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Due to the large number of power transformers (ETs) in the distribution system, there is a need for a relatively simple representation of the status of each unit in order to more easily determine where and how to allocate the budget for preventive and corrective maintenance. In recent years, the concept of the transformer health index (HI) as an integral part of resource management was adopted for the condition assessment and ranking of ETs. HI algorithms take different forms and can be determined based on a large number of specific parameters. However, the main problem in HI methodology or any modern diagnostic technique is the existence of regular measurements and inspections and accurate test results. The paper proposes a solution in the form of the upgraded HI and the novel methodology for ET ranking including the value of available information to describe ET current state. The confidence to the measurement results is calculated using evidential reasoning (ER) algorithm based on Dempster–Shafer theory. The contribution to the ER methodology is the calculation of the initial degrees of belief using Markov chains. The aging process of an ET and transition probabilities from state to state are modelled using the statistical data for the population of 300 ETs and 20 years monitoring data. The proposed methodology is tested on the real data for 110/35 kV transformer, and in the second case, compared to the sample of 30 110/x kV transformers with traditional HI calculation

Determining the health index (HI) of a transformer is a suitable tool that should provide in a reproducible and consistent way information about its condition, the operational correctness, and availability. Transformer indexing by operating condition, with additional risk analysis, enables a better understanding of the availability and reliability of large transformer populations [

Certain measurement methods are performed on a regular basis, such as oil diagnostics, insulation resistance tests, turns ratio measurements, and inspection of accessories. They are performed relatively often and in the state of normal trouble-free operation. Some methods such as the measuring of partial discharges, in spite of their great importance for the assessment of the condition, are not usually used in determining the HI. The reason is possible financial losses resulting from the interruption of electricity supply that can be caused by unnecessary inspections. The advanced methods are used to assess the condition of ETs with developing defects or aged units, such as frequency domain spectroscopy (FDS), frequency response analysis (FRA), advanced bushings, and on-load tap changer (OLTC) diagnostics, as well as measurement of partial discharges.

With the advance of prognostics and health management applications, it is possible to enhance traditional transformer health monitoring techniques. For instance, in estimating the remaining life of a transformer, besides the data of paper insulation condition, it is necessary to know the aging kinetics of the oil-impregnated cellulose insulation, which depends on the temperature and water content in the paper. AC conductivity of the composite of cellulose, mineral oil, and water nanoparticles was investigated in [

As stated before, the advanced measurements are required only for aged ETs with developing defects, but for the vast majority of units, a practical condition index is required. This index should overcome the main problems of previous condition assessment approaches: (a) the rational aggregation of different ET components, (b) uncertainties, accuracy, and confidence of the inspection results, and (c) consistent grade assessment and weighting of different ET components. Recently, the concept of the transformer health index (HI) as an integral part of resource management was adopted for the condition assessment and ranking of ETs. HI calculation method that combines the impact of all available data and criteria based on the industry’s common practices and technical standards is presented in [

Using machine learning techniques, the collected data can be used for the HI prediction in the future period. Various classification techniques have been investigated to reduce ET assessment complexities and decrease the number of features by extracting the most influential ones when determining the HI [

The evidential reasoning (ER) approach is a suitable method for dealing with the aggregation problem. The process developed on the basis of Dempster–Shafer evidence theory [

The methodology of how to transfer a transformer condition assessment problem into a multicriteria decision solution under an ER framework is presented in [

The integrated fuzzy and evidential reasoning model is presented in [

To overcome the problem of subjective treatment of old, dubious, and uncertain data, the hybrid model of ER and Markov chains is proposed in this paper. A basic tree structure necessary for ER assessment is developed based on the complete transformer model and individual HI of every component, and a general, multilevel evaluation process is used for dealing with multicriteria decision problems. The ET condition is represented as a probability distribution over all possible health states using the Markov chain model of component ageing. The confidence to the measurement results is calculated using evidential reasoning (ER) algorithm based on Dempster–Shafer theory. The contribution to the ER methodology is the calculation of the initial degrees of belief using Markov chains. The proposed methodology is tested on the real data for 110/35 kV transformer, and in the second case, compared to the sample of 30 110/x kV transformers with traditional HI calculation

