Remnant Life Estimation of Power Transformers Based on Chemical Diagnostic Parameters Using Adaptive Neuro- Fuzzy Inference System

Transcription

1 Faculty of Science and Engineering Department of Electrical and Computer Engineering Remnant Life Estimation of Power Transformers Based on Chemical Diagnostic Parameters Using Adaptive Neuro- Fuzzy Inference System Mohammadsaleh Forouhari This thesis is presented for the Degree of Master of Philosophy of Curtin University January 207 I

2 Declaration To the best of my knowledge and belief this thesis contains no material previously published by any other person except where due acknowledgment has been made. This thesis contains no material which has been accepted for the award of any other degree or diploma in any university. Signature: Date: 26/0/207 II

3 Abstract Power transformer plays a critical role in the reliability of the electrical networks. Failure of power transformers may lead to catastrophic consequences. Thus, continuous monitoring of power transformers is of great importance to utilities across the world. As the age of numerous power transformers operating worldwide are close to or have even surpassed their designed life expectation, utilities have recently been accentuating on the transformer condition-based maintenance so as to elongate transformers operational lifetime. In addition, establishing life estimation and asset management decision models which is able to estimate the extent of criticality and age of a power transformer is a great contribution to utilities to best formulate an asset management strategy. Among several contributing factors to the failure of a power transformer, pre-mature ageing of the transformer insulation system is one of the major causes which mostly stem from the accumulated impact of three processes of pyrolysis, hydrolysis as well as oxidation. The extent of criticality and ageing of a power transformer can be determined by using several parameters which are of diagnostic importance in the condition monitoring field of power transformers. Thus far, several attempts in developing life estimation and asset management decision models have been made. However, the common feature of all these investigations is using inference systems which are based on static rules. In order to eradicate this constraint, this research study aims at developing an integrated life estimation and asset management decision model based on adaptive neuro fuzzy inference system, ANFIS. Diagnostic indicators which are utilized in the proposed model, such as interfacial tension of the oil, moisture content of the paper insulation and 2-FAL content of the oil show a strong correlation with ageing of power transformers insulation system. Implementation of this ANFIS III

4 methodology is expected to project patterns existing in the practical measurements history of power transformers by adaptive and real-time updating of the inference system s rules and to provide utilities with a more reliable asset management and condition monitoring tool. Keywords power transformer; adaptive neuro fuzzy inference system; life estimation; asset management; dissolved gas analysis; moisture content; 2-FAL content; IFT number; acidity. IV

5 Acknowledgments I would like to first thank my wife for her great support during my studying at Curtin University. Special thanks to my supervisor, Associate Professor Ahmed Abu-Siada, for being always approachable, supportive and inspiring as well as my co-supervisor, professor Syed M. Islam for his undeniable help. Also, sincere gratitude must be expressed towards all the electrical and computer engineering department staff for providing endless technical and administrative support to students and their efforts in building an environment in which students can have the most out of their potential. At the end, I am so grateful of Dr Zahra Jabiri, Kerry Williams and Emmanuel Santos at Western Power Corporation in Western Australia for their guidance and support over the course of this research study. V

6 Publications Over the course of this research study, the outcome has been published as follows:. Saleh Forouhari, A. Abu-Siada, Integrated Life Estimation and Asset Management Decision Model for Power Transformers Using ANFIS, Submitted to IEEE Transaction on Dielectrics and Electrical Insulation Society. 2. Saleh Forouhari, A. Abu-Siada, Remnant Life Estimation of Power Transformer Based on IFT and Acidity Number of Transformer Oil, International Conference on the Properties and Applications of Dielectric Materials (ICPADM), Australia, 205. VI

7 Table of Contents Introduction.... Background....2 Scope of Work Research Methodology Thesis Outline Power Transformer Diagnostic Indicators Dissolved Gas Analysis (DGA) DGA Measurement Methods DGA Interpretation Methods: Key Gas Method (KGM): Doernenburg Ratio Method (DRM): Rogers Ratio Method (RRM) Duval Triangle Method (DTM): Transformer Cellulose Insulation: Cellulose Insulation Degradation: Insulation Life Plots Furan Compounds Formation of Furan Compounds Furan Compounds Stability Correlation between Paper Insulation DP and Furan Content of the Oil 30 VII

8 2.5.4 Effective Factors on the Furan Production Rate Moisture in Oil-Paper Insulation System of Power Transformers Acid in Power Transformer Insulation System Interfacial Tension Number of the Insulting Oil Fundamentals of Fuzzy and Adaptive Neuro Fuzzy Inference Systems The Architecture of ANFIS ANFIS Modelling Life Estimation Model Integrated Life Estimation and Asset Management Decision Model Oil Criticality Sub-model Paper Criticality Sub-model Electrical Criticality Sub-model Asset Management Decision Sub-model Conclusion and Future Work Conclusion Future Work References Appendix Oil Criticality Sub-Model Heating Criticality Sub-model Paper Degradation Criticality Thermal Criticality Sub-model VIII

9 7.5 Paper Criticality Sub-model Partial Discharge Criticality Sub-model Arcing Criticality Sub-model Electrical Criticality Sub-model Overall Criticality Sub-model Asset Management Decision Sub-model Case Studies IX

10 List of Figures Figure.. Power transformer structure... 2 Figure 2.. A basic setup of gas chromatograph [2]... 8 Figure 2.2. Duval triangle with fault zones and associated coordinates [2]...3 Figure 2.3. Complementary Duval triangle 4 [6]...4 Figure 2.4. Complementary Duval triangle 5 [2]...4 Figure 2.5. Different transformer parts formed from pressboard [24]...7 Figure 2.6. Power transformer HV coil wrapped by paper [24]...7 Figure 2.7. Cellulose polymer [24]...8 Figure 2.8. Hydrolytic degradation reaction of cellulose [29]...2 Figure 2.9. An instance of oxidative cellulose degradation [3]...2 Figure 2.0. Cellulose degradation mechanisms [4]...23 Figure 2.. The relation between mechanical properties of crepe kraft paper and ageing [4]...24 Figure 2.2. Different Arrhenius life plots for different types of cellulose insulation [4]...26 Figure 2.3. Chemical structure of furan compounds [44]...29 Figure 2.4. The relation between DP of the kraft paper samples and 2FAL content of the oil obtained from an accelerated ageing test conducetd at different temperatures [7]...3 Figure 2.5. The relation between DP and 2-FAL content of the oil [4]...33 Figure 2.6. Moisture content of paper insulation as a function of temperature and percentage of relative humidity [52]...36 Figure 2.7. Piper charts for lower paper insulation moisture contents [4]...38 Figure 2.8. Moisture equilibrium curves [4]...39 X

11 Figure 2.9. Transformer insulating oil oxidation [30]...40 Figure Acid hydrolysis paper degradation [30]...43 Figure 2.2. Interfacial tensiometer [70]...44 Figure Relation between acidity, IFT number of the oil and in-service years of a transformer [7]...44 Figure 3.. Qualitative classification of transformer diagnostic indicators [72]...46 Figure 3.2. Fuzzy inference system decision-making structure [76]...48 Figure 3.3. Type-3 fuzzy inference and corresponding equivalent ANFIS structure [77]...50 Figure 3.4. Physical effect of the bell-shaped membership function parameters [77]...5 Figure 3.5. A 2-input ANFIS network with nine rules and how it relates to fuzzy subspaces [77]...54 Figure 3.6. A generic example of how ANFIS training results in more precise membership functions [77]...55 Figure 3.7. Flowchart of ANFIS learning [8]...56 Figure 4.. Membership functions of 2-Furfural content...58 Figure 4.2. Membership functions of cellulose insulation moisture content...58 Figure 4.3. Membership functions of IFT number of the oil...58 Figure 4.4. Fuzzy rules of the proposed FIS-based model...60 Figure 4.5. Three-dimensional display of the proposed FIS-based mapping...6 Figure 4.6. ANFIS training error...62 Figure 4.7. ANFIS-based model network...63 Figure 4.8. Adjusted membership functions of 2-FAL content in oil...65 XI

12 Figure 4.9. Adjusted membership functions of the paper insulation moisture content...65 Figure 4.0. Adjusted membership functions of interfacial tension number of the oil...65 Figure 4.. Generated rules of the proposed ANFIS-based model...66 Figure 4.2. The ANFIS-based model validation against testing data...67 Figure 4.3. Integrated life estimation and asset management decision model of power transformer...78 Figure 7.. Adjusted membership functions of interfacial tension number...97 Figure 7.2. Adjusted membership functions of acidity...97 Figure 7.3. Adjusted membership functions of paper insulation moisture content...98 Figure 7.4. Adjusted membership functions of ethane concentration...98 Figure 7.5. Adjusted membership functions of ethylene concentration...98 Figure 7.6. Adjusted membership functions of carbon-monoxide concentration...99 Figure 7.7. Adjusted membership functions of carbon-dioxide concentration...99 Figure 7.8. Adjusted membership functions of carbon-oxides ratio (CO2/CO) Figure 7.9. Adjusted membership functions of paper degradation criticality Figure 7.0. Adjusted membership functions of heating criticality Figure 7.. Adjusted membership functions of thermal criticality... 0 Figure 7.2. Adjusted membership functions of 2-FAL content of the oil... 0 Figure 7.3. Adjusted membership functions of hydrogen concentration Figure 7.4. Adjusted membership functions of methane concentration Figure 7.5. Adjusted membership functions of hydrogen concentration Figure 7.6. Adjusted membership functions of acetylene concentration Figure 7.7. Adjusted membership functions of partial discharge criticality XII

13 Figure 7.8. Adjusted membership functions of arcing criticality Figure 7.9. Adjusted membership functions of oil criticality Figure Adjusted membership functions of paper criticality Figure 7.2. Adjusted membership functions of electrical criticality Figure Adjusted membership functions of overall criticality Figure Adjusted membership functions of life estimation XIII

