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Novel modeling for the prediction of aged transformer oil characteristics
Electric Power Systems Research 51 (1999) 61 – 70
Novel modeling for the prediction of aged transformer oil characteristics Mohamed A.A. Wahab a,*, M.M. Hamada a, A.G. Zeitoun b, G. Ismail a a b
Faculty of Engineering, Electrical Engineering Department, Minia Uni6ersity, Minia, Egypt Faculty of Engineering, Electrical Engineering Department, Cairo Uni6ersity, Cairo, Egypt Received 5 August 1998; accepted 27 October 1998
Abstract The effect of aging on transformer oil physical, chemical and electrical properties has been studied using the international testing methods for the evaluation of transformer oil quality. The study has been carried out on twelve transformers in the field and for monitoring periods up to 8 years. The properties which are strongly time dependent have been specified and those which have a great impact on the transformer oil breakdown voltage have been defined. Mathematical models for the breakdown voltage, total acidity and water content as a function of service periods have been given. The validity and applicability of these models for future prediction of these properties have been verified by the good agreement between the measured end predicted values. A multiple linear regression model for each transformer oil breakdown voltage as a function of its water content, total acidity and service period has been introduced and its adequacy has been illustrated by statistical analysis. Another multiple linear regression model has been developed by combining the results of a group of transformers into that of a single equivalent transformer. This model has been validated by predicting the properties of some other transformers and comparing them with the measured values. The comparison showed a good agreement for the results of transformers which have either been used or not in the derivation of the model. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Aged transformer oil characteristics; Multiple linear regression model; Statistical analysis
1. Introduction Oil insulation has proved to be very effective in HV power apparatus for several decades. However, oil suffers continuous deterioration and degradation due to the sustained application of the electric and cyclic thermal stresses because of loading and climatic conditions. The deterioration of oil characteristics under working conditions may be hazardous to the electric equipment and installation. Continuous monitoring of oil insulation would be effective from the view point of preventing its deterioration, judgment of its quality and the reliability of the electric supply. Therefore the monitoring of insulation characteristics has become an important task [1]. Accumulated experience has led to the development of diagnostic processes for oil insulated apparatus. Diagnostic processes may be real time methods which include partial discharge measurement [2–4] * Corresponding author.
or delayed time methods such as chemical analysis of oil [5]. The diagnosis of degradation of oil insulation characteristics may help to prevent deterioration hazards. Modeling of monitoring results is of growing importance. These models may be used as a feedback for the evolution of monitoring and diagnostic systems. For example the continuous modifications of the IEEE model of transformer top oil temperature rise over ambient temperature in order to achieve accurate prediction is still in progress [6,7]. Artificial neural network simulation has been applied to existing diagnostic systems which depend on the chemical composition of gases evolved on transformer oil [8]. The simultaneous monitoring of different phenomena such as partial discharge and unsolved gases for the judgment of transformer insulation has also been carried out [9]. Artificial (accelerated) aging has also been studied in order to evaluate its effect on different properties of transformer oil mixtures [10]. However, monitoring and modeling of the effects of actual aging on the physical,
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chemical and electrical characteristics on continuously stressed transformer oils have scarcely been reported. The purpose of this study is to derive mathematical models for aging effects on the characteristics of transformer oil based on delayed-time monitoring of its physical, chemical and electrical properties. The main concern is to predict their change with service period. An individual model for each property has been deduced and a model for the breakdown voltage as a function of its water content, total acidity and service period has been derived for each transformer oil. A general model for the transformer oil breakdown voltage as a function of the previously mentioned properties has also been given by combining the results of the monitored transformer oils into that of a single equivalent transformer. The results showed good agreement between the predicted and measured values. The contribution of this study can be summarized in the following points: 1. Depending on the results of measurements of the physical, chemical and electrical properties for several large power transformers in the field for long periods of time (up to 8 years) the properties affecting the breakdown voltage have been revealed. 2. Models for these properties as a function of service period have been deduced and the adequacy of the models has been verified. 3. Two models for the breakdown voltage either as a function of service period or as function of the total acidity, water content and service period have been introduced. The latter can be used for management of transformer maintenance and economy of oil supply. 4. These models are adaptable which means that their parameters can be tuned to each transformer and also the model parameters can be improved with accumulation of the measurement results which achieves the best fit of the intermediate results and good prediction for short term. 5. The deduced models have been implemented for the prediction of transformer oil properties as a function of service period and prediction of breakdown voltage as a function of total acidity, water content and service period of transformer oil. Deviation of the measurements from the model would indicate the probability of a major disturbance in the transformer.
main criteria for the judgment of the transformer oil insulation quality. The tests include the determination of transformer oil breakdown voltage, total acidity, water content, viscosity, ash content and flash point. Periodical testing has been carried out for long period of time (about 8 years) and twelve large power transformers have been tested in the field. Monitoring of transformer oil properties had started after replenishing with fresh (new) oil or after purification of the ‘currently in use’ transformer oil.
