# Multiparameter-Based Fuzzy Logic Health Index Assessment for Oil-Immersed Power Transformers

Authors: Edwell Tafara Mharakurwa; Rutendo Goboza
Journal: Advances in Fuzzy Systems
 (2019)

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## Abstract

The health index scheme can be the most fundamental tool that unifies all transformer condition status information into a singular outcome, thereby enhancing the power transformer asset management and life longevity strategies. This study aims at establishing a multiple parameter-dependent transformer health index estimation model cascaded with a fuzzy logic inference system. This strategy is centered on the effect of dynamic loading regime, varying hotspot temperatures and multiple attesting results of the insulation system. Furthermore, a nonintrusive degree of polymerization (DP) model based on furans and carbon oxide ratios as DP pointers is also factored in developing the health index model. The general outcome of the health index depends on entirely considered elements, but not on any isolated attribute. Data obtained from in-service transformers were used to validate the proposed model. The outcome of the model mirrors the practical condition of the evaluated transformers. Therefore, the proposed health index model can be a vital tool to asset managers and power utilities.


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## Body

## 1. Introduction

Ageing infrastructure of electrical energy systems has lately calls for concern and challenge to power utilities around the globe. Catastrophic failures of ageing electrical equipment, especially power transformers in a power grid, can cause interruptions which result in both social and economic losses. Therefore, it is very important to pay sufficient attention to their maintenance and diagnostic and life span issues [1]. Due to the extensive investment in power transformers and their prominence as key elements which can affect system availability, the transformer asset management system is presumed to be the key aspect of equipment asset management in the field of power engineering [1–3].Transformer health index can be utilized as an asset management decision support tool, residual life valuation, risk pointer, and as a blueprint of maintenance scheme [4–6]. The health index (HI) has emerged to be the most fundamental tool that unifies all transformer condition status information into a singular outcome [6]. The HI highlights a threshold centered principle that allows power utilities to classify the condition of an individual transformer from being in an excellent to a degraded state of operation. Accordingly, asset maintenance, refurbishment, or replacement decisions can be centered on a conjoint pointer. Based on the information gathered during transformer operation not limited to physical transformer and auxillary equipment tests, transformer fault history, parameter lab tests (oil quality lab tests), loading history, and a power transformer health index can be established [1, 7].Different health index models have been established in different literature based on synthesis of different developers using information attained from the insulation system in order to minimize transformer outages [1, 5, 7–15]. Nevertheless, transformers are exposed to different stresses which act simultaneously inside the transformer making the analysis challenging. This makes it difficult to assess and accurately interpret the power transformer’s health condition as well as estimate its technical end of life. Due to these complications in diagnosis, a significant number of transformers are failing before attaining the expected technical life. However, being able to establish transformer health index can avert possibilities of transformer outages. The weighting factor approach of data extracted from field tests, laboratory, and operation history of transformers has been the most used technique is computation of transformer HI. Nevertheless, health index based on soft-computing techniques have brightened the future of many power utilities as these HI methodologies are easy to comprehend. As highlighted in [1, 9–15], fuzzy logic HI approach based on several transformer tests have been proposed in transformer condition and health index assessment. Additionally, probabilistic approaches [16], Bayesian networks [17], and artificial neural networks have been used in determining health index [18].Since there is no standardized approach in defining the scores and weights given to input parameters for health index calculation based on weighting factor, the HI outcome will differ as per the developer. However, this subjective scoring and weighting strategy can be merged with intelligence-based algorithms to mimic the utility experience in determining the asset health index. Even though the fuzzy logic models conveyed in different texts have their peculiar significance in defining the overall HI of transformers, most of them consider limited variables which are influential in deciding the health state of power transformers [14]. However, a multicriterion [1] and multiattribute [5] transformer condition based on fuzzy logic was proposed. In [1], the strategy was centered on the data-correlated auxillary equipment and physical condition of the transformer. However, in this technique, substantial diagnostic information related to internal transformer degradation and ageing was overlooked. Additionally, the limitation of the approach used in [5] arises when a thermally upgraded insulation paper comes into play. Thus, some variables such as the degree of polymerization (DP) and operational stress should be factored in when calculating transformer health index. Furthermore, as observed in [13], it is also essential to include the impact of transformer age and loading profile as pointers in establishing an overall transformer health index. However, DP measurement is an intrusive test which requires de-energizing of the power transformer and take paper samples, thereby disrupting continuity of power supply. Furthermore, gas evolution can be due to insulation ageing or through incipient faults. Thus, the impact of the evolved gases should be considered in determining the health index by also assessing the origin of gas manifestation. Accordingly, implementation of a probable health index calls for great caution in choosing the variables that have great significant effect on the index outcome such that a reasonable and reliable transformer condition is estimated.This paper aims at developing a multiparameter-dependent transformer health index estimation model established upon an integrated fuzzy inference system. It considers the effect of loading regime, varying hotspot temperatures and all attesting results of the insulation system. The general outcome of the established HI centers on entirely reflected elements, not on any sole attribute. Additionally, a nonintrusive DP estimation based on indicating factors, furans and carbon oxides ratio, is also factored in the health index model. Having a reasonable health index can facilitate power transformer reliability and also enhance its residual life span.


## 2. Transformer Health Index Pointers

In order to formulate a probable health index model of a power transformer, careful determination and analysis of the influencing parameters that leads to deterioration of a transformer needs to be performed first. The significance and interpretations of some of the parameters that have influence in the life span and insulation degradation of power transformers in service are summarized in this section.


