A Novel Fuzzy Logic Technique for Power Transformer Asset Management

A Novel Fuzzy Logic Technique for Power Transformer Asset Management

M. Arshad British Columbia Hydro

Burnaby, V3N 4X8, Canada [email protected]

S.M. Islam Curtin University of Technology

Perth 6845, PO Box U1987, Australia [email protected]

Abstract—Due to deregulation, increased demand, economic pressures, and profit constrains transformer management has gained remarkable recognition. Asset management is becoming increasingly important as the average age of transformer increases. Existing assets serving closer to their expected life or beyond are being considered for further utilization in order to reduce capital expenditure as the replacement cost of these transformers is too high. Irrespective of the failure rate, transformers are also of higher concern from the asset management view point. The asset management aims to have a flexible decision on transformer retirement/ replacement or relocation. An accurate asset management ensures that a transformer will serve closer to its rated output and life without sacrificing its practical integrity. Transformer’s performance, reliability and technical life can be increased with the implementation of better management strategies and correct operational criteria. Using fuzzy modeling, this paper presents asset management strategies based on transformer remnant life and rate of aging assessments.

Keywords-Aging; Asset Management; Fuzzy logic; Life estimation; Maintenance; Reliability; Power transformers

I. NOMENCLATURE

A End of life criteria B Aging coefficient CBM Condition based maintenance DGA Dissolved gas analysis

nAAF Aging acceleration factor for the

temperature that exist during nt∆

EQAF Equivalent aging factor for total time period

FRA Frequency response analysis HST Hot spot temperature HV High voltage kWh Kilowatt hours MRTTF Mean residual time to failure MTBF Mean time between failures MTTF Mean time to failure n Index for the time interval, t N Total number of time interval PD Partial discharge

RCM Reliability centered maintenance RVM Return voltage measurement TBM Time based maintenance

HST Hotspot temperature TTFF Time to first failure

Aθ Average ambient temperature

Hθ∆ Winding hotspot temperature

TOθ∆ Top oil temperature

nt∆ Time interval, hours

II. INTRODUCTION RANSFORMER life management has gained remarkable recognition in the recent years due to economic and technical reasons [1]. According to an

IEEE survey, oil immersed transformer failure rate per unit year is 0.00625. Therefore in a fleet of 100 transformers, ten will have problem within the next 16 years. According to the international survey conducted by CIGRE, typical failure rates is in the range of 1-2% per year for the large power transformers (operating voltages up to 300 kV) [2]. Load growth has contributed to an increase in the transformer HST. The estimated HST in 1974 was 50°C and today it would be around 73°C [3]. This gradual increase in hotspot temperature has an effect of reducing insulation life when it is operating at peak load. Transformers operating beyond their ratings experience the following:

• Increase in temperature of windings, insulation and oil.

• Increase in leakage flux density outside the core, causing additional eddy current heating in the metallic parts.

• Moisture and gas content increases with the increase in temperature.

• Bushings, tap-changers, current transformers and cable end connections are exposed to a higher stresses.

• Insulation deterioration increases with higher thermal stresses.

BC Hydro, Canada and the Department of Electrical and Computer Engineering, Curtin University of Technology, Perth Western Australia

T

1-4244-0365-0/06/$20.00 (c) 2006 IEEE

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The failure rate is three times higher in utilities with poor maintenance programs then others, having better maintenance programs [4]. In the absence of effective asset management, many transformers have failed before reaching their designed technical life. Average age of the transformers that failed due to insulation deterioration during the last ten years was around 18 years, [5-7]. It is expensive to replace the existing aging transformer fleet, and some may still be in good working condition [8]. Condition monitoring of power transformers has gained support in the recent years. The factual cost of not having sufficient online monitoring is much greater then the event of an avoidable incident.

Dielectric response is an effective tool for transformer condition assessment as cellulose insulation material degrades with age. The increase in operating temperature, oxygen and moisture causes accelerated insulation degradation, and are important factors in the asset management. The degradation includes both electrical and mechanical properties of the cellulose. Dielectric response is based on the change in the behavior of the insulation system with frequency, temperature and chemical properties [9]. The insulation is very much responsive in transformer serving closer to their design life, influenced by operating and environment conditions. The failure probability increases with the age, in particular where online monitoring and periodic diagnostics are not applied.

