit load corresponding to these temperatures cannot be determined straightforward. It
depends on the transformer dynamics. The time constant (i.e. how fast a transformer heats up or
cools down) depends on for example the quantity of oil, the weight of the transformer (core,
winding), geometry of the windings and ambient temperature.
In Appendix E, values from literature are compared and average per unit loading values are
calculated. With these values, the applied field strengths and the expected lifetimes at different
temperatures are calculated, as shown in Table 4-2. These values will be used as ‘normal insulation
life’ in Equation 4.4. The fourth column shows the new accelerated ageing factors which are based on
the measurement data.
Table 4-2 The expected lifetimes according to the Arrhenius rate of insulation degradation from Table 4-1 can be
compared with the lifetimes based on the measurement. It can be seen that when the properties of the oil are taken into
account, the expected lifetime decreases. The equivalent ageing factors change as well
Temperature
40°C
60°C
80°C
Applied field strength
[kV/mm]
25.3
35.1
42.9
Measurement data
expected lifetime [yr]
1494
90.65
20.53
Equivalent ageing
factor FAA
0,01374
0,2265
1,000
Finally, the effect of transients is incorporated. For two reasons the 1kHz, 5kHz and 10kHz transients
50
are combined to a variable called ‘transient mix’. The first reason is to increase the number of data
points to increase reliability as no clear distinction can be made between the individual frequencies
with the current number of samples. The second reason is that when operating in the grid, a
transformer will not encounter DC spikes at one individual frequency and it will always be a mix of
different frequencies.
Temperature vs. tan delta
0,0045
Tangents delta
0,0044
0,0043
0,0042
0,0041
AC only
0,0040
Transient mix
0,0039
0,0038
40
50
60
70
80
Temperature [°C]
Figure 4-3 A comparison between stressing with AC and stressing with AC with a transient mix superimposed. It can be
seen that for every temperature, the tangents delta increases when transients are applied
A new and non-aged sample has a tangents delta of 0.0287 when the average in the trajectory from
100-300V in Figure D-3 is calculated. In Table 4-3 the increase in tangents delta is calculated. For
clarity the percentage of lifetime consumed while stressing for 22 hours at 2.22kV i.e. 37kV/mm
applied field is displayed in the final column.
Table 4-3 An increase in tangents delta compared with a new sample can be observed. The third column shows how
much lifetime is consumed during the 22 hours stressing period
Temperature
40˚C
60˚C
80˚C
Increase in tangents delta
9.88%
3.35%
6.00%
Lifetime consumed
0.213 %
0.0123 %
2.63 106 %
It is not straightforward to quantify the accelerated ageing due to increase in tangents delta. What
can be assessed from this information is that the resistive component of the leakage current
increases. This increase in leakage current takes place with the same applied field as would have
been applied at new insulation. The leakage current increases the losses in the transformer. This
does not mean that an increase in tangents delta will directly result in a large increase in generated
heat in a transformer. In the model from the 28MVA example transformer from [36], the insulation
losses are not even taken into account. The magnitude or absolute value of the leakage current can
still be regarded as small i.e. not generating a large amount of heat.
However, increases in tangents delta over time are regarded as a sign of deterioration of the
insulation condition [23]. Therefore lifetime is expected to decrease when an increase in tangents
delta is observed. The critical value for the tangents delta, the end of life, as well as the exact
51
trajectory it undertakes is unknown.
In Table 4-3, a lower value for tangents delta at 60˚C and 80˚C can be observed. This should be
regarded as a result of the fact that 22 hours of stressing at these temperatures consumes less
lifetime compared to stressing for 22 hours at 40˚C. The percentages of consumed lifetime drops
faster than the tangents delta value decreases (a factor 105 increase for lifetime vs. a 1.6 times
decrease for the tangents delta). Therefore the relative influence of transients at high temperatures
can be considered large.
For the aforementioned reasons (to increase the number of samples and to model a mix of
transients), an increase in ageing of 6.4% i.e. the average observed increase in tangents delta, is
assumed at all temperatures. The 6.4% increase will be used in the next section for calculations
incorporating the increased applied field strengths from Table 4-2 (modeling an increase in ageing at
80˚C compared with for example 60˚C). The increased accelerated ageing due to transients at higher
temperatures is accounted for this way.
4.2.5 Asset strategy
Scenario 1: A normal loading day
To design an asset strategy, calculations for ageing are made based on two scenarios. The first
scenario is based on a ‘normal’ day as defined in Figure 3-1. Standard [36] states that for the maxima
and minima in the hot spot temperature, the average can be used. Therefore, the continuous
temperature fluctuations from Figure 3-1 are converted into discrete temperature steps as shown in
Figure 4-4.
90
Temperature *˚C+
80
70
60
50
40
30
20
10
0
0:00
4:00
8:00
12:00
16:00
20:00
0:00
Time [h]
Figure 4-4 Daily load cycle on a normal day. The graph shows discrete temperature fluctuations and is based on the
average values from a load cycle according to [27]
Now a similar ageing calculation as shown on page 103 of the [36] can be made. In Table 4-4, a
calculation is made of the equivalent ageing (Equation 4.3) of one day loading according to Figure
4-4.
52
Table 4-4 Calculation of equivalent ageing for a normal day. The equivalent ageing factor is calculated according to
formula 4.3 using the values from Table E-2. The columns FAA and Ageing are equal, but this is not the case if the ageing
calculation would be based on time slots of for example 30 minutes
Time
0:00
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
Hot spot
temp. *˚C+
40
60
80
80
60
60
80
80
60
60
60
60
80
80
80
60
60
60
60
40
40
40
40
40
Load [p.u.]