### 2.1. Oil Quality Analysis (OQA)

Attesting oil quality is usually authenticated by a variety of electrical, physical, and chemical tests conducted on oil test samples. Methods and standards used in this study to measure and determine the oil characteristics are highlighted in Table1.Table 1
Oil quality parameters.
Serial no.
Oil quality parameter
Testing method/instrument
Standards
1
Breakdown voltage (kV)
Megger OTS100AF and Foster OSTS100F (0–100 kV)
IEC 60156
2
Water content moisture (ppm)
Karl Fischer Titration (KFT) method Moisture-in-oil sensor
ASTM D1533
3
Acidity
Chemistry neutralization method
ASTM D947
4
Colour and appearance
Transmitted light and visual inspection
IEC-ISO 2049 ASTMD-1524
5
Dielectric dissipation factor (DDF)
Oil tan delta & resistivity test kit ex. MOTR
IEC 60247
6
Interfacial tension (IFT)
Tensiometer
ASTM D-971


### 2.2. Dissolved Gas Analysis (DGA)

Interpretation of DGA techniques was performed after testing samples of transformer oil to quantify the composition of principle fault gases. Internal electrical or thermal faults manifest through insulation decomposition producing gases such as H2, CH4, C2H2, C2H4, C2H6, CO, and CO2. Manifestation of CO2 and CO discloses paper degradation-related faults whilst C2H4 and C2H6 are significant indicators of oil thermal activities inside the transformer. Faults due to partial discharge can be detected through increase of H2 and CH4, whereas arcing can be can be mirrored by the progression of C2H2 and H2. In this paper, DGA data acquired using a Total Oil Gas Analyzer (TOGA) gas chromatography technique was used in quantifying the concentration of dissolved gases.


### 2.3. Furanic Content in Oil Analysis (FA)

Although furans can exist in five different forms [19, 20], this study focused on 2-FAL since it has been found that its concentration in oil is directly correlated with the DP of the solid insulation that relates to transformer age. 2-FAL content in the transformer mineral oil was detected and well quantified by using the high-performance liquid chromatography (HPLC) under ASTM D-5837 test standards.


### 2.4. Degree of Polymerization (DP)

The degree of polymerization is a valuable indicator of the degradation condition of the transformer insulation paper and its mechanical properties [19, 21]. DP measurement is an intrusive test that requires sampling of insulating paper from a disassembled transformer, thus making it impossible to do on-line measurements. Moreover, this approach requires utmost care, labor intensive, and is pricey and time consuming. This has led to alternative techniques of DP estimation through usage of chemical indicators such as furans, and/CO2/CO concentration ratio, and methanol concentration in oil [19, 22–25]. In addition, mathematical models based on relationships between 2-FAL concentration and DP values have been formulated, and some of them are summarized in [19]. Although, exclusive furan analysis being the most dominant method of DP value estimation in transformer insulation, its results are inconsistent depending on the type of insulation paper, loading regime, and location of the transformer. In this paper, an alternative of DP estimation is proposed as highlighted in the foregoing sections.


## 2.1. Oil Quality Analysis (OQA)

Attesting oil quality is usually authenticated by a variety of electrical, physical, and chemical tests conducted on oil test samples. Methods and standards used in this study to measure and determine the oil characteristics are highlighted in Table1.Table 1
Oil quality parameters.
Serial no.
Oil quality parameter
Testing method/instrument
Standards
1
Breakdown voltage (kV)
Megger OTS100AF and Foster OSTS100F (0–100 kV)
IEC 60156
2
Water content moisture (ppm)
Karl Fischer Titration (KFT) method Moisture-in-oil sensor
ASTM D1533
3
Acidity
Chemistry neutralization method
ASTM D947
4
Colour and appearance
Transmitted light and visual inspection
IEC-ISO 2049 ASTMD-1524
5
Dielectric dissipation factor (DDF)
Oil tan delta & resistivity test kit ex. MOTR
IEC 60247
6
Interfacial tension (IFT)
Tensiometer
ASTM D-971


## 2.2. Dissolved Gas Analysis (DGA)

Interpretation of DGA techniques was performed after testing samples of transformer oil to quantify the composition of principle fault gases. Internal electrical or thermal faults manifest through insulation decomposition producing gases such as H2, CH4, C2H2, C2H4, C2H6, CO, and CO2. Manifestation of CO2 and CO discloses paper degradation-related faults whilst C2H4 and C2H6 are significant indicators of oil thermal activities inside the transformer. Faults due to partial discharge can be detected through increase of H2 and CH4, whereas arcing can be can be mirrored by the progression of C2H2 and H2. In this paper, DGA data acquired using a Total Oil Gas Analyzer (TOGA) gas chromatography technique was used in quantifying the concentration of dissolved gases.


## 2.3. Furanic Content in Oil Analysis (FA)

Although furans can exist in five different forms [19, 20], this study focused on 2-FAL since it has been found that its concentration in oil is directly correlated with the DP of the solid insulation that relates to transformer age. 2-FAL content in the transformer mineral oil was detected and well quantified by using the high-performance liquid chromatography (HPLC) under ASTM D-5837 test standards.


## 2.4. Degree of Polymerization (DP)

The degree of polymerization is a valuable indicator of the degradation condition of the transformer insulation paper and its mechanical properties [19, 21]. DP measurement is an intrusive test that requires sampling of insulating paper from a disassembled transformer, thus making it impossible to do on-line measurements. Moreover, this approach requires utmost care, labor intensive, and is pricey and time consuming. This has led to alternative techniques of DP estimation through usage of chemical indicators such as furans, and/CO2/CO concentration ratio, and methanol concentration in oil [19, 22–25]. In addition, mathematical models based on relationships between 2-FAL concentration and DP values have been formulated, and some of them are summarized in [19]. Although, exclusive furan analysis being the most dominant method of DP value estimation in transformer insulation, its results are inconsistent depending on the type of insulation paper, loading regime, and location of the transformer. In this paper, an alternative of DP estimation is proposed as highlighted in the foregoing sections.


## 3. Transformer Health Index Estimation

Estimation of the HI was centered on the fuzzy inference tool based upon the calculation of five cumulative factors that signifies the transformer condition established on DGA, OQA, furans, DP, and operational ageing stress (OAS). The final HI value is the linguistic output of the fuzzy logic model. The assigned inputs are based on the aggregation of each of the subsystem factor with respect to scores, weights, or impact on the transformer’s insulation condition. Data used to validate the HI model was obtained from transformers from different substations in South Africa and Zimbabwe.