14 List of Tables Table.. Typical sources of power transformers failure []... Table 2.. Comparison between gas chromatography (GC), hydrogen on-line monitor and photo-acoustic spectroscopy (PAS) techniques [2]... 9 Table 2.2. L Concentrations of Doernenburg ratio method []... Table 2.3. Associated faults with fault-gas concentrations ratios in Doernenburg method [2]...2 Table 2.4. Suggested diagnoses by Rogers ratio method [2, 3]...2 Table 2.5. Comparison between DGA interpretation methods [2]...5 Table 2.6. Typical paper and pressboard specifications [24]...9 Table 2.7. Significance of paper degree of polymerisation and 2-FAL content of the oil in paper insulation ageing interpretation [5]...33 Table 2.8. Diagnostic significance of paper insulation moisture content and interfacial tension of the oil [42, 72]...45 Table 4.. Membership functions parameters of the ANFIS-based model...64 Table 4.2. Comparison between FIS- and ANFIS-based models life estimation...68 Table 4.3. Management decisions as per the output of the proposed integrated model...73 Table 4.4. Comparison between actual and estimated asset management decision numbers...79 Table 7.. Adapted parameters of oil criticality membership functions...97 Table 7.2. Adapted parameters of heating criticality membership functions...98 Table 7.3. Adapted parameters for paper degradation criticality membership functions...99 Table 7.4. Adapted parameters of thermal criticality membership functions XIV

15 Table 7.5. Adapted parameters of paper criticality membership functions... 0 Table 7.6. Adapted parameters of partial discharge membership functions Table 7.7. Adapted parameters of arcing criticality membership functions Table 7.8. Adapted parameters of electrical criticality membership functions Table 7.9. Adapted parameters of overall criticality membership functions Table 7.0. Adapted parameters of asset management decision membership functions Table 7.. Case Studies XV

16 Introduction. Background Power transformers are crucial assets and play a crucial role in the continuity and reliability of electric power systems. Rising demand of energy as well as increase in the number of operating transformers which either are close or have already exceeded their expected technical life have resulted in a high failure rate of power transformers in service []. A survey conducted by the IEEE organisation points out that during a period of 6 years, a fleet of oil-immersed power transformers is expected to have a significant failure rate of 0% [2]. As failure of in-service transformers has catastrophic consequences on the electric power network in terms of economical and operational aspects, regular condition monitoring of power transformers to detect incipient faults is necessary. This fact has encouraged transformer operators, including utilities across the world to employ more efficient condition-based asset management and monitoring strategies [3]. Table. [] summarises typical sources of power transformers failure and Figure. shows a typical structure of a power transformer. Table.. Typical sources of power transformers failure [] Internal Causes Insulation degradation Overheating Oxygen and moisture Solid contamination in transformer oil Partial discharge activity Design problems Winding clamping loss and deformation of windings Resonance of windings External Causes Lightning strikes Switching operations in power system Overloading of transformers Faults occurrence in power system, e.g. short circuit

17 Figure.. Power transformer structure A noticeable part of failures in power transformers originate from their insulation system. Therefore, in order to define effective maintenance schemes, it is essential to obtain a thorough understanding of transformer insulation system ageing process and determine the insulation integrity extent. The cumulative effect of oxygen, temperature, and moisture along with mechanical and electrical stresses which a transformer undergoes over its operational course are contributing parameters to the ageing of the insulation system [4]. Although insulation system normal ageing is an expected event once a power transformer is put into service, accelerated ageing of the insulation system is what should be avoided to elongate transformer operational lifetime. Restricted financial resources call for the utilization of uncomplicated, 2

18 economical and reliable life estimation and asset management decision models based on minimum number of condition monitoring parameters. In line with this necessity, some models have been suggested by IEEE [5] and IEC [6], which give an estimation of transformer remnant life by considering merely the effect of operating temperature of power transformers. Even though transformer operators are now more equipped to sense power transformer temperature data due to recent technological innovations in the field of condition monitoring of power transformers, there is still an uncertainty regarding temperature distribution within a transformer [7]. Another criticism which can be directed towards these efforts is that models which are established based on only operating temperature of transformers do not account for the impact of the other ageing factors, such as moisture and oxygen. An age estimation and condition monitoring model for power transformers developed based on fuzzy logic inference system was proposed in the literature [8]. Although this model takes into consideration almost all diagnostic parameters of power transformers, there are some limitations on regular application of this model. Firstly, this model includes some parameters which are not measured at routine transformer testing intervals. Secondly, for measurement of some parameters used in this model, such as sweep frequency response, a transformer needs to be off-line. Additionally, so far, all suggested models concerning life estimation and management decision of power transformers have been based on fuzzy logic inference system or fixed artificial neural network, ANN, methodologies in which corresponding rules cannot be automatically adapted based on future measurements and feedbacks. In order to tackle these issues, a life estimation model of power transformers is proposed, which is based on adaptive neuro fuzzy inference system (ANFIS). One of the advantages this model brings into practice is utilizing parameters which are frequently measured during transformer routine maintenance. 3

19 Also, using the ANFIS technique enables this model to enhance its precision with deploying repeated self-assessments based on the newly measured parameters and the model s output..2 Scope of Work This thesis is aimed at achieving following objectives: Acquiring comprehensive knowledge of transformer s insulation system ageing factors and corresponding diagnostic indicators used in the integrated age estimation and asset management decision model for power transformers. Developing a model based on fuzzy logic for estimating the age of power transformers. Although fuzzy logic inference system has already been applied in other research works in the literature for life estimation and asset management of power transformers, the purpose of using such a technique in this thesis is only to compare its performance with the ANFIS model proposed in this thesis and highlighting the advantages of the applications of neuro fuzzy logic inference system in this field. Introducing an integrated neuro fuzzy logic-based model for life estimation and asset management decision of power transformers, which is the main contribution of this research work in this area. The outcome of this thesis is expected to help transformer operators monitoring the condition of their power transformers fleet more regularly with less cost over the operational course of power transformers. Also, it can have a remarkable contribution to life cycle management of transformers. 4

20 .3 Research Methodology To verify the above-mentioned objectives, this study covers a thorough investigation on the contributing factors to the ageing of power transformers insulation system. Therefore, it examines ageing mechanism of the insulation system and all the diagnostic indicators showing a correlation with ageing of power transformers. Adaptive neuro fuzzy logic inference system is implemented to develop an integrated life estimation and asset management decision model of power transformers..4 Thesis Outline Following chapters are organised as below: Chapter 2 covers the knowledge required for understanding power transformers insulation system ageing mechanism along with diagnostic parameters used in determining power transformers condition and management decision. Chapter 3 brings a short summary of fuzzy logic, only giving an idea to the readers on the principles of fuzzy inference system. Then, it covers adaptive neuro fuzzy inference method as used in this thesis. Chapter 4 explains the details of integrated life estimation and asset management decision model proposed in this thesis along with case studies, and obtained results from the model. Chapter 5 draws the main conclusions form this research and presents some recommendations for future work on this subject. 5

21 2 Power Transformer Diagnostic Indicators Oil-immersed transformers are indispensable assets in the power generation, transmission and distribution networks. The major function of a transformer is to increase or decrease the level of voltage throughout the electric network. After electric energy is generated in a power plant, by means of a step up generation power transformer, the voltage level elevates in order to diminish the amount of loss of the transmitted electric energy for long distances. On the other hand, when electric energy reaches distribution network where it should be delivered to the end consumers, the voltage needs to be reduced to different levels. At this stage, a step down transformer is utilized for this purpose. Power transformers which in majority are present in the generation and transmission networks are one of the most expensive assets of electric utility companies, playing a crucial role in continuity of the electric energy delivery to consumers. A great deal of money is annually spent on the operation, maintenance and repairing of these transformers. Continuity and reliability of power transformers operation are key factors affecting the profitability of the electric energy networks. Due to limited financial resources and considering the immense cost of power transformers replacement, avoiding power transformers failure is number one priority for all the utility companies throughout the world. The following section presents the main condition monitoring tests for power transformers. 2. Dissolved Gas Analysis (DGA) Owing to oil and paper insulation decomposition in an oil-immersed power transformer, fault-gases are produced inside transformer tank, which are dissolved in the oil and decrease dielectric strength of the oil [9]. Dissolved gas analysis, DGA, is used as a reliable method to detect incipient and/or active faults in transformers based on the concentrations of the fault gases dissolved in the oil [0]. Basically, 6

22 transformers experience thermal and electrical faults over the course of their operational lifetime. The thermal energy originated from these stresses result in the generation of five major gases, including hydrogen (H2), methane (CH4), ethane (C2H6), ethylene (C2H4), and acetylene (C2H2), related to the oil decomposition, and carbon-monoxide (CO) and carbon-dioxide (CO2), due to the cellulose degradation[]. The type and criticality extent of each fault, such as partial discharge, thermal faults of different temperatures or high intensity electrical discharge, sustained arcing, can be detected based on the fault-gas concentrations by deploying DGA measurement and interpretation techniques, which assist in condition monitoring of power transformers [2]. Dissolved gas analysis is now regarded as one of the regular measurements performed by utilities on the insulating oil of in-service power transformers as part of preventive maintenance schemes [3]. Data collated form the analysis of dissolved gases in the oil over a period of time can be used for the purpose of not only identifying existing faults, but also determining the progress of the faults by considering fault-gas generating rates, which facilitates asset management decision of power transformer []. 2.2 DGA Measurement Methods Different techniques are currently used in the analysis of gases dissolved in transformer oil. Gas chromatography (GC) is one of these methods, which need to be conducted in the laboratory environment as it requires sophisticated equipment. Whilst gas chromatography is unanimously identified as the most reliable technique in analyzing dissolved gases in the oil, it is deployed annually due to being timeconsuming and relatively higher costs incurred. If the analysis detects noticeable concentration of the gases, it is however necessary to consider this analysis with a higher frequency as per the recommendations of the IEEE standard C

23 []. It is worth mentioning that GC method can also be utilized to quantify the content of free gases existing in for instance, gas blanket of transformers. Figure 2. [2] illustrates a basic setup of a gas chromatograph which is used in the laboratory to measure the concentration of the gases dissolved in the oil. Figure 2.. A basic setup of gas chromatograph [2] As another solution to monitor fault-gas concentrations dissolved in the oil, online hydrogen monitoring device has first been designed and proposed by Syprotec [2]. The ideology behind using this device to monitor condition of power transformers is that it is agreed that most of the faults occurring in the electrical apparatus which use oil as insulating medium result in the generation of hydrogen [0]. Therefore, deploying hydrogen online monitoring device may detect faults, especially hot spots, partial discharges and arcing at an early stage. Furthermore, photo-acoustic spectroscopy (PAS) is a relatively new technique in determining the concentration of fault-gases in the oil [3]. 8