2.1. Transformer oils The transformer oils are given the designations Tr. 1, Tr. 2…up to Tr. 12. Transformer oils from Tr. 1 to Tr. 9 and Tr. 12 are used and purified oils, while Tr. 10 and Tr. 11 are fresh (new) oils. The transformer oils Tr. 11 and Tr. 12 have been used as test cases of the introduced models.
2.2. Breakdown 6oltage Determination of breakdown voltage of each transformer oil sample has been carried out according to the IEC 156 testing procedure [11]. The apparatus used to carry out the tests is PGOS-3 BAUR with automatic voltage rising up to 75 kV. A schematic diagram of the electric circuit of the system is given in Fig. 1(a). Fig. 1(b) gives the main configuration and dimensions of the test cell. In the IEC 156 test the breakdown events are repeated six times, then the average of the breakdown voltage values is obtained and given as the breakdown voltage test result in kV. The rate of voltage rising is 2 kV/s and the electrodes have spherical shape of 13 mm diameter. The spacing is adjusted to be 2.5 mm. Testing starts with 3 min stand time and breakdown events are separated by intermediate stir time and stand time of 1 min each.
2.3. Total acidity Total acidity determination is a chemical neutralization process. The total acidity for a given oil sample has been determined according to the procedure given in IP 139/64 [12]. The total acidity is given as (mg KOH/g of oil).
2.4. Flash point 2. Experimentation The main feature of this study is the use of the internationally adopted testing procedures for the acceptance of transformer oils. These tests are specified by the International Electrotechnical Commission (IEC) and similar bodies and they are considered to be the
Flash point of the transformer oil sample has been determined by Pensky Martin open cup method [12]. It is the minimum temperature at which transformer oil will flash. Low values of flash point will cause the oil to flash inside the transformer by sparks due to tap changing etc.
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2.5. Water content
3. Experimental results and discussion
The apparatus used for the determination of water content is automatic Karl Fischer Titration. The water content is given as particle per million (ppm) in the transformer oil. The testing procedure has been carried out according to IP 356/78 standards [13].
As mentioned previously the experiments which are described in Section 2 have been carried out on each transformer oil periodically. Table 1 shows the results of transformer oil Tr. 10. The values in this table represent a sample of the results obtained for each transformer oil with differences in the intervals of monitoring periods. The results of transformer oils Tr. 11 and Tr. 12 will be used for testing the introduced models as will be explained in Section 4.
2.6. Ash content In the determination of ash content, any ash forming materials are considered to be undesirable impurities or contaminants. The procedure used to evaluate the ash content of an oil sample is given in [14].
2.7. Transformer oil 6iscosity Transformer oil viscosity affects the cooling efficiency of the transformer and hence its temperature rise which in turn affects the oil oxidation and acidity. The heat generated inside the transformer oil accelerates the chemical processes occurring inside it [15]. The testing procedure is given in [16].
3.1. Transformer oil breakdown 6oltage Transformer oil breakdown voltages as a function of their service periods are given in Fig. 2. The first point of each transformer oil result represents the beginning of the monitoring period. From this figure it can be seen that the breakdown voltage of transformer oil starts with a high value and then decreases with the course of time. For the purified transformer oils the initial breakdown voltages are relatively high when
Fig. 1. (a) A schematic diagram of the apparatus used for the determination of transformer oil breakdown voltage, (b) the configuration and main dimensions of the test cell.
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Table 1 The physical, chemical and electrical properties of transformer oil Tr. 10 Time (months)
BDV (kV)
Water content (ppm)
Total acidity (mg KOH/g oil)
Flash point (°C)
Ash content
Viscosity engler
0 12 24 36 48 60 72 78 84
52 54 48 46 42 36 36 34 32
19 21 26 28 32 42 39 40 42
0.001 0.001 0.001 0.030 0.048 0.060 0.080 0.090 0.096
154 154 154 154 154 154 154 154 154
Nil Nil Nil Nil Nil Nil Nil Nil Nil
1.59 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6
compared with that of the fresh (new) transformer oil. This may be due to purification. However, for all cases the breakdown voltages are still higher than the acceptable value specified by the IEC standards (between 30 and 50 kV) [11]. As found in literature, experiments confirmed that filtration and careful drying of the insulating liquid both could increase the breakdown voltage [17]. Abundant experimental evidence [18 – 20] showed that the dielectric strength of transformer oil with uniform fields drops sharply with a slight increase of moisture content, after which the dielectric strength becomes insensitive to any further increase in the moisture [21].The initial rates by which the breakdown voltages of purified transformer oils decrease are higher than that of fresh (new) oil. This may be due to the fact that a high initial breakdown voltage resulted from the large number of purification cycles which makes the transformer oil dry. In fact the presence of moisture has a drastic effect on the breakdown voltage of meticulously dried liquids [22]. The service periods after which the breakdown voltages of the considered transformer oils violate the IEC acceptable level are given in Table 2. The indicated service periods are the periods at which the first violation of the standard acceptable value of the property occurs. Two asterisks (**) indicates that violation has occurred before and has been recorded at this value, and three asterisks (***) means that violation hasn’t been recorded until this point. From Table 2 it can be seen that there is no correlation between the initial value of the breakdown voltage and the service period taken to violate the IEC acceptable level. This means that there are some other properties which are also time-dependent and may have great influence on the behavior of transformer oil breakdown voltage with the service period. These properties will have a great impact on the proposed models for the breakdown voltage. As the initial water content of most of the transformer oils is low this indicates that purification makes the transformer oils meticulously dry and this increases their water absorption from the atmosphere. The rate at which the breakdown voltages decrease between 50 and 30 kV is approximately the
same for all transformer oils. This may be due to the fact that the water contents in the transformer oils have reached the values after which the breakdown voltages become insensitive to further increase in water content. Further decrease in the breakdown voltage with low rate of increase of water content and high rate of increase of total acidity as shown at the end of monitoring periods in Figs. 3 and 4, respectively, may be due to the increase in transformer oil temperature and the probability of gas formation due to water evaporation, as will be discussed in the following subsections.
