IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2018

Investigation of the effect of moisture in transformers on the aging of the solid insulation for dynamic rating applications

CHRISTOS STEFANOU

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Investigation of the effect of moisture intransformers on the aging of the solid insulation for

dynamic rating applications

Undersökning av fukthaltens inverkan på pappersåldring i

transformatorer för dynamiska lastbarhetsapplikationer

Christos Stefanou

Examiner: Patrik HilberSupervisors: Kateryna Morozovska, Tor Laneryd

Master Thesis

KTH Royal Institute of Technology

School of Electrical Engineering

Division of Electromagnetic Engineering

Stockholm, Sweden 2018

AbstractIn the present thesis an investigation is performed for the effect of moisture contenton the aging of the solid insulation for transformers that are dynamically loaded. Theinvestigation is based on a theoretical analysis and a model.

First, a literature review is conducted on the basics of transformer operation, trans-former insulation and moisture in oil-paper systems. Furthermore, a model is developedbased on moisture equilibrium curves created by Oommen and MIT, moisture diffusionprocesses in oil-paper insulation systems and calculations for the aging of cellulose insu-lation from IEC 60076-7. The model represents an experimental system which is loadedon different load patterns that simulate dynamic loading. The aim of the model is toconclude whether the load patterns will cause the paper to age differently dependingon the frequency that the moisture migration phenomenon between paper and oil occurs.

The result of the modeling part is that the aging process is affected by the load pattern,and that the higher the frequency the moisture migration phenomenon occurs within aloading cycle, the larger the impact on insulation degradation. This difference, though,is too small to be measured experimentally in terms of DP and it is suggested thatdifferent load patterns are used in the experiment than those used in the model, whichwill amplify the effect of moisture migration even further.

Finally, experimental work is conducted in the thesis, which focuses on implementingthe LabVIEW design from previous work into hardware, debugging the system andpreparing the experimental set-up on practical matters that occurred in the lab. Somefinal work is required before the experiment is able to run, such as preparation of theexperimental units.

Keywords: Dynamic rating, dynamic transformer rating, moisture in transformers,aging of transformer insulation, cellulose aging, solid insulation aging, experiment.

i

SammanfattningI detta examensarbete undersöks effekten av fuktinnehåll på åldring av fast isolations-material i transformatorer med dynamisk last. Arbetet är baserat på en teoretisk analysoch en modell.

Först genomförs en litteraturstudie på grundläggande transformatorfunktion, transfor-matorisolation och fukt i oljeimpregnerade papperssystem. Vidare utvecklas en modellbaserad på jämviktskurvor for fukt skapade av Oommen och MIT, fuktdifussionspro-cesser i isolationssystem baserade på oljeimpregnerat papper och beräkning av åldringav cellulosaisolation från IEC 60076-7. Modellen representerar ett experimentellt sys-tem som lastas för att simulera dynamisk last. Målet med modellen är att avgörahuruvida lastprofilen påverkar åldrandet av pappret beroende på frekvensen av fuktmi-grationen mellan papper och olja.

Resultatet av modelleringen är att åldrandet påverkas av lastprofilen och desto oftarefuktmigrationen sker inom en lastcykel, desto större är effekten på isolationsdegraderin-gen. Skillnaden är dock för liten att mäta experimentellt med avseende på DP och andralastprofiler föreslås i framtida experiment, för att förstärka effekten av fuktmigration.

Slutligen utförs experimentellt arbete som fokuserar på implementation av LabVIEW-designen från tidigare arbete i hårdvara, felsökning av systemet samt förberedelse av denexperimentella installationen för praktiska bekymmer som uppstått i laboratoriemiljön.En liten mängd arbete återstår före experimentet kan utföras, såsom förberedelse av deexperimentella enheterna.

Sökord: Dynamisk last, dynamisk transformatorklassificering, fukt i transformatorer,åldrande av transformatorisolation, åldrande av cellulosa, åldrande av fast isolation,experiment.

iii

AcknowledgmentsI want to thank my supervisors Kateryna Morozovska at KTH Royal Institute of Tech-nology and Tor Laneryd at ABB Corporate Research for giving me the opportunity towork with this very interesting topic. The experience I acquired from working in thisproject is irreplaceable and has given me a lot to proceed in my future career. I gained alot of valuable knowledge from both my supervisors and their help and guidance playedan important role in the completion of this thesis. I thank them for all the knowledgeand advice they gave me and for our excellent collaboration throughout the thesis.

I would like to thank my examiner, Docent Patrik Hilber at KTH Royal Institute ofTechnology, for his valuable feedback on my report. Also, I want to thank PatrikGustafsson, who designed the experimental set-up, for our great collaboration and thequality time we spent working together in the lab.

I would also like to thank my beloved Angeliki who stood by my side through good andbad, joy and sadness. I wouldn’t be where I am today if it weren’t for her love andsupport all these years. I love her and I appreciate everything she has done for me. Lastbut not least, I want to thank my family for all their love, support and deprivations allthese years to help me get at this point in my life: I want to express my love for myparents Vaso and Stefanos, and my grandparents Stathoula and Christos who supportedme financially through very difficult times and made sure I would complete my studies.Angeliki, Vaso, Stefanos, Stathoula and Christos your love and support will always bein my heart.

v

Contents

Abstract i

Sammanfattning iii

Acknowledgments v

List of abbreviations ix

List of Figures xi

List of Tables xii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Overview of the power transformer 42.1 Operating principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Oil-paper transformer insulation . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Solid insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Liquid insulation . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.3 Cooling of transformers . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Dynamic transformer rating . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Overview of moisture in oil-paper insulation systems & modeling ofthe experimental system 103.1 Moisture in oil-paper insulation systems . . . . . . . . . . . . . . . . . 10

3.1.1 Moisture equilibrium in oil-paper systems . . . . . . . . . . . . 113.1.2 Diffusion of moisture . . . . . . . . . . . . . . . . . . . . . . . . 173.1.3 Estimation of the aging of solid insulation . . . . . . . . . . . . 20

3.2 Modeling of the experimental system . . . . . . . . . . . . . . . . . . . 243.2.1 Representation of the experimental system . . . . . . . . . . . . 253.2.2 Moisture equilibrium in the system at 25 oC and the effect of the

air-gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.3 Moisture equilibrium in the system at 130 oC . . . . . . . . . . 293.2.4 Diffusion time constant . . . . . . . . . . . . . . . . . . . . . . . 353.2.5 Aging of the solid insulation . . . . . . . . . . . . . . . . . . . . 37

3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

vii

4 Experimental 484.1 Design of the experimental set-up . . . . . . . . . . . . . . . . . . . . . 48

4.1.1 Programming in LabVIEW . . . . . . . . . . . . . . . . . . . . 484.1.2 Hardware implementation . . . . . . . . . . . . . . . . . . . . . 52

4.2 Equipment of the experimental set-up . . . . . . . . . . . . . . . . . . . 534.2.1 Cartridge heaters . . . . . . . . . . . . . . . . . . . . . . . . . . 544.2.2 Glass tube containers . . . . . . . . . . . . . . . . . . . . . . . . 584.2.3 Design of the aluminum cylinders . . . . . . . . . . . . . . . . . 594.2.4 Electrical topology of the set-up . . . . . . . . . . . . . . . . . . 634.2.5 Safety equipment . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2.6 Preparation of the experimental units . . . . . . . . . . . . . . . 664.2.7 Additional equipment . . . . . . . . . . . . . . . . . . . . . . . . 67

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Conclusions and future work 695.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

References 71

viii

List of abbreviationsAC Alternating current

DAQ Data acquisition system

DC Direct current

DP Degree of polymerization

DR Dynamic rating

DTR Dynamic transformer rating

EMF Electromotive force

LP1 Load Pattern 1

LP2 Load Pattern 2

LP3 Load Pattern 3

LP4 Load Pattern 4

LP5 Load Pattern 5

LP6 Load Pattern 6

LP7 Load Pattern 7

NI National Instruments

PPM Parts per million

PWM Pulse-width modulation

RMS Root mean square

SSR Solid state relay

w/w Weight-by-weight

ix

List of Figures1 Ideal transformer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Cellulose polymer [5] © 2006 IEEE. . . . . . . . . . . . . . . . . . . . 73 Fabre-Pichon & Oommen’s curves for moisture distribution in oil-paper

systems [23] © 1984 IEEE. . . . . . . . . . . . . . . . . . . . . . . . . 144 Moisture equilibrium curves for oil-paper systems in the low moisture

region [23] © 1984 IEEE. . . . . . . . . . . . . . . . . . . . . . . . . . 155 Moisture equilibrium in oil-paper systems according to Pahlavanpour’s

equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Moisture equilibrium in oil-paper systems according to Serena’s equation. 177 Effect of temperature and moisture concentration on the diffusion coef-

ficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Effect of temperature and moisture concentration on the diffusion coef-

ficient for temperatures between 90 oC and 100 oC. . . . . . . . . . . . 199 Effect of temperature on diffusion time constant for temperatures from

20 oC to 100 oC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2010 Arrhenius plot for the aging rate of the cases of table 3. . . . . . . . . . 2411 Unit of the oil-paper system. . . . . . . . . . . . . . . . . . . . . . . . . 2512 Moisture equilibrium curves in oil-paper systems for high moisture con-

centrations [27] © 1999 IEEE. . . . . . . . . . . . . . . . . . . . . . . . 3013 Moisture equilibrium curves - reproduction of figure 12. . . . . . . . . . 3114 Moisture equilibrium curves and fitting curves from 60 oC to 100 oC. . 3215 Estimation of moisture equilibrium curves from 70 oC to 100 oC. . . . . 3316 Fitting of moisture equilibrium curves for temperatures between 60 oC

and 100 oC and estimated 130 oC curve. . . . . . . . . . . . . . . . . . 3517 Illustration of moisture migration and injected energy in the system for

the three different load patterns (inspired by [18]). . . . . . . . . . . . . 3818 Regression of values of A from table 3. . . . . . . . . . . . . . . . . . . 4019 Moisture concentration c(t) in paper during the migration process from

paper to oil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4120 Moisture concentration c(t) in paper during the migration process from

oil to paper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4121 Block in LabVIEW that controls the solid-state relay of one load pattern. 4922 Block in LabVIEW that acquires and stores the temperatures of the

system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5023 Front panel of the design in LabVIEW. . . . . . . . . . . . . . . . . . . 5124 NI hardware equipment: (a) PXIe-1073 chassis with PXIe-6368 card,

(b) BNC-2120 connector block, (c) SCB-68 pin connector block, (d) NIequipment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

25 TC-08 Thermocouple Data Logger from Pico Technology. . . . . . . . . 53

x

26 Drawing of the cartridge heater. . . . . . . . . . . . . . . . . . . . . . . 5527 Cartridge heater used in the experiment. . . . . . . . . . . . . . . . . . 5628 Approximation of the behavior of the resistance of the cartridge heaters. 5829 Glass tube and cartridge heater used in the experiment. . . . . . . . . . 5930 Technical drawing of the aluminum cylinder. . . . . . . . . . . . . . . . 6031 Illustration of an experimental unit inside an aluminum cylinder. . . . . 6432 Electrical topology diagram. . . . . . . . . . . . . . . . . . . . . . . . . 6433 Safety box used in the experiment. . . . . . . . . . . . . . . . . . . . . 66

xi

List of Tables1 Values of D0 and Ea [27]. . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Values of D and τ for oil-free and oil-impregnated paper for T = 50 oC,

d = 0.5 mm, C = 1 % and single-sided moisture diffusion. . . . . . . . . 183 Values of EA and A for non-thermally upgraded paper and for various

combinations of oxygen content (O2) and moisture content (H2O) [29],[30]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Values of EA and A for thermally upgraded paper and for various com-binations of oxygen content (O2) and moisture content (H2O) [29], [30]. 22

5 Expected lifetime for non-thermally upgraded paper and for four combi-nations of oxygen content (O2) and moisture content (H2O), and for avariety of hot-spot temperatures. . . . . . . . . . . . . . . . . . . . . . 23

6 Dimensions of the equipment depicted in figure 11. . . . . . . . . . . . 267 Dimensions of the moisture equilibrium system depicted in figure 11. . 268 Oil volumes and paper weight needed for the analysis of the samples [18]. 279 Moisture content in paper and oil at equilibrium at 25 oC. . . . . . . . 2810 Moisture content in paper and oil and at equilibrium at 25 oC along with

the global moisture of the system. . . . . . . . . . . . . . . . . . . . . . 2911 Parameters of equation (30) for each curve. . . . . . . . . . . . . . . . . 3112 Mean ratios between the curves of figure 14. . . . . . . . . . . . . . . . 3313 Max error between estimation and actual curves in figure 15 calculated

as max(Pi+10(x)− Pi(x))/Pi(x). . . . . . . . . . . . . . . . . . . . . . . 3414 Moisture content in paper and oil and at equilibrium at 130 oC along

with the global moisture of the system. . . . . . . . . . . . . . . . . . . 3515 Diffusion parameters of the experimental system. . . . . . . . . . . . . 3716 Time intervals where energy is injected in the system with reference to

figure 17 presented in [18]. . . . . . . . . . . . . . . . . . . . . . . . . . 3917 Estimation of aging of the solid insulation considering the moisture trans-

port phenomenon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4418 Time intervals where energy is injected in the system for a set of prelim-

inary load patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4519 Estimation of aging of the solid insulation considering the moisture trans-

port phenomenon for all load patterns. . . . . . . . . . . . . . . . . . . 4520 Cartridge heaters initial resistor values at 25 oC. . . . . . . . . . . . . . 5521 Cartridge heaters resistor values at 25 oC after being loaded. . . . . . . 5722 Dimensions of the aluminum cylinder. . . . . . . . . . . . . . . . . . . . 6323 Equipment used in the experiment. . . . . . . . . . . . . . . . . . . . . 67

xii

1 Introduction

1.1 Background

The invention of the power transformer over a century ago, drastically changed the land-scape of the power system. The power transformer made possible the transportationof electric power over long distances in an efficient way using alternating current (AC),as until then the main source of generation was from direct current (DC) sources. ACsystems proved to be highly beneficial compared to DC, as they facilitated the trans-portation of large amounts of power over long distances, while significantly reducingthe losses. This made it possible for generation stations to be located hundreds oreven thousands of kilometers away from consumption, which was an advantage for thesystem’s growth [1].

The electric power system is an efficient and safe system that covers society’s needsfor electricity where and when it is required. The generators operating in the systemare most commonly synchronous generators, and usually their insulation does not allowvoltage levels larger than 25 kV [2]. The generation is often located far from the con-sumption, thus, creating the need for transporting the energy. The power transformeris a key component in this process, helping in reducing the losses on the power lines andmaking the transportation of the energy more efficient. This is achieved by increasingthe voltage level from generation to transportation, which in turn leads to a reductionof the line current for a given amount of power, and finally a reduction of the powerlosses on the lines. These losses are given by

Ploss = 3I2lineRline (1)

for a 3-phase system, where Iline is the RMS value of the line current and Rline is theohmic resistance of the line. The power transformer also adjusts the voltage to theappropriate respective levels for the various segments of the system (for example house-hold consumers, distribution level, industrial level).

Large power transformers are among the most expensive devices in the system as theyneed to operate safely and continuously for many decades. Failures of large transform-ers can have significant impacts in the power system, from expensive repair costs, tolarge outages and instabilities. The life expectancy of transformers is primarily limitedby their insulation which degrades due to natural processes that take place within atransformer, such as moisture ingression, high temperatures and acid concentration. Itis, thus, understandable that transformers play a critical role in the system and theirinvestigation is of high interest.