FAA
Ageing [h]
0,59
0,82
1,00
1,00
0,82
0,82
1,00
1,00
0,82
0,82
0,82
0,82
1,00
1,00
1,00
0,82
0,82
0,82
0,82
0,59
0,59
0,59
0,59
0,59
0,01374
0,2265
1,000
1,000
0,2265
0,2265
1,000
1,000
0,2265
0,2265
0,2265
0,2265
1,000
1,000
1,000
0,2265
0,2265
0,2265
0,2265
0,01374
0,01374
0,01374
0,01374
0,01374
0,01374
0,2265
1,000
1,000
0,2265
0,2265
1,000
1,000
0,2265
0,2265
0,2265
0,2265
1,000
1,000
1,000
0,2265
0,2265
0,2265
0,2265
0,01374
0,01374
0,01374
0,01374
0,01374
Cumulative
age [h]
0,01374
0,24024
1,24024
2,24024
2,46674
2,69324
3,69324
4,69324
4,91974
5,14624
5,37274
5,59924
6,59924
7,59924
8,59924
8,82574
9,05224
9,27874
9,50524
9,51898
9,53272
9,54646
9,56020
9,57394
The equivalent loss of lifetime according to formula 4.4 is 0.00532%.
Scenario 2: A day with abundant wind energy
The second scenario contains a day including full transport of wind energy, which is shown in Figure
4-5. As explained in the introduction, renewable energy generation can be associated with increasing
transport and transients. Therefore a scenario is designed in which the loading of the transformer is
maximized to 1 per unit from 6.00-19.00 hour and transients are assumed to be present in this
period.
53
90
80
Temperature *˚C+
70
60
50
40
30
20
10
0
0:00
4:00
8:00
12:00
16:00
20:00
0:00
Time [h]
Figure 4-5 Daily load cycle on a windy day. From 6.00-19.00 hours the transformer is operated at 80˚C and transients are
assumed to be present during this period
Table 4-5 Ageing calculations for a windy day. It can be seen that transients are added to the accelerated ageing factor
FAA from 6.00-19.00 hours.
Time
0:00
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
Hot spot
temp. *˚C+
40
60
80
80
60
60
80
80
80
80
80
80
80
80
80
80
80
80
80
60
40
40
40
40
40
Load
[p.u.]
0,59
0,82
1,00
1,00
0,82
0,82
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
0,82
0,59
0,59
0,59
0,59
0,59
FAA
Ageing [h]
0,01374
0,2265
1,000
1,000
0,2265
0,2265
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
0,2265
0,01374
0,01374
0,01374
0,01374
0,01374
0,01374
0,2265
1,000
1,000
0,2265
0,2265
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
1,064
0,2265
0,01374
0,01374
0,01374
0,01374
0,01374
54
Cumulative age
[h]
0,01374
0,24024
1,24024
2,24024
2,46674
2,69324
3,75724
4,82124
5,88524
6,94924
8,01324
9,07724
10,14124
11,20524
12,26924
13,33324
14,39724
15,46124
16,52524
16,75174
16,76548
16,77922
16,79296
16,8067
16,82044
The equivalent loss of lifetime according to Equation 4.4 has now almost doubled to 0.00934%
compared with the 0.00532 from scenario 1. Meanwhile, the per unit loading only increased from
0.806 p.u. to 0.873 p.u. i.e. an increase of only 9.8%.
In case the aforementioned calculations are made with an aged transformer, the loss of lifetime has
to be added to the loss of lifetime caused by its history. In the practice, the transformer can be
loaded above nameplate rating. This has neither been done in scenario 1 nor scenario 2 as no
measurement data was available for these calculations. When a closer look is taken at Equation 4.5,
it can be understood that the equivalent ageing factor excluding transients will be larger than 1
(which in practice means accelerated ageing compared to the rated nameplate temperature). This
will increase the speed of ageing and repetitive overloading will drop transformer lifetime below its
rated lifetime, especially when transients are added as well.
55
56
5 Conclusion
5.1 Conclusions
Literature study
 The dielectric properties of transformer paper insulation are mainly determined by
environmental ageing factors.
 Ageing of transformer insulation is determined by temperature, moisture and oxidation.
Measurements
 The breakdown voltage of the transformer paper increases from 3.11kV to 3.59kV (11V/˚C)
when the temperature is increased from 16.6˚C to 60˚C. In the range from 60˚C to 80˚C, the
breakdown voltage decreases from 3.59kV to 3.12kV (23.5V/˚C) when temperature is
increased.
 The time to breakdown at 2.91kV when 63.2% of the samples fail increases with increasing
temperature. The time to breakdown increases from 48.4 to 82.1 and 147 hours when
temperature is increased from 40˚C to 60˚C and 80˚C, respectively.
 When transient spikes of 1kV superimposed on a 2.22kV AC waveform are applied in the
range from 1kHz up to 10kHz, the tangents delta increases. The average increase in tangents
delta is 6.4% compared with stressing with 2.22kV AC only.
Model consequences
 When modeling transformer ageing, temperature is the most important factor. The ageing
of the insulation will be accelerated when temperature is increased.
 An ageing model can be used to calculate the accelerated ageing factors of the insulation.
With these factors, the rate of ageing at a certain temperature can be expressed in terms of
the ageing at rated temperature.
 To incorporate the interaction between oil and paper correctly, measurement data should be
used to calculate the loss of life due to daily loading cycles. Using measurement data from
lab experiments and data from the field under operating conditions increases the accuracy of
the calculation. Performing calculations on different daily loading cycles increases the asset
managers insight in transformer ageing.
 When renewable energy sources increase transport and introduce transients in the grid,
ageing of transformers is accelerated.
5.2 Recommendations
To increase accuracy
 A measurement setup could be built where the moisture is continuously filtered out of the
oil. This effect of a high relative humidity at low temperatures will then be offset.
 To further investigate the effect of the magnitude and frequency of transient spikes and to
increase accuracy, a moisture free experiment should be performed with the tangents delta
measurement device in a moisture and oxygen free room.
57
For further research
 An alternative and perhaps more realistic measurement method could be used to design a
sensor that measures online tangents delta and to build it in a real-life transformer.
 The dependency between tangents delta and the applied measurement voltage can be
further investigated. However, measures should be taken to protect the sensitive
measurement equipment against breakdown.
58
Appendix A: Raw measurement data
Initial results AC breakdown tests
The initial results of the AC breakdown tests are shown in Table A-1. The outliers, i.e. the most offaverage data points, are removed in Table A-2.
Table A-1 Raw measurement data of the initial AC breakdown tests
Date
In oven?
