Power transformers are the most important components of electricity transmission and distribution networks. The interruptions in power system generate different stresses, including thermal, electrical, chemical, and mechanical stresses inside the transformers [3]. These stresses accelerate the deterioration of the transformer insulation, and finally leads to failure of the device. Electrical stress and thermal stress are the two dominant stresses, which deteriorate the transformer insulation rapidly. Electrical stress are normally developed by overloads, short circuits, lightning, etc [4]. Dielectric heating, higher ambient temperatures, and unpredictable loads are the main origins for higher thermal stress [5]. These two stresses inside the transformers slow down their age, and reduce their expected life. As a result, a huge revenue loss has been faced by the utility managers and the consumers [1]. Therefore, continuous health assessment of transformer is very essential for their successful operation. In general, the health condition of power transformers is predicted from their insulating oil and paper health conditions [6]. Several condition monitoring methods, including Breakdown Voltage (BDV), Interfacial Tension (IFT), Flash Point (FP), Dissolved Gas Analysis (DGA), etc., have been used to determine the health condition of the transformer oil [7]. Similarly, Furan Analysis (FA) and Degree of Polymerization (DP) have been utilized to determine the health condition of the transformer insulating paper [8] . Each of the methods mentioned above determines the present health condition as well as the remnant life of the transformers. However, none of these methods does consider the effect of load, moisture, and ambient temperature on the health of the transformers [7]. Hence, the remnant life assessment of transformers using the above mentioned methods is not accurate. Also the ambient conditions are neither consistent nor predictable [9, 10]. Such situations necessitated further investigations, which incorporate the information obtained from the various test data and the ambient conditions (load, moisture, and ambient temperature) for an accurate health assessment of transformers.

In this paper, the combined effect of load, moisture and ambient temperature on various dielectric properties of transformer insulation has been investigated. Further, a multi-regression technique has been proposed to determine the influence of transformer oil temperature as well as moisture content present in the transformer. Two different transformers owned by Himachal Pradesh State Electricity Board (HPSEB) located at Anu substation, India were tested to prove the robustness and efficacy of the present study. The present approach has been found to be an accurate and more practical solution for transformer remaining health evaluation.

A statistical regression correlates two or more variables in such a manner that one variable can be predicted or explained by using information of the other variables [11]. In simple regression analysis, a single response measurement Y is related to a single predictor X for each observation as given in equation (1). The critical assumption of the model is that the conditional mean function is linear [12].

(1)

where, a is the intercept and b is the slope of X and Y. Similarly, standard multiple regression is used to evaluate the relationship between a set of independent variables and a dependent variable. In multiple regression, all independent variables are entered into the regression equation at the same time [13]. It is computed by (2).

(2)

where, X₁ to X_n are dependent variables and b_n is the slope coefficient of n^th input. Multiple R and R² measure the strength of the relationship between the set of independent variables and the dependent variables respectively. If the value of R² is less than 0.95 then it may imply an unsatisfactory fitness [11]. As its value is near or equal to unity, it shows the variables in the relation are having a strong co-relation. R² value can be further improved by considering the number of higher order coefficients.

As everyone is aware that the atmospheric conditions gradually change as per three different seasons such as winter, summer, and rainy seasons. In general, in upper North region of India, December to March is to be well thoughtout as winter, whereas, April to July treated as summer and August to November as the rainy season. Monthly average ambient temperature is always alternating in nature from season to season. It results in an accelerating deterioration of the transformer insulation. Therefore, the effect of annual load, moisture and ambient temperatures on transformer insulating properties have been investigated in this study. The details of the two test case transformers are given in Table 1. The oil samples were drawn from these transformers at the end of every month, and then various diagnostic tests were performed on the transformers. Annual load, oil temperature, and winding temperature data were collected from Anu sub-station, HPSEB-India. Annual ambient temperature data of Anu sub-station area was collected from an Indian weather report.

Table 1. Details of Test Case Transformers

Annual average winding and oil temperatures of transformers 1 and 2 are shown in Figures 1(a) and (b) respectively.

Figure 1. Annual Average Winding and Oil Temperatures for (a) TF-1 (b) TF-2

It is noticed from Figure 1, that the load and the ambient temperatures are high in summer season. It leads to higher degradation of the insulation in summer. Further, the annual load on these two transformers is shown in Figure 2. Also the average load of the two test transformers is high in summer season. Figure 3 represents the annual ambient temperature in Anu sub-station area.

Figure 2. Annual Average Load of Test Case Transformers

Figure 3. Annual Average Ambient Temperatures

As per the above discussed regression methods, correlations have been obtained between the load, ambient temperature, winding temperature, and oil temperature. These are given from equations (3) to (6).

(3)

(4)

(5)

(6)

The oil samples collected from two transformers have been examined by BDV, moisture content, DGA, and degree of polymerization tests. These tests were performed as per IEC, ASTM, IEEE recommendations, with a span of 720-745 hours. It was continued up to 11310 hours (i.e. 1 year). The significances and interpretations of these tests have been discussed in the following subsections.