1

With the increase of renewable energy sources, the importance of dynamic rating isamplified as it is possible to use smaller equipment of lower cost while retaining thereliability and safety standards of the system. This is especially true for transform-ers connected to renewable generation, such as wind farms and solar parks, where thegenerated power varies over time. Current standards concerning insulation degradationand dynamic rating applications, take into consideration temperature as the dominantfactor in the aging process, neglecting other parameters such as moisture transportdynamics. In the present project, the effect of moisture in the aging of transformerinsulation for dynamic rating applications is investigated.

The results of this work could potentially contribute to improvements in the existingstandards and models concerning transformer insulation aging, by taking into accountmoisture transport dynamics. This can have a positive impact in society by improvingthe power system in terms of reliability and cost, which would prove beneficial forconsumers and producers alike. The improvement in reliability can come in the form ofhaving a lower number of faults in the power transformers of the system, which will leadto fewer disruptions and to providing a higher quality service to the consumers, whilethere will be a reduced number of repairs for the producers. The cost reductions can beachieved by utilizing dynamic rating in a power transformer of lower cost and smallerstatic rating in the place of a more expensive one by having a better understanding onthe underlying destructive factors that affect the transformer’s lifetime. Furthermore,by reducing the cost of transformers connected to renewable energy parks, and thusbeing dynamically loaded, the overall cost of the initial investment for building thepark would decrease, making it financially more feasible to establish green energy intoour society. The ethical aspects of this work can be found in the utilization of cleanerand more environmentally friendly energy sources which has obvious benefits for theworld, with improvement of the living conditions and reduction of greenhouse gasesbeing prominent positive impacts of green energy. Using green energy protects theplanet and helps in making the world better (improves public health, preserves wildlifedue to clean energy, saves energy resources) and much more sustainable for futuregenerations. Lastly, due to the fact that, aside from the initial investment and themaintenance costs, green energy comes directly from energy sources that are free andexist in abundance in nature (for example wind or solar energy) the cost of energy couldbe reduced if the system consists of enough renewable parks, making electrical energyaffordable for all people in the world.

1.2 Thesis objectives

The objectives of the present thesis is to model the effect of moisture content on theaging process of the solid insulation in transformers for dynamic rating applications,and, to implement the experimental design from [18] into hardware. The modeling is

2

based on industrial standards and aims at investigating whether the presence of mois-ture and its migration pattern between oil and paper affects cellulose degradation intransformers. This is performed by testing several load patterns on a theoretical level,and then, the conclusions of the model can be added into the experimental design. Theimplementation of the experimental design into hardware deals with more practicalmatters in the laboratory where the programming in LabVIEW from [18] is tested andapplied into hardware. In this process, the system is debugged and technical difficultiesare dealt with.

The design of the experimental set-up in [18] is realized in LabVIEW, and three loadpatterns are developed which represent intermittent loading. The control and dataacquisition systems are developed in LabVIEW and communicate with the appropriatehardware that interacts with the experimental units. These units represent the oil-paper insulation systems that will be analyzed in the process of investigating the effectof moisture transport dynamics in the aging of the solid insulation.

1.3 Thesis outline

In chapter 2, an overview of the basics of the operation of power transformers and theirinsulation is presented. Also, the cooling of transformers and the concept of dynamicrating (DR) are discussed.

Furthermore, in chapter 3, a thorough discussion about moisture in oil-paper insulat-ing systems is presented along with the model of the experimental system. Literaturereview is conducted and the choice of method for the model and its results are discussed.

Moreover, in chapter 4, the experimental design from [18] is presented along with adescription of the equipment, a discussion about the construction of the experimentalset-up and practical matters that need to be considered.

Finally, in chapter 5, the conclusions of the thesis are discussed and suggestions forfuture work are given.

The degree project is a cooperation between the RCAM group at KTH Royal Instituteof Technology in Stockholm and ABB Corporate Research Center in Västerås.

3

2 Overview of the power transformer

2.1 Operating principle

A typical transformer consists of two (or more) windings which are magnetically coupledthrough a magnetic core. The operation of transformers is based on Faraday’s law ofinduction

E =dϕ

dt(2)

where E represents the electromotive force (EMF) and ϕ represents the magnetic flux.According to Faraday’s law of induction, the rate of change of ϕ is equal to E.

The operating principle will be presented by assuming a single-phase ideal transformer.This means that the windings have zero resistance, there is no leakage flux, the magneticcore has infinite relative permeability µr = ∞, and there are no losses or hysteresis inthe core [2]. Figure 1 illustrates an ideal transformer, where the primary winding hasN1 turns and the secondary winding has N2 turns. Also, a load is connected at thesecondary side which allows the secondary current to flow.

Figure 1: Ideal transformer.

The following analysis is based on section 2.3 from [3]. A time-varying voltage sourceu1 is connected at the primary winding of the transformer, as seen in figure 1, andconsequently a magnetic flux ϕ is created in the core resulting in an EMF e1 = u1. Themagnetic flux will also generate an EMF e2 = u2 at the secondary winding as seen in

4

figure 1. According to Faraday’s law of induction, the following equations are valid

u1 = e1 = N1dϕ

dt(3)

u2 = e2 = N2dϕ

dt(4)

By combining equations (3) and (4), the relation between u1 and u2 can be obtained as

u1N1

=u2N2

=⇒ u1u2

=N1

N2

(5)

It can be seen that the voltage in the secondary winding of the ideal transformer followsa linear relation with the input voltage in the primary, with the factor of proportionalitybeing α = N2/N1. In the ideal transformer case, there are no power losses, meaningthat the instantaneous input power must equal the instantaneous output power

p1 = p2 (6)

It is known that the instantaneous power is the product of voltage times current, p1 =u1i1 and p2 = u2i2, and by combining these with (6) it results into

u1i1 = u2i2 =⇒ i2 =u1u2i1 =⇒ i1

i2=N2

N1

(7)

It can be seen that α is an important parameter in transformer operation and design,and depending on the application (step-down or step-up transformer) the ratio of num-ber of turns between the primary and secondary windings can be larger or smaller than1. For step-down transformers, the voltage in the secondary winding is lower thanthe primary but the secondary current has to be higher than the primary for equation(6) to be true. Larger currents will cause higher losses, which translates into highertemperatures that can severely affect transformer insulation and expected lifetime asdiscussed next. On the other hand, for step-up transformers the secondary voltage ishigher than the primary, while the secondary current is lower than that of the primary.The increase in voltage causes the need for stronger insulation, as the risk of havingelectrical breakdowns or arcing within the transformer increases with voltage.

2.2 Oil-paper transformer insulation

Transformers are among the most expensive and vital components in the power systemand they are expected to operate for decades, thus, they must have high reliability.Large transformers can be rated at 1500 MVA [5] having high voltages and large cur-rents. As a result strong electrical fields and high temperatures can be created inside thetransformer. At this moment, a large number of transformers in operation were installed

5

during the 1970s, meaning that they are approaching the end of their lifetime, with thelife expectancy of transformers predominantly depending on their solid insulation [6].Transformers most commonly have solid and liquid insulation, with paper/pressboardand mineral oil being prevailing choices respectively.

2.2.1 Solid insulation

The preference for solid insulation in transformers, and other electrical applications ingeneral, is cellulose as it has good insulating properties but mainly because it exists inabundance in nature. A cellulose polymer is illustrated in figure 2. Transformers’ insu-lation is expected to last for many years to ensure the normal operation of the devices,though, natural chemical processes gradually lead to degradation and depolymerizationof the material causing it to lose its properties over time, and eventually leading to theend of life of the transformer.

The tensile strength of the paper insulation is one of the most important factor inthe aging of the solid insulation, as a majority of evidence indicates that transformerfailure is closely related to mechanical failure of the insulation, resulting to electricalbreakdowns within the transformer. It is not feasible to extract paper samples froma transformer in use in order to measure the tensile strength, but it is known thatthe tensile strength is proportional to the change in the degree of polymerization (DP)value of the cellulose insulation, thus aged paper will have lower tensile strength [10].The DP value is one of the most common indexes of paper degradation, with a lowvalue of DP indicating higher degradation, tendency for the cellulose to be hydrolyzedeasier and lower tensile strength [5], [6], [7]. The main downside of cellulose insulationis its tendency to absorb moisture which leads to premature aging and reduction of itsinsulating properties which can consequently lead to failures in the devices. In general,the process of drying the solid insulation before using it can be tedious, but it is crit-ical to be performed to ensure minimal moisture ingression in the transformer. Othersynthetic materials have been created which can have better insulating properties andlower moisture absorption, but their cost is significantly higher compared to cellulose.It is stated in [5] that upgraded papers can last up to 10 times more compared to non-upgraded paper.

6

Figure 2: Cellulose polymer [5] © 2006 IEEE.

The presence of moisture in transformers is unavoidable. Moisture can enter the trans-former either through the insulating paper during the construction phase or during theoperation of the transformer. A moisture equilibrium is reached after the oil-paperinsulation is exposed to a specific temperature for a prolonged time, and depending onthe levels of moisture in paper the aging rate can be increased leading to prematuredegradation. Paper samples for testing cannot be obtained during the operation of atransformer, and it is quite tough to do so even when repairing the transformer as itrequires for the transformer to be disassembled [8]. Thus, it is important to be able toestimate the DP value and a method to do that is discussed in subsection 3.1.3.

Other parameters that have a significant effect on the aging of the paper insulationare heat, oxygen and acid. These parameters can cause various chemical reactions thathave a significant effect on the degradation of the solid insulation. In general, the higherthe levels of their concentration, the faster the aging occurs. Temperature is among themost important factors, and a rule of thumb is that for every 10 oC rise the chemicalreaction rates double resulting into quicker degradation in both oil and paper, or inother words for every 10 oC rise in temperature the life of the insulation is reduced tohalf. Though, high temperatures are bound to exist due to losses at the windings or thecore of the transformer which are essentially a heat source. Moreover, cellulose reactswith oxygen, and, water, carbon dioxide and carbon monoxide are produced. Thesecan increase the oxidation process and the aging rates of both oil and paper. Last, acidin oil can also affect the aging of the solid insulation, and used oils have a higher levelof acidity than new ones [9].

2.2.2 Liquid insulation

Mineral oil is the most common material used as liquid insulation in electrical equip-ment as it combines very good dielectric and thermal properties at a low price. Otheralternatives exist that may possess better dielectric or thermal properties than mineraloil, though none can combine both at a competitive price. Mineral oil provides electricalinsulation, heat dissipation and can be used for diagnostic purposes. Mineral oil has

7

quite good dielectric properties, thus acting as an electrical insulator is its primary use,as there are high intensity electric fields within a transformer, and electrical breakdowncan occur if proper measures are not in place. Moreover, the heat generated within thetransformer has to be dissipated in the ambient, and mineral oil distributes this heatwithin the transformer which is finally dissipated in the ambient air through externalheat exchangers or directly through the tank for smaller transformers. In addition,as discussed, in order to assess the operating conditions and the health of the trans-former, it is necessary to be able to run tests without dismantling the device. Theliquid insulation can be used as means of assessing the chemical and electrical proper-ties of the oil-paper insulation and deduce important conclusions about the state of thetransformer, as discussed next. Lastly, factors such as heat, oxygen, partial discharges,arcing and acid affect the aging of the oil [9].

The insulating oil is used in tests such as dissolved gas analysis, furan analysis, moistureconcentration and acid number in transformer diagnostics. During normal operation,several chemical reactions occur within the transformer insulation, such as generationof gases, moisture, acid and furanic compounds. The gas analysis in transformerscan provide information about its state in terms of insulation aging, partial dischargesand electrical breakdowns, thus being a useful tool in transformer diagnostics. More-over, when cellulose molecules break down, residual water is created along with furaniccompounds. These furanic compounds are correlated with the aging of the celluloseinsulation and are partly dissolved in the liquid insulation. Thus by taking oil samplesthe degradation of paper can be estimated through the correlation of the DP value withthe furanic compounds.

2.2.3 Cooling of transformers

Heat generation within the transformer causes the temperature to rise with detrimentaleffects on the insulation’s lifetime. For this reason, cooling is very important in trans-formers and in general the rating of the device is limited by its ability to dissipate thisheat to the ambient. The primary source of heat generation is through the windingsand the core of the machine. The liquid insulation circulates within the transformerhelping to distribute the heat and dissipate it towards its tank. Moreover, fans can beused to increase the heat dissipation [9].

The cooling process can be classified in certain cooling classes, which are characterizedby certain codes. These codes consist of four letters that describe the mechanisms andmedia that participate in the cooling process. The first two letters in the code indicatethe internal cooling of the machine, with the first letter in the coding indicating thecooling medium of the transformer, while the second letter describes the cooling mech-anism. The third and fourth letters describe the external cooling of the transformer

8

with the third letter indicating the cooling medium and the fourth the cooling mech-anism. For the internal cooling, oil (O) is among the best choices, where the coolingmechanism could be either natural (N) or forced (F), while for the external cooling, air(A) and water (W) are usual alternatives, with either natural (N) or forced (F) coolingmechanism. This leads to cooling classes such as ONAN and ONAF which are quitecommon in transformers.

2.3 Dynamic transformer rating

As mentioned, power transformers are among the most expensive devices in the sys-tem, thus their utilization to their full extent is desired. Their manufacturers, though,provide the nominal rating or static rating of the transformers [19]. This limit is rarelyreached, and the transformer is often operating below its full capacity. For this reason,Dynamic Transformer Rating (DTR) is applied. With DTR the transformer works inDynamic Rating (DR) rather than static rating, which allows it to adjust to the condi-tions of its environment on each occasion.

The temperature and environment that the transformer operates at can significantlyaffect its expected life-time, as the life-time depends on the insulation which in turnlargely dependents on temperature. Therefore, for temperatures lower than the condi-tions that the transformer was rated for, the capacity of the transformer can be higherthan the rated. According to [19], the average DR of a transformer can lie between 1.06to 1.10 times its static rating, meaning that it can serve additional loads between 6% to10 % its nominal power. It can be seen that when the conditions allow it, a transformerwith a smaller nominal rating can be used with DTR in the place of a larger and moreexpensive one. This can be applied also in distributed generation systems where theproduction is not always at its maximum (for example solar systems and wind turbines),reducing the total cost of the system.

Moisture has a detrimental effect on the life-time of transformer insulation, and itseffect in combination with DTR should be investigated. The scope of this thesis is theinvestigation of moisture transport in oil-paper systems under DTR. The effect of DRis modeled by increasing the temperature above the normal operating temperature oftransformers and implementing intermittent loading, while aiming for an acceleratedaging of the transformer insulation, as they are devices operating for decades while thetarget is to investigate the effect on a much short period of time with the experimentalset-up.

9

3 Overview of moisture in oil-paper insulation sys-tems & modeling of the experimental system

Moisture in a transformer can have a detrimental consequence on the insulation longevity,as the thermal aging and the tensile strength of the paper insulation is highly corre-lated with its moisture content. Water concentration in areas of high electrical fieldscan also initiate partial discharges as the dielectric strength of the oil is reduced [20],[21]. Thus, it is important to be able to understand and describe the mechanisms andeffects of moisture in transformer insulation. In this chapter, the existence of moisturein oil-paper insulation systems is discussed, the moisture equilibrium is described, theconcept of moisture diffusion is presented and a method that calculates the aging of thepaper is described. Furthermore, the model describing the system of the experiment isdeveloped.