Economically, deferral of investment on costly assets by driving them harder has been always recognized as a preferred strategy. On the contrary, by correlating the cost of depreciation on a transformer with usage (kWhs) facilitates more financially reasonable method for asset performance assessment. This enables the asset managers with a flexible decision to retire the aged transformer at the appropriate time. It also assists to plan the network growth and reduces the expensive risks [10]. Due to restructuring and deregulation of energy market utilities are forced to cut operational and maintenance costs without sacrificing the continued reliability of power supply. This could be achieved by switching from the time based maintenance (TBM) to condition based maintenance (CBM). Costs can not be reduced with unscheduled maintenance and reactive mode of operation. Forced outages and maintenance is more expensive then planned maintenance [9, 11, 12].

The risk of unexpected transformer failure ranges from minimal to very high depending upon the concerned utility’s level of redundancy. The risk management would reduce the overall risk exposure in terms of costs, service reliability and availability. Transformer failure rate due to insulation related problems is 11% and is increasing [13]. Transformer management is vital to determine its technical end of life, practicable performance, strategic and economic impacts. To develop advanced asset management strategies for transformer, the following criteria provides basis to maintain its good operational reliability and availability:

• Identification and impact of major risks that may be present in the transformer.

• Identification and impact of existing risks on the system and environment.

• Implementation of cost effective procedures to reduce the failure risk.

• Alternate action in the absence of failure prevention.

Economic and end of life assessment are essential for the existing aged assets to plan for the maintenance, relocation or retirement. Successful life management of power transformers produce financial benefits with increased reliability and extension in life.

III. TRANSFORMER CRITICALITIES Dielectric response assessment determines the

transformer performance subject to its condition, as cellulose degrades with age. Dielectric response is an important factor in the transformer risk assessment. The failure probability increases exponentially with poor dielectric response. The degradation of oil/paper insulation depends on thermal, hydrolytic, oxidative, electrical and mechanical conditions within the transformer. Thermal degradation tends to breakdown the hydrogen bonds and this process results formation of carbon oxides, organic acids and moisture. The degradation includes both electrical and mechanical properties of the cellulose. The cellulose degradation trend assessment requires transformer historical test data. Dielectric response is based on the change in the behavior of the insulation system with frequency, temperature and chemical properties, Figure 10 [9].

Due to the winding movement, inter-strand insulation breakdown in transformer occurs causing the overheating of insulation. Also due to the circulating currents, the hotspots could be produced at the point of fault. A turn to turn fault produces more energy and can usually be detected and identified. The types of failure which may occur within the transformer tank are many. Insulation aging in transformer is irreversible phenomena. Stresses due to operation (normal to extreme), ambient conditions and contamination contribute to the deterioration of the insulation chain thus shortening the transformer design life. Transformer various criticalities are categorized in Table 1, and explained using fuzzy modeling.

TABLE 1. TRANSFORMER CRITICALITIES

S No. Criticalities Indicators 1 Thermal

Oil DGA-Ethylene and Ethane

Paper DGA-Carbon Monoxide and Carbon Dioxide

2 Electrical Partial

Discharge DGA-Hydrogen and Methane Arcing DGA-Hydrogen and Acetylene

3 Active

Prognostic DGA-Rate of Gas Evolution and Hotspot Temperature

Operational Loading and Environmental effects 4 Winding Integrity

Electrical Partial Discharge [PD] and Leakage Reactance

Mechanical Frequency Response Analysis [FRA] and Dielectric Dissipation Factor [DDF]

5 Oil Quality

Electrical Dielectric Breakdown Voltage [BDV] and Power Factor [PF]

Physical Interfacial Tension [IFT] and UV Spectrophotometry

6 Insulation

Deterioration Moisture [RVM] and Hotspot Temperature [HST]

Power transformer condition monitoring plays a decisive role in the reliability of power system operation. Strategic

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maintenance and operational procedures are best formulated where the performance of existing plant has been accurately assessed. Significant investment in terms of expertise and finance is required for monitoring and diagnostics to ensure regular insulation assessment. Utilities are now focusing seriously on the cost and importance of diagnostic and maintenance practices such as CBM [14, 15]. Transformer failure is directly proportional to the dielectric response. Through faults also have considerable effect on the integrity of insulation system and accelerate the aging phenomenon. Mineral oil and insulation paper should have sufficient dielectric strength to withstand these faults. The aging of cellulose/ oil is mainly due to the change in the chemical and physical properties of the dielectric and can be measured [13, 16, 17]. Transformer failure rate due to insulation related problems is 11% and is increasing [13].