T *˚C+
Sample
1
2
3
4
5
6
7
8
[kV]
Average
Pos. error
Neg. error
Max. error
from avg
1
2
3
4
5
6
7
8
11-12011
16.6˚C
55,2
46,0
54,0
49,4
57,3
55,9
53,3
59,4
18-12011
4 days
45.3
16.6˚C
61,5
52,1
54,0
51,8
52,2
53,0
53,1
54,1
25-12011
24h
65.4
16.6˚C
45,1
64,4
55,1
52,2
56,5
57,2
53,0
59,2
26-12011
48h
65.4
16.7˚C
57,7
53,0
56,2
53,8
63,0
66,9
63,1
55,3
dec10
40˚C
44,1
52,4
47,1
50,1
45,3
11-12011
40˚C
48,8
57,4
46,1
55,4
55,4
53,2
55,4
50,8
dec10
50˚C
39,8
43,2
41,5
56,0
46,0
dec10
60˚C
51,3
54,9
51,6
48,2
55,8
dec10
80˚C
49,1
53,8
58,1
56,0
55,9
17-12011
3 days
45.3
80˚C
53,3
57,3
55,8
56,8
47,5
59,2
58,5
64,0
3,19
2,66
3,12
2,85
3,31
3,23
3,08
3,43
3,11
0,32
0,45
0,45
3,55
3,01
3,12
2,99
3,01
3,06
3,07
3,12
3,12
0,43
0,13
0,43
2,60
3,72
3,18
3,01
3,26
3,30
3,06
3,42
3,19
0,52
0,59
0,59
3,33
3,06
3,24
3,11
3,64
3,86
3,64
3,19
3,38
0,48
0,32
0,48
2,55
3,03
2,72
2,89
2,62
2,82
3,31
2,66
3,20
3,20
3,07
3,20
2,93
3,05
0,26
0,39
0,39
2,30
2,49
2,40
3,23
2,66
2,96
3,17
2,98
2,78
3,22
2,83
3,11
3,35
3,23
3,23
2,62
0,62
0,32
0,62
3,02
0,20
0,24
0,24
3,15
0,20
0,32
0,32
3,08
3,31
3,22
3,28
2,74
3,42
3,38
3,70
3,26
0,43
0,52
0,52
59
2,76
0,27
0,21
0,27
Table A-2 Corrected data of the initial AC breakdown tests
Date
In oven?
T *˚C+
Sample
[kV]
Average
Pos. error
Neg. error
Max. error
from avg
1
2
3
4
5
6
7
8
11-12011
16.6˚C
3,19
3,12
2,85
3,31
3,23
3,08
3,13
0,18
0,28
0,28
18-12011
4 days
45.3
16.6˚C
3,01
3,12
2,99
3,01
3,06
3,07
3,12
3,05
0,07
0,06
0,07
25-12011
24h
65.4
16.6˚C
3,18
3,01
3,26
3,30
3,06
3,42
3,21
0,21
0,19
0,21
26-12011
48h
65.4
16.7˚C
3,33
3,24
3,11
3,64
3,64
3,19
3,36
0,28
0,25
0,28
60
dec10
40˚C
2,55
2,72
2,89
2,62
2,69
0,20
0,15
0,20
11-12011
40˚C
2,82
3,20
3,20
3,07
3,20
2,93
3,07
0,13
0,25
0,25
dec10
50˚C
2,30
2,49
2,40
dec10
60˚C
2,96
3,17
2,98
2,66
3,22
dec10
80˚C
3,11
3,35
3,23
3,23
17-12011
3 days
45.3
80˚C
3,08
3,31
3,22
3,28
3,42
3,38
2,46
0,19
0,16
0,19
3,08
0,14
0,12
0,14
3,23
0,12
0,12
0,12
3,28
0,14
0,20
0,20
Final results AC breakdown test
The final results of the AC breakdown tests are shown in Table A-3. When the outliers are removed,
Table A-4 can be made.
Table A-3 Raw measurement data of the final AC breakdown tests
Date
Sample
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
Average
Pos. error
Neg. error
Max. error
from avg
11-12011
16.6˚C
55,2
46,0
54,0
49,4
57,3
55,9
53,3
59,4
31-12011
40˚C
62,9
64,1
58,4
55,0
55,0
56,9
64,2
56,4
31-12011
50˚C
52,1
67,1
56,9
57,4
64,7
64,9
58,2
62,5
1-22011
60˚C
65,3
65,7
57,1
60,0
64,7
64,2
63,1
57,3
3-22011
70˚C
52,4
65,0
61,6
56,9
55,0
55,6
49,8
55,1
1-22011
80˚C
57,9
57,9
55,9
40,0
56,9
45,0
54,1
57
80˚C
54
61,0
58,3
57,1
57,1
40
56,4
55,1
80˚C
54,4
3,19
2,66
3,12
2,85
3,31
3,23
3,08
3,43
3,11
0,32
0,45
0,45
3,63
3,70
3,37
3,18
3,18
3,29
3,71
3,26
3,41
0,29
0,24
0,29
3,01
3,87
3,29
3,31
3,74
3,75
3,36
3,61
3,49
0,38
0,48
0,48
3,77
3,79
3,30
3,46
3,74
3,71
3,64
3,31
3,59
0,20
0,29
0,29
3,03
3,75
3,56
3,29
3,18
3,21
2,88
3,18
3,26
0,50
0,38
0,50
3,34
3,34
3,23
2,31
3,29
2,60
3,12
3,29
3,12
3,52
3,37
3,30
3,30
2,31
3,26
3,18
3,14
61
3,12
0,40
0,81
0,81
3-22011
90˚C
51,1
58,2
65,0
61,1
57,1
57,1
63,3
58,9
2,95
3,36
3,75
3,53
3,30
3,30
3,65
3,40
3,40
0,35
0,45
0,45
Table A-4 Corrected data of the final AC breakdown tests
Date
Sample
1
2
3
4
5
6
7
8
Average
Pos. error
Neg. Error
Max. error
from avg
11-12011
16.6˚C
3,19
3,12
2,85
3,31
3,23
3,08
3,11
0,20
0,26
0,26
31-12011
40˚C
3,63
3,70
3,37
3,18
3,18
3,29
3,71
3,26
3,41
0,29
0,24
0,29
31-12011
50˚C
3,29
3,31
3,74
3,75
3,36
3,61
3,51
0,24
0,22
0,24
1-22011
60˚C
3,77
3,79
3,30
3,46
3,74
3,71
3,64
3,31
3,59
0,20
0,29
0,29
62
3-22011
70˚C
3,03
3,56
3,29
3,18
3,21
3,18
3,24
0,32
0,21
0,32
1-22011
80˚C
80˚C
3,12
80˚C
3,14
3,34
3,23
3-22011
90˚C
3,36
3,29
3,30
3,30
3,12
3,29
3,26
3,18
3,23
0,11
0,11
0,11
3,53
3,30
3,30
3,65
3,40
3,42
0,23
0,13
0,23
Appendix B: Weibull plots
Analysis AC breakdown tests
This section contains the Weibull plots made with ReliaSoft Weibull++7, a program designed for
calculating and plotting Weibull distributions. For every temperature at which measurements have
been performed (16.6˚C, 40˚C, 50˚C, 60˚C, 70˚C, 80˚C and 90˚C), an individual fit is made. The graphs
associated with these fits can be found in Figure B-1 up to Figure B-12. For the 80˚C measurement,
shown in Figure B-9, the fit could be improved when removing three data points. This improved fit is
shown in Figure B-10.