### 3.1. Fuzzy Inference Health Index Model

#### 3.1.1. Determination of Parameter Score

Several attributes of a transformer can be used in ascertaining its health index. The fuzzy logic HI model inputs are centered on the concentration of dissolved gases factor (DGAF), oil quality factor (OQF), furan content factor (FF), degree of polymerization (DP), and the operational ageing stress factor (OASF). DGAF comprises seven variables, OQF involves six attributes, OASF consists of two parameters. DP is a result of the estimated value from furan content and carbon oxide ratios while furans represent FF. Power utilities can differ on the limits of transformer attributes. Accordingly, variation in transformer health index for similar data can be observed, depending on which organization limits are implemented. The commonly accepted transformer attribute thresholds are highlighted by IEEE, IEC, Dornenburg, California State University Sacramento, and Bureau of Reclamation [1, 26]. In this paper, the IEEE standard C57.104–2008 parameter limit was adopted as summarized in Table 2. Using data from different transformers, fuzzy logic HI was established initially by transforming the inputs into dimensionless variables between 0 and 1. This was attained by normalizing the data using limits that symbolize normal and extreme values which are highlighted in Table 2. Additionally, the ranges of the variables have been partitioned into four conditions. Accordingly, by subjective reasoning, the four conditions of each parameter are given suitable weights (w) spanning between 0 and 10, as indicated in Table 3.Table 2
Transformer standard parameter limits [1, 26].
Category
Parameter
Condition
Normal
Caution
Alarm
Failure
DGAF
Dissolved gases
H2 (ppm)
0–100
101–700
701–1800
>1800
CH4 (ppm)
0–120
121–400
401–1000
>1000
C2H2 (ppm)
0–1
2–7
7–35
>35
C2H4 (ppm)
0–50
51–100
101–200
>200
C2H6 (ppm)
0–65
66–100
101–150
>150
CO (ppm)
0–350
351–700
701–1400
>1400
CO2 (ppm)
0–2500
2501–4000
4001–10000
>10000
OQF
Oil quality
BDV (kV)
100–50
49–40
39–30
<30
IFT (mN/m)
50–30
30–23
23–18
<18
Moisture (ppm)
0–15
16–20
21–25
>25
Acidity (mg KOH/g)
0–0.05
0.051–0.1
0.11–0.2
>0.2
DDF
0-0.1
0.1–0.5
0.5–1
>1
Colour
0–1.5
1.5–2
2–2.5
>2.5
FF
Furans
Furans (ppm)
0–0.1
0.1–1
1–10
>10Table 3
Weights assigned to each of the parameters of the four conditions.
Condition
Condition representation
Weights (w)
Normal
Good
[w ≤ 2.5]
Caution
Acceptable
[2.5 <w ≤ 5.0]
Alarm
Poor
[5.0 <w ≤ 7.5]
Failure
Worst
[7.5 <w ≤ 10]Computation of the exact weight of the variable of a given concentration was performed by using equations (1), [5], and (2).(1)Parameter score=Ki+xi−aibi−ai×2.5.Equation (2) only corresponds with breakdown voltage (BDV) and interfacial tension (IFT) parameters whose values the higher the better and vice versa and thus (1) had to be modified by rearranging it presented as follows:(2)Parameter score=Ki+bi−xibi−ai×2.5,where, Ki signifies the assigned minimum weight in the four conditions of the parameters, xi is the current value of the parameter considered (xi is represented by xi′ for DGAF parameters, xi″ for FF parameter, and xi″ for OQF parameters), ai and bi are the lower and the upper limits of the conforming cluster of the parameter, and xi−ai/bi−ai denotes normalization expression of assessing inputs, whilst normalization of BDV and IFT was done using bi−xi/bi−ai.


#### 3.1.2. DP Estimation Model

The main byproducts of transformer solid insulation considered in this paper mirror the DP value of paper insulation constitute of furans (2-FAL), CO2, and CO concentration. To map the transformer insulation DP values, the proposed fuzzy logic model is developed under MATLAB/Simulink platform. The model is shown in Figure 1, where furan (2-FAL) and CO2/CO are the model inputs, whilst the output represents the insulation DP value.Figure 1
Fuzzy logic model for DP estimation.The associated membership functions as input attributes are set based on the concentration of furan (2-FAL) considered on a scale of 0–12 (ppm) and amount of CO2 and CO as a ratio from 0–12 based on various transformer test data, as shown in Figures 2 and 3, respectively. The five trapezoidal membership linguistic values considered for the furan input variable are normal (N), low (L), medium, high, and critical, whilst CO2/CO input variable uses bad, low, medium, high, and critical.Figure 2
Input parameter membership function-furans (2-FAL) (ppm).Figure 3
Input parameter membership function-CO2/CO ratio.The membership functions of the output variable signifying the DP value are established on a scale of 0 to 1200 where linguistic values of End-of-life, Weak, Normal, Healthy, and Very Healthy are used as indicated in Figure4.Figure 4
Output variable membership function-DP value.A set of “IF-THEN” statements as rules governing the mapping of inputs into outputs were formulated. Illustrations of the conveyed rules for DP estimation are as follows:IF (Furans is normal) and (CO2/CO is low) THEN (DP is V.Healthy)IF (Furans is medium) and (CO2/CO is medium) THEN (DP is Normal)IF (Furans is high) and (CO2/CO is bad) THEN (DP is End-of-Life)


#### 3.1.3. Operational Ageing Stress Factor (OASF)

Transformer loading profile and temperature variations (hotspot temperatures (HST)) are the characteristic attributes governing the operational ageing stress of the transformer insulation system. A fuzzy logic model for determining the transformer operational stress level is established upon load and HST as inputs on membership function scaling of 0–1.2 pu (load) and 0–140°C (HST). The loading and temperature regime were taken to be of equal significance during fuzzy logic rule formulation. The magnitude and rate of change of these parameters determines the pace of operational criticality. The operational stress level of the transformer is upon a scale of 0 to 1 in which the worst condition is reflected by values nearing 1. The transformer fuzzy logic model for operational ageing stress is shown in Figure5.Figure 5
Fuzzy logic model for operational ageing stress.


