Khulna University of Engineering and Technology
A Project on
Regression Analysis of Transformer Aging: Predicting
remaining Life Based on Operational Parameters
Course No: EE 3122
Course title: Sessional on Numerical Methods and Statistics
Date of Submission:20 May ,2024S
Submitted to:
Dr. Md. Mohiuddin Ahmad
Professor,
Department of Electrical
and Electronic Engineering,
KUET.
Submitted by:
Dr. Md. Shahjahan
Professor,
Department of Electrical
and Electronic Engineering,
KUET.


Md Rezaul Islam
Roll : 2003078


Shariar Khan Shetu
Roll : 2003070
2
Abstract:
Power transformer is the most expensive equipment in electrical network and the mineral oil has the main
roles of insulating and cooling in it. Oil is subjected to the degradation because of the ageing, high temperature
and chemical reactions such as the oxidation. Then the oil condition has to be checked regularly and reclaimed
or replaced when necessary, to avoid the sudden failure of the transformer. It will be very desirable also if we
can predict the transformer oil remaining lifetime, from time to time. By using MATLAB codes , we will operate
and calculate the remaining life of a transformer.
Introduction:
Power transformers play a vital role in maintaining reliable and efficient electricity supply. The life of a power
transformer mainly depends on the condition of the paper-oil insulation system. Nowadays, there are many
condition monitoring techniques available for transformers and some measured conditions such as
temperature, moisture, furan content have paper which can be interpret mathematically direct relationship
with transformer insulation. Furan compounds are generally recognized as the most practicably obtainable
reliable indicator of cellulose insulation degradation. Furfural is a chemical byproduct formed when the
cellulose in the transformer insulation degrades. It dissolves in the transformer oil and can be measured
through oil analysis.
Proposed Mathematical Model:
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Condition monitoring data are collected for a fifty number of 3-phase transformers in different capacities ranging
60MVA to 200MVA.
The Factors are:
1.Data of furan
2.Age
3.Moisture content in insulation paper
4.Temperature
5.Oxygen content
6.Total gas amount
7.Capacity in kVA
8.Acidity and breakdown voltage
are collected for the same date
results are shown in Fig. 1.
The expected mathematical model is in the form of,Y=β0+β1x+β2x2+β3x3.Null HypothesisH0:β0=β1=β2=β3=0
The regression line obtained using stepwise selection is as follows.
Furfural=−0.935+0.03018×T+0.03399×A+0.3883×M+O.000048×GO2−0.000023×GTOT−0.000007×C
where,
T
=Temperature (C)
A =Age (Years)
M =Moisture in ppr(%)
GO2 =O2 (ppm)
Gtot=Total Gas (ppm) and
C= Capacity of transformer (KVA)
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dd
The DP value can be calculated by using the above formula.
Further the normal probability plot and verses
fits plot is scattered with no patterns and hence the
variance is constant.
Fitted plot have been drawn in Fig-3 and Fig-4.
A linear regression was conducted for transformers with furan more than 0.6 to identify the significant
parameters. When performing this linear regression, above regression results were considered as one
parameter.
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After identifying the significant factors, a nonlinear
regression was performed to obtain a relationship between
furan and other parameters which are moisture in paper,
temperature, oxygen content, current age of the transformer,
breakdown voltage and capacity of the transformer.
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Conclusion:
The reliability of a power system depends on the condition of its critical assets and power
transformers are vital component in the power systems. Therefore, estimating the remaining lifetime
of power transformers is essential in order to maintain a reliable supply. DP is normally determined
using furan analysis. Different types of relationships between DP and furan are currently used in the
power industry. The remaining lifetime of a transformer can be calculated using DP. the DP value was
calculated using the resulted furan value and then remaining lifetime of the transformer was
calculated. The developed mathematical model estimates the remaining lifetime of a transformer
accurately. It is important to prevent the failures of power transformers to ensure the stability of the
power system. Therefore having an idea regarding the remaining lifetime of a transformer is vital.
References:
1.
Q. Fu, Z. Li and Y. Lin, "Recent advances on analysis and explanation of aged insulation in operating power
transformers", 2010 Asia-Pacific Power and Energy Engineering Conference, 2010.
2.
P. V. Notingher et al., "Transformer board lifetime estimation using activation energy", XV InternationalSymposium
on Electromagnetic Fields in Mechatronics Electrical and Electronic Engineering, 2011.
3.
F. Ortiz et al., "Estimating the age of power transformers using the concentration of furans in dielectric oil",
international Conference on Renewable Energies and Power Quality, May 2016.
4.
L. Hamrick, "Dissolved Gas Analysis for Transformers", ESCO Energy Services International Electrical Testing
Association.
Appendix:
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The regression analysis of the transformer’s remaining life by using MATLAB codes is given below:
below:
function estimateTransformerAge()
% Define specific data points (age, furfural content, degree of polymerization)
age = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]; % years
furfuralContent = [0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55]; % ppm
degreePolymerization = [0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65]; % arbitrary units
units
% Plotting graphs
figure;
subplot(2,1,1);
scatter(age, furfuralContent, 'b', 'filled');
xlabel('Age (years)');
ylabel('Furfural Content (ppm)');
title('Furfural Content vs Age');
grid on;
subplot(2,1,2);
scatter(age, degreePolymerization, 'r', 'filled');
xlabel('Age (years)');
ylabel('Degree of Polymerization');
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% Perform linear regression
furfuralRegression = polyfit(age, furfuralContent, 1);
degreePolyRegression = polyfit(age, degreePolymerization, 1);
% Display regression equations
disp(['Furfural Regression Equation: y = ' num2str(furfuralRegression(1)) 'x + '
num2str(furfuralRegression(2))]);
disp(['Degree of Polymerization Regression Equation: y = '
num2str(degreePolyRegression(1)) 'x + ' num2str(degreePolyRegression(2))]);
% Estimate transformer age based on regression coefficients
estimatedAge = estimateAgeFromFurfuralAndDP(furfuralRegression,
degreePolyRegression);
% Display the estimated age
disp(['Estimated Transformer Age: ' num2str(estimatedAge) ' years']);
end
function estimatedAge = estimateAgeFromFurfuralAndDP(furfuralRegression,
degreePolyRegression)
% Use regression coefficients to estimate transformer age
% Example estimation: estimatedAge = (furfuralRegression(1) +
degreePolyRegression(1)) / 2;
% Adjust the estimation method according to your data or model
estimatedAge = (furfuralRegression(1) + degreePolyRegression(1)) / 2;
end