The rest of the paper is organized as follows. Section

In recent years, the numerical assessment (indexing) of the current state of an ET and other high-voltage equipment in plants assigning a health index (HI) emerges as a tool that could effectively provide a transition to condition-based maintenance. HI is a numerical value that can be used to estimate the overall condition of an ET. By individually evaluating the most representative key factors that are vital to the reliable operation of transformers and mathematically aggregating them into a quantitative index, this value provides information on the “health” of ET.

With this index, it will be possible to evaluate the state of a large population of distribution transformers and group them according to the state. Introducing this concept will increase availability and reliability while reducing maintenance costs. The assessment of the condition of the ET should include an assessment of the condition of the key parts: magnetic core and coil, solid insulation and insulating oil, bushings and voltage regulators, cooling system, transformer tank, expansion tank, and auxiliary equipment. The assessment is based on the results obtained by applying appropriate test methods in the field of chemical and electrical testing and visual inspection as well as evaluation of load histories [

Given that the assessment of the condition of an ET is based on the following [

Results of electrical and chemical tests

Maintenance information

Work history—exploitation events

Condition of equipment: isolators, cooling system, transformer tank, expansion tank, and auxiliary equipment

The estimated condition of the paper insulation

Expert opinion

HI represents the sum of these estimates. It is very important to view the health index as a variable parameter because by performing a multiparameter analysis of the condition, it changes over the life of the ET [

Based on the previous analysis, the calculation of the transformer HI in the proposed methodology includes an assessment of the condition of its key parts listed in Table

Weighting factors for different ET components.

No | ET component | Weighting factor ( |
---|---|---|

1 | Magnetic core | 3 |

2 | Geometry end electric contacts of windings | 4 |

3 | Insulation | 4 |

4 | Bushings | 5 |

5 | On-line tap changer | 5 |

6 | DGA analysis for the active part | 5 |

7 | Transformer oil | 4 |

8 | Transformer tank and auxiliary equipment | 2 |

9 | Work history | 3 |

Different test methods are used to evaluate the condition of each part of the ET mentioned in Table

Weighting factors of different inspection methods.

ET component | Inspection method | Weighting factor ( |
---|---|---|

Magnetic core | Open-circuit test/SFRA | 5 |

Geometry end electric contacts of windings | Resistance testing | 5 |

Leakage inductance test/SFRA | 5 | |

Insulation | Insulation resistivity/tg | 5 |

PDC/RVM/FDS/water content in oil | 4 | |

Furan derivative analysis | 3 | |

Bushings | tg | 4 |

On-line tap changer | Static/dynamic resistance testing | 5 |

DGA analysis for the active part | Dissolved gas analysis (DGA) | 4 |

Transformer oil | Physical and chemical oil characteristics | 5 |

Content of water in oil | 4 | |

Transformer tank and auxiliary equipment | Testing of cooling system and auxiliary equipment | 2 |

Visual inspection/leakage control | 2 | |

Work history | Loading and operation history | 3 |

Since the DGA analysis of the transformer oil sample may indicate a problem of overheating or the occurrence of particles, but it cannot reliably define the location of the resulting fault, it is singled out as special. This limited its impact on the value of total HI but not on specific components, such as windings or cores.

The overall health index of a transformer can be calculated using the following expression:

In expression (_{di} is a grade for each individual _{di} ≤ 3 calculated in the following:

The estimation of the _{m} method is given by an expert on the basis of the results of the last and previous tests, experience, and specificity of individual ETs and using the criteria given in the applicable standards and technical recommendations. The possible range is 0 ≤ _{m} ≤ 3. Alternatively, HI can be calculated with expression (

_{1} and _{2} represent the weighting factors for the transformer and load tap changer, respectively, while DI_{i} represents the diagnostic index of the

Comparison of electrical and chemical test scores with appropriate numerical estimates for health index calculations.