### 3.2. Transformation of HI Model Inputs into Fuzzy Variables

Instead of using individual parameters as inputs to the HI fuzzy logic model, summed scores for three transformer parameter categories obtained using equation (1) and (2), DP, and operation ageing stress factor were employed as the underlining fuzzy inputs. These inputs are mapped into five assessing fuzzy logic variable states using simple and computational efficacy trapezoidal membership functions (MF). These assessing states (Excellent, Good, Moderate, Bad, and Worst) signify the health index of transformer insulation. Excellent designates the best condition whereas worst signifies immediate attention to the transformer. The associated membership function scale and their linguistic labels for the summed inputs are shown in Table 4. These scales are calculated by multiplying the lower and upper limits of weights of the four conditions by the number of parameters in DGAF, OQF, and FF. Furthermore, the DP and OASF membership function was established upon a scale of 0–1200 and 0-1, respectively. The crisp HI output was obtained through the center of gravity defuzzification method. Although the centroid method is computationally intensive, it was chosen due to its intuitive plausibility [27].Table 4
Ranges obtained for summed parameters.
Summed parameters
Input category ranges
Low (L)
Moderate (M)
High (H)
Critical (C)
DGAF
0 ≤ 17.5
17.5 < M ≤ 35
35 < H ≤ 52.5
52.5 < C ≤ 70
OQF
0 ≤ 15
15 < M ≤ 30
30 < H ≤ 45
45 < C ≤ 60
FF
0 ≤ 2.5
2.5 < M ≤ 5
5 < H ≤ 7.5
7.5 < C ≤ 10The proposed fuzzy logic health index model for the power transformer condition assessment process is depicted in Figure6. Figures 4 and 7–10 show the inputs membership functions utilized in mapping the health index output, whereas Figure 11 depicts the membership functions for the established transformer health index output, whilst Figure 12 shows the established rules associated with the proposed fuzzy logic model. The output of the DP model shown in Figure 4 was also used as an input to HI.Figure 6
Fuzzy-based transformer health index model.Figure 7
Input variable membership function-DGA Factor (DGAF).Figure 8
Input variable membership function-oil quality Factor (OQF).Figure 9
Input variable MF-furans content factor (FF).Figure 10
Input variable MF-operational ageing stress factor (OASF).Figure 11
Output variable MF-health index.Figure 12
Rules for the developed fuzzy logic-based transformer health index model.


## 3.1. Fuzzy Inference Health Index Model

### 3.1.1. Determination of Parameter Score

Several attributes of a transformer can be used in ascertaining its health index. The fuzzy logic HI model inputs are centered on the concentration of dissolved gases factor (DGAF), oil quality factor (OQF), furan content factor (FF), degree of polymerization (DP), and the operational ageing stress factor (OASF). DGAF comprises seven variables, OQF involves six attributes, OASF consists of two parameters. DP is a result of the estimated value from furan content and carbon oxide ratios while furans represent FF. Power utilities can differ on the limits of transformer attributes. Accordingly, variation in transformer health index for similar data can be observed, depending on which organization limits are implemented. The commonly accepted transformer attribute thresholds are highlighted by IEEE, IEC, Dornenburg, California State University Sacramento, and Bureau of Reclamation [1, 26]. In this paper, the IEEE standard C57.104–2008 parameter limit was adopted as summarized in Table 2. Using data from different transformers, fuzzy logic HI was established initially by transforming the inputs into dimensionless variables between 0 and 1. This was attained by normalizing the data using limits that symbolize normal and extreme values which are highlighted in Table 2. Additionally, the ranges of the variables have been partitioned into four conditions. Accordingly, by subjective reasoning, the four conditions of each parameter are given suitable weights (w) spanning between 0 and 10, as indicated in Table 3.Table 2
Transformer standard parameter limits [1, 26].
Category
Parameter
Condition
Normal
Caution
Alarm
Failure
DGAF
Dissolved gases
H2 (ppm)
0–100
101–700
701–1800
>1800
CH4 (ppm)
0–120
121–400
401–1000
>1000
C2H2 (ppm)
0–1
2–7
7–35
>35
C2H4 (ppm)
0–50
51–100
101–200
>200
C2H6 (ppm)
0–65
66–100
101–150
>150
CO (ppm)
0–350
351–700
701–1400
>1400
CO2 (ppm)
0–2500
2501–4000
4001–10000
>10000
OQF
Oil quality
BDV (kV)
100–50
49–40
39–30
<30
IFT (mN/m)
50–30
30–23
23–18
<18
Moisture (ppm)
0–15
16–20
21–25
>25
Acidity (mg KOH/g)
0–0.05
0.051–0.1
0.11–0.2
>0.2
DDF
0-0.1
0.1–0.5
0.5–1
>1
Colour
0–1.5
1.5–2
2–2.5
>2.5
FF
Furans
Furans (ppm)
0–0.1
0.1–1
1–10
>10Table 3
Weights assigned to each of the parameters of the four conditions.
Condition
Condition representation
Weights (w)
Normal
Good
[w ≤ 2.5]
Caution
Acceptable
[2.5 <w ≤ 5.0]
Alarm
Poor
[5.0 <w ≤ 7.5]
Failure
Worst
[7.5 <w ≤ 10]Computation of the exact weight of the variable of a given concentration was performed by using equations (1), [5], and (2).(1)Parameter score=Ki+xi−aibi−ai×2.5.Equation (2) only corresponds with breakdown voltage (BDV) and interfacial tension (IFT) parameters whose values the higher the better and vice versa and thus (1) had to be modified by rearranging it presented as follows:(2)Parameter score=Ki+bi−xibi−ai×2.5,where, Ki signifies the assigned minimum weight in the four conditions of the parameters, xi is the current value of the parameter considered (xi is represented by xi′ for DGAF parameters, xi″ for FF parameter, and xi″ for OQF parameters), ai and bi are the lower and the upper limits of the conforming cluster of the parameter, and xi−ai/bi−ai denotes normalization expression of assessing inputs, whilst normalization of BDV and IFT was done using bi−xi/bi−ai.