3.1 Moisture in oil-paper insulation systems

In transformers, there is always moisture content that can be the result of moisture in-gression during operation, residual moisture during the drying and assembling processes,and water generated by the chemical reactions between the solid and liquid insulation.The reliability and safe operation of transformers are affected by this moisture content.Consequently, it is clear that it is of great importance to have knowledge about themoisture content in a transformer. For this reason, methods have been developed toestimate this content as it is not possible to measure it when a transformer is operatingsince the solid insulation is not accessible without dismantling the transformer. Themoisture content in the oil can be measured straightforwardly by extracting oil samples,while the moisture content of the paper can be estimated using various methods as dis-cussed in section 3.1.1. Paper insulation has much larger water affinity than oil, though,the moisture distribution among them depends on the operation of the transformer, es-pecially on temperature. As a result, the largest part of the water can be found in thepaper insulation. It is worth noting that even slight alterations in temperature can havea large effect on the moisture content in oil, but a rather small effect in paper [20], [21].

10

3.1.1 Moisture equilibrium in oil-paper systems

In this section, the moisture equilibrium is described and a literature review for meth-ods that estimate it is conducted. Moreover, factors such as the solubility and thesaturation of water in oil are discussed and moisture equilibrium curves are presented.Lastly, a method is selected to proceed with the modeling of the experimental system.

When the transformer is operating at a specific temperature for a certain amount oftime, an equilibrium is reached between the moisture distribution in the paper and inthe oil. This equilibrium depends on the temperature of the transformer and severalformulas and curves have been proposed to describe and estimate it. The liquid in-sulation in a transformer can act as a mean for the moisture to transport within thetransformer. Also, water in oil can be found in a soluble state and the relation betweenthe solubility of water in oil and temperature [21] is given by

S = WOil e(−B/T ) (8)

where S is the solubility of water in oil,WOil and B are constants that depend on the oil(and are similar for many oils but may vary for some others) and T is the temperaturein Kelvin. In oils that have significantly aged, the solubility can be two times that ofnew oils. Another relation for solubility is presented in the equations of [21], havingthe general form of

S = 10(k1−k2/T ) (9)

where k1 and k2 depend on the specific formula describing the solubility, and T is thetemperature in Kelvin.

In [21], there are models that correlate the moisture distribution between paper andoil, as well as models that estimate the solubility of water in oil. These are namely"Pahlavanpour’s equation", "Serena’s equation", "Shkolnik’s models", "Griffin’s for-mula for solubility in mineral oil", and, "Oommen’s formula for solubility in mineraloil". Additionally, in [23] another set of moisture equilibrium sets is constructed andpresented by Oommen, which is among the most reliable ones.

The following models are presented in [21].

Pahlavanpour’s equation Pahlavanpour’s equation is given by

[H2O]paper(%) = 2.06915 e−0.02970t · ([H2O]oil)0.40489t0.09733 (10)

where [H2O]paper is the moisture in paper given in percentage (%), [H2O]oil is themoisture content in oil given in mgH2O/kgoil and t is the temperature in oC.

11

Serena’s equation Serena’s equation is given by

[H2O]paper(%) = 1.75 · 10−8 · [H2O]oil e4953/T (11)

where [H2O]paper is the moisture in paper given in percentage (%), [H2O]oil is themoisture content in oil given in mgH2O/kgoil and T is the temperature Kelvin.

Shkolnik’s models Shkolnik’s model is given by

[H2O]paper(%) = c · [10(8.94−2254/T ) · ([H2O])oil/S]n (12)

where [H2O]paper is the moisture in paper given in percentage (%), [H2O]oil is the mois-ture content in oil given in mgH2O/kgoil, S is the solubility of water in oil, T is thetemperature Kelvin, while c = a · e−bt, n = k+ dt with t the temperature in oC, and k,d, a and b are constants depending on the insulating material of the solid insulation.

For oils with an acidity equal to 0.02 mgKOH/goil, the solubility is given by

S = 10(7.86−1836/T ) (13)

where T is the temperature in Kelvin. For oils with an acidity equal to 0.3 mgKOH/goil,the solubility is given by

S = 10(8.42−1921/T ) (14)

where T is the temperature in Kelvin. These two different equations for the solubility ofwater in oil can be used for new and used oils respectively, where low acidity indicatesa new oil and high acidity a used one.

Griffin’s formula Griffin’s formula for solubility in mineral oil is given by

S = 10(7.0895−1567/T ) (15)

where S is the solubility in mgH2O/kgoil and T the temperature in Kelvin.

Oommen’s formula Oommen’s formula for solubility in mineral oil is given by

S = 10(7.42−1670/T ) (16)

where S is the solubility in mgH2O/kgoil and T the temperature in Kelvin.In [24], the saturation of oil is defined as the "actual amount of water in the oil inrelation to the solubility level at that temperature" and is given by

Saturation(%) = [Concentration of water in oil (mgH2O/kgoil)/S] · 100 (17)

12

There is a close relation between saturation given in (17) and the dielectric breakdownvoltage in a transformer, and this relation can be approximated by an inversely pro-portional linear function, where with the increase of the saturation level in the oil, thedielectric breakdown voltage decreases [24].

Concerning moisture content in paper, equations (10) and (12) for low acidity oilsare in good agreement, while equation (11) matches (12) for high acidity oils. Oilsaturation calculated by (15) and (16) using moisture concentration in oil match eachother, though the preferred method to calculate the solubility of water in mineral oil isGriffin’s formula (15) [21].

Apart from the equations presented for moisture equilibrium in oil-paper systems, setsof curves have been also developed, with the most widely known ones being the Fabre-Pichon curves, which were published in CIGRÉ in 1960 [23]. These curves are presentedin figure 3a. A similar set of curves is constructed in [23] by Oommen and presentedin figure 3b. This figure illustrates both adsorption and desorption curves, with theadsorption ones being indicated with the letter ’a’ in the figure, and the desorptioncurves being illustrated with the broken lines.

The measuring unit mg/kg is also widely known as parts per million or PPM, as shownin figures 3a and 3b. These curves can have numerous applications, such as determiningthe moisture distribution between paper and oil when the system is in equilibrium at aspecific temperature, but another important utilization is the estimation of the moisturein the paper by knowing the moisture in the oil and the temperature of the interfacebetween oil and paper, for example by extracting oil samples from the transformer andby measuring the temperature using special sensors. It is important that the system isin equilibrium, otherwise the curves will not provide the correct estimation.

13

(a) Fabre-Pichon curves for moisture distribution in Kraft pa-per/Oil systems [23] © 1984 IEEE.

(b) Moisture equilibrium curves for oil-paper systems [23] ©1984 IEEE.

Figure 3: Fabre-Pichon & Oommen’s curves for moisture distribution in oil-paper sys-tems [23] © 1984 IEEE.

14

Oommen constructed the set of equilibrium curves in figure 3b and the motivationbehind the construction of those curves is that the Fabre-Pichon curves may not beapplicable to all systems because the specific types of oil and paper that are modeledmay be different than the ones used in those curves. The method used by Oommen inthe construction of those curves is the "combination of the moisture equilibrium curvesfor oil and paper obtained independently" [23]. This technique presents advantages ofreaching equilibrium state faster in paper that is not oil-impregnated and obtaining theequilibrium moisture in the oil by the solubility information at several relative humidi-ties. Figure 3b is in agreement with figure 3a at high temperatures, but there are somedifferences at lower temperatures that could be the result of the paper-oil system notbeing in complete equilibrium at low temperatures according to Oommen.

It can be observed that both figure 3a and 3b do not include information for lowmoisture contents as those may be unreliable according to [23], though there are meth-ods to construct them. Such a set of curves is presented in [23] and was constructed byBeer et. al. in 1966. These curves are presented in figure 4. It can be observed in thefigure that the solubility limit is also given for each curve.

Figure 4: Moisture equilibrium curves for oil-paper systems in the low moisture region[23] © 1984 IEEE.

15

In figures 5 and 6 the plots of equations (10) and (11) are illustrated for temperaturesbetween 20 oC and 100 oC, for moisture concentration in oil up to 80 PPM and 10 %w/w in paper. Pahlavanpour’s equation matches data for new oils (low acidity) whileSerena’s equation matches those for used oils (high acidity), and the differences in theshape of the curves of those models can be observed. Equation’s (10) curvature is closerto the Fabre-Pichon curves (figure 3a) while equation (11) is closer to a straight line.

From the models and curves reviewed in the literature for moisture equilibrium in oil-paper systems, the curves constructed by Oommen will be used in the modeling of theexperimental system. This selection is based on the accuracy of the curves which is aresult of the construction procedure followed by Oommen, and verified by the Fabre-Pichon curves. It is worth noting that the models described by equations (10) and(11) have been used in other scientific publications, but it was not possible to find theoriginal source of those equations, so it was selected not to use them in the modelingphase.

0 10 20 30 40 50 60 70 80

0

1

2

3

4

5

6

7

8

9

10

Figure 5: Moisture equilibrium in oil-paper systems according to Pahlavanpour’s equa-tion.

16

0 10 20 30 40 50 60 70 80

0

1

2

3

4

5

6

7

8

9

10

Figure 6: Moisture equilibrium in oil-paper systems according to Serena’s equation.

3.1.2 Diffusion of moisture

Moisture equilibrium in the complex oil-paper system requires a specific amount oftime to occur depending on the conditions that govern the system, such as temperatureand moisture content, and this amount of time can be estimated by the diffusion timeconstant τ [seconds] in the system. The time constant is given in [27] by the followingequations

τ =d2

π2D(18)

if moisture is diffusing from both sides of the paper, or by

τ =4d2

π2D(19)

if moisture diffuses from one side of the paper. In equations (18) and (19) d is thethickness of the paper insulation in [m] and D is the diffusion coefficient in [m2/s].

The moisture diffusion coefficient is given in [27] as

D = D0 e(0.5C+Ea(1/T0−1/T )) (20)

where the values of D0 [m2/s] and Ea [K] depend on if the paper is oil-free or oil-impregnated, T0 = 298 K, C is the moisture concentration in percent weight and T [K]is the temperature at which the diffusion coefficient is calculated. The values of D0 andEa are given in table 1.

17

Table 1: Values of D0 and Ea [27].

Coefficient Oil-free paper Oil-impregnated paperD0 [m2/s] 2.62·10−11 1.34·10−13

Ea [K] 8140 8074

For a given paper thickness d, moisture concentration C and temperature T , the diffu-sion coefficientD for oil-free paper is larger than that of oil-impregnated paper, resultingin a smaller diffusion time constant for the oil-free paper, meaning that moisture can bediffused faster in this case. An example is given in table 2 for T = 50 oC, d = 0.5 mm,C = 1 % and single-sided moisture diffusion. As can be seen in that example, there isa significant difference on both D and τ depending on if the paper is oil-impregnatedor not. Having as a reference the present example, it should be noted that in equation(20) the moisture concentration C should be inserted as C = 1 % = 1/100 = 0.01, andnot just as C = 1.

Table 2: Values of D and τ for oil-free and oil-impregnated paper for T = 50 oC, d = 0.5mm, C = 1 % and single-sided moisture diffusion.

Coefficient Oil-free paper Oil-impregnated paperD [m2/s] 2.181·10−10 1.0965·10−12

τ [minutes] 7.7 1540

Moisture diffusion in oil-impregnated paper depends on the moisture concentration andtemperature as equation (20) indicates. In figure 7 the effect of temperature and mois-ture concentration on the diffusion coefficientD is presented for moisture concentrationsfrom 1 % to 5 % and temperatures from 20 oC to 100 oC in oil-impregnated paper wheresingle-sided diffusion is considered. The thickness of the paper in this example is d = 0.5mm.

Moisture concentration seems to have a small effect on D as can be seen in figure 7,while temperature has a significant impact on it. In figure 8 the effect of the moisturecontent on D can be observed for temperatures between 90 oC and 100 oC.

18

20 30 40 50 60 70 80 90 100

0

0.5

1

1.5

2

2.5

3

3.510

-11

Figure 7: Effect of temperature and moisture concentration on the diffusion coefficient.

90 92 94 96 98 100

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.210

-11

Figure 8: Effect of temperature and moisture concentration on the diffusion coefficientfor temperatures between 90 oC and 100 oC.

It can be deduced that the moisture content has a small effect on the diffusion coeffi-cient, at least for moisture levels in this range which are considered indicative of those

19

that can be found in transformers.

The effect of temperature on the diffusion time constant is presented in figure 9 ford = 0.5 mm, C = 1 % and single-sided moisture diffusion. It can be observed thatfor lower temperatures, the diffusion of moisture needs a significantly larger amount oftime compared to higher temperatures. For comparison, the diffusion time constant at20 oC is equal to τ ≈ 14 days or τ ≈ 19910 minutes, while for 100 oC it is equal toτ ≈ 54 minutes.

20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

12

14

Figure 9: Effect of temperature on diffusion time constant for temperatures from 20 oCto 100 oC.

In conclusion, the diffusion coefficient, and in turn the diffusion of moisture from thesolid insulation, depends on several factors with the prominent one being temperature.Moreover, if the paper is oil-free, moisture can diffuse much easier and faster comparedto oil-impregnated paper. Lastly, the thickness of the insulation affects the diffusiontime constant, as does the type of the diffusion (single-sided or double-sided), while themoisture content has a smaller impact.

3.1.3 Estimation of the aging of solid insulation

Several factors can affect the degradation of the insulation and consequently the longevityof the transformer, thus it is important to be able to estimate the aging of the insulationas this can provide important information about the state of the transformer. Next,the estimation of the life expectancy of transformers considering oxygen and water is

20

described according to the IEC 60076-7 standard [28].

The DP is an index of the aging of the insulation, with low values indicating agedinsulations. In [28] the change of the DP value is given as

1

DPend

− 1

DPstart

= A · t · e−EA

R(θh+273) (21)

where DPend is the DP value of the solid insulation after the end of the loading cycle orat the moment that it is measured, DPstart is the initial DP value of the insulation, A isthe pre-exponential or environment factor [1/h], EA is the activation energy [kJ/mol],t is the duration of the loading under which the change of the DP value is estimated,R = 8.314 [J/(K·mol)] is the gas constant, and θh is the hot-spot temperature at whichthe insulation is subjected to [oC].

Equation (21) can be used to estimate the end DP value of the insulation under knownconditions regarding A, EA, θh and t as

DPend =

(1

DPstart

+ A · t · e−EA

R(θh+273)

)−1(22)

or it can be used to estimate the life expectancy of the transformer with knowledge ofDPend, DPstart, A, EA and θh. In [28] the life expectancy texp [years] is expressed byrearranging the terms of equation (21) and solving for t as

texp =1

DPend− 1

DPstart

A · 24 · 365· e

EAR(θh+273) (23)

Typical values of DPstart for new paper insulation is 1000, while a DP value of 200is characterized as the "end-of-life criterion" for a transformer [28]. Parameters EA

and A are related with the environmental conditions that the insulation is subjectedto (oxygen and moisture content) and the type of the paper (thermally upgraded ornon-thermally upgraded) and come in pairs.

In table 3 the values of EA and A are given for four combinations of oxygen andmoisture contents for non-thermally upgraded paper, presented in [29] and [30]. It canbe observed that when no oxygen is present in the system the value of EA remainsconstant independently from the moisture content, while the value of A increases withmoisture content. In systems with the presence of oxygen the values of EA and A arelower than those where no oxygen is present.

21

Table 3: Values of EA and A for non-thermally upgraded paper and for various combi-nations of oxygen content (O2) and moisture content (H2O) [29], [30].

Parameter Without O2 & Without O2 & Without O2 & With O2 &0.5 % H20 1.5 % H20 3.5 % H20 0.5 % H20

EA [kJ/mol] 128 128 128 89A [1/h] 4.1·1010 1.5·1011 4.5·1011 4.6·105

In table 4 the values of EA and A are presented for thermally upgraded paper for thesame combinations of oxygen and moisture content as in table 3. Both parametersare smaller than the respective ones for non-upgraded paper. It can be deduced fromequation (23) that the life expectancy texp of the thermally upgraded paper is longercompared to non-upgraded paper if both are subjected in the same conditions.