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 16. 6C
99,000
Probability -Weibull
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
1,000
10,000
Breakdown voltage [kV]
               
Figure B-1 Weibull plot of the breakdown voltage at 16.6˚C
63
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 40C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
0,010
0,100
1,000
10,000
Breakdown voltage [kV]
                   
Figure B-2 The 3-parameter Weibull plot of the breakdown voltage at 40˚C
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 40C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
1,000
10,000
Breakdown voltage [kV]
               
Figure B-3 The 2-parameter Weibull plot of the breakdown voltage at 40˚C
64
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 50C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
0,100
1,000
10,000
Breakdown voltage [kV]
                   
Figure B-4 The 3-parameter Weibull plot of the breakdown voltage at 50˚C
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 50C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
1,000
10,000
Breakdown voltage [kV]
               
Figure B-5 The 2-parameter Weibull plot of the breakdown voltage at 50˚C
65
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 60C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
1,000
10,000
Breakdown voltage [kV]
               
Figure B-6 Weibull plot of the breakdown voltage at 60˚C
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 70C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
0,100
1,000
Breakdown voltage [kV]
                   
Figure B-7 The 3-parameter Weibull plot of the breakdown voltage at 70˚C
66
10,000
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 70C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
1,000
10,000
Breakdown voltage [kV]
               
Figure B-8 The 2-parameter Weibull plot of the breakdown voltage at 70°C
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 80C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
2,000
4,000
Breakdown voltage [kV]
               
Figure B-9 Weibull plot of the breakdown voltage at 80˚C (raw data)
67
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 80C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
2,000
4,000
Breakdown voltage [kV]
               
Figure B-10 Weibull plot of the breakdown voltage at 80˚C (after deleting datapoints)
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Breakdown voltage at 90C
99,000
90,000
U n r e lia b ilit y [-]
50,000
10,000
5,000
1,000
1,000
10,000
Breakdown Voltage [kV]
               
Figure B-11 Weibull plot of the breakdown voltage at 90˚C
68
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
1,000
Reliability
16.6\Data 1
Weibull-2P
RRX SRM MED FM
F=8/S=0
Reliability Line
0,800
R e lia b ilit y , R (t )= 1 -F (t )
40\Data 1
Weibull-3P
RRX SRM MED FM
F=8/S=0
Reliability Line
50\Data 1
Weibull-3P
RRX SRM MED FM
F=8/S=0
0,600
Reliability Line
60\Data 1
Weibull-2P
RRX SRM MED FM
F=8/S=0
Reliability Line
70\Data 1
Weibull-3P
RRX SRM MED FM
F=8/S=0
0,400
Reliability Line
80\Data 1
Weibull-2P
RRX SRM MED FM
F=14/S=0
0,200
Reliability Line
90\Data 1
Weibull-2P
RRX SRM MED FM
F=8/S=0
Reliability Line
0,000
2,500
2,900
3,300
3,700
4,100
4,500
Time, (t)
16.6\Data 1:                
40\Data 1:                    
50\Data 1:                    
60\Data 1:                
70\Data 1:                    
80\Data 1:                
90\Data 1:                
Figure B-12 Reliability plot of the breakdown voltages at different temperatures
As shown in Table B-1 for the 40˚C, 50˚C and 70˚C measurement the best fit, i.e. the highest value for
ρ, could be accomplished by using a 3-parameter Weibull distribution. This distribution can be used
for different purposes than the 2-parameter Weibull distribution. The location parameter γ, for
example, could be used to find the voltage corresponding to 0% failure. This is however not further
investigated and 63.2% failure times for the 2-parameter Weibull distributions (for 40˚C, 50˚C and
70˚C measurement) have been calculated as well. Table 3-5 shows the results when fitting with 2parameters Weibull distribution.
Table B-1 The 3-parameter Weibull distributions for 40˚C, 50˚C and 70˚C. Displayed as these values for ρ were higher
than the corresponding ρ’s at the 2-parameter Weibull distribution. This information is unused in the thesis but the
location parameter γ could be used to find the voltage corresponding to 0% failure
3-parameter
16.6°C
40°C
50°C
60°C
70°C
80°C
80°C*
90°C
0,7848
5,0044
0,2809
1,5773
3,1532
2,0404
0,9565
0,9794
1,7938
2,7269
2,7269
0,9791
69
Analysis time to breakdown tests
Weibull parameter calculations
The Weibull parameters are calculated differently when censored data is used. When only failure
data is used, the percentage of the population which fails before time t, can be expressed by ̂ ( ).
This would mean for the 40°C measurement (shown in Table 3-6) that the 4th data point indicates the
moment where all samples fail, hence ̂ ( )
.