### 3.1.2. DP Estimation Model

The main byproducts of transformer solid insulation considered in this paper mirror the DP value of paper insulation constitute of furans (2-FAL), CO2, and CO concentration. To map the transformer insulation DP values, the proposed fuzzy logic model is developed under MATLAB/Simulink platform. The model is shown in Figure 1, where furan (2-FAL) and CO2/CO are the model inputs, whilst the output represents the insulation DP value.Figure 1
Fuzzy logic model for DP estimation.The associated membership functions as input attributes are set based on the concentration of furan (2-FAL) considered on a scale of 0–12 (ppm) and amount of CO2 and CO as a ratio from 0–12 based on various transformer test data, as shown in Figures 2 and 3, respectively. The five trapezoidal membership linguistic values considered for the furan input variable are normal (N), low (L), medium, high, and critical, whilst CO2/CO input variable uses bad, low, medium, high, and critical.Figure 2
Input parameter membership function-furans (2-FAL) (ppm).Figure 3
Input parameter membership function-CO2/CO ratio.The membership functions of the output variable signifying the DP value are established on a scale of 0 to 1200 where linguistic values of End-of-life, Weak, Normal, Healthy, and Very Healthy are used as indicated in Figure4.Figure 4
Output variable membership function-DP value.A set of “IF-THEN” statements as rules governing the mapping of inputs into outputs were formulated. Illustrations of the conveyed rules for DP estimation are as follows:IF (Furans is normal) and (CO2/CO is low) THEN (DP is V.Healthy)IF (Furans is medium) and (CO2/CO is medium) THEN (DP is Normal)IF (Furans is high) and (CO2/CO is bad) THEN (DP is End-of-Life)


### 3.1.3. Operational Ageing Stress Factor (OASF)

Transformer loading profile and temperature variations (hotspot temperatures (HST)) are the characteristic attributes governing the operational ageing stress of the transformer insulation system. A fuzzy logic model for determining the transformer operational stress level is established upon load and HST as inputs on membership function scaling of 0–1.2 pu (load) and 0–140°C (HST). The loading and temperature regime were taken to be of equal significance during fuzzy logic rule formulation. The magnitude and rate of change of these parameters determines the pace of operational criticality. The operational stress level of the transformer is upon a scale of 0 to 1 in which the worst condition is reflected by values nearing 1. The transformer fuzzy logic model for operational ageing stress is shown in Figure5.Figure 5
Fuzzy logic model for operational ageing stress.


## 3.1.1. Determination of Parameter Score

Several attributes of a transformer can be used in ascertaining its health index. The fuzzy logic HI model inputs are centered on the concentration of dissolved gases factor (DGAF), oil quality factor (OQF), furan content factor (FF), degree of polymerization (DP), and the operational ageing stress factor (OASF). DGAF comprises seven variables, OQF involves six attributes, OASF consists of two parameters. DP is a result of the estimated value from furan content and carbon oxide ratios while furans represent FF. Power utilities can differ on the limits of transformer attributes. Accordingly, variation in transformer health index for similar data can be observed, depending on which organization limits are implemented. The commonly accepted transformer attribute thresholds are highlighted by IEEE, IEC, Dornenburg, California State University Sacramento, and Bureau of Reclamation [1, 26]. In this paper, the IEEE standard C57.104–2008 parameter limit was adopted as summarized in Table 2. Using data from different transformers, fuzzy logic HI was established initially by transforming the inputs into dimensionless variables between 0 and 1. This was attained by normalizing the data using limits that symbolize normal and extreme values which are highlighted in Table 2. Additionally, the ranges of the variables have been partitioned into four conditions. Accordingly, by subjective reasoning, the four conditions of each parameter are given suitable weights (w) spanning between 0 and 10, as indicated in Table 3.Table 2
Transformer standard parameter limits [1, 26].
Category
Parameter
Condition
Normal
Caution
Alarm
Failure
DGAF
Dissolved gases
H2 (ppm)
0–100
101–700
701–1800
>1800
CH4 (ppm)
0–120
121–400
401–1000
>1000
C2H2 (ppm)
0–1
2–7
7–35
>35
C2H4 (ppm)
0–50
51–100
101–200
>200
C2H6 (ppm)
0–65
66–100
101–150
>150
CO (ppm)
0–350
351–700
701–1400
>1400
CO2 (ppm)
0–2500
2501–4000
4001–10000
>10000
OQF
Oil quality
BDV (kV)
100–50
49–40
39–30
<30
IFT (mN/m)
50–30
30–23
23–18
<18
Moisture (ppm)
0–15
16–20
21–25
>25
Acidity (mg KOH/g)
0–0.05
0.051–0.1
0.11–0.2
>0.2
DDF
0-0.1
0.1–0.5
0.5–1
>1
Colour
0–1.5
1.5–2
2–2.5
>2.5
FF
Furans
Furans (ppm)
0–0.1
0.1–1
1–10
>10Table 3
Weights assigned to each of the parameters of the four conditions.
Condition
Condition representation
Weights (w)
Normal
Good
[w ≤ 2.5]
Caution
Acceptable
[2.5 <w ≤ 5.0]
Alarm
Poor
[5.0 <w ≤ 7.5]
Failure
Worst
[7.5 <w ≤ 10]Computation of the exact weight of the variable of a given concentration was performed by using equations (1), [5], and (2).(1)Parameter score=Ki+xi−aibi−ai×2.5.Equation (2) only corresponds with breakdown voltage (BDV) and interfacial tension (IFT) parameters whose values the higher the better and vice versa and thus (1) had to be modified by rearranging it presented as follows:(2)Parameter score=Ki+bi−xibi−ai×2.5,where, Ki signifies the assigned minimum weight in the four conditions of the parameters, xi is the current value of the parameter considered (xi is represented by xi′ for DGAF parameters, xi″ for FF parameter, and xi″ for OQF parameters), ai and bi are the lower and the upper limits of the conforming cluster of the parameter, and xi−ai/bi−ai denotes normalization expression of assessing inputs, whilst normalization of BDV and IFT was done using bi−xi/bi−ai.