3.2. Water content Transformer oil is hygroscopic and tends to absorb water from the atmosphere. Minute quantities of moisture are always present in insulating (transformer) oil of commercial purity [21]. Water is generated in the transformer oil by absorption from the atmosphere or by oxidation. The initial values of water content in the transformer oils and the time to violate the IEC limits are given in Table 2. The IEC limits the water content in the transformer oil to between 15–30 ppm [23]. As indicated for the transformer oil breakdown voltages there is no correlation between the initial water content and the time to violate the IEC limits. This may indicate that water content interacts with (or depends
Fig. 2. Transformer oil breakdown voltages as functions of service periods.
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Table 2 Time to violate IEC standard limits for the transformer oil breakdown voltage, water content and total acidity Property
Breakdown voltage
Water content
Transformer
Initial BDV (kV) Time to violate IEC (months)
Initial water content (ppm)
Time to violate IEC (months)
Initial total acidity (mg KOH/g oil)
Time to violate IEC (months)
Tr.1 (Pur.*) Tr. 2 (Pur.) Tr.3 (Pur.) Tr. 4 (Pur.) Tr. 5 (Pur.) Tr. 6 (Pur.) Tr. 7 (Pur.) Tr. 8 (Pur.) Tr. 9 (Pur.) Tr.10 (new)
74 70 75 80 78 71 73 72 63 52
8 10 8 11 16 16 17 27 30 19
**13 **12 **5 **15 **12 **8 **27 **5 **5 **48
0.006 0.01 0.128 0.016 0.064 0.008 0.014 0.096 0.03 0.001
**7 **36 0 **15 0 **44 **34 0 0 **48
**19 **48 ***44 **33 **45 **53 ***46 **53 ***55 ***84
Total acidity
* : Purified. ** : Violation occurred before this period. *** : Violation not recorded.
on) other properties. Fresh (new) transformer oil Tr. 10 has the longest service period to violate the IEC limits in spite of its relatively high water content when compared with that of other transformer oils. The results of water content for the transformer oils as a function of service periods are given in Fig. 3. The figure shows that water content increases in the transformer oil with the increase in service period. The initial rate of water increase is high then it decreases after the water content reaches a certain value. As mentioned previously water appears in the transformer oil as a result of the oxidation process. Some of the oxidation products do inhibit the reaction which thus stabilizes with time [22] and hence limits the water formation in transformer oil. This may explain the decrease in the rate of increase of water content after its initial high value. Transformer oil-bases affect their tendency to absorb water from the atmosphere. Transformer oils with nephthenic base tend to absorb a higher amount of water than those with paraffinic base. For each transformer oil, this may produce a different initial rate of increase of water content. The slight decrease in water content at the end of the monitoring period may be due to the increase in the total acidity which increases the transformer oil temperature and the evaporation of water from the transformer oil. Also the high increase of transformer oil temperature may decompose the oil and generate gases [8]. This may indicate that there is some interdependence or mutual interaction between water content and total acidity.
present originally in the crude transformer oil and not be completely eliminated during distillation [22]. Table 2 shows that the initial total acidity of new transformer oil is the lowest among all the considered transformer oils. Therefore it has the largest time to violate the standard acceptable level which specifies the total acidity to be less than 0.03 mg KOH/g oil [23]. The most important observation is that the rate of increase of water content in transformer oil decreases when the rate of increase of total acidity is high. This can be seen clearly at the end of monitoring periods. This may be due to evaporation of water from transformer oil by the rise in its temperature which increases the concentration of acids. Total acidity increases the temperature of transformer oil. In general, the service period after which the total acidity violates the standard specification limits depends on the initial values of the total acidity. However, for the first two transformer oils a noticeable difference is obtained between the initial total acidity, for transformer oils Tr. 1 (0.006 mg KOH/g oil, B 7 months) and Tr. 2 (0.01 mg KOH/g
3.3. Total acidity Fig. 4 shows the dependence of the total acidity of the transformer oils on service periods. In fact acids could result from the refining processes or they could be
Fig. 3. Dependence of transformer oil water content on the service periods.