Weibull data is plotted on a logarithmic scale, so for the data points on the horizontal axis, the
̂ ( )) is calculated as
column ( ) was calculated. For the vertical axis, the column
(
(
for the cumulative distribution function of a Weibull it holds that:
( )
( )
(B-1)
( )
(B-2)
Rearranging gives:
( )
( ))
(
(
( ))
(
(B-3)
( )
( )
( )
(B-4)
A line is fitted through the data points in these two columns. This line can be written as
( ).
where
and
When then
(
(
̂ ( ))
it holds that
( )
( ) . Now it is possible to
determine the point on the horizontal axis where η can be found. Once is known, β can be
calculated using the parameters of the aforementioned line as shown in Figure B-13 and Table B-2.
Table B-2 The ranks can be calculated for the failure data points
Rank 40°C
datapoints
1
18,07
2
39,74
3
42,12
4
44,54
̂( )
( )
0,25
0,50
0,75
1,00
2,8943
3,6824
3,7405
3,7964
(
̂ ( ))
(
-1,2459
-0,3665
0,3266
inf
70
0.5
0
log(-log(1-F(t)))
-0.5
-1
-1.5
-2
-2.5
-3
2
2.5
3
3.5
4
4.5
log(t)
Figure B-13 Weibull plot around the point log(-log(1-F(t))) = 0 so that the value for log(η) can be read off the horizontal
axis.
When using suspended data, a revised rank ( ) is calculated instead of using ̂ ( ). This rank can be
calculated by using the so called adjusted rank. The adjusted rank is calculated by:
(
)
Where N is the total number of data points, k and k’ are suspended components. Then rank j is
calculated for a component for which holds that
. The adjusted rank is calculated and
shown in column 5 of Table B-3.
( ) can then be calculated by using a commonly used median rank
The revised rank
approximation:
( )
Table B-3 Adjusting the ranks so that the suspended data points are taken into account
Rank 40°C
datapoints
1
18,07
2
25,12
3
39,74
4
42,12
5
44,54
6
44,74
State
F
S
F
F
F
S
( ) Adjusted rank
( )
(
(
̂ ( ))
2,8943
1,0000 0,1094
-2,15562
3,6824
3,7405
3,7964
2,2000 0,2969
3,4000 0,4844
4,6000 0,6719
-1,0435
-0,41192
0,108281
71
Using this algorithm, found in literature in [33], = 54,2 and = 0.503 are calculated as 2-parameter
Weibull distribution. This deviates from the parameters calculated with Weibull++ software as this
uses its own (optimized) median rank approximation.
Weibull plots
The Weibull fitting plots are shown in Figure B-14, Figure B-15 and Figure B-16. The blue line
indicates the fit when only failure data is used. When suspended data is used (black line), the fit
shifts down and the probability that 63.2% of the samples fail increases.
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Time to breakdown at 40C
99,000
U n r e lia b ilit y [-]
90,000
50,000
10,000
10,000
100,000
Time to breakdown [s]
40C \Data 1:    
40C +S\Data 1:    
Figure B-14 The blue line shows a Weibull fitted on the faillure data only. When the suspension data points are added,
the Weibull distribution shifts down and η, the probability that 63.2% of the samples fail, increases from 40.8 to 48.4
72
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Time to breakdown at 60C
99,000
U n r e lia b ilit y [-]
90,000
50,000
10,000
1,000
10,000
100,000
Time to breakdown [s]
60C \Data 1:    
60C +S\Data 1:    
Figure B-15 The blue line shows a Weibull fitted on the faillure data only. When the suspension data points are added,
the Weibull distribution shifts down and η, the probability that 63.2% of the samples fail, increases from 22.8 to 82.1
ReliaSoft Weibull++ 7 - www.ReliaSoft.com
Time to breakdown at 80C
99,000
U n r e lia b ilit y [-]
90,000
50,000
10,000
1,000
10,000
100,000
Time to breakdown [s]
80C \Data 1:    
80C +S\Data 1:    
Figure B-16 The blue line shows a Weibull fitted on the faillure data only. When the suspension data points are added,
the Weibull distribution shifts down and η, the probability that 63.2% of the samples fail, increases from 22.2 to 147
73
Extra measurements with transients
Some try-out experiments were performed where transients were added to the AC waveform. The
times to breakdown recorded are shown in Table B-4. First the experiment was performed with a
2.91kV AC waveform with 5kHz transients superimposed. Due to the very small breakdown times,
the voltage was decreased to 2.22kV. Here a lot of early breakdowns took place as well, but the
sample that survived, survived for a very long period of time. To eliminate that the temperature
makes the paper unstable, the experiment was repeated at ambient temperature with the 2.91kV
waveform. This also showed a large number of early breakdowns.
Table B-4 Results of the try-out experiment where an attempt was done to do ‘time to breakdown’ tests with transients
superimposed on the AC waveform
UAC
2.91kV
40˚C
Toil
Utransient 5kHz @700V
Sample Time
State
1 0,04
F
2 0,13
F
3 0,53
F
4 0,56
F
5
6
7
8
9
10
11
12
2.22kV
40˚C
5kHz @1kV
Time
0,04
0,13
0,53
0,56
0,17
0,97
24,48
24,48
0,52
0,73
169,67
169,67
State
F
F
F
F
F
F
S
S
F
F
S
S
2.91kV
18.6˚C, ambient
1kHz @1kV
Time
State
0,19
F
0,19
F
0,37
F
0,37
F
3,48
S
3,48
S
A conclusion was drawn that transients decrease the time to breakdown and increase the measured
differences in time. This is one of the reasons why the voltage of the AC waveform is lowered to
2.22kV in the forthcoming tangents delta measurements.
74
Analysis tangents delta tests
A detailed plot of the measured tangents delta at 2.22kV is shown in Figure B-17. The dashed lines
are the actual performed measurements and their average is indicated by the same colored solid
line. The raw measurements data is shown in Table B-5. When transients are superimposed on the
AC waveform during the 22 hours stressing period prior to measuring, Table B-6 can be made.
2.22kV AC waveform
0,0045
0,0044
40C AVG
Tangents delta
0,0043
40C (1)
0,0042
40C (2)
0,0041
60C AVG
0,0040
60C (1)
0,0039
60C (2)
0,0038
80C AVG
0,0037
80C (1)
0,0036
0
50
100
150
200
250
300
350
80C (2)
400
Vapplied
Figure B-17 Detailed plot of all measured tangents delta values when samples are stressed with a 2.22kV AC waveform.