Test results | HI |
---|---|

Good condition | 3 |

Moderately good | 2 ≤ HI < 3 |

Moderately bad | 1 ≤ HI < 2 |

Poor | <1 |

The “moderately good” rating indicates dubious results but without major changes over time, e.g., comparing the last two to three trials and continuing the follow-up with more frequent testing. On the contrary, the rating “moderately bad” indicates a growing trend of deterioration of the transformer state, and it tightens control by more frequent testing, recommends additional testing, or emphasizes the need to plan for a specific intervention in the coming period.

Because of the irregular inspection period, it is hard to perform accurate yearly ET condition assessment. Some data may be several years old, and the main problem in interpretation is the lack of confidence of testing results. The validity of results can be treated by the similar grading system (from 0 for results older than the maximal inspection period and 3 for actual measurement results). The validity of the _{Ei} with

Then, the HI value composed of

Because this treatment of old measurements is very simplified and not based on the complete transformer aging model, the ET condition must be represented as a probability distribution over all possible health states. In this paper, this distribution is determined using the Markov chain model of component ageing, and evidential reasoning is used for the quantification of different parameters. The integrated methodology is presented in the sequel.

To evaluate the state of a power transformer, large amount of qualitative and numerical information needs to be interpreted on different hierarchical levels. The ER approach is a suitable method for dealing with the aggregation problem, and the original ER model and algorithm, based on Dempster–Shafer theory [

In a two-level hierarchy of attributes with a general attribute at the top level and _{i} (

The weights of the attributes are presented by _{1}, …, _{i}, …, _{L}}, where _{i} is the relative weight of the _{i}) with value between 0 and 1 (0 ≤ _{i} ≤ 1). The evaluation grades are represented by the following:

It is assumed that _{n+1} is preferred to _{n}.

The methodology for the evaluation grades for transformer components presented in Table

The evaluation grades for solid insulation.

Dielectric losses | Insulation state | _{n} |
---|---|---|

tg | Good condition | 3 |

1% < tg | Moderately good | 2 |

1.5% < tg | Moderately bad | 1 |

tg | Poor | 0 |

An assessment for the _{i} may be represented by the following distribution:_{n,i} denotes the degree of belief and _{n,i} ≥ 0, _{i}) is complete. In the opposite case, assessment _{i}) is incomplete. Equation (_{i}:

Let _{n} be a grade to which the general attribute is assessed with certain degree of belief _{n}. The problem is to generate _{n} by aggregating the assessments for all associated basic attributes _{i}. For this purpose, the following algorithm is used.

Let _{n,i} be a basic probability mass representing the degree to which basic _{i} supports judgment that the general attribute _{n}, respectively; let _{H,i} be a remaining probability mass unassigned to any individual grade after all the _{i} attribute, are considered. Next expression explains how basic probability mass is calculated:

Remaining probability mass is calculated as

Suppose that _{I(i)} is a subset of the first _{I(i)} = {_{1}, _{2}, …, _{i}}, and according to that, _{n,I(i)} can be the probability mass defined as the degree to which all the _{n}. Also, _{H,I(i)} is the remaining probability mass unassigned to individual grades after all the basic attributes in _{I(i)} have been assessed. Probability masses _{n,I(i)} and _{H,I(i)} for _{I(i)} can be calculated from basic probability masses _{n,j} and _{H,j} for all _{I(I+1)} is a normalizing factor so that _{I(i)} are numbered arbitrarily and that initial values are _{n,I(1)} = _{n,1} and _{H,I(1)} = _{H,1}. And finally, in the original evidential reasoning algorithm, combined degree of belief for a general attribute _{n} is given by_{H} denotes the degree of incompleteness of the assessment.