IV. AGING MECHANISMS The majority of solid insulation is based on cellulose in

the form of paper, pressboard or timber. In the presence of heat, oxygen, water and other chemicals the cellulose molecules undergo into chemical changes. This causes the degradation in term of its electrical and mechanical properties. The increase in operating temperature, oxygen and moisture causes accelerated degradation. One product of these reactions is a glucose, which undergoes further degradation and yields a group of chemicals called furans. Furans are significant because they are more soluble in oil than glucose and can be used as an indicator of cellulose aging. Carbon monoxide and carbon dioxide are also produced together with water and some hydrogen. The cellulose molecules become shorter on average, reducing its dielectric and mechanical strength.

Due to the hygroscopic nature of oil, water and oxygen in the insulation system will further accelerate the aging process. Moisture is the main cause of the accelerated aging process in cellulose. Major part of water is contained in the solid insulation. The water in oil and its movement from solid to oil is highly temperature dependant. Transformer reliability and aging highly depend on the dryness of cellulose. The dryness of cellulose can not be ensured from the measurement of water in oil [18]. With the increase in moisture level, cellulose breakdown and its tensile strength decreases. Also sludge and metal particles affects the degradation process. The activation energy of cellulose degradation in oil is of the order of 85kJ/mole for the oxidative degradation reaction and 120 KJ/mole for the hydrolytic degradation reaction. The cellulose degradation increases significantly above 140°C [19]. The cellulose aging rate is approximately proportional to the amount of water in it. This simply means going from 0.5 % moisture to 1.0 % accelerates the aging rate by two. Faults levels such as short circuits and over voltages have significant contribution in insulation deterioration. The relation between aging factors is synergistic in nature and not just additive that makes the aging mechanism extremely complex. The aging mechanism of the insulation system, within the high voltage (HV) system can be split in to two categories as stated below [20].

A. Intransitive Aging The ability of the insulating material with the passage of

time to withstand the designed stresses such as electrical, mechanical, thermal, chemical, and physical.

B. Transitive Aging It is the rapid aging of the insulating material when

subjected to abnormal condition.

The multi-stress aging is very complex in terms of the large matrix of measurement, interpretation and analysis. The lack of appropriate diagnostics and associated equipment that are non-intrusive, efficient and economical makes the multi-stress aging difficult. Historical data analysis revealed that increase in temperature for every 10°C will cause the insulation life to be halved [21].

Transformer insulation deterioration or aging is a function of time and temperature. Due to temperature non uniformity in transformer, part operating at the high temperature will normally experience accelerated deterioration. Therefore, aging studies consider the effects produced by the highest temperature as well. The loss of thermal life has been evaluated based on IEEE Standard C57.91-1995 using hotspot temperature [22, 23]:

HTOAHST θθθ ∆+∆+= (1)

According to the IEEE Standard C57.91-1995 the life per unit is calculated using Archennous-Dakin method [1, 22, 23]:

Remaining Life TBAe /= (2) )273/(

.+= HSTB

up eALife (3)

Where A and B are constants and typically; 18108.9 −×=A

15000=B

Therefore, )]273/(15000[18

. 108.9 +−×= HSTup eLife (4)

The accelerated aging factor has a value greater than 1 for a winding hotspot reference temperature more then 110°C and less than 1 for temperature below 110°C. The insulation accelerated aging factor is calculated as [23]:

+−

= 27315000

38315000

HSTAA eF (5)

The equivalent aging of the transformer:

∑

∑

=

=

∆

∆= N

nn

N

nnAA

EQA

t

tFF

n

1

1 (6)

Insulation life in percent in the time period is give by:

% Loss of Life = )100( ×× tFEQA / Normal Insul. Life (7)

The other approach for reaming life is evaluated on the basis of partial pressure. For oil reaching saturation with hydrogen or carbon dioxide will cause bubble formation if exceeds 50000µL/L and 610 µL/L in amount approximately. The aging of the oil is determined by the sum of all the pressures over the range of working temperature. The sum of

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the partial pressures ∑ tiP equal or exceed the working

pressure P will start the oil to boil. The difference between the working pressure and sum of partial pressures is an expression of the reaming life (%) [24].