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cantly over the considered monitoring periods. This indicates that the flash point has little or approximately negligible dependence on the service periods of the transformer oils and hence its effect on transformer oil aging can be neglected for the practical service periods of the transformer oils. Therefore this property will be excluded from the proposed model.
3.5. Viscosity
Fig. 4. Transformer oil total acidity as function of service periods.
oil, B 36 months) and the periods to violate the standard acceptable level. This may be due to the effect of purification cycles on the concentration and balance of additives such as oxidation inhibitors and hence their effect on the thermal stability of transformer oil. The purification cycles of transformer oil Tr. 1 and Tr. 2 are 50 and 40 cycles, respectively. As indicated in the literature the course of the aging process may be different for various types of oil. Addition of inhibitor may play a decisive role [24]. Also the rate of dissipation of oxidation inhibitors affects the aging of transformer oils.
3.4. Flash point From IEC specifications the minimum value of flash point should not be less than 145°C [23]. Table 3 shows the measured values of the flash points. This table indicates that the flash point does not change signifi-
Table 3 shows the variation of transformer oil viscosity’s for different periods of time. This table indicates that the changes in transformer oil viscosity are negligibly small and it can be excluded from the modeling of the transformer oil breakdown voltage as a function of its physical properties.
3.6. Ash content Table 3 shows that ash content has not been formed in the transformer oil for relatively large observation periods. Therefore the exclusion of ash content from the model of breakdown voltage is justified and will not introduce error in the model.
3.7. Transformer oil properties considered in the models From the previous subsections it has been found that transformer oil breakdown voltage, total acidity and water content are functions of the service period while ash content, viscosity and flash points are approximately constant for different and long service periods. The discussion of the results indicated that transformer
Table 3 The variation of the transformer oil ash content, viscosity and flash point with service period Transformer oils
Ash content
Viscosity
Flash point (°C)
Tr. 1
Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months)
43
1.6 (up to 43 months)
150 (up to 43 months)
48
1.55(up to 48 months)
155 (up to 48 months)
41
1.7 (for 6 months, then 1.72 for 41 months)
148 (up to 41 months)
39
1.59 (for 15 months, then 1.6 up to 39 months)
144 (up to 39 months)
48
1.6 (up to 48 months)
155 (up to 48 months)
56
1.72 (for 44 months, then 1.7 up to 56 months)
150 (up to 56 months)
46 53
1.6 (for 39 months, then 1.7 for 6 months and 1.65 for 46 months) 1.55 (up to 53 months)
149 (for 39 months then 150 up to 46 months) 150 (up to 53 months)
55
1.6 (up to 55 months)
152 (up to 55 months)
84
1.59 (for 12 months, 1.5 for 12 months, then 1.6 up to 84 months)
154 (up to 84 months)
Tr. 2 Tr. 3 Tr. 4 Tr. 5 Tr. 6 Tr. 7 Tr. 8 Tr. 9 Tr. 10
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Table 4 Sample of breakdown voltage, water content and total acidity of transformer oils as functions of service period Transformer oils
Prop.*
A0
A1
A2
Pred.**
Exp.***
% Error
Tr.7
BDV W.C. T.A.
53.8572 17.7673 −0.004777
−0.2116 0.3659 0.000579
−0.0007 −0.0008 0.0000081
30.1479 43.55 0.10660
30 44 0.1
0.5 1.04 6.2
Tr.8
BDV W.C. T.A.
64.6567 30.3308 00.0976
−0.8861 −0.073 −0.00114448
0.0047 0.0138 0.000046
29.74 69.52 0.1777
28 65 0.16
5.85 6.50 9.9
Tr.12
BDV W.C. T.A.
62.688 22.7055 0.0337499
−0.7809 −0.1167 −0.0002222
0.0065 0.0073 0.0000283
39.29 43.0 0.13219
36 45 0.12
8.4 4.0 9.2
* Property. ** Predicted. *** Experimental.
oil breakdown voltage is strongly dependent on its total acidity, water content and service period. Also there is a mutual dependence and interaction between total acidity and water content. Therefore it can be concluded that a model for the breakdown voltage that incorporates total acidity, water content and service period will be comprehensive and this represents a justified conclusion from this study.