3.1 BDV Test

The maximum voltage that can be applied across the solid or liquid insulation without any electrical breakdown is called as dielectric strength of paper or oil [13] . BDV decreases as per the aging of the transformer [6]. Any significant reduction in the dielectric strength indicates that the oil is no longer capable of performing its vital function. ASTM D 877, ASTM D 1816, IEC 60156, BS 5730a, BS 148, BS 5874 are the various standards for BDV testing [10]. The test results of two transformers are given in Figure 4.

Figure 4. Breakdown Voltage Test Results of Two Transformers

3.2 Degree of Polymerization

The mechanical properties of the transformer insulating paper can be established by the direct measurement of its tensile strength or degree of polymerization (DP) [14]. It is generally suggested that DP values between 150 and 250 represent the lower limits for end-of-life criteria for the paper insulation. If its value is below 150, then the paper has zero mechanical strength [15]. IEC 60450 is the standard test code of DP test. DP results of the two transformers correspond to every month of 2015 are given in Figure 5.

Figure 5. DP Test Results of Two Transformers

3.3 Total Dissolved Gas Content

Dissolved gas analysis is the most widely used method to determine the health index of transformer oil, and identify incipient faults present within transformers. It uses the concentrations of various gases dissolved in the oil. As per IEEE standard C57.104–2008. The overall condition of the transformer is determined by the Total Dissolved Combustible Gas (TDCG) concentration, which is the sum of the concentrations of all the gases, excluding CO₂ . CO₂ is excluded because it is incombustible.

Dissolved gas concentrations in the oil such as nitrogen, oxygen, carbon monoxide, carbon dioxide, hydrogen, methane, ethane, ethylene, and acetylene are determined by using DAG test [16]. The concentrations and relative ratios of these gases can be used to diagnose certain operational problems with the transformer, which may or may not be associated with a change in a physical or chemical property of the insulating oil [17]. DGA test of the transformers oils of the age below 10 years should be done after every two years and of more than 10 years, it should be done every year [2]. DGA results obtained are given in Figure 6.

Figure 6. DGA Test Results of Two Test Transformers

3.4 Moisture Test

An increase in the moisture content causes reduction in the insulating properties of the transformer oil [18, 19]. It may result in dielectric breakdown. Many transformers contain cellulose-based insulating paper in the windings. Excessive moisture content in the transformers results breakdown of the paper insulation. Ultimately, it results in the loss of the insulation performance. Figure 7 shows the variation of moisture content in the two test transformers during 2015-2016.

Figure 7. Moisture Test Results of Two Transformers

Based on the above test results of two transformers, the remnant life of the insulation as per the various properties is determined using simple regression analysis. These are given in Table 2.

Table 2. Remnant Life to Reach Failure Level

A multi-regression analysis has been used to find the combined effect of moisture and oil temperature on transformer properties. It gives the expected life based upon particular oil temperature and moisture level. R value fitted to unity to make the strong strength of correlation between the variables.

From Table 3, it has been noticed that the effect of load and ambient temperatures within limited ranges is almost constant. These ambient conditions do not have higher impact on the insulating properties of the two considered test case transformers. The reason is that the test case transformers operate at half load and an average ambient temperature of 500^o C. Thus the impact is negligible. Further, the effect of moisture on BDV, TDCG, and DP is determined. The obtained relations are shown in Table 4. Also the remaining life of transformer insulation at different moisture levels has been determined, and given in Table 5.

Table 3. Remnant Life Based on Ambient Conditions to Reach Failure Level

Table 4. Effect of Moisture Content on Various Dielectric Properties

Table 5. Remaining Life of Transformers based on Different Moisture Levels, to Reach Failure Level

It has been found from Table 5 that the effect of moisture content is high on dielectric strength of transformer insulation as compared to their DP and TDCG. Finally, it has been found from the analysis that the effect of moisture content is very high on all insulating properties of transformer as compared to that of load and ambient temperature. At the end it is suggested from the analysis that the transformers should operate without moisture content to improve its remaining health. It results a huge revenue save for the utilities as well as customers.

This paper analyzed the effect of load, moisture and ambient temperatures on various properties of solid and liquid insulations. Load data as well as oil and winding temperatures data have been collected from its substation. Test samples of two transformers have been collected every month and various diagnosis tests were conducted, including BDV, moisture, degree of polymerization, DGA, and furan analysis tests. Further, correlation analysis has been done between various dependent and independent variables by using linear regression analysis as well as multi-regression analysis with a string strength of correlation factor. From multiregression analysis, the combined effect of existing moisture level on its BDV and other properties has been evaluated. Furthermore, the remaining life of insulation at any oil temperature and moisture content has been estimated using MRA. Proposed methodology is very accurate and can be easily implemented even by an inexperienced person to compute the condition of the transformer. Subsequently, appropriate remedial actions to improve the health of the transformer can be initiated.

The authors would like to thank the authorities of TEQIP–II of NIT Hamirpur, India for providing financial support with grant number NIT/HMR/TEQIP–II/Research & Develpoment –19/2015/2157–63. They are also thankful to the Himachal Pradesh State Electricity Board (HPSEB)–India for providing the transformer oil samples, and the authorities of TIFAC–CORE Centre of NIT Hamirpur India for providing the necessary facilities to perform the experiments of the present research.