Table 4: Values of EA and A for thermally upgraded paper and for various combinationsof oxygen content (O2) and moisture content (H2O) [29], [30].

Parameter Without O2 & Without O2 & Without O2 & With O2 &0.5 % H20 1.5 % H20 3.5 % H20 0.5 % H20

EA [kJ/mol] 86 86 86 82A [1/h] 1.6·104 3·104 6.1·104 3.2·104

Using equation (23) and the values of EA and A from table 3, the life expectancy texpof non-thermally upgraded paper is calculated for temperatures from 70 oC to 130 oCand is presented in table 5. It is observed that temperature can have a quite largeimpact in the longevity of transformer insulation, as for hot-spot temperature 70 oC,no oxygen and 0.5 % moisture content the expected lifetime is 347 years, but for 100oC it is reduced to just under 10 years for the same oxygen and moisture levels. Inthe cases where no oxygen is present in the system, a drastic reduction of the lifetimeoccurs with the increase of the moisture content. For example, at 70 oC when themoisture content is 0.5 % the expected lifetime is 347 years and when 3.5 % moisture ispresent the lifetime decreases approximately by an order of magnitude. Similarly, whenoxygen is present in the system the expected lifetime experiences a substantial decreasecompared to the case where there is no oxygen in the system.

22

Table 5: Expected lifetime for non-thermally upgraded paper and for four combinationsof oxygen content (O2) and moisture content (H2O), and for a variety of hot-spottemperatures.

Expected lifetime [years]Hot-spot temperature Without O2 & Without O2 & Without O2 & With O2 &

θh [oC] 0.5 % H20 1.5 % H20 3.5 % H20 0.5 % H2070 347 95 31.6 35.580 97.3 26.6 8.9 14.790 29.3 8 2.7 6.4100 9.4 2.6 0.86 2.9110 3.2 0.9 0.3 1.4120 1.15 0.3 0.1 0.67130 0.43 0.12 0.04 0.34

The aging rate k is defined in [28] as

k = A · e−EA

R·(θh+273) (24)

and in figure 10 the Arrhenius plots for the aging process of non-thermally upgraded pa-per are given for the cases of table 3 and for absolute hot-spot temperatures T = θh+273[K] from 303 K to 403 K. In these graphs the natural logarithm of the aging rate kis plotted against the absolute hot-spot temperature. It can be observed that for thecases without oxygen the moisture content has a significant effect on the aging rate, asthe higher the moisture content the faster the insulation ages. For high temperatures(low values of 1/T ) by comparing the two cases with 0.5 % moisture content, it can beobserved that they have similar aging rates, which is an indicator that high tempera-ture has a more severe effect on insulation longevity than oxygen content. For lowertemperatures (high values of 1/T ) though, the aging rate is significantly higher whenoxygen is present.

23

2.5 2.6 2.7 2.8 2.9 3

10-3

-24

-22

-20

-18

-16

-14

-12

-10

Figure 10: Arrhenius plot for the aging rate of the cases of table 3.

3.2 Modeling of the experimental system

The moisture equilibrium in oil-paper systems depends on the temperature of the in-terface between oil and paper and the global moisture content of the system. When thesystem reaches steady state after a specific amount of time at a certain temperature,the share of moisture between oil and paper is determined and can be estimated withthe use of equilibrium curves. In the experimental setup of the present thesis, twodistinct equilibrium states are desired: in the first state (State 1) the whole systemis at room temperature 25 oC, while in the second state (State 2) the paper wrappedaround the cartridge heater is at 130 oC (measured in the second layer of the wrappedpaper). In between those states, dynamic phenomena take place where the moisture istransporting between the paper and the oil depending on if the system goes from State1 to State 2 or the other way around.

In this section, a calculation model is created that assesses the aging of the paperinsulation of the experimental setup. This model will be used for comparing the resultsfrom the laboratory experiment to the theoretical results. The system will be modeledin terms of its moisture equilibrium states according to subsection 3.1.1, the diffusionprocesses according to subsection 3.1.2 and the aging of the solid insulation accordingto subsection 3.1.3 while implementing the moisture dynamic phenomenon into thecalculations. In this modeling process, the distribution of the moisture between oiland paper is determined along with the diffusion time constants and the total moisture

24

that should be inserted into the system to reach a specific moisture percentage in thepaper at 25 oC. Also, the value of the degree of polymerization (DP) at the end of theexperimental cycle will be estimated using the method presented in subsection 3.1.3.The model aims to approach the phenomena that take place in the experiment andgive an estimation of the primary parameters that describe the system. As described insubsection 3.2.5, there are three different load patterns proposed by [18] that simulatedynamic loading of a transformer. These load patterns will be used in the modelingphase and their results will be compared in terms of DP values to conclude about theeffect of moisture on the aging of the paper insulation.

3.2.1 Representation of the experimental system

The experimental system is presented in figure 11. In this figure, the oil is representedwith the gold-yellow color and the paper wrapped around the cartridge heater is repre-sented with brown stripes.

L1

L2

L3

L4

D1

D2

L1

L2

L3

L4

D1

D2

L5

D3

Figure 11: Unit of the oil-paper system.

The oil-paper system is enclosed in a glass tube which is sealed with a cork. A smallair-gap is left in the tube for safety reasons as the top part of the cartridge heatersshould not come in contact with liquids since this might cause an electrical fault to thecomponent. The lengths which are illustrated in the figure will be used in the modeling

25

phase for the calculation of the various volumes of the system. The glass tube has aheight equal to 200 mm, an outer diameter equal to 38 mm and glass thickness equal to1.4 mm, as described in section 4.2. The cartridge heater has a total height 126.5 mm(the heating zone together with the cold zone are 125 mm, and the flange is 1.5 mm),a diameter of the heating zone cylinder (where the paper is wrapped around) equal to10 mm and a diameter of the flange equal to 27 mm (section 4.2). Table 6 containsthe dimensions of the glass tube and the cartridge heater, while table 7 contains thelengths which will be used in the modeling along with typical values that can be used inthe construction phase of the experimental set-up. Having figure 11 as a reference, thevolume of the oil and the air-gap in the system will be calculated, as this will providethe amount of the total moisture to be added in the system, as described in subsection3.2.2.

Table 6: Dimensions of the equipment depicted in figure 11.

Length Dimensions [mm]Tube height 200

Total cartridge height 126.5Cartridge height (hot & cold zones) 125

Flange height 1.5Glass tube outer diameter 38Glass tube inner diameter 35.2

Cartridge diameter 10Flange diameter 27

Table 7: Dimensions of the moisture equilibrium system depicted in figure 11.

Symbol Length Dimensions [mm]L1 Air-gap height 20L2 Oil-level height 160L3 Cartridge immersed in oil height 105L4 Cartridge exposed in air-gap height 20L5 Flange height 1.5D1 Cartridge diameter 10D2 Glass tube inner diameter 35.2D3 Flange diameter 27

26

3.2.2 Moisture equilibrium in the system at 25 oC and the effect of theair-gap

The moisture specifications that the experiment aims at have need to be taken intoconsideration. The moisture content in the paper is selected to be equal to 5 % weight-by-weight (w/w) at 25 oC, indicating a rather increased water content that will acceler-ate the aging process of the solid insulation. This percentage value indicates the watercontent of the solid insulation per weight paper. The weight of the paper, though, is afactor that has to be selected in accordance with the analysis requirements, as indicatedin [18] which states that the total weight of the paper that is needed for the DP analysisis equal to 0.8 grams. The total weight of the paper is selected at 1 gram, resulting into

H2Opaper =5

100· 1 · 103 = 50 mg (25)

of moisture in paper at 25 oC. Moreover, [18] states that the total oil volume that isneeded for the oil analysis is equal to 42 mL. This information, along with the varioustests to be conducted, are presented in table 8.

Table 8: Oil volumes and paper weight needed for the analysis of the samples [18].

Material Test Minimum quantityDissolved gas analysis 16 mL

Furan analysis 10 mLOil Acid number 6 mL

Moisture content in the oil 10 mLMethanol and ethanol content Reuse oil from previous tests

Paper DP test 0.8 grams

The first step is to calculate the equilibrium in the oil-paper system with the help ofOommen’s moisture equilibrium curves (figure 3b) at 25 oC. Since the targeted moisturecontent in the paper is 5 % weight-by-weight at 25 oC, the corresponding water contentin the oil can be estimated by using the set of curves in figure 3b. It can be observedthat there are no curves for this temperature, but there are curves for 20 oC and 30oC. These appear to follow a linear relation, thus a good approximation is to considerthat the curve at 25 oC can be estimated by using linear regression. From the curve of20 oC and for 5 % moisture in paper, the corresponding moisture in oil is equal to 17.4PPM, while from the curve of 30 oC and for 5 % moisture in paper, the correspondingmoisture in oil is equal to 30.15 PPM. This results in a moisture content of 23.775 PPMin the oil for 5 % moisture in paper at 25 oC. These values are presented in table 9.

27

Table 9: Moisture content in paper and oil at equilibrium at 25 oC.

Material Moisture contentPaper 5% w/wOil 23.775 PPM

Second, the volume of the mineral oil in the system is calculated as this, along with themoisture content in oil in table 9, will determine the total moisture content of the oil-paper system. The geometry of the glass tube is not precisely cylindrical, as its radiuson the bottom decreases, approaching a spherical shape. Also, the air-gap is not purelycylindrical as well as the cork has the shape of a flat cone. These deviations though,do not have a noticeable impact on the result and the calculations will be executed asif both geometries were cylindrical. The volume of the oil is given by

Voil = π

(D2

2

)2

L2− π(D1

2

)2

L3 (26)

resulting in Voil = 147.46 mL using the values from table 7. Thus, the moisture contentof oil at 25 oC with density equal to 913 kg/m3 [26] (typical value for transformermineral oils) is

H2Ooil = 23.775 · 10−6 · 913 · 106 · 147.46 · 10−6 = 3.2 mg (27)

Third, the air-gap in the tube may affect the total moisture content of the system, andpotentially have a significant effect on the paper moisture content and on the aging ofthe solid insulation. For this reason, the effect of the air-gap in the moisture of the sys-tem will be investigated. The air will be considered to be at a saturated state when thetube is sealed, which will indicate the maximum moisture content that the air can insertinto the system at room temperature of 25 oC, which is considered the temperature atwhich all tubes will be sealed. This moisture content is considered to be transferredcompletely to the paper insulation as this is the worst case in terms of aging, and theinvestigation will determine if the moisture content of the solid insulation experiencesa significant increase. Last, the moisture of the air-gap will be considered only if itseffect results in a noteworthy alteration of the moisture content of the paper, otherwiseonly the moisture content of oil and paper will be taken into account in the equilibriumcalculations.

The volume of the air-gap can be calculated by

Vair−gap = π

(D2

2

)2

L1− π(D1

2

)2

L4− π(D3

2

)2

L5 (28)

28

which results in Vair−gap = 17.03 mL with use of the values from table 7. The maximummoisture content that the air can hold at 25 oC is 23.85 gr/m3 [25], resulting in

H2Oair−gap = 17.03 · 10−6 · 23.85 · 103 = 0.406 mg (29)

of moisture for the air-gap of the experimental system. This value is significantly smallerthan the moisture contents of paper and oil, and if it were to be considered it wouldamount to 0.76 % of the total moisture in the system. As a result, it is concluded thatthe air-gap has no noteworthy effect in the system’s total moisture and can be neglectedin the calculations.

The information about the moisture content in the complex oil-paper system is sum-marized in table 10.

Table 10: Moisture content in paper and oil and at equilibrium at 25 oC along with theglobal moisture of the system.

Material Moisture content [mg]Paper 50Oil 3.2

System 53.2

3.2.3 Moisture equilibrium in the system at 130 oC

In subsection 3.2.2, the moisture equilibrium at 25 oC was estimated and used to deter-mine the share of moisture between oil and paper and to estimate the global moisturecontent in the system. This was performed with use of Oommen’s curves in figure 3b,which contain information about moisture concentration in oil up to 80 PPM. At highertemperatures, though, the equilibrium may dictate that the moisture content in oil islarger than 80 PPM, thus another set of curves that contains higher moisture concen-trations in oil and is considered reliable should be used. Such a set of curves availablein the literature is given in [27]. These curves originate from the same source as Oom-men’s curves and were developed by MIT. The advantage compared to the curves fromfigure 3b is that the equilibrium is calculated for oil moisture content up to 800 PPM,providing information for high water concentrations in the oil-paper system. This setof curves is presented in figure 12.

29

Figure 12: Moisture equilibrium curves in oil-paper systems for high moisture concen-trations [27] © 1999 IEEE.

Furthermore, figures 3a, 3b and 12 contain information for temperatures up to 100 oC,while State 2 in the experiment reaches 130 oC. This creates the need to estimate theequilibrium curve at that temperature. The 130 oC curve could be estimated math-ematically by having knowledge of the 100 oC curve, as the graphs appear to followa pattern, especially from 60 oC to 100 oC and for the levels of moisture content inpaper considered in the present model (≤ 5% w/w). In the following, the mathematicalexpressions of the equilibrium curves from 60 oC to 100 oC are derived as these will beused in the procedure to estimate the curve at 130 oC. The derivation of these mathe-matical expressions is done by firstly taking multiple points on the graphs and creatingan array for each curve of figure 12. Secondly, by using MATLAB’s Curve Fitting ap-plication, the curves can be approximated by a known mathematical expression withvery good precision for the range of the input data. The reproduction of figure 12 isshown in figure 13, where the obtained data points are plotted.

30

0 100 200 300 400 500 600 700 800

0

2

4

6

8

10

12

14

16

Figure 13: Moisture equilibrium curves - reproduction of figure 12.

Next, the curves from figure 13 for temperatures between 60 oC and 100 oC are approx-imated by fifth degree polynomials using the Curve Fitting application, which has theform

Pi(xi) = pi1 · x5i + pi2 · x4i + pi3 · x3i + pi4 · x2i + pi5 · xi + pi6 (30)

In equation (30) Pi(xi) is the moisture concentration in paper in [w/w %], xi representsthe respective oil moisture concentration in [PPM] and index i indicates the temperature(in oC) of the corresponding curve that is approximated. The values of the parametersfor each curve are presented in table 11 where the respective boundaries for xi for eachgraph are given.

Table 11: Parameters of equation (30) for each curve.

i xi pi1 pi2 pi3 pi4 pi5 pi6100 [0 - 800] 2.146 · 10−13 −3.860 · 10−10 2.674 · 10−7 −8.7480 · 10−5 0.02152 −0.237790 [0 - 592] 8.512 · 10−13 −1.153 · 10−9 6.113 · 10−7 −1.5540 · 10−4 0.02978 −0.194680 [0 - 429] 4.005 · 10−12 −4.054 · 10−9 1.614 · 10−6 −3.0920 · 10−4 0.04372 −0.229970 [0 - 306] 2.003 · 10−11 −1.469 · 10−8 4.283 · 10−6 −6.1040 · 10−4 0.06429 −0.211360 [0 - 216] 1.219 · 10−10 −6.494 · 10−8 1.361 · 10−5 −1.3750 · 10−3 0.09855 −0.1660

In figure 14, the original curves are presented with solid colored lines while the fittedcurves that are expressed by equation (30) and the values from table 11 are illustratedwith broken black lines.

31

0 100 200 300 400 500 600 700 800

0

1

2

3

4

5

6

7

8

9

10

Figure 14: Moisture equilibrium curves and fitting curves from 60 oC to 100 oC.

It can be observed that the fitting is accurate for values of the x-axis indicated in table11 and values of the y-axis up to 10 % w/w. Thus, the graphs described by equation(30) can mathematically represent the original curves with adequate precision.