## 3.1.2. DP Estimation Model

The main byproducts of transformer solid insulation considered in this paper mirror the DP value of paper insulation constitute of furans (2-FAL), CO2, and CO concentration. To map the transformer insulation DP values, the proposed fuzzy logic model is developed under MATLAB/Simulink platform. The model is shown in Figure 1, where furan (2-FAL) and CO2/CO are the model inputs, whilst the output represents the insulation DP value.Figure 1
Fuzzy logic model for DP estimation.The associated membership functions as input attributes are set based on the concentration of furan (2-FAL) considered on a scale of 0–12 (ppm) and amount of CO2 and CO as a ratio from 0–12 based on various transformer test data, as shown in Figures 2 and 3, respectively. The five trapezoidal membership linguistic values considered for the furan input variable are normal (N), low (L), medium, high, and critical, whilst CO2/CO input variable uses bad, low, medium, high, and critical.Figure 2
Input parameter membership function-furans (2-FAL) (ppm).Figure 3
Input parameter membership function-CO2/CO ratio.The membership functions of the output variable signifying the DP value are established on a scale of 0 to 1200 where linguistic values of End-of-life, Weak, Normal, Healthy, and Very Healthy are used as indicated in Figure4.Figure 4
Output variable membership function-DP value.A set of “IF-THEN” statements as rules governing the mapping of inputs into outputs were formulated. Illustrations of the conveyed rules for DP estimation are as follows:IF (Furans is normal) and (CO2/CO is low) THEN (DP is V.Healthy)IF (Furans is medium) and (CO2/CO is medium) THEN (DP is Normal)IF (Furans is high) and (CO2/CO is bad) THEN (DP is End-of-Life)


## 3.1.3. Operational Ageing Stress Factor (OASF)

Transformer loading profile and temperature variations (hotspot temperatures (HST)) are the characteristic attributes governing the operational ageing stress of the transformer insulation system. A fuzzy logic model for determining the transformer operational stress level is established upon load and HST as inputs on membership function scaling of 0–1.2 pu (load) and 0–140°C (HST). The loading and temperature regime were taken to be of equal significance during fuzzy logic rule formulation. The magnitude and rate of change of these parameters determines the pace of operational criticality. The operational stress level of the transformer is upon a scale of 0 to 1 in which the worst condition is reflected by values nearing 1. The transformer fuzzy logic model for operational ageing stress is shown in Figure5.Figure 5
Fuzzy logic model for operational ageing stress.


## 3.2. Transformation of HI Model Inputs into Fuzzy Variables

Instead of using individual parameters as inputs to the HI fuzzy logic model, summed scores for three transformer parameter categories obtained using equation (1) and (2), DP, and operation ageing stress factor were employed as the underlining fuzzy inputs. These inputs are mapped into five assessing fuzzy logic variable states using simple and computational efficacy trapezoidal membership functions (MF). These assessing states (Excellent, Good, Moderate, Bad, and Worst) signify the health index of transformer insulation. Excellent designates the best condition whereas worst signifies immediate attention to the transformer. The associated membership function scale and their linguistic labels for the summed inputs are shown in Table 4. These scales are calculated by multiplying the lower and upper limits of weights of the four conditions by the number of parameters in DGAF, OQF, and FF. Furthermore, the DP and OASF membership function was established upon a scale of 0–1200 and 0-1, respectively. The crisp HI output was obtained through the center of gravity defuzzification method. Although the centroid method is computationally intensive, it was chosen due to its intuitive plausibility [27].Table 4
Ranges obtained for summed parameters.
Summed parameters
Input category ranges
Low (L)
Moderate (M)
High (H)
Critical (C)
DGAF
0 ≤ 17.5
17.5 < M ≤ 35
35 < H ≤ 52.5
52.5 < C ≤ 70
OQF
0 ≤ 15
15 < M ≤ 30
30 < H ≤ 45
45 < C ≤ 60
FF
0 ≤ 2.5
2.5 < M ≤ 5
5 < H ≤ 7.5
7.5 < C ≤ 10The proposed fuzzy logic health index model for the power transformer condition assessment process is depicted in Figure6. Figures 4 and 7–10 show the inputs membership functions utilized in mapping the health index output, whereas Figure 11 depicts the membership functions for the established transformer health index output, whilst Figure 12 shows the established rules associated with the proposed fuzzy logic model. The output of the DP model shown in Figure 4 was also used as an input to HI.Figure 6
Fuzzy-based transformer health index model.Figure 7
Input variable membership function-DGA Factor (DGAF).Figure 8
Input variable membership function-oil quality Factor (OQF).Figure 9
Input variable MF-furans content factor (FF).Figure 10
Input variable MF-operational ageing stress factor (OASF).Figure 11
Output variable MF-health index.Figure 12
Rules for the developed fuzzy logic-based transformer health index model.