24 Table 2.. Comparison between gas chromatography (GC), hydrogen on-line monitor and photoacoustic spectroscopy (PAS) techniques [2] Method Advantage Disadvantage GC Hydrogen on-line monitor PAS Can detect and analyse each gas dissolved in transformer oil Has the highest accuracy and repeatability Results can be utilized to identify the fault type Rugged, relatively cheaper, and continual on-line monitoring Detects imminent faults Continuous on-line monitoring Can measure a broad range of fault gases content Results can be used to identify the fault type Can be conducted only in the laboratory because of the sophistication of the equipment Time-consuming Expensive A trained person is required to perform the test and interpret the results Only detects H2, CO, C2H2, and C2H4 Provides the most accurate concentration only within the monitor temperature range of 20 to 40 degrees centigrade Results are not usable to determine the type of fault Sensitive results to the wave number range of the optical filters and their absorption characteristics Concentration accuracy influenced by the external temperature and pressure, and by vibration Still undergoing development In this method, pressure waves are produced after the conversion of infrared light energy of different wavelengths which are absorbed by fault gases into kinetic energy. These pressure waves are detected through a microphone and consequently the 9

25 concertation of fault-gases can be identified based on the intensity of these waves [4]. Table 2. [2] compares the positives and negatives of the three mentioned techniques in analysing concentration of fault gases dissolved in the oil samples extracted from in service power transformers. 2.3 DGA Interpretation Methods: So far, several methods have been put forward to interpret dissolved gas analysis results of samples extracted from oil-immersed electrical apparatus. The common feature of all of them is utilizing absolute or ratios of the main hydrocarbon gases generated by degradation of the oil/paper as mentioned earlier. For instance, 2-gas ratios are proposed in IEEE [] and IEC [5], 3-gas ratios in Duval Triangles to 7 [6] and recently proposed 5-gas ratios in Duval Pentagon [7] as a complementary tool to the Duval Triangles. Some of these interpretations commonly used by asset management expert teams so as to determine the condition of power transformers are explained below Key Gas Method (KGM): Once an electrical or thermal fault happens inside the transformer tank, chemical bonds of the insulating oil break, resulting in the production of fault gases. Key gas method, KGM, uses the concentrations of six fault gases of carbon-monoxide (CO), hydrogen (H2), methane (CH4), Ethane (C2H6), Ethylene (C2H4), and Acetylene (C2H2) to identify four different faults based on the percentage concentrations of the mentioned gases, which are obtained from practical experience [8] Doernenburg Ratio Method (DRM): DRM is one of the DGA interpretation methods which deploys the ratios of fault-gas concentrations in order to determine the type of faults []. In this method, faults are 0

26 distinguished according to pre-defined limits for the gas concentrations ratios of CH4/H2, C2H2/C2H4, C2H2/CH4 and C2H6/C2H2 as shown in Table 2.2 []. To use this interpretation method, two criteria must be met. Firstly, the content of at least one of the key fault gases of H2, C2H4, CH4, and C2H2 must be more than two times of the corresponding L limit and secondly, the content of at least one of the gases used in each ratio must exceed related L limit. Table 2.3 [2] contains associated faults with the quantity of the four gas ratios utilized in this method. Table 2.2. L Concentrations of Doernenburg ratio method [] Key Gas L Concentration (ppm) Hydrogen (H2) 00 Methane (CH4) 20 Carbon Monoxide (CO) 350 Acetylene (C2H2) 35 Ethylene (C2H4) 50 Ethane (C2H6) Rogers Ratio Method (RRM) In contrast to Doernenburg ratio method, it is not needed to have remarkable concentrations of fault-gases to apply Rogers ratio method, RRM so as to identify fault types. Once fault-gas concentrations surpass the L limits suggested in Table 2.2, the requirement has been addressed and this method is applicable. Although Rogers ratio method first included four fault-gas concentrations of C2H6/CH4, C2H2/C2H4, CH4/H2, and C2H4/C2H6, the ratio of C2H6/CH4 was then disregarded due to having less diagnostic value [9]. Currently, 5 different fault types together with normal condition may be identified using the proposed fault-gas ratios ranges in

27 Table 2.4 [2, 3]. Table 2.3. Associated faults with fault-gas concentrations ratios in Doernenburg method [2] CH4/H2 C2H2/C2H4 C2H2/CH4 C2H6/C2H2 Faults Oil Gas Space Oil Gas Space Oil Gas Space Oil Gas Space Thermal Fault > >0. <0.75 < <0.3 <0. >0.4 >0.2 PD <0. <0.0 Not significant <0.3 <0. >0.4 >0.2 Arcing >0. to < >0.0 to <0. >0.75 > >0.3 >0. <0.4 <0.2 Table 2.4. Suggested diagnoses by Rogers ratio method [2, 3] Case C2H2/C2H4 CH4/H2 C2H4/C2H6 Fault Diagnoses 0 <0. >0. to < < Normal <0. <0. < Partial discharge of low energy density 2 0. to 3 0. to >3 Arcing 3 <0. >0. to < to 3 Thermal fault of low temperature (T < 300 C) 4 <0. > to 3 5 <0. > >3 Thermal fault of medium temperature (300 C < T < 700 C) Thermal fault of high temperature (T > 700 C) 2

28 2.3.4 Duval Triangle Method (DTM): This method was established using IEC ratio method and IEC TC0 databases [6]. It is represented by a triangle using the concentrations of CH4, C2H2, C2H4 shown on the sides of this triangle []. This method facilitates the identification of seven different faults, including partial electrical discharge (PD), electrical discharges of low energy (D) as well as high energy (D2), thermal faults at varying temperatures (T, T2, T3), and a combination of thermal faults and electrical discharges (DT) as displayed in seven different zones on the triangle in Figure 2.2 [2]. As a disadvantage of this method, Duval triangle cannot recognize the conditions in which power transformers have a normal operation, leading to inability of this method to identify incipient faults. Furthermore, Duval has also put forward some other triangles using the same principles and methodology, such as DTM 2 [6], which is developed for the detection of faults in oil-filled load tap changers, DTM 3 [6] for electrical apparatus utilizing non-mineral insulating oils and DTM 4 together with DTM 5 [6], which are used in order to have a particular attention to cases when the occurrence of partial discharge (PD), thermal fault of T and thermal fault of T2 are detected using the original Duval triangle. Figure 2.2. Duval triangle with fault zones and associated coordinates [2] 3

29 In addition, Duval pentagon [7] has recently been introduced as a new complementary technique for the interpretation of dissolved gas analysis in power transformers. The triangles of DTM 4, and DTM 5 are displayed in Figure 2.3 [6] and Figure 2.4 [2] respectively. Figure 2.3. Complementary Duval triangle 4 [6] Figure 2.4. Complementary Duval triangle 5 [2] Table 2.5 [2] compares the key gas method (KGM) with all well-known ratio methods for the interpretation of DGA results. 4

30 Table 2.5. Comparison between DGA interpretation methods [2] Type Method Fault Types Gases Involved CO, CO2, KGM Deploys individual gas contents, convenient to apply, very conservative PD, arcing, overheated oil, overheated cellulose H2, CH4, C2H2, C2H4, and C2H6 Utilizes four gas concentration DRM ratios (CH4/H2, C2H2/C2H4, C2H2/CH4, and C2H6/C2H2) to distinguish three different fault types, deploys specified concertation limits to identify Thermal decomposition, PD, arcing H2, CH4, C2H2, C2H4, and C2H6 faults Utilizes three gas RRM concentration ratios (C2H2/C2H4, CH4/H2, and C2H4/C2H6) to distinguish five different fault types, deploys specified concentration limits PD, arcing, low temperature thermal fault, thermal fault <700 C, thermal fault >700 C H2, CH4, C2H2, C2H4, and C2H6 to identify faults Analogous to RRM, however PD, low energy electrical excluding the C2H6/CH4 ratio, discharge, high energy H2, CH4, IRM identifies six fault types, deploys specified electrical discharge, thermal faults <300 C, C2H2, C2H4, and concentration limits to identify between 300 and 700 C, C2H6 faults and greater than 700 C 5

31 DTM Deploys triangles to identify six faults, not able to detect the normal condition of a power transformer PD, low energy discharge, high energy discharge, thermal faults <300 C, between 300 and 700 C, and greater than 700 C CH4, C2H2, and C2H4 As stated above, several interpretation techniques of DGA results have so far been established. However, some inconsistency in the application of these methods to recognize fault types have been reported [20]. In order to address this issue, researchers have suggested AI methods, such as fuzzy logic [20] and neural network [2, 22], yielding a higher precision in transformer diagnoses. 2.4 Transformer Cellulose Insulation: Due to the abundance of cellulose in nature, which can be obtained from soft wood, it has been the first option to be used as solid insulation in power transformers. Cellulose is consumed as an insulating medium not only in transformers, but also in condenser bushings, HV power cables and power capacitors [23]. It is reported that the quantity of cellulose consumption in electrical equipment in the year 939 in the United States was 8 million kilograms the majority of which was used in manufacturing power transformers and HV power cables [24]. However, cellulose insulation shows a great affinity for moisture, identified as the main disadvantage of the utilization of cellulose in high voltage electric apparatus, especially power transformers. In power transformers, it is strongly recommended to dry out cellulose insulation as it improves dielectric properties of cellulose although drying-out process is time-consuming and sophisticated [25]. Generally, cellulose insulation is considered in oil-filled power transformers ranging from small ones, such as pole-mounted transformers to large ones in substations with 40,000 to 00,0000 litres of oil. Cellulose insulation in power 6

32 transformers comprise the HV and LV windings insulation together with support structures, spacers etc. as illustrated in Figure 2.5 [24]. Figure 2.6 [24] also shows the high voltage, HV, coil of a power transformer wrapped by paper tapes [24]. Figure 2.5. Different transformer parts formed from pressboard [24] Figure 2.6. Power transformer HV coil wrapped by paper [24] 7