In the following, with knowledge of these mathematical expressions, it will be investi-gated if the i + 10 curve can be linearly approximated with satisfactory precision byhaving knowledge of the corresponding i curve, for example if the 80 oC curve can beestimated by the 70 oC curve. A factor of proportionality c is desired that can be mul-tiplied with the polynomial of the i curve and can adequately express the i+ 10 curve.This is formulated mathematically as

Pi+10(x) ≈ c · Pi(x) (31)

The c factor is derived by firstly calculating the mean ratio between the i + 10 and icurves (for moisture concentrations in oil in the span of xi), for i = 60, 70, 80, 90, andafterwards calculating the average of these four mean ratios. This way, an average valueof c is obtained that can be used in equation (31) for the curves between 60 oC and 100oC to investigate if the i + 10 curve can be approximated this way. The values of themean ratios are presented in table 12.

32

Table 12: Mean ratios between the curves of figure 14.

i Mean ratio (Pi+10(x)/Pi(x))90 0.686180 0.711670 0.695860 0.6729

The average value of these ratios is c = 0.6916. Equation (31) can be rewritten as

Pi+10(x) ≈ 0.6916 · Pi(x) (32)

By using equation (32), the curves for temperatures from 70 oC to 100 oC are estimatedand plotted together with the original curves for comparison in figure 15. The estimatedcurves are illustrated with black broken lines while the original curves are presentedwith solid colored lines. It can be observed that the estimated curves have an errorcompared to the original ones, but they follow them closely for moisture contents inpaper up to 4.5 % w/w. The maximum error that each estimation curve has is calculatedas max(Pi+10(x)− Pi(x))/Pi(x) and is presented in table 13.

0 100 200 300 400 500 600

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Figure 15: Estimation of moisture equilibrium curves from 70 oC to 100 oC.

33

Table 13: Max error between estimation and actual curves in figure 15 calculated asmax(Pi+10(x)− Pi(x))/Pi(x).

i Max error in %90 6.457480 8.424170 5.747560 6.6263

By observing figure 15 it can be deduced that curve i + 10 can be mathematicallyapproximated with knowledge of curve i. It should be noted that the estimation of themoisture equilibrium in this way underestimates the moisture content of the paper forvalues between ≈ 1 % w/w and ≈ 4.5 % w/w. Equation (32) will be used to expressthe 130 oC curve and estimate the moisture equilibrium between oil and paper at thistemperature. Equation (32) can be rewritten in a general form as

Pi+k·10(x) ≈ 0.6913k · Pi(x) (33)

for (i+k ·10) ≥ 100 where i ≥ 60 and k ∈ N. The equilibrium state at 130 oC (i = 100,k = 3) can be estimated by

P130(x) ≈ 0.69163 · P100(x) (34)

It is known beforehand that this method will introduce a larger error in the moistureshare in the oil-paper system than that indicated in table 13 as there is no knowledgeof the 110 oC and 120 oC curves, and the 130 oC is estimated directly from the 100oC curve. Equation (34), though, will provide an indication for the levels of moistureshare between paper and oil at 130 oC, which is the initial aim. The estimated curve isillustrated in figure 16 along with the curves of figure 14.

The moisture equilibrium at 130 oC is calculated using equation (34) as

P130(x)

100· 1 · 103 + x · 10−6 · 913 · 106 · 147.46 · 10−6 = 53.2 mg (35)

and is presented in table 14. As mentioned before, the moisture content of paper islikely to be underestimated at 130 oC calculating the equilibrium in this way. By havingas a reference the maximum value in table 13, the error between estimation and actualmoisture share could be of the order of 1.0842413 − 1 = 1.2746− 1 = 27.46 %.

34

0 100 200 300 400 500 600 700 800

0

1

2

3

4

5

6

7

8

9

10

Figure 16: Fitting of moisture equilibrium curves for temperatures between 60 oC and100 oC and estimated 130 oC curve.

Table 14: Moisture content in paper and oil and at equilibrium at 130 oC along withthe global moisture of the system.

Material Moisture content Moisture content [mg]Paper 1.03 % w/w 10.3Oil 318.64 PPM 42.9

System 53.2 mg 53.2

For comparison, the equilibrium at 100 oC can be found by solving

P100(x)

100· 1 · 103 + x · 10−6 · 913 · 106 · 147.46 · 10−6 = 53.2 mg

and it results to moisture concentration in paper equal to 2.33 % w/w and in oil equalto 222 PPM.

3.2.4 Diffusion time constant

The moisture diffusion time constants for the two states of the system will be calculatedaccording to subsection 3.1.2. With reference to figure 11 the system experiences single-sided diffusion, thus equation (19) will be used to calculate the diffusion time constant,while the diffusion coefficient D is calculated from equation (20). The temperatures atthe two states of the system are 25 oC and 130 oC respectively. Equations (19) and(20) are rewritten below.

35

Single-sided diffusion time constant (equation (19)):

τ =4d2

π2D

Diffusion coefficient (equation (20)):

D = D0 e(0.5C+Ea(1/T0−1/T ))

In equation (19) the total thickness of the paper insulation d is required for the calcula-tion of the time constant and this depends on the paper that is used in the experiment.The heating zone of the cartridge heaters is 80 mm and the paper needs to be wrappedaround this region of the cartridge, thus a height equal to 75 mm is selected for theinsulation paper sheet. The density of the paper is equal to 72 µg/mm2 and the thick-ness of one layer of paper is 90 µm. Furthermore, for paper weight equal to 1 gramthe length of the paper is equal to 185 mm. Lastly, the radius of the heating zonethat the paper is wrapped around is 5 mm, resulting to v 6 layers of paper. Thus, thetotal thickness of the paper insulation wrapped around the cartridge heater is equal tod = 0.54 mm.

From State 1 to State 2 The system is assumed to be initially at equilibrium at25 oC (State 1) with a starting moisture content 5 % w/w and then the temperatureis assumed to increase instantaneously to 130 oC (State 2) for simplification, thus themoisture will start migrating from paper to oil to reach an equilibrium at this tem-perature, which was previously estimated at 1.03 % w/w. The diffusion coefficient iscalculated using equation (20) for T = (273 + 130) K and C = 5 % which results toD = 1.5986 · 10−10 m2/s. The diffusion time constant at this state is calculated usingequation (19) and is equal to τ = 12.3 minutes.

From State 2 to State 1 Moreover, when the system goes from State 2 to State 1,the temperature is assumed for simplification to go from 130 oC to 25 oC instantaneouslywith an initial moisture content 1.03 % w/w. In this case, the moisture transports fromoil to paper to reach an equilibrium at State 1 at 5 % w/w. The diffusion coefficientis calculated in the same way for T = (273 + 25) K and C = 1.03 % which results toD = 1.3469 · 10−13 m2/s. The diffusion time constant at this state is calculated usingequation (19) and is equal to τ = 10.15 days.

The parameters are summarized in table 15. The difference in the order of magnitudeof the time constants is obvious and is a result of the temperature difference in the twoprocesses.

36

Table 15: Diffusion parameters of the experimental system.

From To D [m2/s] τ

State 1 State 2 1.5986 · 10−10 12.3 minutesState 2 State 1 1.3469 · 10−13 10.15 days

The time constants of the diffusion processes presented in table 15 will be used insubsection 3.2.5 to mathematically model the moisture migration phenomenon as anexponential procedure.

3.2.5 Aging of the solid insulation

In subsection 3.1.3 the methodology for estimating the aging of solid insulation was pre-sented according to IEC standard 60076-7 [28]. In the present subsection, the methodaccording to [28] will be implemented to the experimental system while taking intoconsideration the moisture migration phenomenon.

The experimental design of [18] consists of three different load patterns, namely LoadPattern 1 (LP1), Load Pattern 2 (LP2) and Load Pattern 3 (LP3). The interest behindthe experiment is to investigate the effect of moisture transport in the aging of oil-paperinsulation systems under different load patterns. Potentially, these load patterns canaffect the aging of the insulation differently due to moisture migration. The oil-paperinsulation is heated in different patterns in terms of the frequency and duration of theheating cycles depending on LP1, LP2 and LP3. This way, the moisture transportphenomenon varies in oil-paper systems subjected at different load patterns, as thephenomenon depends on the temperature equilibrium between oil and paper.

The load patterns that were designed in [18] are depicted in figure 17 for one cycle. Thelength of one cycle is 36 days, and is the same for all load patterns. The total amountof energy Q that is injected into the system in one cycle is the same for the three loadpatterns. As it can be seen from the figure, though, the energy is injected in threesegments in LP1, in two segments in LP2 and in one segment in LP3. This way, themoisture transport phenomenon in one cycle will occur three times in LP1, two timesin LP2 and one time in LP3. According to [18], the experimental set-up is designedso that the following relations are valid for the time intervals, with reference to figure 17:

Time intervals where energy is injected (on-time):

t′1 + (t′3 − t′2) + (t′5 − t′4) = t′′1 + (t′′3 − t′′2) = t′′′1 (36)

Time with no heat generation (off-time):

(t′2 − t′1) + (t′4 − t′3) + (t′6 − t′5) = (t′′2 − t′′1) + (t′′4 − t′′3) = (t′′′2 − t′′′1 ) (37)

37

End of cycle:t′6 = t′′4 = t′′′2 (38)

t [days]

t [days]

t [days]0

0

0

Q, c

Q, c

Q, c

t1’’’

t1’

t1’’

Q: injected heat, red color

c: moisture concentration in paper, blue color

Q: injected heat, red color

c: moisture concentration in paper, blue color

LP 1

LP 2

LP 3

t2’ t3’ t4’ t5’ t6’

t2’’ t3’’ t4’’

t2’’’

t [days]

t [days]

t [days]0

0

0

Q, c

Q, c

Q, c

t1’’’

t1’

t1’’

Q: injected heat, red color

c: moisture concentration in paper, blue color

LP 1

LP 2

LP 3

t2’ t3’ t4’ t5’ t6’

t2’’ t3’’ t4’’

t2’’’

Figure 17: Illustration of moisture migration and injected energy in the system for thethree different load patterns (inspired by [18]).

In figure 17, the moisture content of the solid insulation is illustrated with the bluecurves while the injected energy is presented with the red lines. At the intervals wherethe moisture is migrating from the paper to the oil and heat is generated in the system,the experimental set-up is at State 2, while when no heat is generated and the moisturemigrates back to the paper the set-up is at State 1. The curves that represent themoisture concentration intend to illustrate the diffusion processes at State 1 and State2 according to the analysis made in subsection 3.2.4. The moisture migration will beconsidered only during State 2 in the estimation of the aging of the paper insulation, asthis is the state where the system experiences significant aging due to the temperatureof 130 oC. The temperature of 25 oC has no noticeable effect in the aging process andthe moisture transport will not be accounted. The process of moisture migration frompaper to oil in one cycle occurs three times in LP1, two times in LP2 and one time inLP3 and potentially this can affect the aging of the insulation differently.

The time intervals selected in [18] for the different load patterns are presented in table16 and will be used in the estimation of the aging of the paper insulation.

38

Table 16: Time intervals where energy is injected in the system with reference to figure17 presented in [18].

Load pattern On-time [days] Off-time [days]LP1 2 10LP2 3 15LP3 6 30

The diffusion time constant for the transition from State 1 to State 2 calculated insubsection 3.2.4 is equal to 12.3 minutes, however table 16 indicates an on-time in thescale of days. This is because the intended result is to expose the paper insulationin high temperature for a prolonged period of time, so significant aging can occur astransformers are in use for many decades and the experiment is targeting at analyzingmeaningful results in the time-scale of months.

In the following, the aging of the solid insulation in the three different load patternsis investigated by means of the DP value with use of equation (21), which is rewrittenbelow.

1

DPend

− 1

DPstart

= A · t · e−EA

R(θh+273)

Table 3 presents values of EA and A only for some moisture contents in paper, thus it isneeded to estimate their values in the moisture contents that the experimental systemwill experience, that is at 5 % w/w and 1.03 % w/w as was previously calculated.The system contains a limited amount of oxygen and as a result the values of EA andA for no oxygen will be used. As mentioned in subsection 3.1.3, when no oxygen ispresent in the system the value of EA is constant and equal to 128 kJ/mol. ParameterA though needs to be estimated and to do so, the values of A from table 3 are plottedin MATLAB and with use of the Curve Fitting application a curve is fitted in the data.This is presented in figure 18.

39

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

1

2

3

4

5

6

7

810

11

Figure 18: Regression of values of A from table 3.

The curve that fits the data in figure 18 is mathematically expressed by

A(c) = 1.367 · 1010 · c2 + 8.167 · 1010 · c− 3.25 · 109 (39)

for concentrations from 0.5 % w/w to 5 % w/w, where A [1/h] is a function of themoisture concentration c [%].

During the moisture transport processes though, the moisture content in paper is notconstant and can be described mathematically by

c(t) = c∞ + (cstart − c∞)e−tτ (40)

where t [minutes] is the time, c(t) [%] is the instantaneous value of the moisture con-centration in paper at time t, c∞ [%] is the final value of moisture concentration at theend of the dynamic phenomenon, cstart [%] is the initial value of moisture concentrationat the beginning of the migration process and τ [minutes] is the diffusion time constantvalues from table 15. This change in the moisture content as described by equation(40) will affect parameter A which in turn will have an effect on the DP value duringthe moisture migration process. Equation (40) is plotted against time in figure 19 forthe transition from State 1 to State 2. It can be seen that after 120 minutes at 130oC, moisture equilibrium has been reached, thus the moisture diffusion process will beincluded into the aging calculations for the first 120 minutes. Moreover, in figure 20the moisture concentration in paper is plotted against time for the moisture migra-tion process from oil back to paper. It can be seen in the figure that it takes a littleless that ten time constants (91 days) for the moisture to migrate entirely back to paper.

40

0 50 100 150 200 250

1

1.5

2

2.5

3

3.5

4

4.5

5

X: 100

Y: 1.031

X: 120

Y: 1.03

X: 240

Y: 1.03

Figure 19: Moisture concentration c(t) in paper during the migration process frompaper to oil.

0 10 20 30 40 50 60 70 80 90 100

1

1.5

2

2.5

3

3.5

4

4.5

5

X: 10

Y: 3.518

X: 91.2

Y: 5

X: 80

Y: 4.999

Figure 20: Moisture concentration c(t) in paper during the migration process from oilto paper.

By combining equations (39) and (40), the value of A as a function of time t during thediffusion process can be estimated as

A(t) = 1.367 · 1010 · c(t)2 + 8.167 · 1010 · c(t)− 3.25 · 109 (41)

Equation (22) can be written with use of equation (41) for times t during the diffusion

41

process as

DP ′end =

(1

DP ′start+ A(t) · t · e−

EAR(θh+273)

)−1(42)

where A is a function of t when moisture transports from paper to oil, while onceequilibrium has been established it has the form of equation (22) where A has a constantvalue, rewritten below

DPend =

(1

DPstart

+ A · t · e−EA

R(θh+273)

)−1First step The calculation of the DP value of the paper starts by assuming a valueof DP ′start = 1000 in equation (42) according to [28]. Then, for the first 120 minutesof the transition phase from State 1 to State 2, the moisture diffusion is taken intoaccount and equation (42) is used. As mentioned, this phase lasts approximately 120minutes, and by dividing this time-frame into smaller segments the value of c(t) andconsequently of A(t) can be calculated into each segment (as a reminder, EA = 128kJ/mol throughout the whole calculation process). In MATLAB this time-frame isdivided into 1-minute segments, resulting in 120 segments in total, thus t in equation(42) equals t = 1/60 [hours] in all three load patterns. Furthermore, the value of DP ′endis calculated recursively for 120 iterations, where in each iteration, except the first iter-ation of the first cycle, the value of DP ′start is the previously calculated value of DP ′end.This first step is identical in all three load patterns and the calculations concerning theDP value during the transitional phase are given by the following equations (based on(42)), where t1 = t2 = t3 = 1/60 hours and θh = 130 oC.