As explained in the introductory section, the hierarchical structure of an ER algorithm proved to be adequate for the condition-based maintenance of the power transformer [_{n,i}_{n}) is the utility of the grade _{n} with _{n} + 1) > _{n}) if _{n} + 1 is preferred to _{n,} then the maximum, minimum, and the average expected utilities on

The process of transition from state to state can be represented by the diagram given in Figure _{3} through _{0} represent the health status of the transformer according to the established health index. The _{ij} labels indicate the transition rates from state

State transition scheme.

The exponential probability distribution (

The failure intensity of this distribution is a constant value, and the time to failure is independent of the operating time of the equipment being observed. By using Markov transition diagrams, degrees of belief in terms of ER methodology can be modelled in the following way. Let the measurement and inspection results indicate the health state Hi. After the period _{ii}) or transitioned to the state _{ij}) can be represented by the following transition matrix:

An

The intensity of leaving the state is equal to the sum of the transitions from the state to the other states of the system so that

Exponential distribution has one important feature that allows relatively simple modelling of systems with exponential residence time distributions in characteristic states. The probability that the system that is on state in _{1} is likely to transition to another state over a period of time (_{1}, _{2}) is

As can be seen from the previous relation, the considered probability depends solely on the length of time interval for which the probability is calculated and not on the length of stay in the previous state. If the time interval is very short, an approximate replacement of the exponential function is obtained from the previous relation:

Using the statistical data from the transformer history, the intensities of transition from state _{ij}) are calculated based on the following relation:_{ij} represents the number of transitions from state _{ij} represents the average number of years staying in state

The algorithm for the ET assessment can be presented in the following steps and graphically presented in Figure

Step 1: define a set of

Step 2: for each attribute, determine the transition probability matrix (

Step 3: depending on inspection accuracy and time, _{i}, and evaluation grade _{n}, a degree of belief _{n} is assigned for each attribute

Step 4: _{n,i}, a basic probability mass, representing the degree to which the _{i} supports a hypothesis that the health index is assessed to the _{n} is calculated

Step 5: the combined probability masses are generated by aggregating all the basic probability assignments using the recursive ER algorithm

Step 6: calculate the combined degrees of belief for a higher-level property

State transition scheme.

The proposed methodology will be illustrated on individual transformer health estimation and on comparative estimation of 30 transformers operating in EPS (Electric Power Industry of Serbia).

The fleet of 344 transformers of 110 kV primary voltage operating in EPS was monitored during 10 years period (2008–2018). Transition probabilities are derived from the measurement databases consisting of more than 10,000 measurements of 18 main transformer components. The proposed methodology will be illustrated on the individual transformer health assessment (Case 1) and the ranking of a sample of 30 transformers (Case 2).

The methodology for the condition assessment will be applied to the existing transformer 110/35/10 kV, 20/20/10MVA. Starting from a complete model presented in Tables

Hierarchical scheme for transformer HI assessment.

Initial data with the available measurements, together with weighting factors for ET component (_{i}) and testing method (_{m}), are presented in Table _{P,C} (1/year) obtained from the 10-year period is given in the following:

Initial data for the degrees of belief calculation.

Oil | Insulation | Active part | Windings | |||||
---|---|---|---|---|---|---|---|---|

0.24 | 0.24 | 0.28 | 0.24 | |||||

0.55 | 0.45 | 0.41 | 0.34 | 0.25 | 0.5 | 0.5 | ||

_{i} | Phys, chem (_{i}, 1) | H_{2}O (_{i},2) | tg_{i},1) | FDS (_{i},2) | Furan (_{i},3) | DGA (_{i}) | _{i},1) | _{i},2) |

3 | 0.75 | 0 | 0 | 0 | 0.8 | 0 | 0.5 | 0.5 |

2 | 0.14 | 0.8 | 0 | 0 | 0 | 0.9 | 0.3 | 0.3 |

1 | 0.08 | 0.2 | 0.8 | 0 | 0 | 0 | 0 | 0 |

0 | 0.02 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

The physical/chemical characteristics have been inspected two years ago, and the state of oil has been graded as “good.” Using expressions (

Recursively using equations (_{3} = “good,” _{2} = “moderately good,” _{1} = “moderately bad,” and _{0} = “poor,” equals 0.17, 0.44, 0.045, and 0, respectively.