The performed measurements and the average are plotted
Table B-5 Measurement data of the tangents delta measurements where a sample was stressed with an AC waveform of
2.22kV prior to testing
Temp.
40˚C
60˚C
Measurement 1
Applied
voltage
54
95
147
200
248
294
355
47
102
156
205
250
298
349
Tangents
delta
0,00401
0,00405
0,00419
0,00423
0,00424
0,00427
0,00431
0,00416
0,00420
0,00426
0,00430
0,00443
0,00443
0,00443
Measurement 2
Applied
voltage
54
109
147
202
243
296
349
47
100
146
200
245
296
350
75
Tangents
delta
0,00396
0,00402
0,00404
0,00408
0,00411
0,00414
0,00416
0,00389
0,00405
0,00413
0,00419
0,00421
0,00422
0,00422
Average
Applied
voltage
54
102
147
201
246
295
352
47
101
151
203
248
297
350
Tangents
delta
0,003985
0,004035
0,004115
0,004155
0,004175
0,004205
0,004235
0,004025
0,004125
0,004195
0,004245
0,00432
0,004325
0,004325
80˚C
47
102
150
199
251
292
348
0,00382
0,00383
0,00384
0,00387
0,00391
0,00391
0,00393
47
101
148
200
250
296
346
0,00410
0,00424
0,00430
0,00432
0,00432
0,00431
0,00429
47
101,5
149
199,5
250,5
294
347
0,00396
0,00404
0,00407
0,00410
0,00412
0,00411
0,00411
Table B-6 Measurement data of the tangents delta measurement where the samples have been stressed for 22 hours
with 1khz, 5kHz and 10kHz transients prior to testing
1kHz
Temp
40˚C
60˚C
80˚C
Applied
voltage
54
101
148
196
242
296
353
54
100
147
201
248
297
353
46
101
147
202
246
296
351
5kHz
Tangents
delta
0,00425
0,00430
0,00442
0,00449
0,00451
0,00452
0,00451
0,00409
0,00422
0,00431
0,00435
0,00436
0,00434
0,00431
0,00394
0,00405
0,00411
0,00416
0,00418
0,00419
0,00420
10kHz
Applied
voltage
45
101
148
201
250
301
348
48
100
151
198
249
304
351
54
101
147
202
249
303
348
76
Tangents
delta
0,00384
0,00390
0,00400
0,00405
0,00409
0,00412
0,00415
0,00396
0,00409
0,00418
0,00425
0,00433
0,00434
0,00435
0,00401
0,00405
0,00410
0,00419
0,00432
0,00433
0,00436
Applied
voltage
46
101
148
197
249
304
352
47
100
149
202
251
298
343
54
97
149
204
248
295
350
Tangents
delta
0,00440
0,00450
0,00455
0,00463
0,00463
0,00463
0,00463
0,00426
0,00436
0,00446
0,00449
0,00452
0,00457
0,00457
0,00419
0,00435
0,00446
0,00451
0,00451
0,00448
0,00441
Appendix C: Extra measurement setup information
Measurement setup AC breakdown tests
The measurement setup used in the AC breakdown tests, is shown in Figure C-1. The earthed wire
enters a deep fryer through a Perspex lit. The high voltage enters the deep fryer via a metal bar.
Figure C-2 and Figure C-3 show how the electrodes look when they are worn-out.
Figure C-1 An overview of the test setup. Earthed wire (left) and high voltage wire (right) coming from the transformer
Figure C-2 A worn out top electrode in which tiny pits filled with carbon traces are formed. The random distribution of
these pits indicate that the electrode was correctly polished prior to use. If this had not been done, a high concentration
on only the edges would have been observed
Figure C-3 Close up of an aged bottom electrode. The pits on this electrode look similar to the pits on the top electrode
77
Measurement setup time to breakdown tests
Figure C-4 and Figure C-5 contain schematic drawings of the test setup discussed in section 3.2.5.
Figure C-4 Side view of the time to breakdown test setup. The base electrode has a diameter of 120mm and is connected
to earth via an earthed copper plate. The four top electrodes (only 2 visible) have a diameter of 25mm and are all
connected to high voltage via metal bars. It is possible to easily disconnect a sample after breakdown has occurred
Figure C-5 Top view of the alignment of the electrodes. The large circle is the bottom electrode of 120mm diameter and
has a round rim. The slightly darker area is the flat area of the bottom electrode and is 100mm in diameter. The four dark
circles are the top electrodes of 25mm in diameter.
78
Measurement setup tangents delta tests
The adapted setup for stressing with transients is shown in Figure C-7. A connection is made to a box
containing a spike generated. The spikes will be superimposed on the AC waveform.
Figure C-7 To stress the samples prior to measuring their tangents delta, a connection is made to a box containing a spike
generator. The spikes will be superimposed on the AC waveform, simulating a ‘dirty’ waveform
79
80
Appendix D: Characterization of the paper
Dielectric spectrograph tests
A new sample is tested in a dielectric spectroscope. This is a frequency dependent tangents delta test as the frequency of the applied AC voltage is varied.
The applied voltage in this test is 1V. The tangents delta is measured at 20°C, 40°C, 60°C and 80°C as can be seen in Figure D-1.
Dielectric spectroscope measurement (new sample)
1,00E+01
tangents delta
1,00E+00
20C
1,00E-01
40C
60C
80C
1,00E-02
1,00E-03
1,00E-02
1,00E-01
1,00E+00
1,00E+01
1,00E+02
1,00E+03
1,00E+04
1,00E+05
1,00E+06
1,00E+07
Frequency (Hz)
Figure D-1 Result of the dielectric spectroscope measurement performed on a new, non-aged sample. The tangents delta is temperature dependent and shifts to the right for increasing
temperatures
81
The tangents delta curve is shifted to the right when temperature is increased. Tangents delta is calculated using the measured permittivity and is defined as
ϵ’’ divided by ϵ’.Therefore the course of these variables are shown in Figure D-2. The value of ϵ’ decays up to 1-10Hz and is constant at higher frequencies.
