Power Transformer Health Concepts

All matters affecting the health of a power transformer are discussed in this section.

Dissolved Gas Analysis

Use this free analysis template to analyse your dissolved gas data to establish general condition.

LEDT - Low Energy Degradation Triangle

The LEDT is a contemporary method to assess the condition of the transformer based on low energy incipient faults. It provides early detetcion of incipient faults which start off from low energy insulation degradation.

Case Studies

Review cases studies of power transformer failures.

Thursday, May 26, 2016

Dornenburg's Method

The Dornenburg ratio method makes use of the ratios of the concentration of the key gases hydrogen, methane, ethane, ethylene and acetylene. The following ratios are used CH4/H2, C2H2/CH4, C2H4/C2H6 and C2H2/C2H4.
For this method to be a viable diagnostic tool a few criteria have to be met. This in itself is the negative aspect of this diagnosis method as there are more frequent than not “no diagnosis” obtained.

The criteria are such that for the transformer to be considered to have a problem at least one of the key gas concentrations must exceed twice a predetermined limit with at least one of the remaining three key gases exceeding its predetermined limit. There is also a further validity check that at least one of the key gases in each of the four ratios must exceed the predetermined limit for the ratios to be significant. Only then can the combination be compared to the codes. Once this criteria is met the combination of the ratios into a code is established, where each four parameter code has a unique diagnosis that is able to identify
thermal faults, corona discharge and arcing [IEEE C57.104].



Use the following link to the "Analysis" section to get the Dornenburg diagnosis of the oil samples. Enter the oil sample under "Sample 5" to get the diagnosis.

Thursday, May 12, 2016

Dissolved Gas Analysis Methods

Power transformers play a key role in any power network and must be maintained and effectively monitored with continuous condition assessment to ensure reliability of the network. Numerous techniques have been developed over the years for the detection of transformer faults. 

Some of the conventional parameters used are dissolved gases, furfuraldehyde, degree of polymerisation of paper insulation and frequency response analysis. Dissolved gas analysis has been extensively utilised for incipient fault detection by some of the following methods; key gas analysis [IEC60567], the Dornenburg [Dornenburg1], Duval [Duval1], Rogers [Rogers1] gas ratio method and those highlighted in the ANSI/IEEE standard [IEEE C57.104]. Other advanced analytical techniques explored are artificial neural networks, fuzzy logic, data mining and cluster analysis with the aim of identifying fault conditions within the transformer.The next few sections provide a short review of the capabilities of the generally accepted fault diagnosis methods.

Use the following link to the "Analysis" section to get the Rogers Ratio diagnosis of the oil samples. Enter the oil sample under "Sample 5" to get the diagnosis.

References

[Dornenburg1]
Dornenburg, E., Strittmater, W., “Monitoring Oil Cooling Transformers by Gas Analysis,” Brown Boveri Review 61.5, pages 238-274, 1974
[Duval1]
Duval, M., “A Review of Faults Detectable by Gas-in-oil Analysis in Transformers,” IEEE Electrical Insulation Magazine, Vol. 18, No. 3, Pages 8-17, May/June 2002
[IEC 60567]
IEC 60567, “Oil-filled Electrical Equipment – Sampling of Gases and of Oil for Analysis of Free and Dissolved Gases – Guidance,” 4th Edition, IEC Publication, 2011
[IEEE C57.104]
IEEE C57.104, “IEEE Guide for the Interpretation of Gases Generated in Oil-immersed Transformers,” IEEE Power Energy Society, 2008
[Rogers1]
Rogers, R. R., “IEEE and IEC Codes to Interpret Incipient Faults in Transformers Using Gas in Oil Analysis,” IEEE Transactions on Electrical Insulation, Vol. 13, No. 5, pages 349-354, October 1978


Monday, May 9, 2016

Solubility of Dissolved Gases

Different gases/parameters have different solubility levels in mineral oil [DiGiorgio1]. It is important to correctly identify the levels of gases produced in the associated defective conditions before any dissolved gas analysis is attempted. The following table provides solubility levels of the gases in transformer mineral oil with a static equilibrium at 760mm Hg and 25 °C [DiGiorgio1]:

Table: Typical solubility levels of gases in mineral oil [DiGiorgio1]
Gases
Solubility
H2
7% by volume
N2
8.6%
CO
9%
O2
16%
CH4
30%
CO2
120%
C2H6
280%
C2H4
280%
C2H2
400%
The figure below provides some indication of the relative solubility of the combustible gases as a function of temperature [DiGiorgio1]. Gases such as hydrogen, nitrogen, carbon monoxide and oxygen have an increasing solubility rate with increasing temperature. The hydrocarbon gases methane, acetylene, ethylene and ethane together with carbon dioxide have a decreasing solubility rate with increasing temperature. It is noted that both hydrogen and carbon monoxide are not very soluble at low temperatures but the solubility rate does improve drastically for hydrogen at operating temperatures around 70-80°C. The solubility rate of methane is moderate, decreasing with increasing temperatures. These aspects play an important role and must be taken into consideration when assessing the gas production rates as assessed from oil samples.
Figure Relative Solubility as a function of Temperature [DiGiorgio1]


References


[Digiorgio1]
DiGiorgio, J. B., “Dissolved Gas Analysis of Mineral Oil Insulating Fluids,” DGA Expert System: A Leader in Quality, Value and Experience 1, Northern Technology and Testing, pages 1-17, http://www.nttworldwide.com/tech2102.htm, 2005

Friday, May 6, 2016

Dissolved Gases

Dielectric oil and solid cellulose dielectric materials when degrading under thermal and electrical stresses produce gases of varying compositions and in concentrations relative to the severity of the stresses applied to these materials [Griffin1]. These gases dissolve in the oil where the nature and concentrations of the dissolved gases sampled provides a good representation of the type and severity of the fault in the transformer [Rogers1]. The changes in the gas production rates form key components in the determination of the type of fault(s) involved where some specific gases form profiles for certain types of faults [Gibeault1].

Dissolved gas data are obtained from oil sample testing [IEC 60567]. The most common gases analysed from oil tests are hydrogen (H2), methane (CH4), acetylene (C2H2), ethylene (C2H4), ethane (C2H6), carbon monoxide (CO), carbon dioxide (CO2), oxygen (O2) and nitrogen (N2) [Wang1]. 
The degradation of oil insulation material produces a fair amount of hydrocarbon compounds, which are composed of hydrogen and carbon atoms that are broken up into two distinct classes, namely aliphatic and aromatic hydrocarbons [Arora1]. 


Aliphatic hydrocarbons are further broken down into three groups, which are alkanes, alkynes and alkenes. Alkanes are composed of single bonds, alkenes consist of double carbon bonds and alkynes consist of triple carbon bonds [Arora1]. This means that more energy is required for the breakdown of double and triple bonds implying that less energy is required for gases such as methane and ethane and higher energy for ethylene and acetylene.
The principle degradation product of low energy electrical discharges found in mineral oil-filled transformers is molecular hydrogen [Rouse1].
The decomposition of methane (CH4) into its elements starts at about 578°C hence competes with its degradation to acetylene [Leroux1].
The formation of ethylene and acetylene has been noted to be specific to high-energy electrical discharges [Arakelian1]. At about 1327°C and higher, acetylene is more stable than other hydrocarbons but decomposes into its elements thus indicating that the conversion or splitting time must be incredibly short (milliseconds) [Leroux1]. The amount of energy needed is very large and in the region of the favourable free energy.


All hydrocarbons release carbon dioxide and H2O as products of combustion [Arora1]. Studies have shown that the thermal decomposition of cellulose insulation produces carbon oxides (CO and CO2), some hydrogen and methane due to the oil impregnation [Kachler1, Wang1]. The oxygen levels in the transformer arise primarily from the atmosphere. Oxygen causes oxidation of the oil, which sustains the insulation degradation process [Liland1].







References


[Arakelian1]
Arakelian, V. G., “Effective Diagnostics for Oil-filled Equipment,” IEEE Electrical Insulation Magazine, Vol. 18, No. 6, pages 26-38, November / December 2002
[Arora1]
Arora, A., “Hydrocarbons (Alkanes, Alkenes, and Alkynes),” Discovery Publishing House, 2006
[Gibeault1]
Gibeault, J. P., Kirkup, J. K., “Early Detection and Continuous Monitoring of Dissolved Key Fault Gases in Transformers and Shunt Reactors,” Electrical Electronics Insulation Conference, Electrical Manufacturing & Coil Winding Conference, IEEE Proceedings, Pointe-Claire, Quebec, Canada, 1995
[Griffin1]
Griffin, P. J., “Criteria for the Interpretation of Data for Dissolved Gases in Oil from Transformers (A Review),” Electrical Insulating Oils, STP 998, American Society for Testing and Materials, Philadelphia, pages 89-106, 1988
[IEC 60567]
IEC 60567, “Oil-filled Electrical Equipment – Sampling of Gases and of Oil for Analysis of Free and Dissolved Gases – Guidance,” 4th Edition, IEC Publication, 2011