For LP1

DP ′end,1 =

(1

DP ′start,1+ A(t) · t1 · e

− EAR(θh+273)

)−1(43)

For LP2

DP ′end,2 =

(1

DP ′start,2+ A(t) · t2 · e

− EAR(θh+273)

)−1(44)

For LP3

DP ′end,3 =

(1

DP ′start,3+ A(t) · t3 · e

− EAR(θh+273)

)−1(45)

In the first iteration of the first cycle it is assumed that the initial moisture content ofthe paper in all 3 load patterns is equal to 5 % w/w. After that, the initial moisturecontent is calculated using equation (40) where t takes the values of the respective off-times of each load pattern. This means that the moisture migration phenomenon from

42

paper to oil happens at different initial moisture concentration levels that depend onthe load pattern. The initial moisture content will be less than 5 % w/w, as the timeconstant of this migration phenomenon was calculated equal to 10.15 days.

Second step After this 120-minute time-frame is over, equation (22) is used, whereDPstart takes the value of DP ′end of the last iteration of the first step. Also, A is cal-culated according to equation (39) for moisture content in paper equal to c = 1.03% w/w, while t depends on the load pattern and the values of table 16. For LP1,t1 = 2 · 24 − 2 = 46 hours, as the on-time for this load pattern is 2 days and themoisture transport phenomenon takes place for 2 hours (120 minutes). For LP2,t2 = 3 · 24 − 2 = 70 hours, while for LP3 t3 = 6 · 24 − 2 = 142 hours. The calcu-lations concerning the DP value during equilibrium in the three different load patternsare realized using the following equations (based on 22) for θh = 130 oC.

For LP1

DPend,1 =

(1

DPstart,1

+ A · t1 · e− EAR(θh+273)

)−1(46)

For LP2

DPend,2 =

(1

DPstart,2

+ A · t2 · e− EAR(θh+273)

)−1(47)

For LP3

DPend,3 =

(1

DPstart,3

+ A · t3 · e− EAR(θh+273)

)−1(48)

Third step After the on-time is over, the system is not supplied with power and thetemperature is supposed to go to 25 oC instantaneously. Equations (46), (47) and (48)are used to calculate the effect of this temperature on the aging of the paper. Thestarting value DPstart,i (where i = 1, 2, 3) in these equations is the value calculated asDPend,i (i = 1, 2, 3) at the end of the second step, θh = 25 oC, while t1 = 10 · 24 = 240hours, t2 = 15 · 24 = 360 hours and t3 = 30 · 24 = 720 hours with reference to table 16.The value of A is calculated for the respective moisture content of each load patternafter t1, t2 and t3 hours for LP1, LP2 and LP3 respectively, according to equation (39).It is noted that the moisture migration effect in this step is not taken into consideration,as the low value of temperature does not have a noticeable impact on the aging.

Fourth step After the first three steps are completed three times for LP1, two timesfor LP2 and one time for LP3, the calculations for one cycle of 36 days have beenperformed. If more cycles are desired, then steps one through three are repeated, withthe only difference being that the value of DP ′start,i (i = 1, 2, 3) in equations (43), (44)and (45) for the first iteration are equal to the respective values DPend,i (i = 1, 2, 3) at

43

the end of the third step.

By performing these four steps for a duration of 6 cycles, the DP values at the endof these 6 cycles of the three different load patterns can be estimated. The resultsare presented in table 17. It can be seen that the DP value differs between the threeload patterns, with LP1 experiencing the largest aging, LP3 the least aging and LP2an intermediate aging. The only difference between these three loading patterns is thenumbers of times that the moisture transport phenomenon occurs. It can be concludedthat the moisture migration phenomenon affects the aging of the paper, and the moretimes it occurs, the largest the impact. Experimentally though, this difference cannotbe observed as it is very small.

Table 17: Estimation of aging of the solid insulation considering the moisture transportphenomenon.

Load pattern DPstart DPend

LP1 1000 317.94LP2 1000 318.50LP3 1000 319.55

For comparison, theDPend value for all three load patterns when the moisture migrationis not taken into consideration is equal to DPend = 321.33 and is the same for all 3load patterns, thus the moisture transport between oil and paper affects the aging ofthe solid insulation as table 17 indicates, but the calculated difference is rather small tobe measured experimentally. Since this difference is small, another set of preliminaryload pattern is examined to investigate further the effects of the moisture transportdynamics on the aging of the solid insulation and potentially amplify the difference inthe DP value of the various load patterns. The load patterns that showcase the largestdifference among them can be potentially used in the experimental phase. The total on-and off-times in one cycle are set to be equal to those dictated by LP1, LP2 and LP3.The ratio between on- and off-times of these load patterns is held constant and equal to1:5 as in LP1, LP2 and LP3. The on- and off-times of the load patterns are presentedin table 18. The illustration of the moisture migration phenomenon and the injectedheat into the system is similar to those depicted in figure 17 and is not repeated here.

44

Table 18: Time intervals where energy is injected in the system for a set of preliminaryload patterns.

Load pattern On-time [days] Off-time [days]LP4 4/24 (4 hours) 20/24 (20 hours)LP5 8/24 (8 hours) 40/24 (40 hours)LP6 0.5 (12 hours) 2.5 (60 hours)LP7 1 5

After implementing the four steps of the calculation method described previously for6 cycles, the results are presented in table 19. The number of times that the moisturemigration from paper to oil occurs in one cycle is presented in column "Frequency".

Table 19: Estimation of aging of the solid insulation considering the moisture transportphenomenon for all load patterns.

Load pattern DPstart DPend FrequencyLP1 1000 317.94 3LP2 1000 318.50 2LP3 1000 319.55 1LP4 1000 315.95 36LP5 1000 316.51 18LP6 1000 316.74 12LP7 1000 317.25 6

3.3 Discussion

In this chapter, an overview of moisture in oil-paper systems was presented where im-portant factors such as the moisture equilibrium between oil and paper, the moisturediffusion and the aging of the paper due to moisture migration and exposure to hightemperatures were analyzed. Furthermore, a calculation model was developed that aimsat estimating the effect of moisture migration in the aging of the solid insulation of theexperimental system. The model takes into account the moisture equilibrium betweenoil and paper, the diffusion of moisture from the insulation, and the aging of the paperdue to the existence of moisture content, moisture dynamics, and high temperatures.The method from [28] was used for calculating the DP value of the paper insulation,while the model created in this thesis adds the effect of moisture dynamics in the agingcalculations.

The modeling starts with calculating the moisture equilibrium at 25 oC by known setsof curves and continues with estimating the equilibrium at 130 oC. Linear regression

45

was used to estimate the equilibrium at State 2, which introduces an error in the cal-culations, however the approximation is considered to be in acceptable levels for thepurpose of the model, which is to investigate the effect of moisture migration in theaging of the paper insulation. The actual moisture content in paper at equilibrium atState 2 can be larger that the calculated value of 1.03 % w/w as per figure 15, which canpotentially further affect the aging. The moisture diffusion in the system was modeledaccording to [27] and the aging according to [28]. The result of the modeling, presentedsubsection 3.2.5, is that the phenomenon of moisture migration between oil and papercan affect the aging of the paper. It is suggested that different load patterns are usedin the experimental part, though, so the effect of the phenomenon can be amplified asexplained in the following.

The differences in the DP values of the load patterns indicated in table 19 are quitesmall to be observed experimentally, as several factors can affect the temperature andthus the aging of the paper as explained in chapter 4. One of those factors is the re-sistance of the cartridge heaters, which could result in differences in temperature thathave a significant effect on the expected aging. It is advised to increase the number oftimes that the moisture migration phenomenon occurs in the load patterns that will beimplemented in the experimental set-up, as was done in the preliminary load patterns(LP4 to LP7). During the modeling phase it was concluded that the loading time afterequilibrium has been established does not contribute to any observable differences in theaging, as the insulation of each load pattern is subjected to 130 oC for approximatelythe same time. LP4 is subjected to this high temperature with a moisture content of1.03 % w/w in paper less total time compared to the other load patterns as the diffusionof moisture happens with higher frequency, but it experiences the largest aging out ofthe seven load patterns, so the moisture migration phenomenon is the differentiatingfactor that affects its DP value. It is known beforehand that the moisture equilibriumat State 1 is not established in any load pattern, but it does not have any impact onthe aging process, other than when the transition from State 1 to State 2 takes place,the initial moisture content of the paper is lower than 5 % w/w. This initial moisturecontent can be easily calculated using equation (40) for a specific time instant t. Itis suggested that the temperature at State 2 is decreased, as this would prolong thediffusion time constant, and thus, the time that the moisture transport phenomenontakes place, allowing for longer exposure under the diffusion process. This investigationis suggested to be performed as future work, where the appropriate time intervals foron- and off-times can be concluded along with the proper temperature at State 2.

Furthermore, it is noted that the term "diffusion time constant" mentioned in thischapter does not provide the time needed for moisture equilibrium to be established.When referring to decreasing processes, the time constant indicates the time needed for

46

the quantity to have decreased to approximately 36.8 % of the initial value, while whenreferring to increasing systems it indicates the time needed to reach approximately 63.2% of the final value.

Lastly, it is noted that the temperature of the cellulose insulation during the modelingprocess was considered to be the same and constant throughout the thickness of thepaper (all layers where supposed to have the same temperature). This is not true forthe experimental system though, as a radial decrease in the temperature of the paperwill occur in reality which will affect the aging of the paper.

47

4 Experimental

In this section, the laboratory work of the present thesis is presented. This workincludes implementing the experimental design into hardware, selecting the appropriateexperimental equipment, designing a heat dissipation system, conducting a sensitivityanalysis on the laboratory set-up & investigating the behavior of the cartridge heaters’resistance under temperature increase and over time, and, conducting preliminary tests.

4.1 Design of the experimental set-up

The design of the experimental set-up is the result of previous work [18]. The designaims to control simultaneously the three load patterns described in subsection 3.2.5(LP1, LP2, LP3) and illustrated in figure 17 in an efficient way. It allows for multipleoil-paper units, such the one presented in figure 11, to be controlled and monitored atthe same time. This way, experimental units can be extracted from the set-up and besent for analysis at selected points in time, for example after one cycle, three cycles orsix cycles.

The injected heat into the system is realized by using cartridge heaters and controllingtheir input voltage using solid-state relays (SSR). The SSRs are controlled by meansof pulse-width modulation (PWM) and the duty cycle of the PWM has to be suchthat the temperature as State 2 is equal to 130 oC. In total, three SSRs are used inthe experimental set-up, where each SSR controls one load pattern. The design allowsto control the duty cycle of the PWM signal of each SSR, and is programmed to in-ject power into each load pattern according to the on and off-times presented in table 16.

The design of the experimental set-up was programmed in LabVIEW [18]. Originally,analog output signals were utilized to generate the PWM waveforms that control theSSRs of all load patterns, but once the program was implemented into the hardwareit was not possible to control all three relays at the same time due to incompatibilitywith the equipment. The design was then slightly altered and digital signals where usedto control the relays instead, which proved to be a much more efficient and accuratemethod, as all switches can be controlled simultaneously and no latency is observedin the signals. The LabVIEW program is implemented into hardware from NationalInstruments (NI) which interacts with the equipment of the experimental set-up.

4.1.1 Programming in LabVIEW

The program in LabVIEW is presented in figures 21, 22 and 23. Figure 21 illustratesthe set-up for controlling one load pattern (in this case LP1), figure 22 presents theblock that measures and stores the temperatures of the system, and figure 23 depicts

48

the front panel of the program. The design is based on control blocks, signal generationblocks, data acquisition blocks, while-loops and flat-sequence structures.

Figure 21: Block in LabVIEW that controls the solid-state relay of one load pattern.

The set-up of figure 21 presents the design in LabVIEW that controls one SSR bygenerating the appropriate PWM signal and setting the desired on and off-times for therespective load pattern. The whole structure is enclosed in one while-loop. Analytically,the control block contains:

• Part 1 consists of one large while-loop embodied in the first frame of the mainsequential structure. It also contains a smaller sequential structure that includesparts 2 and 3. The while-loop contains an elapsed-time block, named "LP1 ON",that controls the on-time of the load pattern. The elapsed-time block receives atime target as an input and ensures that all operations contained in the while-loopcontinue running until the targeted time is reached. In the example of the picturethe input time is 2 ·86400 seconds, which corresponds to 2 days. The elapsed timeand the time left in the loop are also displayed in the front panel of figure 23.Once the targeted time has elapsed, the operations of the while-loop are finishedand the program proceeds to the second sequence frame, indicated by number 4.

• Part 2 consists of a while-loop that contains a data acquisition (DAQ) assistantand an elapsed-time block. The DAQ assistant communicates with the NI hard-ware and generates a digital signal of amplitude +5 V DC when the the loopis active which closes the SSR of the respective load pattern. The elapsed-timeblock controls the time that the loop is active, which essentially indicates the dutyratio of the PWM control signal. Once time has elapsed the operation continuesto the next sequential frame, which is indicated by 3.

49

• In part 3, similarly to part 2, the while-loop controls the off-state of the SSR withan elapsed-time block and a DAQ assistant. When this loop is active the digitalsignal that controls the relay is deactivated (amplitude equal to 0 V DC) and theSSR is open. The sequence returns to part 2 once the time has elapsed and thewhile-loop of part 1 is active. The combination of parts 2 and 3 creates the PWMcontrol signal.

• In part 4 the while-loop controls the off-time of the load pattern and is activatedonce time has elapsed in part 1. It contains an elapsed-time block and a DAQassistant. The elapsed-time block controls the time when no energy is injectedinto the load pattern (off-time), while the DAQ assistant dictates that the controlsignal of the respective SSR is deactivated (amplitude equal to 0 V DC) and therelay is open. Once time elapses in this part, the sequential structure will activatepart 1 once again.

• Lastly, part 5 consists of lamp indicators which are controlled by the local variablesof the while-loops that communicate with the front panel of figure 23 indicatingif the load pattern is active or inactive and if the SSR is on or off.

Figure 22: Block in LabVIEW that acquires and stores the temperatures of the system.

Figure 22 presents the temperature measurement structure. This design, collects thetemperatures of the experimental set-up and logs them to the computer. More analyt-ically:

• Element 1’ is a DAQ assistant which communicates with the NI hardware toacquire the temperature measurements. The number and type of thermocouplesconnected to the hardware can be selected, while the received data are plotted inthe front panel of figure 23 using the ’Waveform Chart’ element.

50

• Element 2’ is a signal collector. This element collects the temperature measure-ments.

• Element 3’ writes the collected signals from 2’ in a text-format file. The type ofthe file can be selected, while a new file is created with each iteration.

• Element 4’ defines the frequency that the measurements are acquired.

Figure 23: Front panel of the design in LabVIEW.

Figure 23 illustrates the front panel of the LabVIEW program. Information concerningthe state of the load patterns and their SSRs are displayed along with the temperaturemeasurements.

• In 1” & 2” the status of the load pattern is visible. This contains informationabout the elapsed time and the time left for both on and off-states. Also, lampindicators visualize if the load pattern is active or inactive.

• The LED of 3” displays the state of the respective SSR. If the LED is on the therelay is closed, while if it is off then the relay is opened.

• In 4” the information concerning the temperature files are displayed. By adjustingthe maximum iteration and delay time settings, the number of measurements

51

written in the file and the frequency that the measurements are acquired can beset.