4. Modeling technique In this section modeling of the results has been carried out as follows: 1. Modeling of the service period dependent properties namely breakdown voltage, total acidity and water content as a function of the service period. 2. Modeling of the breakdown voltage of each transformer oil as a function of its total acidity, water content and service period. 3. Combining the results of breakdown voltage, water content, total acidity and service period for all the monitored transformer oils into that of a single equivalent transformer and modeling of these results as indicated in item (ii). This will be called the general model. The model parameters can be modified by the consecutive measurement results of the studied transformer oils. Also the general model will be used to predict the properties of other transformer oils whose measurement results have either been considered or not, in the derivation of the model. Applying different modeling techniques and the measurement results to model transformer oil breakdown voltage, total acidity and water content as a function of service period concluded that the polynomial regression should be applied. For modeling the breakdown voltage as a function of its water content, total acidity and service period, a multiple linear regression model
should be used. The least squares technique is implemented for the derivation of these models [25–27]. The least squares estimation technique is usually reliable and is unlikely to be the source of significant error [6].
4.1. Modeling of transformer oil breakdown 6oltage, total acidity and water content as function of ser6ice period The results of each transformer oil which are shown in Figs. 2 and 3, and Fig. 4 are modeled using the least squares technique [25–27]. The general model for transformer oil breakdown voltage, water content or total acidity as a function of its service period has the following form: Y(x)=A0 + A1x+ A2x 2 + A3x 3 + ...
+ Anx n
(1)
where: Y(x) is the dependent variable (i.e. breakdown voltage, total acidity or water content) A0, A1, A2, A3,... and An are the model constants which are required to be determined, and x is the service period. The method for computing the constants A0, A1, A2, A3,... and An is given in [25–27]. A sample of modeling results of transformer oils Tr. 8, Tr. 10 and Tr. 12 are given in Table 4. In this table the constants (A0, A1, and A2) for the model for each transformer oil property are given. The models are used to predict these properties, using their corresponding constants, after a service period of three months of the last measurements given in Figs. 2–4 to be compared with measurement results which are obtained at that time. The breakdown voltage predicted by Eq. (1) will be given the designation Pred. (1). The absolute percentage errors between the measured and predicted values are also given in the table. Some of the results showed good agreement between the measured and predicted values while others showed some deviations. From the view point of modeling these differences can be reduced by different methods [25] among them is the increase of measurement
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‘R 2’ has been computed by the following equation [25,26]:
data which can be accomplished by reducing the service period between consecutive measurements and it can easily be carried out. However, from the experimental results it has been found that the deviation occurs when there is an abrupt change of the property with time which may indicate a certain disturbance in the transformer itself.
n
(3) where Yexp. is the experimental values of Y, Ymodel is the computed value of Y, Yav. is the average value of Y, and Y is the property which is required to be modeled (in this case the breakdown voltage.) The value ‘R 2’, for a model implies that ‘R 2’% of the sample variation is attributable to, or explained by one or more of the variables. Thus ‘R 2’ tells how well the model fits the data and thereby represents a measure of the adequacy of the overall model. Another test is the ‘F’ test. The values of ‘F’ are computed according to the following equation [25,26]:
4.2. Modeling of transformer oil breakdown 6oltage as a function of its water content, total acidity and ser6ice period From the previous section it has been concluded that the breakdown voltage of a transformer oil is mainly dependent on its water content, total acidity and service period. Therefore the authors proposed that the breakdown voltage of a transformer oil can be modeled by a multiple linear regression model [25 – 27] having the following form: F(x1, x2, x3)=B0 +B1x1 +B2x2 +B3x3
,
R 2 = 1− % (Yexp. − Ymodel)2 % (Yexp. − Yav.)2
F=
(2)
(R 2/k) ((1−R )/[n − (k+ 1)])
(4)
2
where n is the number of data points, k is the number of parameters (coefficients of the variable) of the model, and R 2 is computed by Eq. (3). The values of ‘F’ are computed and compared with the critical values of the ‘F’ distribution fa.(y1, y2) [25,26]. Where y1 and y2 are the degrees of freedom in the numerator (k) and denominator (n− k−1), respectively, and a is the level of significance. When the value of ‘F’ is greater than fa (y1, y2) this indicates that the multiple linear regression model is useful to predict the breakdown voltage of the transformer oils. The measured and predicted values for the breakdown voltages are also included in Table 5. The prediction of the breakdown voltage has been carried out by two differ-
where: F(x1, x2, x3) is the transformer oil breakdown voltage (kV), x1, is the transformer oil water content (ppm), x2 is the transformer oil total acidity (mg KOH/ g oil), x3 is the transformer oil service period (months), and B0, B1, B2 and B3 are the model constants.The constants B0, B1, B2 and B3 are determined by the least squares technique [25 – 27]. The model constants for some of the transformer oils are given in Table 5. The modeling method has been carried out for different numbers of measurements, and samples of the constants for each number of points used in the models are indicated in the table. To assess the utility of the hypothesized model the coefficient of determination
Table 5 Sample of the results obtained for model constants, ‘F’ test, and values of measured and predicted values for breakdown voltages Prop.