[Rogers1]
Rogers, R. R., “IEEE and IEC Codes to Interpret Incipient Faults in Transformers Using Gas in Oil Analysis,” IEEE Transactions on Electrical Insulation, Vol. 13, No. 5, pages 349-354, October 1978
[Kachler1]
Kachler, A. J., Hohlein, I., “Ageing of Cellulose at Transformer Service Temperatures. Part1: Influence of Type of Oil and Air on the Degree of Polymerisation of Pressboard, Dissolved Gases and Furanic Compounds in oil,” IEEE Electrical Insulation Magazine, Vol. 21, No. 2, pages 15-21, 2005
[Leroux1]
Leroux, P. J., Mathieu, P. M., “Kinetics of the Pyrolysis of Methane to Acetylene,” Chem. Eng. Prog. Vol. 57, pages 54-59, 1961
[Liland1]
Liland, K. B., Kes, M., Ese, M. H. G., Lundgaard, L. E., Christensen, B. E., “Study of Oxidation an Hydrolysis of Oil Impregnated Paper Insulation for Transformers Using a Microcalorimeter,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 18, No. 6, pages 2059-2068, December 2011
[Rouse1]
Rouse, T. O., “Mineral Insulating Oil in Transformers,” IEEE Electrical Insulation Magazine, Vol. 14, Issue 3, Pages 6-16, May-June 1998
[Wang1]
Wang, H., Butler, K. L., “Modeling Transformers with Internal Incipient Faults,” IEEE Transactions on Power Delivery, Vol. 17, No. 2, pages 500-509, April 2002

Thursday, May 5, 2016

Ageing Components and By-products: Organic


The power transformer basic components, which are organic in nature, are the insulating oil and cellulose based insulation (paper, insulation boards and blocks) [Heathcote1]. These components form the basis for the transformer health or life, as these are usually the fastest degrading materials making up the transformer [Emsley2].

Solid Insulation
The solid insulation is composed of Kraft paper, pressboard, transformer board and cellulose made up of electrical grade paper insulation manufactured from unbleached sulphate cellulose [IEEE 60641-3-1]. 


Acid-hydrolysis, pyrolysis and oxidation are processes, which causes the depolymerization of paper [McNutt1, Lundgaard1, Unsworth1]. Oxidation is a process that is considered a form of combustion where the products of the reaction are water and carbon dioxide. Pyrolysis and thermal heating of the paper insulation produces significant amounts of CO and CO2 [Emsley2, Griffin1].
Studies have found that Insuldur upgraded paper does not produce as much 2FAL as Kraft paper concluding that 2FAL cannot be used as an indicator of ageing for all paper types [Lundgaard1, Prevost1]. Although both water and oxygen play an important role in the paper degradation process, water is the most significant contributor because the catalytic efficiency of dry acids is low [Lundgaard1].  


For thermal conditions such as pyrolysis in oil significant levels of ethylene are produced supported by hydrogen and methane [Wang1]. Arcing in oil causes significant levels of both hydrogen and acetylene to be produced [Kelly1]. 
Kraft paper has a cellulose base that is composed of linear, polymeric chains of cyclic b-D-glucopyranosyl units [Lundgaard1]. These chains consist of linear condensation polymer, which is composed of a hydrocarbon glucose molecule that is formed by D- anhydroglucopyranose units joined by ß 1.4 – glucosidic bonds. Paper insulation has a general molecular formula of [C12H14O4(OH)6]n with n in the range of 300 to 750 [DiGiorgio1]. The cellulose breaks down causing the lengths of the chains to become smaller with the process generating CO, CO2 and H2O [Wilkinson1]. Other products produced during this breakdown process like –OH and –OH2OH groups further promote the cellulose to become both hygroscopic and vulnerable to oxidative degradation [Oommen3, Unsworth1]. Water is found in the paper insulation as a vapour, absorbed to surfaces, as free water in the capillaries and as imbibed free water [Du1]. The presence of moisture plays a critical role in the life of the transformer insulation [Lundgaard1].