• In 5” the waveform chart for the temperatures is illustrated.

4.1.2 Hardware implementation

The programming in LabVIEW is implemented into hardware using equipment fromNI. This equipment consists of an NI PXIe-1073 chassis, an NI PXIe-6368 card, an NIBNC-2120 connector block and an NI SCB-68 pin connector block. These devices arepresented in figure 24.

Figure 24: NI hardware equipment: (a) PXIe-1073 chassis with PXIe-6368 card, (b)BNC-2120 connector block, (c) SCB-68 pin connector block, (d) NI equipment.

The card is inserted in the chassis which is connected to the computer running theLabVIEW program. The connector blocks are connected with the card, and this waythey can be controlled from the computer. The two connector blocks (BNC-2120 andSCB-68) have analog and digital inputs and outputs making the interaction with the

52

experimental set-up feasible. The SCB-68 block is a screw-terminal device, while theBNC-2120 connector has BNC terminals as well. The SSRs are connected to the digi-tal outputs of the BNC-2120 connector, while the inputs from the thermocouples thatmeasure the temperatures of the solid insulation of the set-up can be connected in bothdevices.

Another temperature logger that can be used in the experiment is the TC-08 Ther-mocouple Data Logger from Pico Technology. This device can be connected to thecomputer via USB and is user-friendly. No programming is required for the TC-08 tomeasure and log the temperatures of the set-up. This device is illustrated in figure 25.

Figure 25: TC-08 Thermocouple Data Logger from Pico Technology.

4.2 Equipment of the experimental set-up

In this section the equipment of the experimental set-up is presented. With reference tofigure 11, the oil-paper insulation of a real transformer is approximated by tightly wrap-ping insulation paper around a cartridge heater which is submersed into transformeroil in a glass tube container. The glass tube container is firmly sealed afterwards,while both the oil and the paper have been appropriately treated with the amounts ofmoisture defined in the previous chapter. This set-up models the heating of the solidinsulation inside an oil-filled transformer with a certain moisture content. The tube isthen inserted in a custom-made aluminum cylinder which acts as a heat sink to dissi-pate the generated heat. For the purpose of the experiment, additional equipment isused, such as thermocouples, solid-state relays, a safety box, and other parts that arepresented in subsection 4.2.7.

53

4.2.1 Cartridge heaters

Cartridge heaters are elements used for heating purposes. They utilize electric powerto generate heat, and their operation is based on resistive heating. This means that theheat is generated in terms of resistive losses in the element following Joule’s law

Pcartridge = I2Rcartridge (49)

where Pcartridge [W] is the power, I [A] is the RMS value of the current flowing throughthe cartridge and Rcartridge [Ω] is the ohmic resistance of the cartridge. The advantageof these devices for the purposes of the experiment is that heat generation depends onthe consumed electric power, thus having the ability to turn them on and off at will,this way having complete control on the generated heat.

The cartridges selected in the present experiment have nominal power equal to 200 Wand nominal operating voltage 230 V. This means that their resistance under nominaloperation should be Rcartridge = 2302/200 = 264.5 Ω. However, after measuring thevalues of the resistors at 25 oC in the lab, the actual values deviate from the nominalone, and the manufacturer claims tolerance levels between -5% and +10% from thenominal value, which corresponds to a span from 251.3 Ω to 291 Ω. The measuredvalues when the cartridges are unused are presented in table 20, in ascending order.

It can be seen that the cartridges can vary over 30 Ω in their resistance. This variationwill create imbalances in the power consumed by each cartridge, and consequently inthe generated heat and temperature on the insulation, as described in subsection 4.2.4.The technical drawing of the cartridge heater used in the experiment is illustrated infigure 26 (from IHP, International Heating Products). The dimensions in the figure aregiven in millimeters (mm). The cartridge heater should not be immersed entirely inoil, as this may cause a fault in the component. The part of it that can be in the oil isindicated in figure 26 as "part into media". A cartridge heater used in the experimentis illustrated in figure 27.

54

Table 20: Cartridge heaters initial resistor values at 25 oC.

Measured value [Ω] Deviation from nominal value [%]236.6 -10.55239.3 -9.53239.7 -9.38241.5 -8.70241.8 -8.58242.3 -8.39243.5 -7.94244.6 -7.52244.8 -7.45246 -7.00246.7 -6.73247.8 -6.31248.8 -5.94252.2 -4.54267.5 1.13268 1.32268.7 1.59269.8 2.00

part into media

125 mm 300 mm

5 mm 80 mm 40 mm

part into media

125 mm 300 mm

5 mm 80 mm 40 mm 1.5 mmheating zone cold zone

cold zone

Φ10 mm

Φ27 mm

part into media

125 mm 300 mm

5 mm 80 mm 40 mm 1.5 mmheating zone cold zone

cold zone

Φ10 mm

Φ27 mm

Figure 26: Drawing of the cartridge heater.

55

Figure 27: Cartridge heater used in the experiment.

Some cartridges were used in preliminary experiments and when their resistance wasmeasured after being used, it was noticed that it increased. This observation led toa sensitivity analysis of the laboratory set-up concerning the behavior of the cartridgeheaters and all cartridges were subjected to loading tests, as the temperature increasein the cartridges is the probable cause of this behavior. These tests aimed at examiningif all cartridges would behave similarly and if their resistance would reach a constantvalue after being loaded for a certain period of time.

During the tests, the cartridges were immersed in water and they were controlled bythe arrangement described in section 4.1, by a PWM signal with a duty ratio equal to0.75 and a period of 40 msec. The cartridges were connected in parallel, thus everycartridge was subjected to the same voltage. Naturally, cartridges with smaller resis-tance consumed larger amounts of power, and thus, generated more energy and theirtemperature was higher compared to cartridges with larger resistance.

56

Table 21: Cartridge heaters resistor values at 25 oC after being loaded.

Rstart [Ω] R∞ [Ω] Deviation from nominal value [%]236.6 253.2 -4.60239.3 253.1 -4.63239.7 254.3 -4.18241.5 256.7 -3.28241.8 256.7 -3.28242.3 256.7 -3.28243.5 255 -3.92244.6 257.2 -3.09244.8 256.9 -3.20246 260.7 -1.77246.7 260.2 -1.96247.8 259.5 -2.22267.5 278.3 4.86268 278.4 4.90268.7 279 5.12269.8 279.3 5.24

During these tests, the value of the resistance of the cartridge heaters was measured atselected points in time, while the cartridges were still hot right after being disconnectedfrom the power source. It was observed that there is a faster increase in resistance atthe beginning of the tests, thus more frequent measurements were made during thisperiod (1 measurement every 30 minutes). These measurements were plotted againsttime and the conclusion of these tests is that the behavior of their resistance follows anexponential relation that can be approximated by

R(t) = R∞ + (Rstart −R∞)e− t

τR (50)

where R(t) [Ω] is the instantaneous value of the resistance at instant t [minutes], R∞[Ω] is the final value of the resistance, Rstart [Ω] is the resistance when the cartridgewas unused (table 20) and τR [minutes] is the time constant of the resistance. The pa-rameters of equation (50) depend on the initial resistor value. It is important that theresistance has come to a constant value before the cartridges are used in the experimentso the correct duty ratio can be found for the temperature of State 2. It is concludedfrom the tests that the cartridges need to be loaded for at least 15 hours before theirresistance reaches a stable value in the conditions described previously, and the timeconstant τR is approximately 120 minutes, but it is different for each cartridge.

57

Figure 28: Approximation of the behavior of the resistance of the cartridge heaters.

4.2.2 Glass tube containers

The oil-paper insulation system should be in a sealed container to have as much controlof the moisture as possible. Options that were considered to be used as containers werethermal resistive bottles and glass tubes. The latter was the selected option, mainlyfor cost-related reasons, as the bottles were significantly more expensive. The selectedglass tubes are made of borosilicate glass 3.3. The glass tubes will be sealed usingcorks, though, this required that the corks are slightly trimmed so that the wires of thecartridge heaters and the thermocouples could exit the containers. Moreover, glue canused in the incision between the glass tube and the cork to reinforce the sealing.

During the selection of the glass tubes, factors that were considered were their thermaldurability and their dimensions. Their dimensions should be such that they can fit thecartridge heaters, while at the same time their volume is such that they can hold enoughoil to perform the necessary analysis described in table 8. The volume of the cartridgeheater itself has to be considered and subtracted from the volume of the glass container(calculations presented in subsection 3.2.2). An important note is that when the sampleis sent for analysis, once the needed oil is extracted from the tube the paper should notbe exposed to air. This means that there has to be enough oil left in the tube after theextraction so that when the cartridge is immersed in the oil, the paper is entirely cov-ered. A glass tube used in the experiment is illustrated in figure 29 with a cartridge in it.

The selected tube has the following dimensions according to the manufacturer: height=200

58

mm, outer diameter=38 mm, glass thickness=1.4 mm. These dimensions are used asa starting point for the heat transfer calculations needed for the construction of thealuminum cylinder as described in subsection 4.2.3.

Figure 29: Glass tube and cartridge heater used in the experiment.

4.2.3 Design of the aluminum cylinders

The samples in the experiment will be subjected to a temperature of 130 oC measuredon the inner layers of the paper wrapped on the cartridge. For this reason, the exper-imental units should have a mechanism to dissipate part of the generated heat to theambient. An initial approach was to use a water bath for the units and this solutionwas used in preliminary tests. Though, this solution is not suitable for the final exper-imental set-up, as a water bath would increase the moisture in the surroundings, andpotentially this could result in insertion of extra moisture into the system.

For this reason, aluminum cylinders were selected as heat sinks. Each unit has itsown aluminum cylinder, as the temperatures in the various cartridges may not be equal(even in the same load pattern) due to the difference in the resistances of the cartridges.Aluminum is a very good heat conductor, and by having the same aluminum block for

59

samples with different temperatures, we may have an increase in temperature in unitsthat originally had lower temperatures. The technical drawing of the aluminum cylin-ders is presented in figure 30. The dimensions Φ2, Φ3, H1 and H3 appearing in thetechnical drawing depend on the selected glass tubes that are going to be inserted inthe aluminum. Also, the thickness of the bottom of the aluminum cylinder H2 is se-lected equal to 20 mm. This thickness will also provide increased weight on the base ofthe cylinder which will make the structure more stable.

H2

TOP VIEW

Φ2Φ2

Φ3Φ3

TOP VIEWH

1

H3

Φ1Φ1

Φ2Φ2

Φ3Φ3

H1

H3

CROSS-SECTIONCROSS-

SECTIONΦ1

indicates concentric geometry in the ‘TOP

VIEW’ diagram

indicates concentric geometry in the ‘TOP

VIEW’ diagram

indicates the axis of symmetry of the geometry in

the ‘CROSS-SECTION’ diagram

indicates the axis of symmetry of the geometry in

the ‘CROSS-SECTION’ diagram

Figure 30: Technical drawing of the aluminum cylinder.

The next step concerns the calculation of the thickness of the aluminum cylinder tohave satisfactory heat dissipation. With reference to figure 30, Φ1 = 80 mm was se-lected as a starting point for the diameter of the aluminum to begin with the heattransfer calculations. The lumped capacitance method was used to determine if thisvalue is satisfactory or not for the purposes of the experiment. According to [4], thelumped capacitance method is used to "determine the time dependence of the tem-perature distribution during a transient process and heat transfer between a solid andits surroundings", when the temperature gradient in the material can be neglected.

60

Aluminum has high thermal conductivity, with a value k = 237 W/m·K for pure alu-minum at 300 Kelvin [4], thus, its temperature gradient can be considered negligibleand the lumped capacitance method can be used. The thermal time constant of thealuminum cylinder can be estimated with this method for a certain thickness. Depend-ing on the value of the thermal time constant, the thickness of the aluminum (diameterΦ1) can be increased or decreased. The following analysis is based on equations from [4].

The thermal time constant τt of a material with volume V , surface area A, density ρ,specific heat cp and heat transfer coefficient (from radiation and convection) h is givenby

τt =1

hAρV cp (51)

The heat transfer in the present experiment is through convection and radiation. Theaverage heat transfer coefficient for free convection flow is given by

h =kNuLL

(52)

where k is the thermal conductivity of the material (aluminum in this case), NuL is theaverage Nusselt number for a vertical plate as the lateral surface of the cylinder can beapproximated by a vertical plate, and L is the characteristic length of the geometry.The average Nusselt number for a laminar (non-turbulent) flow is given by

NuL =

0.825 +

0.387Ra1/6L

[1 + (0.492/Pr)9/16]8/27

2

(53)

where RaL is the Rayleigh number and Pr is the Prandtl number. The Prandtl numbercan be found in tables for air, while the Rayleigh number is calculated by

RaL =gβ(Ts − T∞)L3

αv(54)

where g is the gravitational acceleration constant, Ts is the surface temperature of thealuminum, T∞ is the temperature of the surroundings of the cylinder (ambient temper-ature), β = 1/T∞, α and v can be found in tables for air, and L is the height of thecylinder.

The radiation heat transfer coefficient is given by

hr = εσ(Ts + T∞)(T 2s + T 2

∞) (55)

61

where ε is the emissivity of aluminum and σ is the Stefan–Boltzmann constant.

The heat transfer from the aluminum surface is given by

q = qconv + qrad = hA(Ts − T∞) + εAσ(T 4s − T 4

∞) (56)

where q is the generated heat, qconv and qrad are the heat transfers from convectionand radiation respectively. In the calculations, only the lateral surface of the aluminumcylinder was assumed to contribute in the heat transfer process, thus A represents thelateral surface of the cylinder. During the preliminary experiments, the power on a car-tridge was controlled through an SSR to get a temperature close to 130 oC. Once thetemperature stabilized near this value, the electric power was calculated by measuringthe RMS voltage and current in the system, as it is known that the electric power insingle-phase systems is given by the product of the RMS values of voltage and current.Assuming that there are no losses in the system and that all the electric power is uti-lized in heat generation in the cartridge, the value of q is obtained, and this value wascalculated at 40 Watts. Furthermore, the value of the surface of the aluminum Ts isneeded to perform the calculations, and this value was selected at 130 oC as a startingpoint. Lastly, the ambient temperature is assumed equal to T∞ = 25 oC and the heightof the cylinder is L = 220 mm.

After having the complete set of equations, the time constant can be calculated byequation (51) for Φ1 = 80 mm. The procedure starts by calculating h from equation(52) and hr from (55) for Ts = 130 oC, and substituting them in equation (56). Then,by solving this equation for Ts, a new value for the surface temperature is obtained.This value is used to calculate new values for h and hr to be used in equation (56). Thisprocedure continues until Ts converges to a value and remains constant. For this finalvalue of Ts, the values of h and hr that will be used in the total heat transfer coefficientcan be calculated. Thus, the total heat transfer coefficient is h = h+ hr. The thermaltime constant of the aluminum cylinder for a diameter of 80 mm can be then calcu-lated by equation (51), where V is the volume of the aluminum cylinder (with an innerdiameter of 40 mm due to the dimensions of the glass tube), cp is the specific heat ofaluminum and can be obtained from tables, and A is the lateral surface of the aluminum.

This results to τt = 4805.3 seconds. That is a long time constant and should bereduced. Solutions to reduce it include: (i) reduction of the radius of the cylinders, (ii)painting the cylinders to increase their radiation, (iii) manufacturing cooling fins on thecylinders, and, (iv) utilizing forced convection by blowing air on the units (for exampleusing a fan). From these options, (ii) would increase the radiation, but cylinders closeto each other would radiate their heat to adjacent ones, thus this is not an option.Option (iii) would be an efficient solution, though it would result in an increased cost,

62

while (iv) would require for all the cylinders to be exposed to the same cooling. Theselected option is (i), with a reduction of Φ1 to 60 mm. The other dimensions of thecylinder were selected after carefully measuring the glass tubes and making sure thatthey would all fit in the aluminum. This included the outer diameters of the rims ofthe glass tubes, the height of the rims, the outer diameters of the glass tubes and theirheight. This results into the values of table 22.