B0 B1 B2 B3 R2 F f0.05 (y1, y2) BDV* pred. (1) BDV** pred. (2) BDV*** pred. (3) Exp.****
Transformer oils Transformer oil Tr. 2 7 points 6 points
Transformer oil Tr. 3 7 points 6 points
Transformer oil Tr. 4 7 Points 6 points
Transformer oil Tr. 5 7 points 6 points
76.0886 −0.7453 145.126 −0.5065 0.9974 383.62 9.28 30.6245 26.6311
97.591 −0.8181 −135.69 0.3423 0.96322 26.1887 9.28 34.3236 30.2332
79.6419 −0.6538 −39.485 −0.2725 0.8899 8.0826 9.28 28.2725 24.73
80.4663 −0.6227 −88.577 −0.2364 0.88509 5.13513 19.16 28.6322 26.9922
69.4156 −0.8403 308.009 −0.5802 0.97496 38.9393 9.28 28.8046 29.7329
40.655 −0.5594 709.480 −1.2239 0.98981 64.757 19.16 28.528 30.6177
75.8226 −0.7324 152.693 −0.5295 0.997554 271.8872 19.16 29.72 31.2578
194.638 0.1298 −951.91 0.5722 0.9705 21.932 19.16 33.1611 33.7376
30.5510
30.
35.1149
33.5763
27.642
26.5387
28.444
32.3488
26
31.5
31
32
28
28
27
28
* Pred. (1), Eq. (1): Y(x) = A0+A1x+A2x2. ** Pred. (2), Eq. (2), F(x1, x2, x3)= B0+B1x1+B2x2+B3x3; where, x1, x2 and x3 are measured values. *** Pred. (3), Eq. (2), F(x1, x2, x3)= B0+B1x1+B2x2+B3x3; where, x1, x2 and x3 are predicted values. **** Experimental value.
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Table 6 Results of testing of the general model for the transformer oil breakdown voltage Transformer oil
Service period (x3) (months)
Water content (ppm)
Total acidity (mg KOH/g Breakdown voltage oil) (measured)
Breakdown voltage (predicted)
Tr. 11
0 24 60 72 96 108 120
16 20 28 29 32 40 51
0.03 0.032 0.04 0.048 0.06 0.064 0.08
64 57 48 46 39 36 36
67.0238 60.2073 48.5039 45.8992 39.9065 31.9825 21.873
Tr. 12
0 11 23 35
18 20 23 31
0.06 0.06 0.064 0.08
63 59 56 48
65.7161 62.5949 58.3155 50.4733
ent methods. The first one depends on the substitution of the measured values of the water content, total acidity at the desired service period in the multiple linear regression model. These predicted values will be given the designation Pred. (2). In the second method the values of total acidity and water content are predicted first from their individual models as a function of service period, Eq. (1) using their corresponding constants, and then these values are substituted in the breakdown voltage multiple linear regression model. The predicted values in this case have been given the designation Pred. (3). Table 5 shows some of the predicted and measured values of the transformer oil breakdown voltages. Predicted values of the individual transformer oil model as function of its service period agree with those obtained from the measurements. Also the substitution of the predicted values of water content, total acidity and service period of a given transformer in its multiple linear regression model gives values approximately the same as those of the individual model and the experimental results. From Table 5 it can seen that the predicted and measured values are in good agreement. This may support the conclusion inferred from the previous section which considered the breakdown voltage as a function of the total acidity, water content and service period. Also the table justifies the applicability and validity of the proposed model.
The model constants C1, C2and C3 are obtained by combining the results of measurements (breakdown voltages, total acidity and service period) of the transformers from Tr. 1 to Tr. 10 and by manipulating them as those of an equivalent transformer. Table 6 shows the measured total acidity, water content and breakdown voltage as functions of service periods of the transformer oils Tr. 11 and Tr. 12 which are fresh (new) and used (purified) oils, respectively. The results from these transformer oils are not used in the derivation of the model. From this table it can be seen that there is a good agreement between the measured and predicted values which justifies the applicability and validity of the proposed model. Table 7 shows the breakdown voltage for different transformer oils whose measurement results are used for the derivation of the model. The table shows the service period and the breakdown voltage which is measured at this time as the first and second values (between brackets), respectively. In general there is a good agreement between the measured and predicted values. There is a difference between the predicted and measured values for some transformer oils against the service period. By inspecting the behavior of these transformer oils it has been found that there is an abrupt increase in the total acidity or water content
4.3. General model for the breakdown 6oltage as a function of water content, total acidity and ser6ice period
Table 7 Sample of the experimental and the general model predicted results Tr. 2
(x3, Exp. BDV) Pred. BDV
(0, 70) 71.42
(45, 32) 31.07
(48, 26) 26.14
The model is obtained by combining the results of measurements of the transformers into that of a single equivalent transformer. The model has the following mathematical form:
Tr. 4
(x3, Exp. BDV) Pred. BDV
(27, 34) 36.62
(39, 28) 28.24
(42, 26) 27.1
Tr. 5
(x3, Exp. BVD) Pred. BDV
(24, 41) 38.61
(45, 28) 27.92
(51, 28) 26.4
Fg (x1, x2, x3)=C0 + C1x1 +C2x2 +C3x3
Tr. 8
(x3, Exp. BDV) Pred. BDV
(5, 52) 52.32
(35, 41) 43.94
(53, 28) 24
Tr. 10
(x3, Exp. BDV) Pred. BDV
(60, 36) 38.06
(78, 34) 36.92
(87, 30) 32.53
(5)
where Fg is the breakdown voltage (kV), x1, x2, and x3 are those defined in Eq. (2), and C1, C2 and C3 are constants computed by the least squares technique.