33 The majority of paper and pressboard which are specifically manufactured for electrical purposes are made up of processed wood pulp by a chemical process identified as kraft process [24]. Kraft is a German word meaning strong. The main part of paper and pressboard in power transformers is cellulose. Cellulose consists of repeated glucose units connected to each other as displayed in Figure 2.7 [24] and can be represented by the chemical symbol of [C5H0O5]n in which n is recognised as the degree of polymerisation (DP) of the cellulose. New kraft paper and pressboard have a DP ranging between 00 and 200. Figure 2.7. Cellulose polymer [24] A few decades after inventing power transformers in 885 by Austrian engineers [26], it was unanimously accepted that a combination of paper insulation with insulating oil was vital to address all the issues with boundary areas in power transformers, such as angels and corners, which were raised due to increasing voltage levels. The usage of insulating oil in power transformers began in 892 by GE company [24]. Impregnating paper with resin which was used prior to this time to improve insulating characteristics of the paper insulation ceased by the introduction of the insulating oil. By increasing the operating temperature of power transformers due to the elevation in transformers rating, the use of thermally upgraded paper insulation in transformers was considered. It is evident that thermally upgraded paper increases insulation life and extends the life of transformers by at least the factor of three [24]. In order to compare the function of thermally upgraded papers with respect to ageing, long-term ageing studies were 8

34 performed in the 960s on different types of these papers each of which was upgraded deploying different upgrading agents [24]. Morrison s studies indicated considerable difference in the lifetime of these papers among which the best ones endured 0 times more than regular kraft papers [27]. Generally, it is believed that thermally upgraded paper designed for up to 65 C rise in insulating oil has at least 2 C improvement in thermal performance as compared with regular kraft papers [24]. As another improvement, some synthetic materials are being used to produce paper and pressboard insulation for power transformers. The advantage of using them is improved thermal capability, 220 C, while it is 05 C for paper insulation made of cellulose [24]. Moreover, synthetic paper insulation has remarkably lower hygroscopicity, adsorbing considerably less moisture [24]. As a result, hybrid solid insulation comprised of both cellulosic and synthetic paper insulation is now commercially utilized in small power transformers to benefit from these advantages. However, it is still not economically viable to use them in medium and large power transformers due to the high cost of synthetic paper insulation. For each transformer, there is a list of all the specifications of the material used for producing paper and pressboard. Table 2.6 [24] contains typical specifications indicating the properties of paper and pressboard insulation. Table 2.6. Typical paper and pressboard specifications [24] Physical and Mechanical Thickness Apparent density Tensile strength Edge tear strength for paper Shrinkage for pressboard Stretch capacity when subject to tension Resistance to air (porosity) Electrical Properties Dielectric breakdown strength at 60 Hz Impulse strength Hold strength at 60 Hz for pressboard Hold strength of impulse for pressboard Dissipation factor at 25 C 9

35 2.4. Cellulose Insulation Degradation: Generally, it is accepted that the condition of power transformer paper insulation determines whether a power transformer is operable. Hence, preserving cellulose insulation integrity and life is necessary. In order to fulfil this goal, it is essential to have a comprehensive understanding of the ageing mechanisms of the cellulose insulation. Contributing factors to cellulose insulation ageing used in power transformers are temperature, water, oxygen and acids formed in mineral oil. They are generally classified into three processes of hydrolysis related to water, oxidation related to oxygen and pyrolysis related to heating [28]. For instance, through hydrolysis which is a reaction involving water and acids, cleavage of cellulosic polymer chain occurs, generating free glucose molecules [7]. Further degradation of these glucose molecules results in the formation of furans which will be elaborated later. It is worth mentioning that the water molecules formed as a by-product of the hydrolysis reaction will contribute to more degradation of the cellulose insulation. This is one the situations in which contributing factors to the ageing of cellulose insulation act in a synergistic way. Degradation rate of the cellulose insulation increases if no remedial actions are performed to recover the condition of cellulose insulation. Figure 2.8 [29] depicts hydrolytic degradation reaction of cellulose. Moreover, there are a number of oxidative reactions which engage cellulose, breaking its polymeric chain and leading to the production of water molecules [30]. Concurrently, this moisture causes more hydrolytic cellulose decomposition. Figure 2.9 [3] demonstrates one of the oxidative reactions contributing to the degradation of cellulose structure. 20

36 Figure 2.8. Hydrolytic degradation reaction of cellulose [29] Several studies have been conducted to examine the effect of oxygen, moisture and temperature on the ageing rate of paper insulation [23, 24, 25] with different conclusions. For example, Lundgaard et al [32] identified that cellulose in oil with excessive oxygen content has 2 to 3 times faster degradation rate compared to vacuum conditions. Figure 2.9. An instance of oxidative cellulose degradation [3] 2

37 The ageing of power transformers has been a continuing concern since the first day of transformer operation due to the significant replacement cost. As mentioned earlier, cellulose insulation consists of long chains of glucose monomers, which breaks when cellulose is exposed to thermal and electrical stresses within a power transformer. Degree of polymerisation (DP) which is a reliable indicator to the extent to which paper insulation has been degraded is a reflective of the average number of the glucose monomers in these chains [33]. For a new paper, DP is expected to be in the range of 00 to 600 although it reduces as the paper insulation depolymerises under the influence of the ageing factors of temperature, oxygen and moisture. Figure 2.0 [4] shows paper degradation mechanisms and the final products of each ageing process. Carbon-monoxide (CO), carbon-dioxide (CO2) and moisture are the ultimate byproducts of cellulose insulation degradation. As a result, CO and CO2 concentrations dissolved in the insulating oil together with their generating rates may be considered as diagnostic indicators for paper insulation degradation in condition monitoring of power transformers [3, 28]. As paper ages, its mechanical properties, such as tensile and burst strength diminishes due to reduction in the length of cellulose polymeric chains. Figure 2. [4] depicts how mechanical properties of thermally crepe kraft paper, a type of kraft paper with more elongation capacity [24], changes as the paper decomposition occurs over time. Identical curves have been also established for noncrepe kraft paper [34]. As DP values of the paper insulation reach between 250 and 300, mechanical strength of the paper considerably decreases, so any induced forces originating from lightning or short-circuit currents could cause catastrophic failures to the transformer. DP value of 200 is considered as the end of practical life of paper insulation. Alongside paper insulation degradation due to thermal stresses, electrical 22

38 faults, such as partial discharge and sustained arcing could also have detrimental impact on the paper insulation and cause further paper decomposition [35]. Additionally, metallic sharp points in the vicinity of paper insulation and wet paper contribute to the occurrence and development of partial discharge affecting cellulose insulation [36]. Paper insulation remarkably degrades in the case of general overheating happens inside a power transformer, mainly due to operating transformers at close or even higher than their nominal power rating. The ratio of carbon-oxide concentrations is one of the diagnostic tools in detection of paper insulation overheating [37]. Typically, the ratio of carbon-oxides, CO2/CO, is in the range of 7 to 0 when paper decomposes normally []. Any acceleration in degradation of the paper insulation could result in ratios less than 3 or more than [37], identified as excessive cellulose decomposition which is caused by oxidation or burning of paper in the presence of significance oxygen. In addition, carbon-oxide content of more than 30% of the overall carbon-oxides concentration is a certain reflection of cellulose overheating [4]. Figure 2.0. Cellulose degradation mechanisms [4] 23

39 2.4.2 Insulation Life Plots The assessment of cellulose insulation life commenced in 930s by conducting accelerated ageing tests in laboratories on regular kraft paper [4]. In 960s when thermally upgraded and creped cellulose insulation were introduced, they regained their popularity. In the beginning, tensile strength retention property was chosen as the criterion for determining cellulose insulation end of life. However, it has recently changed to degree of polymerisation (DP) in the IEEE standard C57.9 as a majority of transformers can live longer even though the tensile strength retention of their paper insulation is less than 50 % [5]. DP of 200 is now deemed as the end of paper insulation life in the IEEE standard C57.9 [5]. Initial paper insulation life plots that were developed based on the tensile strength of 50 % end-of-life criterion showed an exponential relationship between cellulose age and the temperature it was exposed to [4]. Figure 2.. The relation between mechanical properties of crepe kraft paper and ageing [4] 24

40 In addition, a research [38] performed in 948 in the Westinghouse Electric Corporation in the USA indicated that thermal deterioration of cellulose comply with Arrhenius relationship, resulting in () [38]. E RT t = Aexp () In this equation, t represents the time spent until a cellulose property diminishes to a certain level, T is the absolute temperature in degrees Kelvin ( K) to which paper is subjected, A is a constant, R is the gas constant and E is the activation energy. Because of some discrepancies in the results obtained from the life equations established by considering cellulose tensile strength as the critical property, DP has been introduced by the IEEE standard C57.9 [5] for the investigation on paper life equations. As mentioned earlier, once DP of 200 is considered as the end-of-life criterion, life equations for thermally upgraded paper insulation, 65 C rise units, is as displayed in (2) [4]. Log 0 Life (Hours) = ( T).754 (2) Figure 2.2 [4] illustrates different Arrhenius life plots for cellulosic insulation. In this figure, D-65 stands for distribution transformers having thermally upgraded paper insulation, PD-65 for power and distribution transformers with thermally upgraded paper, P-65 for power transformers with thermally upgraded cellulose insulation, D- 55 for distribution transformers with non-upgraded paper and P-55 refers to power transformers which have non-upgraded cellulose insulation. For instance, for thermally upgraded paper insulation in both power and distribution transformers, the expected life at the reference hot-spot temperature of 0 C is estimated to be 80,000 hours which is approximately 20 years. It is evident form the Arrhenius life plots which temperature has significantly detrimental impact on the cellulose insulation life. For 25

41 instance, Arrhenius relationships indicate that for every 6 to 7 C increase in temperature, cellulose life may halve when the hot spot temperature ranges between 80 C and 00 C. As a result, in order to elongate transformer lifetime, all the proper precautions, such as proper cooling of transformers to stay within the temperature rise limit should be taken into consideration so as to maintain the operating temperature of power transformers at the lowest possible level. During the intervals when transformers are overloaded, the life aging of cellulose is more than normal situations and loss of life can be estimated deploying Arrhenius equations [5]. Using thermally upgraded papers in warmer climates in which hot spot temperature is normally higher than regions with cold weather could be a solution to prolong the life of cellulose insulation. Figure 2.2. Different Arrhenius life plots for different types of cellulose insulation [4] 26