Table 22: Dimensions of the aluminum cylinder.

Φ1 60 mmΦ2 48 mmΦ3 40 mmH1 220 mmH2 20 mmH3 5 mm

Figure 31 illustrates a cross-section of an aluminum cylinder with a glass tube thatcontains the oil-paper system.

4.2.4 Electrical topology of the set-up

The electrical connection of the experimental set-up is illustrated in figure 32. Theresistors in the figure represent the cartridge heaters, the solid-state relays used forcontrol of the power are indicated with ”SSR” and the voltage source models the con-nection with the grid on the 230 V voltage level. Figure 32 intends to present the maintopology of the set-up on a higher level, as there are more components that are notillustrated in the figure (for example, the control signals of the relays). The cartridgesof each load pattern experience the same voltage as they are connected in parallel andare controlled by the same SSR.

63

Figure 31: Illustration of an experimental unit inside an aluminum cylinder.

Voltage source

SSR 2 SSR 3SSR 1

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15

LP1 LP2 LP3

Voltage source

SSR 2 SSR 3SSR 1

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15

LP1 LP2 LP3

Figure 32: Electrical topology diagram.

64

The design allows multiple samples in the same load pattern to be controlled simulta-neously. However, since the resistances vary among the cartridges, the consumed powerand temperature are expected to vary. If the applied voltage from the source (wallsocket) is V [Volts (RMS)], the consumed power of a cartridge with resistance R [Ω]will be equal to P = V 2/R [Watts]. Moreover, since the resistors vary the consumedpower will differ. It is important to connect cartridges in the same load pattern withas close resistances as possible. With reference to table 21, there are cartridges withresistances very close to each other, but in total in the same load pattern there will becartridges with different resistances which may cause a noticeable difference in temper-ature. The cartridges with the lower resistance are expected to consume more powerand have higher temperatures.

4.2.5 Safety equipment

The solid-state relays are connected to the power supply at the 230 V level. For safetyprecautions it is important that the relays are enclosed in an insulating structure toavoid the risk of electric shock. A plastic safety box is used as illustrated in figure 33.The box is modified for the purposes of the experiment as can be seen in the figure.Its dimensions are 31 cm x 24 cm x 11 cm. As seen in subfigure 33a, the power supplyis connected with the relay power inputs, while the control signals (red and black lowvoltage wires) are connected to the NI equipment. Subfigures 33b & 33c illustrate thenecessary modifications made on the box.

65

(a) Top view.

(b) Side view 1.

(c) Side view 2.

Figure 33: Safety box used in the experiment.

4.2.6 Preparation of the experimental units

When preparing the experimental units, it is of high importance that all are treatedequally. The insulating paper needs to be dried in the oven to avoid having additionalmoisture in the system. Also, the tubes, the cartridges, the corks and the oil need tobe dried prior to the experiment to minimize the ingression of extra moisture in thesystem. The paper needs to be cut in stripes of the same length for all units and becarefully placed in the hot zone of the cartridge. The oil that will be added in the glasstubes needs to be measured and the same volume of oil should be filled in all units.Furthermore, when wrapping the paper around the cartridges it is important to wrapit as tightly as possible, while the thermocouples should be placed in the intermediatelayers of the paper (for example the second layer) on the same spot in all units.

The addition of moisture in the units should be performed very carefully so the correctamount is added in the system in all units. This can be done by using a pipette. Also,

66

when placing the experimental units, the same distance should be kept between allsamples in order to avoid increase in temperature. Lastly, when an experimental unitshould be extracted and sent for analysis, it is of high importance that there should beno power in the system during the extraction.

4.2.7 Additional equipment

Additional equipment is needed in order to construct and run the experiment, such asthermocouples to measure the temperatures, BNC connectors to connect the thermo-couples with the NI equipment, cables to realize the necessary electrical connectionsand corks to seal the glass tubes. In table 23, an overview of the equipment used in theexperiment is presented.

Table 23: Equipment used in the experiment.

Equipment Quantity Details DimensionsComputer 1 LabVIEW compatible -

PXIe-1073 chassis 1 National Instruments -PXIe-6368 card 1 National Instruments -

BNC-2120 connector block 1 National Instruments -SCB-68 pin connector block 1 National Instruments -

Solid-state relays 3 Comus -Thermocouples 15 Type-K -

Safety box 1 - 310 x 240 x 110 [mm]Cartridge heaters 15 200 W at 230 V -

Glass tubes 15 Borosilicate glass 200 x 38 [mm]Aluminum cylinders 15 - 220 x 60 [mm]

Cellulose paper 15 Munksjö Thermo 70 75 x 185 [mm]Transformer oil 2000 mL Nytro 10 XN -

Corks 15 - -PVC-isolated cable - Blue 1.5 mm2

PVC-isolated cable - Black 1.5 mm2

Power cable 1 - -Cable glands 7 - -Counter nuts 7 - -

Terminal blocks 35 - -Ring terminals 6 - -Drying oven 1 - -

67

4.3 Discussion

The main experimental work performed in this thesis is focused on the implementationof the design and the sensitivity analysis of the equipment, including the alteration ofthe initial design where digital signals where used instead of the analog ones to controlthe SSRs. The experimental set-up is designed, tested and implemented into hardware,but still there are some actions to be taken before the test starts. One of these actionsis to carefully tune the duty cycle of the load patterns to achieve a temperature of 130oC in the units. Moreover, as discussed in chapter 3, the load patterns could be changedin order to achieve a larger difference in the DP value of the samples of the various loadpatterns.

There are certain practical matters that need to be handled carefully, such as managingto wrap the paper as tightly as possible and minimizing the gap between the paperlayers where the thermocouple is placed. Also, when the tube is sealed, the cartridgesshould be placed on the appropriate height within the tube. If these aspects are notfulfilled, they can lead to unreliable results concerning the aging of the paper.

As discussed in [18], the paper-to-oil ratio in real transformers is 53 mg of paper for1 mL of oil, which is not fulfilled in the present experiment for practical reasons, asthe thickness of the paper wrapped around the cartridges would increase significantlyand the temperature would be far from uniform within the paper layers. This is notexpected to affect the results though.

68

5 Conclusions and future work

5.1 Conclusions

The work of this thesis is focused on creating a calculation model that estimates theeffect of moisture dynamics in transformer insulation on the aging of the solid insulationfor DR applications, and on implementing the experimental design of [18] in hardware.The model is based on industrial standards and scientific articles, and is implementedin the frame of the experimental set-up designed in [18]. The model is focused on ap-proximating the phenomena that occur during this process and estimating the result ofthe experiment. It was concluded that the moisture migration phenomenon contributesto further aging of the sold insulation, and the higher the frequency that it occurs,the more severe the effect. However, these results cannot be observed experimentallyif the differences in the DP values are less than 40 DP. It is important to consider theconclusions that were stated in the modeling part when executing the experiment asthese can provide useful information and directions on altering the load patterns of theexperimental design in LabVIEW. This model does not include practical issues that arepresent in the experimental set-up, such as the non-uniform temperature distributionwithin the paper insulation and the difference in the resistance of the cartridges thatcan lead to temperature deviations within the experimental units.

Also, a large part of the thesis was laboratory work, and as mentioned, there are practi-cal matters to be considered when executing the experiment, with the most importantones being treating all experimental units in the exact same way when preparing them,and tuning the duty cycles of the load patterns to achieve a temperature of 130 oC. Ifthe results of the experiment are promising, further investigation can be conducted intesting different moisture contents, temperatures, load patterns or types of paper andsolid insulation. Potential improvements on the existing thermal models of transformerscould be possible if the results of the experiments are calling for further research. Thepreliminary results of the model indicate that potentially there could be differences inthe aging, if the correct load pattern is implemented.

5.2 Future work

Before starting the experiment, there are certain tasks that need to be addressed. Onetask could be to investigate possible alternative load patterns that may reveal largerdifferences in the DP value by following the methodology described in 3.2.5. The in-vestigation could aim at examining alternative temperatures and on- and off-times forthe load patterns that would maximize the effect of moisture transport dynamics onthe aging of the insulation so the analysis of the experimental units is more likely toreveal fruitful results.

69

A second task is to tune the duty cycles of the PWM signals that control the SSRs ofeach load pattern to achieve the temperature of 130 oC. Additional protection equipmentcould be added, such as over-temperature protection equipment that can be realized byusing thermostats of the appropriate operating range. Though, this could potentiallyincrease the already existing gap of the layers of the paper wrapped around the car-tridges, leading to a further non-uniform temperature distribution.

Lastly, it is advisable to run the experiment for a shorter period of time, for example 1 or3 cycles, in order to receive some preliminary results from the analysis that can be usefulconcerning possible alterations or adjustments that may be needed in the experimentalset-up. In case there are deviations between the experimental results and the resultsfrom the model, further investigation of the effects and factors that affect the agingof oil-paper insulation systems should be conducted, focusing on better understandingand interpreting the relation between cause and effect.

70

References

[1] Martin Heathcote, "J & P Transformer Book", Thirteenth edition, Elsevier.

[2] Olle I. Elgerd, "Electric Energy Systems Theory, An Introduction", Second edition,McGraw-Hill.

[3] Stephen D. Umans, "Fitzgerald & Kingsley’s Electric Machinery", Seventh edition,McGraw-Hill.

[4] Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine,"Fundamentals of Heat and Mass Transfer", Sixth edition, John Wiley & Sons.

[5] Thomas A. Prevost, T. V. Oommen, "Cellulose Insulation in Oil-Filled PowerTransformers: Part I – History and Development", IEEE Electrical InsulationMagazine, Volume: 22, Issue: 1, Jan.-Feb. 2006.

[6] A. J. Kachler, I. Höhlein, "Aging of cellulose at transformer service temperatures.Part 1: Influence of type of oil and air on the degree of polymerization of press-board, dissolved gases, and furanic compounds in oil", IEEE Electrical InsulationMagazine, Volume: 21, Issue: 2, March-April 2005.

[7] Bassem B. Hallac, Arthur J. Ragauskas, "Analyzing cellulose degree of polymeriza-tion and its relevancy to cellulosic ethanol", Biofuels, Bioproducts and Biorefining,Volume 5, Issue 2, March/April 2011, Pages 215–225.

[8] C. Homagk, K. Mossner, T. Leibfried, "Investigation on Degradation of PowerTransformer Solid Insulation Material", Electrical Insulation and Dielectric Phe-nomena, CEIDP 2008.

[9] James H. Harlow, "Electric power transformer engineering", CRC Press 2004.

[10] A.M. Emsley, R.J. Heywood, M. Ali, X. Xiao, "Degradation of cellulosic insulationin power transformers. Part 4: Effects of ageing on the tensile strength of paper",IEE Proceedings - Science, Measurement and Technology, Volume: 147, Issue: 6,Nov 2000.

[11] T. V. Oommen, Thomas A. Prevost, "Cellulose Insulation in Oil-Filled PowerTransformers: Part II – Maintaining Insulation Integrity and Life", IEEE Electri-cal Insulation Magazine, Volume: 22, Issue: 2, March-April 2006.

[12] T. O. Rouse, "Mineral insulating oil in transformers", IEEE Electrical InsulationMagazine, Volume: 14, Issue: 3, May-June 1998.

71

[13] Huo-Ching Sun, Yann-Chang Huang, Chao-Ming Huang, "A Review of DissolvedGas Analysis in Power Transformers", Energy Procedia, Volume 14, 2012, Pages1220-1225, Elsevier.

[14] Lynn Hamrick, "Dissolved Gas Analysis for Transformers", NETA World, Winter2009-2010.

[15] Luiz Cheim, Donald Platts, Thomas Prevost, Shuzhen Xu, "Furan analysis forliquid power transformer", IEEE Electrical Insulation Magazine, Volume: 28, Issue:2, March-April 2012.

[16] A. A. Pollitt, "Mineral oils for transformers and switchgear", Journal of the Insti-tution of Electrical Engineers - Part II: Power Engineering, Volume: 90, Issue: 13,February 1943.

[17] IEC, "Power transformers – Part 5: Ability to withstand short circuit", IEC 60076-5 International standard, Third edition, 2006-02.

[18] Patrik Gustafsson, "Design of Experimental Setup for Investigation of Effect ofMoisture Content on Transformer Paper Ageing during Intermittent Load", MasterThesis, KTH Royal Institute of Technology, April 2018.

[19] Tahereh Zarei, "Analysis of reliability improvements of transformers after applica-tion of dynamic rating", Master Thesis, KTH Royal Institute of Technology, June2017.

[20] Belén García, Juan Carlos Burgos, Ángel Matías Alonso, and Javier Sanz, "AMoisture-in-Oil Model for Power Transformer Monitoring—Part I: TheoreticalFoundation", IEEE Transactions on power delivery, Volume: 20, No: 2, April2005.

[21] Pahlavanpour, M. Martins and Eklund, "Study of Moisture Equilibrium in Oil-Paper System with Temperature Variation", Proceedings of the 7th InternationalConference on Properties and Applications of Dielectric Materials, 2003, pp. 1124-1129 vol.3.

[22] Victor Sokolov, Jacques Aubin, Valery Davydov, Hans-Peter Gasser, Paul Grif-fin, Maik Koch, Lars Lundgaard, Oleg Roizman, Mario Scala, Stefan Tenbohlen,Boris Vanin, "Moisture equilibrium and moisture migration within Transformerinsulation systems", Technical Brochure: "A2 Transformers", CIGRÉ, June 2008.

[23] T. V. Oommen, "Moisture equilibrium in paper-oil insulation systems", 1983 EIC6th Electrical/Electronical Insulation Conference, Chicago, IL, USA, 1983, pp.162-166.

72

[24] Lance Lewand, "Understanding Water in Transformer Systems: The RelationshipBetween Relative Saturation and Parts per Million (ppm)", NETA World Journal,Spring 2002.

[25] Engineering ToolBox, (2008). "Maximum Moisture Carrying Capacityof Air" [online]. Available at: https://www.engineeringtoolbox.com/maximum-moisture-content-air-d_1403.html [Accessed 04/04/2018].

[26] Engineering ToolBox, (2010). "Densities of Common Materials" [online]. Availableat: https://www.engineeringtoolbox.com/density-materials-d_1652.html[Accessed 04/04/2018].

[27] Du Y., Zahn M., Lesieutre B.C., Mamishev A.V., Lindgren S.R., "Moisture equi-librium in transformer paper-oil systems", IEEE Electrical Insulation Magazine,Volume: 15, Issue: 1, Jan.-Feb. 1999.

[28] IEC, "Power transformers – Part 7: Loading guide for mineral-oil-immersed powertransformers", IEC 60076-7 International standard, Edition 2.0, 2018-01.

[29] Nick Lelekakis, Daniel Martin, Jaury Wijaya, "Ageing Rate of Paper Insulationused in Power Transformers Part 1: Oil/paper System with Low Oxygen Concen-tration", IEEE Transactions on Dielectrics and Electrical Insulation, Volume: 19,Issue: 6, December 2012.

[30] Nick Lelekakis, Daniel Martin, Jaury Wijaya, "Ageing rate of paper insulation usedin power transformers Part 2: Oil/paper system with medium and high oxygen con-centration", IEEE Transactions on Dielectrics and Electrical Insulation, Volume:19, Issue: 6, December 2012.

73

TRITA TRITA-EECS-EX-2018:106

ISSN 1653-5146

www.kth.se