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between two successive points during the course of measurements. This deviation continues for some time until the property takes a smooth course of variation with time. This abrupt increase indicates a certain disturbance in the transformer. This depicts another applicability of the model which gives an indication of the occurrence of a disturbance in the transformer under service conditions. This model can be valuable to electric power companies whose transmission and distribution networks are spread over large areas with different climatic and loading conditions by depending on the measurements for samples of the transformers in each location and deducing a general model for their transformer oil properties.
[3]
[4]
[5]
[6]
[7]
5. Conclusions Experimental studies and modeling of the effects of aging on the transformer oil properties have been carried out by monitoring large number of transformers in the field by internationally adopted testing methods and for long periods of time, up to 8 years. The following conclusions are inferred: 1. The transformer oil breakdown voltage, water content and total acidity are continuously deteriorating with extended service periods while the values of flash point, viscosity and ash content are approximately constant. 2. Mathematical models for the transformer oil breakdown voltage, total acidity and water content as a function of service period have been introduced, their adequacy has been proved and their applicability for the prediction of these properties has been justified. 3. A mathematical model for the breakdown voltage of transformer oil as a function of its water content, total acidity and service period has been given. The application of this model for the prediction of the breakdown voltage using the measured and predicted values of its water content and total acidity at a given service period illustrated its validity. 4. A general model for the transformer oil breakdown voltage as a function of its water content, total acidity and service period has been deduced by using the testing results of a group of transformers as those of an equivalent transformer. Predicting the breakdown voltage for transformer oils whose measured properties either have been used or not in the derivation of the model proved the model to be accurate.
[8]
[9]
[10]
[11]
[12] [13] [14] [15]
[16] [17]
[18] [19]
[20] [21]
[22] [23]
References [1] R. Malewski, K. Feser, A. Claudi, E. Gulski, Digital techniques for quality control and in-service monitoring of high voltage apparatus, CIGRE, International Conference on Large High Voltage Electric Systems, Paris, paper 15/21/33-03, 1996. [2] A. Zielonka, E. Gulski, Application of digital measuring techniques for the diagnosis of high voltage generator insulation,
[24] [25] [26] [27]
CIGRE, International Conference on Large High Voltage Electric Systems, Paris, paper 15/12/33-06, 1996. D. Wenzel, H. Borsi, E. Gockenback, Pulse shaped noise reduction end partial discharge localization on transformer using the Karhunen – Loeve-Transform, 9th International Symposium on HV Engineering, Graz, August 1995, paper 5627. K.B. Cho, H. Park, H.W. Ryou, T.S. Kim, Survey and evaluation of neuro-fuzzy-logic theory to partial discharge pattern classification, International Conference on Large High Voltage Electric Systems, Paris, paper 15/33-18, 1996. T. Kawamura et al., Technique of diagnosis for electrical facilities, Institute of Electrical, Electronic Engineers of Japan IEEJ, OUMU Company 1989, pp. 188 – 204. B.C. Lesieutre, W.H. Hagmn, J.L. Kirtley, An improved transformer top oil temperature model for use in an on-line monitoring and diagnostic system, IEEE Trans. Power Deliv. PWRD 12 (1) (1997) 249 – 256. J.L. Kirtley, W.H. Hagman, B.C. Lesieutre, M.J. Boyd, E.P. Warren, H.P. Chou, R.D. Tabors, Model-based monitoring of transformers, IEEE Computer Application in Power, Vol. 9, 1996. O. Vanges, Y. Mizuno, K. Naito, T. Kamiya, Oil diagnosis of oil insulated power apparatus by using neural network simulation, IEEE Trans. Dielectrics Electr. Insul. 4 (3) (1997) 290 –299. H. Borsi, Methods for the sensitive judgment of the insulation of the fluid insulated transformers during operation, 9th International Symposium on HV Engineering, Graz, August 1995, paper 1026. M. Elshazly-Zaghloul, B.A. Badawy, A. El-Melegy, Aging effects in transformer oil mixtures, Annual Report of the IEEE CEIPD, Pennsylvania, PA, USA, 1990, pp. 660 – 666. IEC Publication No. 156, Method for the determination of the electrical strength of insulating oils, International Electrotechnical Commission, Geneva, 1963. ASTM Designation D974, Standard method of test for acidity of petroleum products, IP 139/64, 1964. IP 356/87, Standard methods for analysis and testing of petroleum end related products, Wiley, 1990. International Chemical