( )P

PPR

ti

res∑−

=100

(8)

Many variables in transformer, including varying load and ambient conditions make it difficult to give precise remnant life estimation rule. Transformer remnant life estimation is not achievable precisely considering single indicator and ignoring other variables. Therefore to judge the transformer with single indicator for its criticality, aging rate and remnant life estimation would be unfair.

The remnant life estimation fuzzy model indicates various criticalities, rate of aging, expected residual life and suggests appropriate asset management strategies, as shown in Figure 10. The main achievement of the asset management fuzzy model is to enhance the reliability, maintainability, availability and utilization of the existing aging transformers fleet. Due to the cumulative effects of various factors it is not possible to develop enhanced asset management strategies with a great degree of accuracy using statistical approach [25]. Remnant life estimation is an effective tool in the asset management in terms of extension in life, retirement, relocation, enhanced reliability and safety.

V. FUZZY LOGIC MODELING TECHNIQUE Due to various reasons many stresses act simultaneously

inside the transformer which increases the complexity and is not possible to build a precise analytical asset management model. The fuzzy knowledge based expert system for power transformer encapsulates the engineer experienced knowledge. The information is mostly inexact and qualitative such as poor, satisfactory and excellent. Expert system using fuzzy logic codifies the experience based diagnosis and facilitates to develop enhanced asset management strategies and ensures transformer better reliability, maintainability and availability. Inaccuracy in the single input variable will not invalidate the result but will reduce the accuracy of the analysis up to an acceptable understanding [26]. All the parameters can be analyzed individually as each rule satisfies the following criteria:

• Relevant measurement with respect to the transformer indicated condition.

• Acceptable range for the measured quantity which includes any uncertainty associated with this measurement or acceptable range.

• Importance of the measurement in determining the condition of the transformer.

Most of the techniques used in transformer assessment are based on ad-hoc basis or stand alone indicator. The fuzzy logic is an effective tool in transformer asst management, identifying its criticality rank, rate of ageing and remnant life [27-29].

A. Membership Functions Let X be a set of transformer diagnostic data, called the

universe, whose elements are denoted x . Membership in a

subset A of X is the membership function, Aµ from X to the real interval [0, 1]. Where A is a fuzzy set and is a subset of X that has no sharp boundary. The Aµ is a grade of membership x in A . The closer the value of Aµ is to 1, the more x belongs to A [26, 30, 31].

)})),(,{( XxxxA A ∈= µ (9)

Also the support of the fuzzy set A in the universal set X is the crisp set that contains all the elements of X .

}0)({ >∈= xXxA Aµ (10)

With the finite support, let ix be an element of the

support of fuzzy set A and iµ a grade of membership in A , then:

∑=

=++=n

i i

i

n

n

xxxxA

12

2

1

1 ........ µµµµ (11)

The degree of membership is expressed as:

[ ] ( ) [ ]1,0: →ℜ=∈ xAxFz Aµ (12)

Where A is the fuzzy set represented by a membership function, all the elements are denoted by a point x on the real lineℜ . This is mapped to a degree of membership value µ , lies somewhere on the real interval of 0 to 1 [26, 32]. Mamdani’s model is used such as:

( ) ( ) ( )( )yBxAVyxMAMD iin

i &, 1== (13)

( ) ( ) ( )[ ] Xxxx xBABA ∈∀⇒=∩ µµµ ,min (14)

Where BA∩µ is the respective membership function of BA ∩

B. Fuzzy Rules In terms of fuzzy logic, a set of knowledge based

linguistic rules are developed made of “IF–THEN” type. In this model a fuzzy set A defined in a universe X and the second set B defined in another universe Y . Therefore the fuzzy implication mapped in YX − surface is given as [26, 30, 33]:

( ) ( ) ( )[ ]yxyx BABA µµµ ,min, =→ (15)

YX yx ∈∀∈∀ , (16)

The knowledge based fuzzy rules are defined in term of input variables to the fuzzy logic model for an output of power transformer assessment. Demi-Cauchy (bell shaped) membership functions are selected for the fuzzy modeling although other types may also apply. Some examples of the rules developed are:

( ) ( ) ( ) ( )[ ]cbacba cBARiµµµµ ,,min,, = (17)

If a is aiA AND b is iB THEN ),( bafc ii =

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C. Defuzzification A centroid method is applied to obtain the crisp value for

transformer assessment level. The centroid or center of gravity method finds the balance point of the solution (fuzzy region) by calculating the weighted mean of the fuzzy region. Arithmetically, for fuzzy solution region A , this is given as [14, 15, 26, 31]:

( )

( )∑

∑

=

=→ℜ n

iiA

n

iiAi

d

dd

0

0

µ

µ (18)

Where d is the ith domain value and ( )dµ is the truth membership value for that domain point.