Mineral Insulating Oil
Transformer mineral insulating oil is composed from naphthenic crude oils which is a mixture of hydrocarbon compounds of alkanes, naphthenes and aromatic hydrocarbons. Mineral oil has a general molecular formula of CnH2n+2 with n in the range of 20 to 40 [DiGiorgio1].

The transformer mineral oil has numerous particles and compounds dissolved within it. These compounds are as a result of byproducts in the degradation process or being introduced from the external environment. The most common are dissolved gases, acids, water, corrosive sulphur, silicon and furans. Insulating oil by nature has a low affinity for water but the solubility increases significantly with an increase in temperature. It is further highlighted that water can exist in transformers in a dissolved state in oil, tightly bound to the oil molecules or as free water [Du1]. 

Aging of oil insulation is markedly different for open (free breathing) and closed systems [Kachler1]. Aging of the oil insulation is accelerated by the high ingress of oxygen, which after reaching equilibrium of approximately 20000 ppm produces a source of additional energy for the ageing of the oil [Ferguson1]. Transformer oil degradation is primarily caused by decomposition, contamination and oxidation [Phadungthin1]. Mineral oil may break down under elevated temperatures due to abnormal loading or fault conditions such localized hotspots and electrical faults. Moisture, dielectric, acidity and oxygen have a major effect on the ageing and break down of the oil [Cigre WG12.18].

References


[Cigre WG12.18]
Cigre Working Group 12.18, “Guidelines for Life Management Techniques for Power Transformers,” Cigre, 22 June 2002
[Digiorgio1]
DiGiorgio, J. B., “Dissolved Gas Analysis of Mineral Oil Insulating Fluids,” DGA Expert System: A Leader in Quality, Value and Experience 1, Northern Technology and Testing, pages 1-17, http://www.nttworldwide.com/tech2102.htm, 2005
[Du1]
Du, Y., Zahn, M., Lesieutre, B. C., Mamishev, A. V., Lindgren, S. R., “Moisture Equilibrium in Transformer Paper-oil Systems,” IEEE Electrical Insulation Magazine, 15(1), pages 11-20, 1999
[Emsley2]
Emsley, A. M., Stevens, G. C., “Review of Chemical Indicators of Degradation of Cellulosic Electric Paper Insulation in Oil-filled Transformers,” IEE Proceedings - Science, Measurement and Technology, Vol. 141, No. 5, pages 324-334, 1994
[Ferguson1]
Ferguson, R., Lobeiras, A., Sabou, J., “Suspended Particles in the Liquid Insulation of Aging Power Transformers,” IEEE Electrical Insulation Magazine, Vol. 18, No. 4, pages 17-23, 2002
[Griffin1]
Griffin, P. J., “Criteria for the Interpretation of Data for Dissolved Gases in Oil from Transformers (A Review),” Electrical Insulating Oils, STP 998, American Society for Testing and Materials, Philadelphia, pages 89-106, 1988
[Heathcote1]
Heathcote, M. J., “The J & P Transformer Book,” Thirteenth Edition, Newnes, 2007
[IEEE 60641-3-1]
IEEE 60641-3-1, “Pressboard and press paper for electrical purposes – Part 3: Specifications for individual materials – Sheet 1: Requirements for pressboard,” IEC Publication, 2008
[Kachler1]
Kachler, A. J., Hohlein, I., “Ageing of Cellulose at Transformer Service Temperatures. Part1: Influence of Type of Oil and Air on the Degree of Polymerisation of Pressboard, Dissolved Gases and Furanic Compounds in oil,” IEEE Electrical Insulation Magazine, Vol. 21, No. 2, pages 15-21, 2005
[Kelly1]
Kelly, J. J., “Transformer Fault Diagnosis by Dissolved-gas Analysis,” IEEE Transactions on Industry Applications, Vol. IA-16, No. 6, pages 777-782 , November / December 1980
[Lundgaard1]
Lundgaard, L. E., Hansen, W., Linhjell, D., Painter, T. J., “Ageing of Oil-impregnated Paper in Power Transformers,” IEEE Transactions on Power Delivery, Vol. 19, No. 1, pages 230-239,
January 2004
[McNutt1]
McNutt, W. J., “Insulation Thermal Life Considerations for Transformer Loading Guides,” IEEE Transactions on Power Delivery, Vol. 7, No. 1, pages 392-401, January 1992
[Oommen3]
Oommen, T. V., Prevost, T. A., “Cellulose Insulation in Oil-filled Power Transformers: Part II Maintaining Insulation Integrity and Life,” IEEE Electrical Insulation Magazine, Vol. 22, No. 2, pages 5-14, 2006
[Phadungthin1]
Phadungthin, R., Chaidee, E., Haema, J., Suwanasri, T., “Analysis of Insulating Oil to Evaluate the Condition of Power Transformer,” Electrical Engineering Electronics Computer Telecommunications and Information Technology (ECTI-CON), pages 108-111, 2010
[Prevost1]
Prevost, T. A., Oommen, T. V., “Cellulose Insulation in Oil-filled Power Transformers: Part 1- History and Development,” IEEE Electrical Insulation Magazine, Vol. 22, No. 1, pages 28-35, 2006
[Unsworth1]
Unsworth, J., Mitchell, F., “Degradation of Electrical Insulating Paper Monitored with High Performance Liquid Chromatography,” IEEE Transactions on Electrical Insulation, Vol. 25, No. 4, Pages 737-746, August 1990
[Wang1]
Wang, H., Butler, K. L., “Modeling Transformers with Internal Incipient Faults,” IEEE Transactions on Power Delivery, Vol. 17, No. 2, pages 500-509, April 2002
[Wilkinson1]
Wilkinson, M. D., Dyer, P., “Continuous Moisture Management: Extending Transformer Service Life,” IEE Conference Publication No. 482, Vol. 1, CIRED 2001, 18-21 June 2001