42 However, despite the fact that thermally upgrading agents used in the structure of cellulose can rise thermal stability and tolerance of the paper insulation, the amount of these agents plays a great role in their performance and must be properly balanced. As extending the life of transformers is of significant importance to transformer operators, efficient maintenance programs together with regular condition monitoring of the suspected units should be formulated. 2.5 Furan Compounds Furan compounds are one of the by-products of cellulose insulation degradation. Therefore, furan testing has obtained a remarkable importance in assessing the condition of paper insulation over the operational course of power transformers. Furan compounds which are dissolved in the insulating oil of transformers are tested as part of routine transformer oil sampling in order to monitor the condition of transformers. It is reported that thermal decomposition of cellulose yields five furan compounds of 2-furaldehyde (2FAL), 5-hydroxymethyl-2-furaldehyde (5H2F), 2-acetyl furan (2ACF), 5-methyl-2-furaldehyde (5M2F), and 2-furfurol (2FOL) [39]. After furan compounds generate through thermal degradation process, they dissolve in oil and the content of furans in the oil can be measured using high performance liquid chromatography (HPLC) [40]. There are two main reasons why furan analysis has gained a lot of popularity in transformers condition monitoring filed. Firstly, furan compounds originate merely from paper insulation degradation [4], so they are direct reflection of the extent of paper insulation degradation, while other diagnostic indicators of paper degradation, such as carbon-oxide concentrations in oil not only come from cellulose thermal decomposition, but also they may come from oil oxidation process. Secondly, in contrast to measuring degree of polymerisation of the paper insulation, furans testing is not an intrusive procedure, i.e., once oil sample form 27

43 transformers is extracted from the sampling point located outside transformers, it can be tested for furans deploying HPLC test method Formation of Furan Compounds Kraft paper insulation is generally produced by the kraft process in which wood pulp delignification is conducted. The major component of paper insulation is cellulose, being a natural polymer of glucose units as displayed in Figure 2.7 earlier. It is commonly accepted that paper insulation decomposition is dependent on the conditions paper experiences. Basically, there are four factors affecting paper insulation life including temperature, oxygen, moisture and acids. Exposure of paper insulation to increased operating temperature of transformers, the presence of acids in the oil and paper [30] and excess moisture in cellulose [42] lead to the paper insulation depolymerisation, which generates free glucose molecules. These glucose molecules degrade further under the impact of the ageing factors and form furan compounds along with moisture and some gases [43]. The chemical structure of the five commonly known furan compounds are displayed in Figure 2.3[7]. Among these five furan compounds, 2FAL is deemed as the most dominant one and mainly used in the interpretation of furan test results for determining the extent of paper insulation degradation [44] Furan Compounds Stability It is of great importance to understand whether furan compounds are stable under the operating conditions in a transformer so as to use furan results in the most efficient way. There have been several studies to probe the stability of these compounds so far. Some laboratory experiments conducted on the furan compounds in the oil for this purpose without the presence of oxygen indicate that at temperatures lower than 00 C, all above-mentioned furan compounds do not show a noticeable decline [7]. 28

44 Figure 2.3. Chemical structure of furan compounds [44] However, 2FOL remarkably degrades as the oil temperature exceeds 00 C and up to 60 C [45]. Therefore, it can be concluded that all the furan compounds in the transformer oil are quite stable because as per the IEEE C57.9 standard for loading of transformers [5], top oil temperature which is considered as the hottest oil should always be maintained lower than 0 C and it scarcely surpasses 00 C. In contrast, it is revealed that in the presence of excessive oxygen, such as in free breathing transformers, furan compounds, especially 2FOL and 5H2F exhibit an unstable behaviour with regards to oxidative stability in the temperature range of 70 C to 0 C [7]. As a result, diagnostic importance of these two furan compounds is lower than the other three ones of 2FAL, 5M2F, and 2ACF when interpreting furan analysis results of an oil sample which has a high oxygen level, normally in the range between 29

45 6500 ppm to ppm [3]. In general, the stability of 2ACF is quite the same as 5M2F compound and having lower stability than these two, the other three compounds come in the order of 2FAL> 5H2F > 2FOL [45] Correlation between Paper Insulation DP and Furan Content of the Oil As degree of polymerisation of cellulosic paper insulation is considered as the most reliable indicator which shows the extent of paper insulation deterioration in a power transformer, there has been much effort in establishing a correlation between DP and furan content of the oil based on laboratory results [39] as well as statistical analysis of field data [46]. Developing this correlation eliminates the need for intrusive measures to extract paper samples from transformers and cellulose insulation degradation level can be determined by only testing oil samples taken from transformers. Degree of polymerisation of cellulosic paper can be measured according to ASTM D (2009) [47] standard test method. IEC standard is a similar test for this purpose as well [48]. Through these test methods, a solution of a small amount of fluffed oil-removed cellulosic paper or board dissolved in cu-priethylenediamine is used for determining the viscosity of the solution. The viscosity of the solution is related to the molecular weight of the cellulose paper at a low concentration. Deploying an experimentally developed equation, the DP of the cellulose can be calculated [47]. Viscometric degree of polymerisation is indicative of the glucose units on average in each cellulose chain. As paper insulation ageing diminishes the number of glucose units, DP has been utilized as the reliable reflection of the paper insulation deterioration. For a new paper insulation after drying out of the transformer through manufacturing process, DP is expected to be between 000 and 200 [4]. Generally, 30

46 as paper insulation DP reaches about 200, this stage is regarded as the end of paper insulation practical life when paper cannot tolerate further mechanical stresses happening during normal operation of a power transformer [49]. However, as some transformers can still be operated even if paper insulation DP is lower than 200, determining end of life criterion with respect to degree of polymerisation remains as an engineering judgment. In order to establish the correlation between furan content in the insulating oil and DP of the kraft paper, accelerated ageing on the paper samples was conducted in several laboratories [4, 44] together with using data gathered from field sample testing [39]. Investigating the test data from accelerated ageing studies, it is proposed that there is an approximately linear relation between the logarithm of the 2-FAL content in the oil and the degree of polymerisation of standard kraft paper samples. Figure 2.4 [7] displays one instance of the relation between DP of the kraft paper samples and 2-FAL content in the oil obtained from an accelerated ageing test which was conducted at different temperatures. Figure 2.4. The relation between DP of the kraft paper samples and 2-FAL content of the oil obtained from an accelerated ageing test conducetd at different temperatures [7] 3

47 Several proposed correlations between cellulose insulation DP and 2-FAL content of the oil are illustrated in Figure 2.5 [4] and their corresponding mathematical equations are listed below [4]: DP =.5 log 0 F (Chendong) (3) DP =.7 log 0 F (Scholnik et al.) (4) DP = 800 (Pahlavanpour) (5) (0.86 F)+ DP = 700 (Depablo) (6) 8.88+F In these equations F denotes 2-FAL content of the oil in parts per million (ppm). In spite of a great deal of effort to establish correlation between DP and 2-FAL content of the oil, there is still some uncertainty in determination of paper insulation DP using 2-FAL content in the oil as there are some discrepancies and variations in the results of the proposed equations [7]. Table 2.7 [5] shows the significance of paper degree of polymerisation and furan content of the oil in the interpretation of paper insulation ageing extent Effective Factors on the Furan Production Rate Although there have been several studies on developing the correlation between furan content of the oil and degree of polymerisation of the paper insulation as mentioned above, there are some technical restrictions which confine the applicability of the proposed outcomes to power transformers under actual operational conditions as well as statistical investigations on furan data gathered from transformers in service [7]. 32

48 The first factor which has to be taken into consideration in interpreting furan test results is the typical hot-spot temperature of each specific transformer together with its loading profile. Figure 2.5. The relation between DP and 2-FAL content of the oil [4] Table 2.7. Significance of paper degree of polymerisation and 2-FAL content of the oil in paper insulation ageing interpretation [5] DP Value 2-FAL (ppm) Significance healthy insulation moderate deterioration extensive deterioration <250 >0 end of life An explanation to this is that the hot spot has the highest temperature across winding insulation, which is regarded as the most important location for paper insulation thermal ageing and consequently, furan production. The second parameter affecting the production of furans in power transformers is differences in transformer design. Most often, two transformers of different make and design with the same operational 33

49 conditions show different behaviour with respect to their thermal features. For example, different specifications in the design of transformers may lead to distinct temperature gradients across windings. As a result, it is obvious that this may have different contribution to the production of furans. Also, it is worth considering in the comparative study of furan production in power transformers that the type of materials used for insulating transformer windings has a great impact on the furan production [7]. This accentuates design dependency problem in examining furan test data collected from actual operating transformers. The temperature of the environment in which a power transformer operates also plays an effective role in the furan production in power transformers. It is expected for transformers functioning in hot climates that furan production rate is higher than that for transformers in cold environments. Along with the effect of operating and ambient temperatures on the furan generation rate, the ageing level of paper insulation is also effective as proved by some laboratory examinations [45]. These studies indicated that when the DP of paper insulation is lower than 500, furan generation rate increases and at DP of 200, production rate starts decreasing. There are some other parameters influencing furan production rate in power transformers to be listed, namely, insulation type to be either standard kraft paper or thermally upgraded paper, moisture concentration within paper insulation, acids and other contaminants in insulating oil, oxygen content in vicinity of paper insulation, furan partition between oil and paper, insulating oil maintenance procedures, such as degassing, drying out and reclamation of the oil. In order to have a justifiable assessment of furan test results, all these factors should be examined. In addition, measuring furan content baseline in new transformers is of diagnostic importance as this baseline is essential in the future assessment of furan testing results. However, a reliable diagnosis of a power transformer should deem not only furan 34