Diagnostic facts are represented by a large number of fuzzy rules for an accurate evaluation to reach a definite outcome in term of criticality, rate of ageing and remnant life. The main target of the model is divided into several sub targets using fuzzification of all the elements. The model is based on the optimization process which includes the combined effect of each sub problem as a multistage decision process (multi- criteria analysis) [14, 15, 30].

VI. TRANSFORMER REMNANT LIFE ESTIMATION In this section to map the transformer remnant life, a

fuzzy logic modeling is carried out with furanic compound and moisture (RVM analysis) as input variables, as shown in Figure 1-3. Membership functions for furan are considered on the scale 0 to 4 (mg/L) and for moisture from 0 to 10 (%), based on the various transformers test data and specified standards.

Figure 1: Fuzzy Model - Remnant Life Mapping Using furan and Moisture

Figure 2: Input Variable MF - Furan (mg/L)

Figure 3: Input Variable MF - Moisture (%)

The model’s output variable membership functions are based on the various transformers test data interpretations and specified standards, measured on the scale from 50 to 0 (new to significantly aged), as shown in Figure 4. Fuzzy rules are developed using transformer diagnostics and interpretation techniques. The remnant life mapping model is tested with furan (3mg/L) and moisture (3%) to map the given transformer remnant life. The model outcome for the defined inputs concludes low residual life, which is approximately 6.376 years on the scale from 50 to 0. It should be noted here that for simplicity a 50 year life has been assumed for a transformer. But the model can be easily modified for a different life cycle. The transformer remnant life can be mapped directly using the model’s surface graph (outcome) for the given inputs, as shown in Figure 5.

Figure 4: Output Variable MF - Remnant Life

Figure 5: Remnant Life Mapping Model Outcome

VII. TRANSFORMER ASSESSMENT The combined evaluation of the diagnostics provides

better estimation of transformer remnant life. Power transformer end of life criteria could be strategic, economic or technical [25]. These assessments are essential for the existing aged assets to plan for the maintenance, relocation or retirement accordingly.

A. Strategic end of life criteria Strategic end of life criteria relates to the transformer’s

ability to carry out the load, short circuit current, network service voltage and over voltages applied to it.

B. Economic end of life criteria This may include the increase in maintenance and

outages costs. A detailed cost benefit ratio study should be performed for the transformer and the economic benefit of investment on maintenance be weighed against replacement of transformer with a new one.

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C. Technical end of life criteria This is a case of true technical failure of a transformer. It

is the ultimate end of transformer life, assessed beyond repair. Technical factors such as mechanical or electrical overstressing or insulation contamination can have significant impact on the remaining life, perhaps resulting in sudden catastrophic failure. This may involve some collateral and environmental damages, personnel safety, unwanted outages, revenue loss and in some cases penalty due to inability to transfer power.

A transformer reaches its end of practical life, when one or more of the diagnostics characteristics decreases to a level where further operation stands inadmissible. The electrical properties should not exceed the recommended levels such as tan δ for insulation, insulation resistance, dielectric strength of oil, oil tan δ. Any change in physico-chemical properties is critical for transformer assessment for example gases and water concentration in oil, tan δ of paper and degree of polymerization [24].

The successful analysis is based on the accuracy of the authenticated data obtained from the actual operational and environmental conditions the transformers are serving or failed. To overcome the issue of accurate remnant life estimation tests were performed and site data was collected from various power transformers at different operating conditions. The considerable difficulty in forecasting the end of life suggests developing a complete life cycle management model using fuzzy logic approach, based on actual test data and sound experience judgment.

VIII. ASSET MANAGEMENT CHALLENGES Transformer life management model depends on its

criticalities, rate of aging (degradation factor) and technical end of life (remaining service life). Transformer management challenges are due to the following reasons [16, 34, 35]:

• Many transformers are expected to operate at or above nameplate ratings.

• Peak loads are exceeding the design limits resulting in smaller safety margins.