## 4. Results and Discussions

Test data from different transformers and sources highlighted in Table5 were used in validation of the developed model. The validation was based on a linguistic label (Worst, Bad, Moderate, Good, and Excellent) assigned to different outcome states of the transformer after inputting test data from the sampled in-service transformers. Table 6 shows the corresponding scores calculated as per the values of transformer parameters and the health indices calculated for a sample of 20 in-service transformers. Using Transformer 8 as an illustration, the established model health index output signifies that the transformer is in the worst state. Its corresponding totals are DGAF = 63.64, OQF = 49.76, FF = 5.81, DP = 262.5, and OASF = 0.25. From Table 4, it is noted that DGAF and OQF fall in the critical range, whereas, FF exists in the high range. Additionally, the estimated DP value (through fuzzy logic sub model) approaches the end-of-life category. The critical state of DGAF is as a result of evolved gases surpassing their limited thresholds. Furthermore, most of the transformer oil quality tests (moisture, BDV, DDF, colour, and acidity) were in high ranges thereby resulting in worst transformer state. In addition, the results of both test data and HI output can be justified as the transformer was installed in 1976, and thus it was 37 years old at the time of the tests (2013).Table 5
Test data of 20 transformers rated between 20MVA and 175MVA (88 kV–420 kV).
Tx no
Year of installation
H2 (ppm)
CH4 (ppm)
C2H2 (ppm)
C2H6 (ppm)
C2H4 (ppm)
CO2 (ppm)
CO (ppm)
Furans (ppm)
Moisture (ppm)
Acidity (mg KOH/g)
BDV (kV)
DDF (%)
IFT (dynes/ cm)
Colour
HST (°C)
Load (pu)
Tx1
1996
234
300
52
56
29
5495
700
0.25
22
0.07
52
0.14
30
1.5
60
0.58
Tx2
—
607
119
3
257
67
2011
189
1.37
23
0.13
44
0.264
24
2
61
0.6
Tx3
1996
32.5
45.8
17
25.54
21.31
3685
697
0.49
16.5
0.058
61
0.174
27
2
49
0.57
Tx4
1986
74
347
35
194
172
22789
8197
4.5
28
0.18
40
0.266
20
2.5
78
0.61
Tx5
—
71
65
18
127
79
4567
582
1.1
19
0.15
38
0.185
23
2.5
58
0.44
Tx6
2000
107
129
0
55
68
7038
892
0.1
26
0.09
48
0.249
25
1.5
66
0.65
Tx7
1981
979
236
112
183
180
2492
1843
5.76
23.2
0.251
51.7
0.458
26
3
75
0.72
Tx8
1976
1498
395
26
323
395
12371
1582
3.9
33
0.19
35
0.593
25
4
66
0.48
Tx9
1996
294
748
6
212
1348
6764
669
0.83
9
0.08
49
0.1
35
2.5
77
0.75
Tx10
—
163
106
9
298
1517
2348
299
4.48
42
0.22
46
0.221
21
3.5
64
0.45
Tx11
1998
151
8
8
151
10
2323
297
0.22
6
0.13
64
0.566
27
2
68
0.5
Tx12
—
678
368
163
92
108
1139
162
0.16
11
0.05
70
0.113
38
1
81
0.82
Tx13
2015
893
724
1
6
18
1883
242
0.03
9
0.04
71
0.068
45
0
56
0.55
Tx14
1995
195
660
22
127
79
3347
356
0.09
6
0.03
66
0.207
41
1
53
0.6
Tx15
1990
440
522
183
31
62
5382
685
0.31
12
0.05
65
0.319
28
2
50
0.66
Tx16
2010
15
8
0
9
5
7135
902
0.1
10
0.03
55
0.15
42
1
61
0.44
Tx17
2005
1176
4
1
4
10
4991
637
0.83
10
0.09
62
0.733
29
1.5
53
0.5
Tx18
—
441
678
55
73
62
13345
1695
5.1
32
0.25
55
0.328
26
3
77
0.62
Tx19
2000
75
44
0
106
13
7846
261
2.4
40
0.092
31
0.416
22
3
61
0.55
Tx20
2002
181
79
21.1
56
29
713
192.6
8.91
21.2
0.349
33.5
0.257
20
3
50
0.5Table 6
Corresponding scores obtained as per the values of the test data and HI results.
Tx. no
H2
CH4
C2H2
C2H6
C2H4
CO2
CO
Moisture
Acidity
BDV
DDF
IFT
Colour
HST (°C)
Load pu
DP∗
DGAF
OQF
FF
Health index
Tx1
3.06
4.1
9.02
2.15
1.45
5.63
5
6
3.5
2.4
2.75
2.5
2.5
60
0.58
643.4
30.41
19.65
2.92
0.278
Good
Tx2
4.61
2.48
3.39
9.7
3.32
2.01
1.35
6.5
5.75
4
3.53
4.64
5
61
0.6
443.5
26.86
29.42
5.1
0.657
Moderate
Tx3
0.81
0.95
5.89
0.98
1.07
4.48
4.98
3.25
2.9
1.95
2.96
3.57
5
49
0.57
725.1
19.16
19.63
3.58
0.28
Good
Tx4
1.85
4.53
5
8.23
6.79
12.83
31.78
9
7
5
3.54
6.5
7.5
78
0.61
172.7
71.01
38.54
5.97
0.992
Worst
Tx5
1.78
1.35
3.48
6.33
3.93
5.24
4.15
4.5
6.25
5.5
3.03
5
7.5
58
0.44
524.8
26.26
31.78
2.53
0.498
Moderate
Tx6
2.53
2.57
0
2.12
3.37
6.27
5.68
8
4.5
3
3.43
4.29
2.5
66
0.65
786.3
22.54
25.72
2.5
0.275
Good
Tx7
5.63
3.53
14.38
9.15
6.99
2.49
9.08
6.6
8.78
2.42
4.74
3.93
12.5
75
0.72
109.9
51.25
38.97
6.32
0.944
Bad
Tx8
6.81
4.96
6.7
16.15
12.38
8.49
8.15
11.5
7.25
6.25
5.47
4.29
15
66
0.48
262.5
63.64
49.76
5.81
0.992
Worst
Tx9
3.12
6.45
4.5
10.6
36.2
7.82
4.78
1.5
4
2.75
2.5
1.88
7.5
77
0.75
494.8
73.47
20.13
4.53
0.528
Moderate
Tx10
2.76
2.21
5.18
14.9
40.43
2.35
2.14
16
8
3.5
3.26
6
12.5
64
0.45
248.7
69.97
49.26
5.97
0.991
Worst
Tx11
2.71
0.17
5.09
7.55
0.5
2.32
2.12
1
5.5
1.8
5.33
3.58
5
68
0.5
665.7
20.46
22.21
2.83
0.248
Good
Tx12
4.91
4.71
18.93
4.41
5.18
1.14
1.16
1.83
2.5
1.5
2.58
1.5
1.67
81
0.82
725.2
40.44
11.58
2.67
0.275
Good
Tx13
5.44
6.34
2.5
0.23
0.9
1.88
1.73
1.5
2
1.45
1.7
0.63
0
56
0.55
992.8
19.02
7.28
0.75
0.12
Excellent
Tx14
2.89
6.08
3.84
6.32
3.93
3.91
2.54
1
1.5
1.7
3.17
1.13
1.67
53
0.6
725.1
29.51
10.17
2.25
0.121
Excellent
Tx15
3.91
5.51
20.71
1.19
3.06
7.24
4.89
2
2.5
1.75
3.87
3.21
5
50
0.66
638.3
46.51
18.33
3.09
0.525
Moderate
Tx16
0.38
0.17
0
0.35
0.25
7.97
5.72
1.67
1.5
2.25
2.81
1
1.67
61
0.44
756.2
14.84
10.9
2.5
0.12
Excellent
Tx17
6.08
0.08
2.5
0.15
0.5
7.08
4.55
1.67
4.5
1.9
6.17
2.86
5
53
0.5
594.4
20.94
22.1
4.53
0.348
Good
Tx18
3.92
6.16
9.29
3.01
3.06
8.89
8.55
11
8.75
2.25
3.93
3.93
12.5
77
0.62
217.4
42.88
42.36
6.13
0.991
Worst
Tx19
1.88
0.92
0
5.26
0.65
8.23
1.86
15
4.6
7.25
4.8
5.5
12.5
61
0.55
325
18.8
49.65
5.31
0.931
Bad
Tx20
2.84
1.65
6.25
2.15
1.45
0.71
1.38
5.6
11.23
6.63
3.48
6.5
15
50
0.5
109.9
16.43
48.44
7.2
0.992