The degrees of belief of the main transformer components.

3 | 2 | 1 | 0 | _{H,i} | |
---|---|---|---|---|---|

Oil | 0.17 | 0.44 | 0.045 | 0 | 0.345 |

Insulation | 0.062 | 0 | 0.14 | 0 | 0.8 |

DGA | 0 | 0.252 | 0 | 0 | 0.748 |

Windings | 0.153 | 0.07 | 0 | 0 | 0.777 |

With the values calculated in step 3, we get the combined degrees of belief for _{3} = “good,” _{2} = “moderately good,” and _{1} = “moderately bad” which equal to 0.32, 0.175, and 0.08, respectively. The average HI, obtained from (_{avg} = 2.03.

Using the traditional HI calculation method, using the data from Table _{d} for oil, insulation, active part, and windings equals 2.56, 1.75, 2, and 3, respectively. Using equation (

Transformer assessment using the traditional HI.

Oil | Insulation | Active part | Windings | |||||
---|---|---|---|---|---|---|---|---|

4 | 4 | 5 | 4 | |||||

5 | 4 | 5 | 4 | 3 | 5 | 5 | ||

Phys, chem | H_{2}O | tg | FDS | Furan | DGA | |||

_{m} | 3 | 2 | 1 | — | 3 | 2 | 3 | 3 |

The estimation of HI was performed on a sample of 30 distributive energy transformers. The complete transformer model with the elements in Table

Figure

HI obtained by different assessment methods.

The HI is calculated using the proposed ER methodology (denoted ER in Figure

Deviations of all ER results from the accurate health state are presented in

Deviations of the real health values from the HI obtained by the ER method.

Maximal deviations from the exact values are obtained with equation (

Inspection grades and assessment results.

Magnetic core 3 | Geometry end electric contacts of windings, 4 | Insulation, 4 | Bushings, 5 | On-line tap changer, 5 | Oil, 4 | DGA, 5 | Tank, 2 | HI [0–3] | Total HI [0–100%] | Validity ažurnost | Expert | Equation ( | ER | E 5 | Dev equation ( | Dev ER | Dev equation ( | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

HI | HI | HI | HI | HI | HI | HI | HI | ||||||||||||||||||||

1 | 1983 | 3 | 10 | 2.5 | 10 | 3 | 6.67 | 0 | 10 | 3 | 10 | 1.44 | 10 | 3 | 10 | 0 | 0 | 2.76 | 0.41 | 0.616716 | 2.76 | 0.41 | 0.616716 | ||||

2 | 3 | 5 | 1.5 | 2.5 | 3 | 6.67 | 0 | 0 | 3 | 0 | 3 | 10 | 3 | 10 | 3 | 10 | 0 | 2.49 | 0.41 | 0.430638 | 2.49 | 0.41 | 0.430638 | ||||

18 | 1986 | 3 | 10 | 3 | 10 | 2.67 | 10 | 0 | 1 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 0 | 1.08 | 0.2 | 1.56625 | 1.08 | 0.2 | 1.56625 | ||||

17 | 1979 | 3 | 10 | 1.5 | 5 | 3 | 6.67 | 3 | 10 | 3 | 0 | 3 | 5 | 3 | 0 | 0 | 0.6 | 1.23 | 1.21 | 0.87096 | 0.63 | 0.61 | 0.27096 | ||||

13 | 1958 | 3 | 10 | 3 | 10 | 2 | 10 | 0 | 1 | 10 | 2 | 10 | 3 | 10 | 2.56 | 10 | 0.75 | 0.93 | 1.47 | 1.44375 | 0.18 | 0.72 | 0.69375 | ||||