• Equipment replacement lead times can be greater than one year.

• Increase in temperature of windings, insulation and oil.

• Increase in leakage flux density outside the core, causing additional eddy current heating in the metallic parts.

• Moisture and gas content increase with the increase in temperature.

• Bushings, tap-changers, current transformers and cable end connections are exposed to a higher stresses.

• Insulation deterioration increases with higher thermal stresses

• Transformer average age continues to increase.

• Spot market replacement power costs are unpredictable and will likely continue to rise.

IX. ASSET MANAGEMENT CRITERIA The operational availability of large power transformers

is of strategic importance for power generation and transmission companies. Main insulation (cellulose and oil) deterioration plays a decisive role in the transformer technical life [36]. Serious failures in power transformers owing to insulation breakdown cause considerable financial losses due to power outage and costs for replacement or repair. Therefore, most power utilities have developed individual inspection methods for the transformer condition assessment by collecting duty time percentage data and information on failure causes. Due to the majority of the transformers reaching significant age, there exists an interest of failure rate reduction. Also an improvement of transformer condition assessment renders benefit by giving a decision basis to the asset managers [37]. The main target of asset management is to manage the transformer to serve longer with reduced lifetime operating cost [1].

Asset management with improved strategies plays an important role in the reliability of the system. A recent survey estimates that power outages cost each of the roughly two million US industrial and digital economy electricity customers more than $23,000 per year. Utilities are interested in safely maximizing the use of assets, minimizing interruptions to customers, and enhancing shareholder’s value. It is essential to achieve goals such as optimization of the maintenance, loading, and life of the key transformers in our system. Transformer failure survey statistics shows that; electrical disturbances (29%), deterioration of insulation (18%), lightning (16%), inadequate maintenance (13%), loose connections (13%), moisture (7%), and overloading (2%) are the main causes of failure [7].

Existing transformer population is an important issue for the utilities. There is an ample safety and environmental risk involved in operating aged units close to loading limits with out surveillance and assessment. The principal categories of deterioration in transformer are solid insulation (oil impregnated paper) and liquid insulation where as mechanical parts can be easily managed during routine maintenance practices. Asset management strategies mainly depend on the preventive, corrective and reliability centered maintenance programs associated with condition monitoring. Condition monitoring is mostly considered for transformer insulation and winding integrity. The asset management criteria would focus on the following identifications of the asset [38]:

• Highest failure rate.

• Strategic importance.

• High concern irrespective of failure rate.

X. ASSET MANAGEMENT Life cycle management cost includes routine

maintenance, reconditioning, major refurbishment and condition monitoring. These factors are important for strategic, economic and technical assessments in order to develop enhanced asset management strategies. Transformer’s performance, reliability and technical life can be increased with the implementation of correct operational criteria and improved management strategies. Also

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transformer’s timely relocation and retirement/ replacement can be planned.

Advanced diagnostics techniques such as DGA, PD, FRA, RVM, furan analysis, peak load and thermal dynamics play a key role in developing maintenance strategies. Most of the transformer faults develop and get active over a period of time. Enhanced maintenance strategies together with critical component surveillance will improve the life cycle management of transformers. To conclude main objective of asset management is to suggest and implement the transformer life cycle management strategies which includes the following:

• Identification of the critical transformer with respect to performance and cost.

• Identification of the transformer criticality rank with respect to its condition, based on technical and end of life assessment.

• Planning, transformer management decision towards enhanced maintenance strategies such as refurbishment, retirement or relocation.

To fulfill these objectives, in-depth knowledge of the transformer design, operation, stresses, monitoring, diagnostics and maintenance is required. The risk and ranking assessment is mainly based on the performance and failures historical data. Causes of transformer failures and respective consequences investigation stand vital for the asset management point of view. Failure probability analysis is also a key parameter in asset management. For asset management the transformers must be categorized according to its assessment and respective strategy is required to be developed for the group of the transformers accordingly.

Asset’s failure probability forecast with in a certain time interval t∆ is given by:

21 ttt −=∆ (19)

Where, 1t is the time at which diagnostics were

performed and 2t is the probable time to fail. Based on criticality, each indicator is required to have the respective rank number [39]:

∑=

=n

mscmsc CC

1, (20)

Where scC is the critical rank of the transformer with respect to severity classification sc, m is the failure mode and n is the total number of failures of the asset.