WorstThe test data used in validating the proposed model were also used in validating some of the models for health index proposed in the literature. A comparative analysis of four approaches is highlighted in Tables7 and 8. The utility Health index estimation was based on Furans analysis and oil quality factors, whereas the model in [8] was centered upon seven inputs which are, moisture, acidity, BDV, DF, Furans calculated DP, and TDCG, whilst a weighting factor of three inputs based on transformer oil and paper tests was established in [5]. It has been observed that though many attributes were used in [8], it was cumbersome to formulate many rules although three membership functions were used in which different experts decision can compromise the accuracy of the model by using fewer membership functions. In [8], the number of rules was reduced; however, variables like DP and loading effect should also be considered in HI estimation of which in [5] they were overlooked. The proposed model utilized the various transformer tests and integrated them into influential factors that mirror the transformer health index. Additionally, loading regime, DP, and hotspot temperatures were considered in HI estimation. In Table 8, different HI estimation methods have been presented. It is observed that some transformers show different health status whereas some show same HI status, but the magnitude of the condition differs by using same data. Bold values indicate where the HI differs for the compared models.Table 7
Health index status by different methods for 20 different test transformers.
Tx. No
Transformer health index level and description
Utility estimation
Method in [8]
Method in [5]
Proposed method
Tx1
Good
0.275
Good
0.275
Good
0.278
Good
Tx2
Moderate
0.552
Moderate
0.572
Moderate
0.657
Moderate
Tx3
Excellent
0.120
Excellent
0.143
Excellent
0.28
Good
Tx4
Worst
0.936
Worst
0.972
Worst
0.992
Worst
Tx5
Moderate
0.5
Moderate
0.452
Moderate
0.498
Moderate
Tx6
Good
0.273
Good
0.275
Good
0.275
Good
Tx7
Worst
0.832
Bad
0.894
Bad
0.944
Bad
Tx8
Worst
0.991
Worst
0.99
Worst
0.992
Worst
Tx9
Moderate
0.752
Bad
0.52
Moderate
0.528
Moderate
Tx10
Bad
0.899
Bad
0.934
Bad
0.991
Worst
Tx11
Good
0.225
Good
0.233
Good
0.248
Good
Tx12
Good
0.264
Good
0.273
Good
0.275
Good
Tx13
Excellent
0.083
Excellent
0.083
Excellent
0.12
Excellent
Tx14
Excellent
0.12
Excellent
0.122
Excellent
0.121
Excellent
Tx15
Moderate
0.45
Moderate
0.51
Moderate
0.525
Moderate
Tx16
Excellent
0.08
Excellent
0.104
Excellent
0.12
Excellent
Tx17
Good
0.25
Good
0.278
Good
0.348
Good
Tx18
Worst
0.887
Bad
0.9
Bad
0.991
Worst
Tx19
Worst
0.913
Bad
0.926
Bad
0.931
Bad
Tx20
Worst
0.98
Worst
0.983
Worst
0.992
WorstTable 8
HI comparison accuracies for different methods for 134 test transformers.
Status
HI comparison of 134 test case transformers
Utility estimation
Method in [8]
Method in [5]
Proposed method
Excellent
7
9
9
6
Good
28
26
26
27
Moderate
65
66
64
64
Bad
11
13
14
13
Worst
23
20
21
24
Total transformers
134
134
134
134
Overall % error against utility HI
7.5%
6.7%
4.5%Taking the Utility HI estimation as the bench-mark, Table8 depicts the accuracy comparison between the fuzzy logic models in [5, 8] and the present proposed method. The three methods showed accuracy levels of 92.5% [8], 93.3% [5], and 95.5% (proposed method) against the utility HI estimation. This shows that all three methods have the capabilities of estimating the health index that can be embraced by utility expects for asset management. The criticality of the estimated HI was based on the parameter threshold values highlighted in Table 2.From Table7, refurbishment, replacement, decision on retirement, or scrapping the transformers in the worst state is recommended since these transformers can fail untimely. However, for transformers in bad state, proper diagnostic measures and condition-based maintenance are suggested and planning for their short term replacement or other remedial actions. Transformers in moderate condition pose for long-term refurbishment or replacement. However, their condition does not promote them to be sidelined for monitoring and diagnosis. Additionally, more frequent sampling intervals should be administered in new transformers in moderate state, so as to investigate any abnormalities that may result in accelerated insulation degradation and ageing. Subsequently, the likelihood of failure for transformers in excellent or good state is very low; thus, only regular maintenance can be practiced as they operate within nameplate specifications.In a nutshell, the variances in transformer health status might be due to variations in loading patterns, the harmonic content of the loads, differences in maintenance strategies, different stresses subjected to the transformers, partial-discharge activities, and problems in the cooling mechanisms or difference in ageing and degradation rate.


## 5. Conclusions

To improve on the consistency of the transformer insulation health index model output, an intelligent health index model was developed based on the transformer multiattributes cascaded with an inference system which relies on the interpretation of an experienced expert. The computation of the HI was centered on the fuzzy inference tool based upon the calculation of cumulative factors that signifies the transformer insulation condition established on dissolved gas analysis factor, oil quality analysis factor, Furans content factor, degree of polymerization (DP), and operational ageing stress factor. The DP value was established from a fuzzy logic-based model using Furans (2-FAL) and carbon oxides ratio as the inputs. The operational ageing stress was framed from the transformer loading and transformer hot spot temperature profile. The overall resultant of the health index assessment was governed by all considered parameters as a whole, not on any specific individual parameter. Hence, this approach reflects a reliable and truthful insulation health index for the transformers. However, transformer health status evaluation can be enhanced by using the rate of change of dissolved gases and oil characteristics. However, in this paper, the data for rate of change of the variables were not available. Having a reasonable health index can facilitate in power transformer reliability and also enhance its residual life span.



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*Source: 2647157-2019-12-13.xml*