Tuesday, May 3, 2016

Ageing Components and By-products: Main Structures

A power transformer is composed of a core, set of windings, oil, tank, bushings, tap changer and other auxiliary equipment. Each of these components is manufactured from either metals or compounds that are organic in nature. The different types of material react differently to the different fault conditions and the rate of energy release in the vicinity. This study examines the effects of the energy dissipated and the rate of breakdown of the different materials. These materials consist of kraft paper, oil, copper, steel and insulating boards.
The transformer tank is manufactured from steel and houses the oil and active part of the transformer. The tank has to be properly earthed and can sometimes be subjected to circulating currents causing localized hot spots.

The transformer core provides the medium for the flux path. It is usually manufactured from steel, which is arranged as thin laminations for reducing the effects of eddy currents. These laminated sheets are usually coated with a layer of special varnish or shellac [Gottlieb1]. The core arrangement is usually constructed in either the core or the shell type arrangement. The core type arrangement is such that the magnetic core is surrounded by the low voltage and high voltage windings [Heathcote1]. In the shell type arrangement the windings are surrounded by the core. GSU Transformers are usually of the core type arrangement. The core arrangement also can have a variation on the number of limbs. In a five limb core type transformer the three phase windings are located in the inner three core legs respectively and the outer legs on either side allow for flux transfer.

GSU transformers are constructed as two winding transformers. The low voltage and high voltage winding per phase are located in close proximity to ensure the maximum mutual coupling between windings [Winders1]. The windings are composed of thin copper strands, which are wrapped with paper insulation. 

References

[Gottlieb1]                  
Gottlieb, I. M., “Practical Transformer Handbook,” Reed Educational and Professional Publishing Ltd., India, 1998
[Heathcote1]              
Heathcote, M. J., “The J & P Transformer Book,” Thirteenth Edition, Newnes, 2007
[Winders1]                  
Winders, J. J., “Power Transformers: Principles and Applications,” Vol. 17,
CRC, Allentown, Pennsylvania: Marcel Dekker Inc., 2002


Transformer Life

Power transformers are generally designed for an operating life of 30 to 35 years. However, depending on how the transformer is operated, maintained and exposed to external risk these values may be less. Over the last 20 years trends have indicated that the transformer life has been much lower than expected. Even within Eskom, from statistics since the early 1990’s it was found that the average life of the larger GSU transformers was around 15 years.

A major contribution to transformer failure is windings, leads, tap changer and bushings. These failures are usually catastrophic to the transformer and in most cases the transformer has to be either rewound or replaced.