EAbscscmC ππδλβ=, (21)

Where scβ is failure effect probability, δ is failure

mode ratio, bλ is failure rate, Aπ is application factor to

adjust bλ between operating stresses of transformer serving

and diagnostics, and Eπ is the environmental factor.

Reliability or risk assessment does not predict a definite time that a transformer will fail but rather an increasing probability of failure and a corresponding reduction in reliability. When reliability has declined to a certain value, the life of the transformer has effectively ended for its

particular application. The insulation life expectancy of a transformer depends to a high degree on extraordinary events, such as over-voltages, short-circuits in the system and emergency loading.

Transformer’s technical, economic and end of life assessment based on diagnostics play critical role in the asset management strategies. It always remains a difficult task to calculate failure probability. Failure could be random or time based with respect to deterioration, where as CBM increases the time between various deterioration stages. Transformer aging behavior comprises of different spans between new and end-of-life. These intervals are not even to calculate MTBF. The deterioration periods could be best judged with experience about transformer’s performance [40]. Transformer failure probability can be predicted based on transformer monitoring, diagnostics and failure historical data. By implementing appropriate CBM the mean time between failures (aging stages) could be increased and reliability can be improved. Impact of CBM on the transformer’s probability of survival and failure is high. The residual life and uncertainty of the transformer at particular instant can be given by [39]:

)Pr{)( tTtR ≥= (22)

}Pr{)( tTtF <= (23) Where: )(tR is the survival probability, )(tF is the

failure probability, t is the age (interval) and T represents the life period.

Expected time to failure is )(),()( 1212 tttFtF >− ,

therefore the failure probability between 21 & tt can be obtained:

∫=−2

1

)()()( 12

t

t

dttftFtF (24)

Where )(tf , is the failure density and is expressed as

dttdF )(

and dttf )( is the probability of the transformer

failure during interval )](,[ dttt + .

To predict time to first failure (TTFF) is not possible therefore the mean time to failure (MTTF) can be calculated by:

∫∞

=0

)( dtttfMTTF (25)

If )(tR decreases to zero, the above equation can be expressed as:

∫∞

=0

)( dttRMTTF (26)

The mean residual time to failure (MRTTF) can be obtained, provided the transformer stands normal at time u :

∫∞ −=0 )(

)()(uR

tfutMRTTF dt (27)

Transformer failure age distribution investigation of a utility shows that most of the transformers failed in early age.

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The failure could have been averted with better monitoring/diagnostics and condition based maintenance. The power transformer assessment could be categories as below [6]:

A. Normal Behavior The transformer is serving according to its design and

normal aging criteria. Unit performance is considered inconsistent with the target reliability. Routine testing and monitoring is suggested.

B. Accelerated Ageing The transformer’s monitoring and diagnostics results

exhibit rapid insulation deterioration with respect to normal aging. It requires identifying the faults and considering for long term management program.

C. Uneconomical Condition The transformer requires a high cost to maintain its

performance and availability. The failure frequency is increasing and the cost benefit ratio, revenue lost verses a transformer’s replacement can’t be satisfied. It requires short term planning to relocate the transformer or otherwise allow serving with restricted operational criteria. Decision can be made for its retirement. Sometimes the unit stands uneconomical due to the upgrading of the system.

D. End of Life Status This is the ultimate end of the transformer, where the

assessment suggests that the transformer can not serve the purpose due to being declared failed or high risk for failure. The refurbishment cost is close to the replacement with a new one or otherwise the required reliability can’t be ensured with the maintenance required.

XI. ASSET MANAGEMENT FUZZY MODELING To have flexible asset management decision, fuzzy

modeling is carried out based on transformer rate of aging and remnant life mapping. Due to variation in operational and climatic condition and many other factors controlling the transformer variables, the asset management polices may differ, from transformer to transformer even having same rating and calendar age. Transformer criticalities, rate of aging and remnant life has significant impact on the asset management strategies. To enable a good decision it is essential to incorporate all these variables into asset management fuzzy model, Figure 10. The input variable to the asset management fuzzy model are the same as the respective out puts of the transformer rate of aging and remnant life mapping fuzzy models, as shown in Figure 6 and 7 respectively. The output variable membership functions are based on the rate of aging and remnant life of the transformer and measured on the scale from 0 to 8, Figure 8.