However, dependent on the temperature measured at, ϵ’’ decreases between 0.01-10Hz. This increase in ϵ’’ at higher temperatures is an indication of
conduction losses [16], in this case most likely caused by the increased conductivity of the oil absorbed by the paper. Around 5 MHz all ϵ’’ values are the
same, this is a measurement error and should be ignored as the dielectric spectroscope used is not suitable for measuring at these frequencies.
Measurement of ε' and ε'' (new sample)
1,00E+01
1,00E+00
20C ε'
Epsilon
40C ε'
60C ε'
1,00E-01
80C ε'
20C ε''
40C ε''
1,00E-02
60C ε''
80C ε''
1,00E-03
1,00E-02
1,00E-01
1,00E+00
1,00E+01
1,00E+02
1,00E+03
1,00E+04
1,00E+05
1,00E+06
1,00E+07
Frequency [Hz]
Figure D-2 The tangents delta values are based on the measurements for ε' and ε '' shown in this graph. It can be seen that the shape of the tangents delta graphs are
directly related to the decrease in ε''
82
When a closer look is taken at the tangents delta at 50Hz, the value measured with the dielectric
spectroscope is between 3.04e-3 and 3.10e-3 for 20°C. This measurement is repeated with an
electronic tangents delta measurement device. As shown in Figure D-3, the value for tangents delta is
dependent on the applied measurement voltage. When extrapolating the curve to the 1 volt,
consistency with the dielectric spectroscopy measurement can be observed.
Reference measurement (new sample)
0,008
0,007
Tangents delta
0,006
0,005
0,004
0,003
0,002
0,001
0
0
200
400
600
800
1000
1200
Vapplied
Figure D-3 The tangents delta is dependent on the applied measurement voltage. This measurement is performed on a
new, non-aged sample at 50Hz
The measured value for tangents delta for this new sample should be the lowest measured value in
this research as it is non-aged and the opportunity for moisture and oxygen to penetrate the sample
are minimal.
As the value for tangents delta is the most constant in the region from 50-600V, it was decided to
perform all future measurements in this region. The effect of ageing on the value of tangents delta at
1kV or higher might be interesting to investigate in future research. However, a warning has to be
given not to apply a voltage close to breakdown as any breakdown has the potential to impair the
measurement device.
83
84
Appendix E: Model calculations
In Table E-1 , some values from literature are compared and average per unit loading values are
calculated. The per unit loading of 40˚C is an estimated value as this could not be easily calculated
from the sources. The transformer from [37] is designed for 110°C and therefore the per unit values
in the range 70°-110°C have been used. Colleagues have their own model [38], the goal is not to redo
their work but to have an example with which it is possible to investigate the measurement data.
Table E-1 Literature values
Temperature
40°C
60°C
80°C
Per unit loading [37]
0.59
0.82
1.00
Applied field strength [kV/mm]
25.3
35.1
42.9
)
From Figure 4-2 it can be seen that at (
year, the applied field strength is 42.85
kV/mm. When using the calculated per unit values from Table E-1Table , the applied field strength
for oil and insulation (Arrhenius law was only considering the insulation) can be calculated.
On a logarithmic scale, a straight line such as a lifeline has the form of
(E-1)
To calculate the point of time at a certain applied field, formula E-1 can be rewritten.
(E-2)
(
)
(
(E-3)
( )
(E-4)
)
The results of this calculation can be found in Table E-2.
Table E-2 Lifetime comparision between Arrhenius expected lifetime (models the insulation) and the measurement data
expected lifetime (models both oil and insulation). In the final column, the expected lifetime is recalculated based on
Temperature Arrhenius
expected
lifetime [yr]
40°C
4687
60°C
263.6
80°C
20.53
Measurement
data expected
lifetime [yr]
1.59*107
90.65
20.53
85
Expected lifetime [yr]
(based on Figure E-3)
Equivalent ageing
factor FAA
1494
90.65
20.53
0,01374
0,2265
1,000
The course of the expected lifetimes from the measured data deviates from the Arrhenius rate of
reaction. As elaborated in section 4.1.1 and 4.1.2, this is a result from the changes properties of the
oil and especially its moisture solving capabilities. Therefore the expected lifetime was recalculated
in Figure E-1 while putting the 40°C lifeline below the other lifelines. The position and steepness of
the 40˚C lifeline is linearly extrapolated to lie below the 60˚C lifeline.
80
40C
60C
70
80C
Applied field [kV/mm]
60
50
40
30
25
-2
10
0
10
2
4
10
10
6
10
Time [h]
Figure E-3 The lifeline of the investigated transformer paper. The 40°C lifeline is calculated to be the linear extrapolation
of the changing steepness and position of the 60°C and 80°C measurements
86
Bibliography
[1] European Union. Roadmap 2050. [Online].
http://www.roadmap2050.eu/attachments/files/Volume1_fullreport_PressPack.pdf
[2] H. William and P.E. Bartley, "Analysis of Transformer Failures," in International Association of
Engineering Insurers, Stockholm, 2003.
[3] The IET. [Online]. http://www.theiet.org/about/libarc/archives/biographies/faraday.cfm
[4] Martin J. Heathcote, The J&P transformer book. Oxford UK: Elsevier Ltd., 2007 (13th edition).
[5] E. Peschke and E. von Olshausen, Cable Systems for High and Extra-High Voltage. Berlin: Publicis
MCD, 1999.
[6] T. Koltunowicz, "Defining a transformers aging factors in the future," CIRED 20th international
conference on electricity distribution, 2009.
[7] L. van der Sluis and P. Schavemaker, Electrical power system essentials - Lecture notes ET2105.
Delft: VSSD, 2007.
[8] Oncor.com. Transmission. [Online]. http://oncor.com/electricity/transmission/
[9] James H. Harlow et al.,.: CRC Press, 2004, p. 56.
[10] Cigré, "Ageing of cellulose in mineral-oil insulated transformers," Cigré Brochure 323, p. 46,
2007.
[11] F.H. Kreuger, Industrial high voltage. Delft: University Press, 1991.
[12] Belén García et al., "A moisture in oil model for power transformer monitoring," IEEE
transactions on power delivery, VOL. 20, NO. 2, APRIL 2005.