50 content of the oil and production rate of furan compounds, but also the trending of oil quality test and DGA results [7]. 2.6 Moisture in Oil-Paper Insulation System of Power Transformers The presence of moisture is an important factor when considering operational reliability of power transformers. Moisture contributes to degrading transformers insulation system by compromising its electrical and mechanical properties. It is believed that the life of regular kraft paper in regards to mechanical properties halves when moisture content within insulation system doubles [52]. Furthermore, cellulose insulation degradation rate is highly dependent on paper insulation moisture content [53] and it is also believed that moisture is a contributing factor to partial discharge occurrence within transformers as well as bubble formation in transformer oil [52]. Therefore, understanding behaviour of moisture in the oil-paper insulation system of a power transformer is of a great importance. Although insulating oil in power transformers show a low affinity for moisture, moisture solubility in insulating oil normally rises with the increase in oil temperature [54]. Generally, moisture can be found in insulating oil in three situations. It is either dissolved in the oil or firmly connected to oil molecules which is more likely in degraded oil. Also, it can be found in the form of free drops or in suspension when the moisture content of the oil is higher than its saturation level. The content of moisture in the oil is quantified in parts per million (ppm), which is the weight of moisture to the weight of oil (µg/g) [55]. Relative humidity is another technical term used in the context of moisture in transformer insulation system. Relative humidity of the oil can be defined as the ratio of moisture content dissolved in the oil to the maximum concentration of moisture which can be dissolved in oil before it reaches its saturation 35

51 level [56, 58]. It is accepted that relative saturation of the oil is a better reflection of the operational changes in power transformers than moisture content of the oil which is measured in ppm [52]. Considering paper insulation in transformers, moisture can be detected in several situations, such as absorbed water to paper insulation surface or vapour. Paper insulation in a power transformer holds approximately all the moisture in a transformer and insulating oil contains a relatively very minor portion of the existing moisture. Moisture content of paper insulation is typically calculated in %M/DW, which is the ratio of the weight of moisture to the weight of dry oil-free bulk cellulose insulation in a transformer expressed in percentage. Furthermore, as it is evident from Figure 2.6 [52], cellulose insulation has significant affinity for moisture. For instance, in the room temperature range of 20 to 25 C, paper insulation can contain 4 to 8 % moisture when the relative humidity ranges from 30 to 70 %. Figure 2.6. Moisture content of paper insulation as a function of temperature and percentage of relative humidity [52] 36

52 As transformer life is adversely affected by the presence of moisture in insulation system of a power transformer, especially solid insulation, it is essential to conduct drying out process of power transformer insulation system in a fastidious way over the course of transformer manufacturing [27]. For example, as paper insulation typically experiences a relative humidity of 30 to 70% through manufacturing process during hot and cold seasons, in a temperature range of 20 to 25 C, it is expected to absorb 4 to 8% moisture, %M/DW, and it must therefore be dried out to about 0.5%, which is the acceptable level of moisture in a new transformer prior to commissioning [4]. In addition, transformer units in operation with high level of moisture content needs to be dried out [25]. Similar to drying out process performed in the factory, the acceptable limit of moisture after field drying out is 0.5%. The drying out methods conducted on power transformers have the same principals originating from Piper charts which is illustrated in Figure 2.7 [4]. These functions express the relation between logarithm of vapour pressure and temperature in degrees centigrade. For the lower moisture contents of the paper insulation, this function can be approximately formulated by (7) [52]. In this formula, PV represents the atmospheric vapour pressure, C is the paper insulation moisture content in percentage and T is the temperature in degree Kelvin. P V = C.4959 ( 7069 T e ) (7) As discussed before, paper insulation degradation yields moisture as one of the byproducts of this deterioration process. As moisture accelerates paper insulation degradation rate [23], it is necessary for transformer users to routinely assess moisture presents in transformer insulation system. Moisture migrates between paper and oil with changes in transformer operating temperature. For example, once operating temperature of a transformer decreases due to load reduction, moisture migrates from the insulating oil to paper insulation [52]. 37

53 Figure 2.7. Piper charts for lower paper insulation moisture contents [4] In order to have an estimation of the paper insulation moisture content, equilibrium curves established based on moisture absorption data of paper and oil [57] are used as depicted in Figure 2.8 [4]. In this figure, equilibrium curves at different temperatures correlate moisture content in the oil measured in ppm with paper insulation moisture content. As a power transformer experiences different temperatures across its cellulose insulation, moisture content of the paper insulation is not necessarily the same in all the locations. In addition, moisture equilibrium curves can be used in order to estimate the average moisture content of the bulk cellulose insulation. Hence, in order to have a better evaluation of the water content in hot spots which are the most vulnerable regions with respect to thermal degradation due to having highest temperatures, some 38

54 modifications in theses curves are needed. Generally, it is expected for hot-spot regions to have lower moisture content than the bulk cellulose insulation as higher temperature causes them to be drier. For example, if water content of the bulk cellulose is estimated to be 2% in an equilibrium situation between oil and paper once the oil temperature is on average at 50 C and its moisture content is 20 ppm, for a hot spot region in the paper insulation with temperature of 70 C, moisture content is approximately %, %M/DW [4]. Nevertheless, there is more limitation on utilizing moisture equilibrium curves at lower oil temperatures as equilibrium status between oil and paper is hardly achievable due to slow transition of moisture between oil and paper. This also reveals the issue that wet oil does not always mean high level of moisture in paper insulation. The reason behind this is that when transformer oil temperature reduces, it takes a relatively long time until moisture migrates back to the paper insulation [56, 60]. Figure 2.8. Moisture equilibrium curves [4] In order to assess moisture content existing in the insulation system of power transformers in a more reliable way, some alternative methods, such as dielectric spectroscopy [59] for which it is not necessary to have the equilibrium status between 39

55 paper and oil and recovery voltage method have been proposed [50, 6, 52]. In addition, a recent study has proposed a method for measuring moisture content of the paper insulation in non-equilibrium conditions [62]. 2.7 Acid in Power Transformer Insulation System To extend life of power transformers, it is vital to identify all the factors affecting insulation system ageing. Acids are another by-product of transformer insulation system degradation process, which accelerate ageing of power transformers whose life is dominantly dependent on their paper insulation condition. It is shown that paper insulation deterioration is caused by heat along with the aid of oxygen, moisture and acids in the insulating oil of transformers [55]. Acids form as a result of reactions involving insulating oil as well as paper insulation [30]. Mineral insulating oil is basically made up of three different hydrocarbon molecules, including paraffins, naphthenes, and aromatics [64]. Over the course of oil oxidation process, dissolved oxygen in the oil reacts with these molecules, generating carboxylic acids as displayed in Figure 2.9 [30]. Figure 2.9. Transformer insulating oil oxidation [30] Using chemical titration method, neutralisation number of transformer oil samples is quantified, which is indicative of the amount of potassium hydroxide, in mg KOH/g oil, needed to neutralize acidic content of the oil samples [65]. Nonetheless, it is proved that neutralization number cannot differentiate between types of acids in oil and their strengths [63]. This necessitates the need for more investigation to establish a more 40

56 reliable correlation between oil acidity and paper insulation ageing rate. The extent to which a specific type of acid is effective on the paper insulation degradation rate through acid hydrolysis reactions depends on its solubility in insulating oil as more soluble acids in insulating oil of power transformers have a less impact on cellulose deterioration [30]. In addition, some researches on acids in transformer insulating oil with respect to their molecular weight suggest that low-molecular-weight acids are more hydrophilic, having a higher affinity for paper insulation and water, while highmolecular-weight acids show a lower tendency to paper insulation, having a lower impact on paper insulation degradation [30]. Over time, aggregation of acids formed by the oxidation process results in the formation of some insoluble materials in oil, called sludge [3]. The presence of sludge can contribute to the thermal degradation of paper insulation when it deposits on paper or internal parts of transformer, such as radiator pipes and reducing transformer cooling [67]. In order to hinder oxidation process in the oil, oxidation inhibitor, such as 2,6-ditertiary-butyl para-cresol is added to the oil. Oxidation inhibitor is consumed while reacting with oxygen dissolved in the oil, slowing down acid formation and elongating transformer operational life. Once oxidation inhibitor in the oil is consumed, oil oxidation accelerates, resulting in rapid formation of acids until acidity reaches a saturation level [30]. As shown in Figure 2.20 [30], acids degrade paper insulation through acid hydrolysis reactions [32]. The reactions indicate that transformer cellulose paper degradation rate is dependent on the moisture content of the paper and H + cations stemming from acids dissociation [30]. In addition to acids originating from oil oxidation, acid hydrolysis of paper insulation in power transformers also lead to the formation of several types of acids, such as levulinic, formic and acetic acid. These acids remain in the paper insulation and show a high willingness to dissociate, leading to an increase in cellulose 4

57 degradation rate [66]. It is also suggested that acid content of the paper is of more importance than acidic content of the oil as the majority of low-molecular acids which mainly aid in paper insulation degradation exist in cellulose insulation [68]. Some methods have been suggested on how to estimate paper acidic content of transformers in service [69], which depend on several factors, including temperature and condition of the paper insulation. 2.8 Interfacial Tension Number of the Insulting Oil Interfacial tension, IFT number, of the insulating oil in power transformers indicates the extent of soluble polar contaminants and oil degradation by-products present in the oil solution. It can also be affected by dissolved moisture in the oil as water consists of polar molecules [3]. Standard ASTM D97 2 [70] is the test method used by laboratories to measure interfacial tension between oil and water. Through this method which is conducted at the room temperature of 25 C, oil sample extracted from an operating transformer is added to distilled water. As oil gravity is less than water s, it tends to float at the top of the solution, so a noticeable border between oil and water is formed. The IFT number is indicative of the amount of force required to pull up a small planar ring for a distance of cm through the border area between the oil and water [7]. Figure 2.2 [70] displays equipment deployed for the interfacial tension measurement. IFT number which is measured in dynes/cm or mn/m shows a strong correlation with oil acidity and the number of years a transformer has been operating as shown in Figure 2.22 [7]. Interfacial tension number of new oil is expected to be around 50 mn/m, while significantly degraded oil has the interfacial number of about 4 mn/m or lower [72]. 42

58 Once transformer insulation system deteriorates, oil and paper degradation byproducts contaminant insulating oil, diminishing interfacial tension number over time. Hence, acidity and IFT number of the oil are considered as diagnostic indicators to identify when remedial actions are required to be performed on oil to avoid formation of sludge. It is recommended to reclaim transformer oil when the IFT number is about 25 mn/m as the sludge formation starts at IFT number of 22 mn/m [7]. Figure Acid hydrolysis paper degradation [30] 43