5 | 1969 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 1 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 1.35 | 1.78 | 1.4 | 1.84 | 0.43 | 0.05 | 0.49 | |||

8 | 1972 | 3 | 10 | 3 | 10 | 2.67 | 8.33 | 3 | 10 | 1 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 1.35 | 2.58 | 1.4 | 1.781962 | 1.23 | 0.05 | 0.431962 | |||

7 | 1968 | 3 | 10 | 2.5 | 10 | 2.38 | 6.67 | 1 | 0 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 1.5 | 2.11 | 1.6 | 1.475118 | 0.61 | 0.1 | 0.024882 | |||

9 | 1962 | 2 | 10 | 1.25 | 10 | 1.42 | 10 | 0 | 3 | 10 | 2 | 10 | 3 | 10 | 3 | 10 | 1.5 | 2.58 | 1.6 | 1.4175 | 1.08 | 0.1 | 0.0825 | ||||

11 | 1978 | 3 | 10 | 3 | 10 | 3 | 10 | 0 | 3 | 10 | 3 | 10 | 3 | 10 | 1.22 | 10 | 1.5 | 2.2 | 1.9 | 1.68875 | 0.7 | 0.4 | 0.18875 | ||||

19 | 1972 | 3 | 10 | 3 | 10 | 3 | 10 | 0 | 1 | 10 | 2.44 | 10 | 3 | 10 | 2.44 | 10 | 1.5 | 2.15 | 1.7 | 1.53125 | 0.65 | 0.2 | 0.03125 | ||||

23 | 1989 | 3 | 10 | 1.5 | 5 | 3 | 6.67 | 3 | 10 | 3 | 0 | 3 | 5 | 3 | 0 | 0 | 1.5 | 2.78 | 2.23 | 0.87096 | 1.28 | 0.73 | 0.62904 | ||||

4 | 1971 | 0 | 3 | 0 | 2.33 | 6.67 | 3 | 10 | 0 | 0 | 1.44 | 5 | 3 | 10 | 0 | 1.65 | 2.64 | 1.8 | 0.27713 | 0.99 | 0.15 | 1.37287 | |||||

12 | 1988 | 0 | 3 | 5 | 3 | 6.67 | 3 | 10 | 3 | 10 | 3 | 5 | 2 | 0 | 0 | 1.65 | 2.78 | 2.24 | 1.288104 | 1.13 | 0.59 | 0.361896 | |||||

20 | 2013 | 0 | 3 | 5 | 3 | 6.67 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 1.65 | 2.11 | 1.8 | 2.3127 | 0.46 | 0.15 | 0.6627 | ||||

6 | 1968 | 0 | 0 | 3 | 5 | 3 | 5 | 0 | 1.44 | 10 | 3 | 10 | 3 | 5 | 1.8 | 2.22 | 1.7 | 0.805 | 0.42 | 0.1 | 0.995 | ||||||

16 | 1980 | 0 | 3 | 5 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 0 | 1.8 | 1.23 | 1.22 | 2.0625 | 0.57 | 0.58 | 0.2625 | |||||

22 | 1971 | 0 | 10 | 0 | 10 | 0.58 | 6.67 | 0 | 3 | 10 | 3 | 5 | 0 | 0 | 0 | 1.8 | 2.95 | 2.74 | 0.203151 | 1.15 | 0.94 | 1.596849 | |||||

21 | 1965 | 3 | 10 | 2.5 | 10 | 3 | 10 | 3 | 10 | 2 | 10 | 2.56 | 10 | 3 | 10 | 2.56 | 10 | 1.95 | 2.72 | 1.9 | 2.7 | 0.77 | 0.05 | 0.75 | |||

24 | 1968 | 3 | 10 | 3 | 10 | 2.67 | 10 | 3 | 10 | 3 | 10 | 2.44 | 10 | 3 | 10 | 3 | 10 | 1.95 | 2.71 | 2.43 | 2.89 | 0.76 | 0.48 | 0.94 | |||