[13] T.V. Oommen and S.R. Lindgren, "Bubble evolution from transformer overload," IEEE, 2001.
[14] A. Akbari, S. DehPahlevan, and H. Borsi, "Analyzing Dynamic of Moisture Equilibrium in Oilpaper Insulation in Power Transformers for Efficient Drying," in Annual Report Conference on
Electrical Insulation and Dielectric Phenomena, Hanover, 2006.
[15] V. Wasserberg, "Challenge of Mixed Insulating liquids for use in high-voltage transformers,"
IEEE, p. 2, 2002.
[16] F.H. Kreuger, Industrial high voltage. Delft: University Press, 1992, vol. 2.
[17] C.F. Ten, M.A.R.M. Fernando, and Z.D. Wang, "Dielectric properties measurements of
transformer oil, paper and pressboard with the effect of moisture and ageing," Annual report
conference on electrical insulation and dielectric phenomena, 2007.
87
[18] Y. Dui et al., "Moisture Solubility for Differently Conditioned Transformer Oils," IEEE
Transactions on Dielectrics and Electrical Insulation, Vol. 8 No. 5, October 2001.
[19] Shell. Shell Diala AX. [Online]. www.shellusserver.com/products/pdf/DialaAX.pdf
[20] Shell. Shell Diala Oil B. [Online]. ptskm.com/GTDS_Diala_B.pdf
[21] H.P. Moser and V. Dahinden, transformerboard II. Rapperswil: Styria Graz, 1987.
[22] PTD T Höhlein / Heinzig Siemens AG, IEEE Transformers Committee Meeting. Jackson (MS): PTD
T Höhlein / Heinzig, 2005.
[23] E. Gulski, J.J. Smit, and J.P. van Bolhuis, "Monitoring and diagnostic of transformer solid
insulation," IEEE, p. Vol.7 No.2, 2002.
[24] R.J. Heywood, G.C. Stevens, C. Ferguson, and A.M. Emsley, "Life assessment of cable paper using
slow thermal ramp methods," Elsevier , p. 2, 1999.
[25] Delft University of Technology. Research in the high voltage laboratory. [Online].
http://www.ewi.tudelft.nl/live/pagina.jsp?id=e63bb4ef-5956-446d-bbdf5a4319bcba6c&lang=en
[26] Frank M. Clark, Insulating materials for design and engineering practice. New York: John Wiley
and Sons, Inc., 1962.
[27] Zoran Radakovic and Kurt Feser, "A new method for the calculation of the hot-spot temperature
in power transformers with ONAN cooling," IEEE, Oktober 2003.
[28] CENELEC, "Electrical strength of insulating materials - Test methods," IEC 60243-1, 1998.
[29] S.Güler H.Yilmaz, "The effect of electrode shape, gap and moisture on dielectric breakdown of
transformer oil," 1996.
[30] ASTM International, "Standard Test Method for Dielectric Breakdown Voltage and Dielectric
Strength of Solid Electrical Insulating Materials at Commercial Power Frequencies," D 149 – 97a,
2004.
[31] IEEE, "Guide for the statistical analysis of electrical insulatino breakdown data," IEEE, 2007.
[32] T.L. Koltunowicz. (2010, Dec.) Sinergie Presentation.
[33] Tim Bedford and Roger Cooke, Probabilistic Risk Analysis: Foundations and Methods.:
Cambridge University Press, 2001.
[34] T.L. Koltunowicz, G. Bajracharya, D. Djairam, and J.J. Smit, "Exploring the feasibility of an aging
model for paper insulation based on the repetition frequency of transcients," ISEI, 2010.
88
[35] Haefely. Haefely.com. [Online]. http://www.haefely.com/pdf/LL_2840_0410_LWA.pdf
[36] IEEE, IEEE Guide for Loading Mineral-Oil-Immersed Transformers, 57911995th ed. New York,
United States of America, 1995.
[37] Cooper Power Systems. (2003, July) Waukesha Electronic. [Online].
http://www.waukeshaelectric.com/assets/documents/25TP03-DR-017.pdf
[38] G. Bajracharya et al., "Optimization of Condition-Based Asset Management Using a Predictive
Health Model," in Proceedings on the 16th International Symposium on High Voltage
Engineering, Johannesburg, 2009, pp. 5-6.
[39] Mathworks. Mathworks. [Online].
http://www.mathworks.com/help/toolbox/physmod/powersys/ref/threephasetransformerindu
ctancematrixtypetwowindings.html
[40] N. Parkman, Electrical Insulation. London: Peter Peregrinus Ltd., 1983.
89
90
Acknowledgements
In this final chapter of my thesis I would like to thank all helpful people from the High Voltage
Management & Technology department. I found out that everyone who does or has done research
related to mine is more than willing to help things get started by i.e. providing literature or explaining
how to handle lab equipment.
A special thanks to my daily supervisor Tom Koltunowicz. Whenever I had questions or wanted to
discuss my results, I could always meet you on a short notice. Another thanks to my weekly
supervisor, Dhiradj Djairam who guided me through the crucial moments of the project. I also
appreciated that you gave me a lot of responsibility as soon as you noticed that I could quite well
monitor my own progress.
Furthermore I would like to mention Wim Termorshuizen and Aad van der Graaf who made some
components of my measurement setup with great craftsmanship. And I would like to thank lab
manager Ing. P. van Nes for the confidence of letting me operate both powerful and expensive high
voltage equipment.
Another thanks to prof. dr. J.J. Smit and dr. M. Gibescu, dipl-ing for participating in my thesis
committee. I appreciate it that you are taking time for this.
With a smile on my face I would like to thank my fellow graduation students. I enjoyed the lightminded atmosphere during the 3 o’clock tea brakes in the High Voltage Laboratory. I think we all
needed that to be able to deal with the sometimes stagnating experimental or editorial progress. 
The second last ‘thanks’ goes to Evert de Haan, my classmate, former roommate and best friend for
all his mental support and editorial assistance. We had a great time at the university and it was really
nice to finish it by graduating together.
Finally I would like to thank Klazien, my wife slash girlfriend (you can still be friends while married,
right?), for her unconditional support. Although you don’t always understand what I’m working on,
you always listen to my nonsensical yet impressive stories.
91