59 Figure 2.2. Interfacial tensiometer [70] Once transformer insulation system deteriorates, oil and paper degradation byproducts contaminant insulating oil, diminishing interfacial tension number over time. Hence, acidity and IFT number of the oil are considered as diagnostic indicators to identify when remedial actions are required to be performed on oil to avoid formation of sludge. It is recommended to reclaim transformer oil when the IFT number is about 25 mn/m as the sludge formation starts at IFT number of 22 mn/m [7]. Figure Relation between acidity, IFT number of the oil and in-service years of a transformer [7] 44

60 Table 2.8 [42, 72] displays diagnostic significance of moisture content of the paper insulation and interfacial tension of the oil. Table 2.8. Diagnostic significance of paper insulation moisture content and interfacial tension of the oil [42, 72] Paper Insulation Moisture Content (%M/DW) Interfacial Tension Number (mn/m) Significance 0.5% -.5% >27 healthy insulation.5%-2.5% entering medium risk zone 2.5%-4% 8-23 entering in high risk zone >4% <8 entering imminent failure zone 45

61 3 Fundamentals of Fuzzy and Adaptive Neuro Fuzzy Inference Systems Ageing of a power transformer is a sophisticated process in which contributing agents act simultaneously and synergistically. Owing to this sophistication, developing analytical equations to precisely calculate ageing dynamics of a power transformer is quite impossible. As a result, available guidelines for power transformer diagnostics are classified in a qualitative way similar to the example shown in Figure 3. [72]. Figure 3.. Qualitative classification of transformer diagnostic indicators [72] An effective modelling tool in addressing such situations is fuzzy logic inference system [73]. Fuzzy logic inference modelling is defined as a soft-computing technique, which is capable of yielding a certain output from ill-defined input data. The variables deployed in the fuzzy logic inference method are in the form of words, which are mapped form input to output variables by fuzzy rules in the form of conditional if-then statements. Using the effectiveness of fuzzy logic inference system in modelling complex systems, many research works have been conducted for different power 46

62 transformer condition monitoring purposes, including DGA interpretation techniques consistency analysis, determining transformer criticality, asset management decision of power transformers, etc. [2, 35, 74, 75]. Accessing enough data of input and output variables, fuzzy logic inference system can be utilized for mapping input variables to output ones. As illustrated by the flowchart in Figure 3.2 [76], fuzzy decision-making procedure is composed of five distinct components as elaborated below: Fuzzification: it is the process of assigning each input variable to its corresponding membership function representing a fuzzy set, and subsequently determining the membership degree of that input variable in the designated membership function. Membership functions: characterizing fuzzy sets and are used in both fuzzification and defuzzification stages. They can be in different shapes, such as bell or Gaussian functions, depending on the features of input and output data. Fuzzy Rules: fuzzy rules are developed through the relationship between input and output data, having a conditional form of IF-THEN or IF-AND / OR- THEN. Fuzzy Inference Engine: at this step, the conversion of fuzzy inputs to fuzzy outputs with the use of fuzzy rules takes place Deffuzification: using deffuzification methods, such as centre of gravity or bisector, fuzzy inference modelling output is quantified from the associated output membership functions. 47

63 Figure 3.2. Fuzzy inference system decision-making structure [76] The basic structure of a model relying on the fuzzy inference system comprises a procedure which includes mapping of input variables characteristics to their corresponding membership functions, input membership functions to fuzzy rules, fuzzy rules to output variables characteristics, output characteristics to their corresponding membership functions, and output membership functions to an outcome in the form of a value or a pertaining decision. In such modelling scenarios, fuzzy inference system rules are developed by the user s understanding to the characteristics of the available data of the modelled system. In addition, mathematical parameters defining each membership function included in the intended model are determined randomly without taking into consideration the features of the system data. Therefore, to increase model s accuracy, it is essential to employ techniques which consider all the changes and features of the input and output data of a system. Adaptive neuro fuzzy inference system (ANFIS) is an artificial intelligence, AI, technique in the framework of adaptive networks which can satisfy this necessity. What is noted as the advantage of ANFIS-based models over models established based on fuzzy inference system, FIS, is that with using ANFIS method, one can customize 48

64 the membership functions parameters and model rules as per the patterns and attributes of the system data. Basically, membership functions are determined by some geometrical parameters defining the shape of each membership function and their covering range. Applying ANFIS method to map input variables to output ones facilitates the adjustment of membership functions parameters to the variations in the input data in an optimal way. Therefore, in establishing estimating model for power transformer remnant life and asset management decision based on insulating oil diagnostic parameters, ANFIS modelling has the advantageous of considering the changes in transformers data, loading profile, environmental and operational factors and design of transformers. 3. The Architecture of ANFIS Different equivalent ANFIS structures have so far been proposed with respect to adaptive networks application to different types of fuzzy logic inference and reasoning systems [77]. This section elaborates on the architecture of adaptive neuro fuzzy inference system, which is embedded into the Takagi and Sugeno type [78] fuzzy inference system as used in the model developed in this thesis. In order to provide a simple explanation of how the adaptive neuro fuzzy inference system functions, it is assumed that fuzzy inference system under study has two inputs, x and y and one output, z. provided that this FIS is based on two fuzzy if-then rules of the Takagi and Sugeno type, these rules are expressed as follows: Rule : if x is A and y is B, then f = p x + q y + r Rule 2: if x is A 2 and y is B 2, then f 2 = p 2 x + q 2 y + r 2 49

65 Type 3 fuzzy inference system and its associated ANFIS structure is depicted in Figure 3.3 [77]. In this ANFIS structure, the nodes in each layer represents functions of the same family as explained below:. In layer, each node is expressed by (8) [77] in which x shows the input of node i and A i serves as the related linguistic variable to this node function. Therefore, it can be concluded that O i represents the associate membership function with A i, which determines the membership degree of the input x. O i = μ Ai (x) (8) In the model presented in this research work, bell-shaped membership functions are utilized which are mathematically presented by (9) [79] and depicted in Figure 3.4. Evidently, characteristics of this type of membership functions are dependent on the parameters a i, b i and c i named as premise parameters. Once any change in the quantity of these parameters occurs, the shape of membership functions varies, representing distinct features. Figure 3.3. Type-3 fuzzy inference and corresponding equivalent ANFIS structure [77] 50

66 μ Ai (x) = + x c 2b (9) i i a i Figure 3.4. Physical effect of the bell-shaped membership function parameters [77] 2. In layer 2, function of each node is to multiply input signals by a weighting factor wi and to send the outcome to the next layer. For example, w i of each node can be calculated as below [77]: w i = μ Ai (x) μ Bi (y) i =, 2. (0) Principally, the outcome of every node in this layer determines the weight of rules and any other generalized AND operator in the content of fuzzy logic can also be utilized as the function of nodes in this step. 3. In the third layer, the output of each node, w i, is the proportion of the weight of associated rule with the node to the summation of all the rules weights as defined by () [77]. The outputs of this layer is also identified as normalized weights. w i = w i w + w 2 i =, 2. () 4. In layer 4, each node s function is defined as (2) [77] in which w i is the normalized weight of the corresponding rule with the node, which is the output 5

67 of the previous layer and p i, q i, and r i are this layer s parameters recognized as consequent parameters. O 4 i = w if i = w i(p i x + q i y + r i ) (2) 5. Layer 5 as the final layer includes only one node whose function is the summation of all the inputs coming from layer 4 as below [77]. O 5 = overall output = w if i = w if i i (3) i i w i As depicted in Figure 3.3, the proposed adaptive network is a multilayer feedforward structure whose node functions have a particular performance on their inputs and associated parameters. Basically, in the adaptive networks, nodes are distinguished as circle or square nodes. Circle nodes present those nodes without any parameters, which are identified as fixed nodes, whereas square nodes indicate nodes with parameters, which are known as adaptive nodes. To obtain an acceptable mapping from input data to output data, the parameters of these adaptive nodes need to be optimized based on available training data. There are several optimisation algorithms, such as back propagation learning algorithm [80], hybrid learning algorithm [77], etc. For the purpose of developing ANFIS model proposed in this thesis, backpropagation algorithm is deployed. It is important to mention that the backbone of all these optimisation procedures is the gradient descent method [77] which is described below. Provided that an adaptive network includes L layers and the kth layer of this structure has k nodes, the ith node of the kth layer can be denoted as (k, i) and its pertaining function as O i k. If we present a training data set of P entries, the error function of the pth entry of this data set, < p < P, can be defined as the summation of squared errors by (4) [77] in which T m,p is the mth element of pth expected output vector and L O m,p is the mth element of pth actual output vector. 52

68 E p = L m= (4) L (T m,p O m,p ) 2 Therefore, the overall error function can be defined as in (5) [77]. P E = p= E p (5) In order to establish an optimum procedure for the parameters of an adaptive network using gradient descent method, it is required to quantify the rate of error, E p, for pth O training data and every node output denoted as O. The rate of error for the output of a node in the ith position of the Lth layer can be calculated as in (6) [77]. E p L O i,p = 2 (T i,p O L i,p ) (6) Using the chain rule, for instance, for an internal node in the ith position of the kth layer, the rate of error is defined as below [77]: E p k O i,p k+ E p = k+ O m,p m= k k L (7) O m,p k+ O i,p As a result, if α is a parameter pertaining to a node in the adaptive network, the rate of error depending on α can be defined as below [77]: E p = E p α O S O O α (8) In the above equation, S refers to the set of nodes whose outcomes are dependent on α. Therefore, the overall error rate regarding α is defined as (9) [77]. E P E p = α p= (9) α According to the above overall error rate equation, the generic formula for updating node parameters can then be expressed as in (20) [77] in which ρ is recognised as the 53

69 rate of learning and can be defined as in (2) [77]. In this equation, k determines the size of each gradient transition step when parameters are being updated, on which the learning algorithm convergence speed is dependent. α = ρ E α (20) ρ = k ( E α α )2 (2) Premise Parameters Consequent Parameters Figure 3.5. A 2-input ANFIS network with nine rules and how it relates to fuzzy subspaces [77] Adaptive networks can be trained in two ways. The first is off-line learning functions in which each parameter of the network is updated after the entire training data has been given to the network. In other words, just following every epoch, the update of network parameters takes place. The second is on-line or pattern learning through which parameters of the network are updated exactly following the presentation of 54