3 | 1978 | 3 | 10 | 3 | 10 | 3 | 10 | 0 | 3 | 10 | 3 | 10 | 3 | 0 | 2.56 | 10 | 2.1 | 2.54 | 2.2 | 2.2275 | 0.44 | 0.1 | 0.1275 | ||||

10 | 1982 | 3 | 10 | 1.5 | 5 | 2.67 | 10 | 3 | 10 | 3 | 10 | 2.56 | 10 | 3 | 10 | 3 | 10 | 2.1 | 1.49 | 1.7 | 1.74375 | 0.61 | 0.4 | 0.35625 | |||

25 | 1980 | 3 | 10 | 1.5 | 5 | 3 | 6.67 | 2 | 5 | 3 | 0 | 3 | 5 | 3 | 0 | 0 | 2.1 | 2.43 | 2.56 | 0.720538 | 0.33 | 0.46 | 1.379462 | ||||

14 | 1954 | 3 | 10 | 3 | 10 | 1.46 | 6.67 | 0 | 3 | 10 | 2.44 | 10 | 3 | 10 | 3 | 10 | 2.25 | 1.38 | 1.23 | 1.533456 | 0.87 | 1.02 | 0.716544 | ||||

26 | 1986 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 2.25 | 2.64 | 2.23 | 3 | 0.39 | 0.02 | 0.75 | |||

27 | 1974 | 3 | 10 | 3 | 10 | 2.58 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 2 | 10 | 0 | 2.25 | 2.11 | 1.56 | 2.4325 | 0.14 | 0.69 | 0.1825 | ||||

15 | 3 | 10 | 2.5 | 10 | 3 | 3.33 | 3 | 10 | 3 | 10 | 0 | 0 | 0 | 3 | 1.53 | 1.24 | 1.57064 | 1.47 | 1.76 | 1.42936 | |||||||

28 | 1978 | 3 | 10 | 3 | 10 | 2.58 | 10 | 0 | 3 | 10 | 1.44 | 10 | 3 | 10 | 0 | 3 | 2.58 | 2.54 | 1.38 | 0.42 | 0.46 | 1.62 | |||||

29 | 1978 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 10 | 3 | 3 | 2.74 | 3 | 0 | 0.26 | 0 | |||

30 | 1974 | 3 | 10 | 3 | 10 | 3 | 6.67 | 3 | 10 | 3 | 10 | 1 | 5 | 3 | 10 | 0 | 3 | 3 | 2.74 | 1.441583 | 0 | 0.26 | 1.558417 |

The main challenge in finding the relation between the HI and all the elements of the calculation is the lack of data. The regular, precisely defined dynamics of the full-scale testing is not present at all power distribution companies. Therefore, there is a difficulty in selecting a mathematical tool to calculate objective transformer state estimates in the absence of some parameters. The integration of evidential reasoning methodology with the Markov chain model of component ageing enables the more accurate estimation of transformer health. The proposed methodology takes the probability that the component remained in the same state or transitioned to another state in a quantitative way.

By calculating the HI for a fleet of transformers in the system, it is possible to rank them according to their current state or HI value. The traditional approaches to HI calculation give the large deviations from the accurate health grades, especially for transformers in poor condition. If the scope of the tests is small and the last tests were performed a long time ago, it is obvious the reliability of the HI is lower. However, the traditional HI methodologies did not give the quantitative evaluation of this reliability. The proposed methodology gives a clear signal that more accurate or full-scale testing should be performed to more accurately assess the current state of the unit. Further research will be focused on the more precise estimation of utility functions, concerning financial losses resulting from the interruption of electricity supply that can be caused by an ET failure or unnecessary inspections.

All the data were generated during the study realized for Electric Power Industry of Serbia. The derived data supporting the findings of this study are available upon request to Srdjan Milosavljevic via smilos@ieent.org.

The authors declare that they have no conflicts of interest.