The two major components of the transformer that have the faster degradation rate are the oil and paper insulation. These components degrade as a result of thermal, electrical and chemical stress. Paper insulation degrades very early with elevated operating temperatures. Chemical stress usually takes a long time to affect transformer health and predominantly affects the oil. Electrical stress is the most destructive and with rapid degrading mechanisms on both oil and paper insulation.

It was clear from the literature thus far that the key components to focus on when assessing transformer health are the oil and cellulose/paper insulation under chemical, thermal and electrical stress. 

The key aspect of transformer winding construction is the insulation of each conductor with paper that is impregnated with insulating oil, providing at least a minimum life of 25 years at an operating temperature of 65-95 °C [Emsley2]. The end of life of a transformer occurs when the mechanical strength of the solid insulation in the windings was lost and failures are then triggered by severe conditions like lightning strikes, switching transients and short-circuits [Emsley2, Kachler1, Wang1]. Wang et al. highlighted that transformer failures can be categorized as electrical, mechanical or thermal where the cause of failure being either internal or external [Wang1].

Generator and furnace transformers exhibit accelerated aging in comparison to grid transformers due to the high loading factors [Kachler1]. Generator transformers are often loaded to full rating, which can increase the aging rate due to higher winding temperatures causing faster rates of insulation paper de-polymerisation [Checksfield1].

Insulating materials age thermally and from chemical reactions occurring within the materials caused by pyrolysis, oxidation and hydrolysis, which are accelerated by increased levels of temperature, oxygen and moisture content [McNutt1, Wang1].

An unusual gassing state defined as ‘stray gassing’ was identified as a phenomenon where some types of insulating oils produced hydrogen and hydrocarbons when heated at low temperatures of around 100°C to 120°C. However, the gas formation subsides to plateau off and this gas level can be removed by filtering the oil [Hohlein1].


External faults easily increase the short circuit forces to dangerous proportions such that any hidden defects and aged insulation causes inter-turn shorting [Wang2]. Internal faults frequently occur on one phase of the HV winding and can be formed either by direct contact or by an electric arc [Jablonski1]. With system growth, transformer loading increases causing the operating stress to increase. This causes the conductor insulation to weaken in an aging transformer to the point where it can no longer sustain mechanical stresses of a fault. Dielectric failure of turn-to-turn insulation causes loosening of winding clamping pressure, which reduces the transformer's ability to withstand future short circuit forces [Bartley1].

References


[Bartley1]                   
Bartley, W. H., “Analysis of International Transformer Failures,” International Association of Engineering Insurers 36th Annual Conference, Stockholm, 2003
[Checksfield1]           
Checksfield, M., Westlake, A., “Experiences with Operating and Monitoring Generator Transformers,” IEE Colloquium on IET, Transformer Life Management (Ref. No. 1998/510), pages 4/1-7, 22 October 1998
[Emsley2]                   
Emsley, A. M., Stevens, G. C., “Review of Chemical Indicators of Degradation of Cellulosic     Electric Paper Insulation in Oil-filled Transformers,” IEE Proceedings - Science, Measurement and Technology, Vol. 141, No. 5, pages 324-334, 1994
[Hohlein1]                 
Hohlein, I., “Unusual Cases of Gassing in Transformers in Service,” IEEE Electrical Insulation Magazine, Vol. 22, No. 1, pages 24-27, 2006
[Jablonski1]                
Jablonski, M., Napieralska-Juszczak, E., “Internal Faults in Power Transformers,” IET Electrical Power Applications, Vol. 1, No. 1, pages 105-111, 2007
[Kachler1]                  
Kachler, A. J., Hohlein, I., “Ageing of Cellulose at Transformer Service Temperatures. Part1: Influence of Type of Oil and Air on the Degree of Polymerisation of Pressboard, Dissolved Gases and Furanic Compounds in oil,” IEEE Electrical Insulation Magazine, Vol. 21, No. 2, pages 15-21, 2005
[McNutt1]                  
McNutt, W. J., “Insulation Thermal Life Considerations for Transformer Loading Guides,” IEEE Transactions on Power Delivery, Vol. 7, No. 1, pages 392-401, January 1992
[Wang1]                     
Wang, H., Butler, K. L., “Modeling Transformers with Internal Incipient Faults,” IEEE Transactions on Power Delivery, Vol. 17, No. 2, pages 500-509, April 2002