70 each input-output data pair. Figure 3.5 displays how a 2-input ANFIS network with nine rules corresponds with fuzzy subspaces. As three membership functions pertain to each input in this structure, fuzzy input space consists of nine fuzzy subspaces and each of the nine fuzzy rules which are in the form of if-then statements determines how their associated subspace changes. Figure 3.6 [77] shows a generic instance of how ANFIS learning procedure leads to adjusted membership functions of the input variables x and y. Parts a and b depict membership functions prior to the implementation of the learning algorithm and parts c and d illustrate membership functions once desired minimum error between actual data and model output has been achieved. Figure 3.6. A generic example of how ANFIS training results in more precise membership functions [77] 55

71 Figure 3.7 [8] shows a generic flowchart of ANFIS learning procedure. start generating initial parameters of neuro fuzzy model presenting input training data set calculating the output of neuro fuzzy model correcting the value of neuro fuzzy model parameters calculating the quantity of error (difference between desired output and model output) is error less than the expected value? No Yes saving adjusted values of parameters of neuro fuzzy system end Figure 3.7. Flowchart of ANFIS learning [8] 56

72 4 ANFIS Modelling 4. Life Estimation Model Degradation of the insulation system of a transformer is a sophisticated process. This complexity originates from synergistic and retrospective participation of factors affecting the ageing process of a transformer. Hence, as mentioned earlier, finding a mathematical equation for transformer ageing process is quite impossible. As a solution, this work implements ANFIS modelling to establish life estimation model for power transformers based on diagnostic indicators which are regularly measured at routine maintenance intervals of a transformer. Applying ANFIS modelling technique accounts for all the variations in the operational and environmental parameters playing a significant role over the course of transformer ageing and results in a higher precision in the model output. This chapter describes the proposed model and highlighting the advantage of using ANFIS method in modelling complex systems over fuzzy inference system, FIS, which has already been used in other research works. Therefore, FIS-based life estimation model of power transformers is firstly presented. Secondly, the ANFISbased model as the main contribution of this thesis is elaborated. Results of these two models are compared in order to give a better understanding of how the ANFIS method improves the accuracy of modelling. Finally, an integrated asset management decision model developed based on the ANFIS learning technique is put forward. The FIS-based model is established by utilizing fuzzy logic toolbox graphical user interface in MATLAB software to map the input variables of 2-FAL content, in mg/kg oil, oil interfacial tension number, in mn/m, and the water content within paper insulation, in %M/DW, to the percentage of transformer remnant life as the output variable. These diagnostic indicators show a strong correlation with ageing of power 57

73 transformers. Membership functions of these variables chosen are displayed in Figure 4., Figure 4.2 and Figure 4.3. These membership functions were defined using qualitative information in Table 2.7, Table 2.8, and Figure 3. and according to the user s perception of available data. Figure 4.. Membership functions of 2-Furfural content Figure 4.2. Membership functions of cellulose insulation moisture content Figure 4.3. Membership functions of IFT number of the oil 58

74 One of the negative points being effective on the accuracy of this FIS-based model is that the parameters determining the physical characteristics of these bell-shaped membership functions are selected randomly. As a result, these membership functions will not reflect all the characteristics and patterns existing between the input and output data. This deficiency can be mitigated to a satisfactory extent by deploying adjusted membership functions through optimised ANFIS technique. Required number of fuzzy rules for this model is 25 as each input variable involves five membership functions. Each of these rules represents a probability in the relation between input variables and output one, being in the form of If-And-Then statements. The graphical illustration of these rules that shape the relation between interfacial tension number, 2-FAL content of the oil, and water content in the paper insulation with the remanent age of a power transformer is shown in Figure 4.4. As an example, for 2-FAL content of 4.3 mg/kg oil or ppm, moisture content within paper insulation of 3.5%, %M/DW and oil interfacial tension number of 22 mn/m, the proposed model yields a percentage of transformer remnant life of 32.2%, based on an average operational life of 40 years. Another disadvantage of using fuzzy logic inference system is that fuzzy rules are defined according to the user s understanding and experience to the investigated problem, which makes it inconsistent; moreover, these rules are static and cannot be dynamically adapted. In contrary with FIS, ANFIS modelling facilitates dynamic change of rules based on the changes in the system data [82]. The mathematical representation of the centre of gravity method is as in (22) [8] where Z0 is the defuzzified output, µc (z) are the output membership functions associated with the input data and fuzzy rules and z is the fuzzy system output variable. Figure 4.5 displays one of the three-dimensional plots of the suggested FIS model, 59

75 showing how 2-FAL content of the oil and cellulose moisture content correlate with the percentage of transformer remnant life. Figure 4.4. Fuzzy rules of the proposed FIS-based model Z 0 = z.μ c(z)dz μ c (z)dz (22) Due to the above-mentioned disadvantages which fuzzy logic inference system has in modelling complex systems and in order to improve the accuracy of the model representing the behavior of the system under study, this research study deploys adaptive neuro fuzzy inference system method to develop an integrated life estimation and asset management decision model as elaborated below. ANFIS learning method 60

76 enables membership functions and rules to be tailored to the features and any changes in the input and corresponding output data. Figure 4.5. Three-dimensional display of the proposed FIS-based mapping ANFIS modelling contributes to better projecting all the features of transformers, sourced by distinctions in the loading profile, environmental factors affecting the operation of a transformer, and design of transformers into the membership functions of the input and output variables and defined rules in the model. The underlying principles of the adaptive neuro fuzzy inference system are identical to the fundamentals of artificial neural networks, ANN. Due to successful implementation of the ANN methods for addressing complex problems and in selflearning algorithms, these principles have gained a significant popularity in establishing algorithms for recognising patterns, predicting trends, etc. [77]. In order to develop ANFIS-based life estimation model of power transformers, diagnostic indicators of interfacial tension number, 2-furafural content of the oil and water content of the cellulose insulation, which are reliable indictors of the ageing of power transformers as described in chapter 2 are used as the input variables. The studied 6

77 transformers are from a wide range of age, design, rating and operational condition. In order to apply ANFIS method, anfis function accessible in the fuzzy logic toolbox of MATLAB software is used. The collated data is separated into two batches of data for training and testing purposes. Training batch includes 60 and testing one contains 40 sets of data. Through training process of the adaptive neuro fuzzy inference system, back propagation algorithm [80] is utilized so as to optimise membership functions parameters and the rules of the proposed model. Backpropagation optimising procedure employs input and output data history in order to adjust the parameters of the membership functions. It computes and adapts random weights as the learning procedure goes forward until the difference between the actual and desired output, model error, meets the specified criterion [83]. The error of model training during the application of ANFIS method to the collected data is illustrated in Figure 4.6. Figure 4.6. ANFIS training error This error expressed in years, which is the difference between actual age of the studied transformers, determined as per their commissioning date, and their estimated age by the model diminishes as training is in progress until it reaches the value of year at the epoch of The typical structure of the adaptive neural fuzzy networks for the 62

78 proposed model is depicted in Figure 4.7. In this architecture input variables, namely 2-FAL content of the oil, paper insulation moisture content and oil interfacial tension number together with the estimated age of power transformers as the single output are displayed. It also shows how multiple layers and nodes of the proposed ANFIS network collaborate with each other. As shown in this structure, input variables are mapped through representative nodes of the input membership functions, and then through the representative nodes of rules and output membership functions into the output variable. Figure 4.7. ANFIS-based model network Following finalization of the training procedure, the proposed model optimised through ANFIS learning algorithm and the adjusted membership functions are the outcome of this learning procedure. The proposed life estimation model in this work uses four generalized bell-shaped curves as the membership functions of each input variable. The equation of this type of function is as in (23). Considering the equation, physical characteristics of this function which define the shape and interval they cover 63

79 are dependent on the parameters of a, b and c. Over the course of ANFIS learning, these parameters are changed until the error of the model reaches a satisfactory level. f(x; a, b, c) = + x c (23) 2b a The parameters of the adapted membership functions are shown in Table 4.. Figure 4.8, Figure 4.9 and Figure 4.0 also display the membership functions of the input variables of the suggested model. Table 4.. Membership functions parameters of the ANFIS-based model Membership Function Paper Insulation Moisture Content (a,b,c) 2-FAL Content (a,b,c) Interfacial Tension Number (a,b,c) Good (0.47,2.2,0.30) (0.86,.74, -0.23) (4.76, 2.08, 43.05) Marginal (0.6,2.5,.39) (0.55, 2.5, 0.98) (6.2,.3, 32.25) Poor ( ) (0.55, 2.69, 2.86) (5.68, 2.46, 23.28) Critical (0.99, 2.02, 4.96) (0.52, 3.20, 4.96) (6.38,.89,5.44) Optimisation of these parameters occurs on the basis of a gradient vector which is basically a mathematical function indicative of the accuracy of the model which maps the presented input data to output data for a specific set of parameters as explained earlier. Once the gradient vector is achieved, optimization methods can be performed on this function so as to minimize the output error of the ANFIS-based model. It is worth mentioning that the ANFIS graphical user interface of MATLAB software also provides the possibility of using an integration of the back propagation algorithm and the least squares estimation as an alternative optimization method for the adjustment of the parameters of the membership functions. Generally speaking, one of the ways 64

80 to improve the performance and reduce the estimation error of this proposed ANFISbased model is to utilize more accurate optimising algorithms which can determine membership functions parameters and model rules in a more precise way. Figure 4.8. Adjusted membership functions of 2-FAL content in oil Figure 4.9. Adjusted membership functions of the paper insulation moisture content Figure 4.0. Adjusted membership functions of interfacial tension number of the oil 65

81 In the above figures, the range of input variables membership functions is selected through the ANFIS training as per the given input data. However, the calculated parameters of each membership function defines the interval they cover. In contrast with FIS-based models which are static, ANFIS training facilitates continuous enhancement of the ANFIS-based models because the parameters of membership functions are updated every time a new set of data is presented to them. Figure 4. depicts corresponding rules with the suggested model, which are automatically generated through ANFIS learning algorithm. Figure 4.. Generated rules of the proposed ANFIS-based model In order to assess the accuracy of the proposed model, testing data consists of 40 sets of the input and output data, which are extracted from different transformers 66