Figure 6: Input Variable MF - Rate of Ageing

Figure 7: Input Variable MF - Remnant Life

Figure 8: Output Variable MF - Asset Management Decision

Fuzzy rules based on input-output mapping are developed using transformer diagnostics and test data interpretation technique and experience, Figure 9.

Figure 9: Fuzzy Rules - Asset Management Decision Model

The asset management decision outcomes on the scale 0 to 8 are classified as given below, Table 2, where “D” is the asset management fuzzy model outcome. The model is tested to determine the asset management criteria with the inputs a , b , c , d , e , f , g , h , i , j , k , l , m , n , o , p , q , r , s , u , v , and w , as shown in Figure 10.

The model outcome for the defined inputs exhibits 7.87 on the scale 0 to 8. The model dictates an asset management decision 87 ≥< D as given in Table 2. The transformer asset management decision can also be judged for any set of inputs using the surface graph mapping, Figure 11.

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TABLE 2. ASSET MANAGEMENT DECISION OUTCOME

Asset Management Fuzzy

Logic Decision Management Strategies

10 ≥≤ D Normal operation and monitoring in accordance with the name plate rating.

21 ≥≤ D Normal operation and specific monitoring.

32 ≥≤ D Normal operation with overall strict monitoring.

43 ≥≤ D Restricted operation (loading below 80%) with strict overall monitoring, schedule diagnostics.

54 ≥≤ D

Restricted operation (loading below 60%) with strict monitoring/ increased interval sampling, schedule diagnostics and predict condition based maintenance.

65 ≥≤ D

Reduced operation (loading below 50%) with strict online monitoring/ increased interval sampling, schedule diagnostics and predict condition based maintenance.

76 ≥≤ D

Reduced operation (loading below 50%) with strict online monitoring/ increased interval sampling, and detailed diagnostics. Arrange major refurbishment, relocation or retirement.

87 ≥≤ D

Critical, immediate shutdown. Apply detail diagnostics and investigation. Arrange for emergency major refurbishment or replacement. Decide to relocate or retire/ scrap.

Figure 11: Surface Graph - Asset Management Decision

Figure 10: Asset management Fuzzy Logic Model

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XII. CONCLUSIONS Asset management provides better maintenance

framework for the transformer and its reliability issue can be met effectively. The residual life can be extended and maximum return on the investment can be achieved. It will limit the failure surprises. It allows planned shutdowns, minimizing the forced outages. The flexible budget and procurement polices can be implemented to arrange spares on competitive rates as well as the work force. Successful life management and life extension in power transformers produce financial benefits with increased reliability.

It maximizes the transformer availability resulting in minimization of capital investment. It also facilitates failure analysis to predict the causes and their impact on the over all system. Diagnostics and monitoring techniques provide useful information for developing and implementing asset management strategies.

The advance asset management strategies will allow the transformer to serve beyond its expected design age. It also provides an acceptable life time before a failure can be concluded or a criticality ranking among a group of transformer can be established.

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XIV. BIOGRAPHIES Arshad M (S’41612155) was born in Pakistan. He received his B.Sc., M.Sc and PhD degrees in Electrical Power Engineering in 1986, 1994 and 2006 respectively. He is currently working as a senior safety engineer with BC Hydro, Canada. He has worked as an electrical engineering instructor in the American

University of Sharjah. He also worked as an electrical engineer in the Ministry of Electricity and Water, United Arab Emirates. Previously he has worked as an electrical protection, instrumentation & control engineer (maintenance) in the Water and Power Development Authority, Pakistan. His primarily research interests are condition monitoring, diagnostics and remnant life estimation of power transformers and generators.

Syed Islam received his B.Sc., M.Sc and PhD degrees in Electrical Power Engineering in 1979, 1983, and 1988 respectively. He is currently a Professor and Head of Department of Electrical and Computer Engineering at Curtin University of Technology, Perth, Western Australia. He is the current chair

of the Australasian Committee for Power Engineers (ACPE). He has previously taught at King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; Sultan Qaboos University, Oman; and The University of Newcastle, Australia. His research interests are in wind energy conversion systems, power systems, power quality and harmonics, and condition monitoring of transformers. He is a fellow of the Engineers Australia, a senior member of the IEEE, and a corporate member of the IEE. He is also a member of the CIGRE panel AP-12 and a chartered engineer in the United Kingdom.

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