Series, 1965. I.A. Metwally, Y.A. Abed, Static electrification phenomena in large forced oil cooled power transformers, 9th International Symposium on HV Engineering, Graz, August 1995, paper 1020. ASTM Designation D 445-65, Standard method of test for viscosity of transparent and opaque liquids, Adopted 1960. T.M.A. Sufian, W.G. Chadband, The evolution of our understanding of electrical conduction and breakdown in liquid insulants, 4th Middle East power systems conference, MEPCON-96, pp. 156– 165. A.A. Zaky, R. Hawley, Conduction and Breakdown in Mineral Oil, Peregrins, London, 1973. J.K. Nelson, B. Salvage, W.A. Sharply, Electric strength of transformer oil for large electrode areas, Proc. IEE (London) 118 (1971) 388 – 393. D.A. Kaplan, G.C. Kutchinski, Influence of humidity on the electric strength of transformer, 35, 1964, pp. 30 – 33. A. Nossier, S. El-Debeiky, I.F. Hashad, H.A. Bary, Effect of temperature on the breakdown probability of liquid dielectrics, IEEE Trans. Electr. Insul. 15 (6) (1980) 502 – 505. M.M. Khalifa, High Voltage Engineering Theory and Practice, Marcel Dekker, New York, 1990. IEC publication No. 296, Specification for new insulating oils for transformer and switchgear, 1982. J. Kedzia, Electrostatic properties of aged transformer oil, IEEE Trans. Electr. Insul. 24 (2) (1989) 175 – 178. R.E. Walpole, R.H. Myers, Probability and Statistics for Engineers and Scientists, 2, Macmillan, New York, 1978. W. Mendenhall, T. Sincich, Statistics for Engineering and Science, Dellen, 1992. S.C. Wheelwright, S. Makridakis, Forecasting Methods for Management, Wiley, New York, 1985.
Novel modeling for the prediction of aged transformer oil characteristics Mohamed A.A. Wahab a,*, M.M. Hamada a, A.G. Zeitoun b, G. Ismail a a b
Faculty of Engineering, Electrical Engineering Department, Minia Uni6ersity, Minia, Egypt Faculty of Engineering, Electrical Engineering Department, Cairo Uni6ersity, Cairo, Egypt Received 5 August 1998; accepted 27 October 1998
Abstract The effect of aging on transformer oil physical, chemical and electrical properties has been studied using the international testing methods for the evaluation of transformer oil quality. The study has been carried out on twelve transformers in the field and for monitoring periods up to 8 years. The properties which are strongly time dependent have been specified and those which have a great impact on the transformer oil breakdown voltage have been defined. Mathematical models for the breakdown voltage, total acidity and water content as a function of service periods have been given. The validity and applicability of these models for future prediction of these properties have been verified by the good agreement between the measured end predicted values. A multiple linear regression model for each transformer oil breakdown voltage as a function of its water content, total acidity and service period has been introduced and its adequacy has been illustrated by statistical analysis. Another multiple linear regression model has been developed by combining the results of a group of transformers into that of a single equivalent transformer. This model has been validated by predicting the properties of some other transformers and comparing them with the measured values. The comparison showed a good agreement for the results of transformers which have either been used or not in the derivation of the model. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Aged transformer oil characteristics; Multiple linear regression model; Statistical analysis
1. Introduction Oil insulation has proved to be very effective in HV power apparatus for several decades. However, oil suffers continuous deterioration and degradation due to the sustained application of the electric and cyclic thermal stresses because of loading and climatic conditions. The deterioration of oil characteristics under working conditions may be hazardous to the electric equipment and installation. Continuous monitoring of oil insulation would be effective from the view point of preventing its deterioration, judgment of its quality and the reliability of the electric supply. Therefore the monitoring of insulation characteristics has become an important task [1]. Accumulated experience has led to the development of diagnostic processes for oil insulated apparatus. Diagnostic processes may be real time methods which include partial discharge measurement [2–4] * Corresponding author.
or delayed time methods such as chemical analysis of oil [5]. The diagnosis of degradation of oil insulation characteristics may help to prevent deterioration hazards. Modeling of monitoring results is of growing importance. These models may be used as a feedback for the evolution of monitoring and diagnostic systems. For example the continuous modifications of the IEEE model of transformer top oil temperature rise over ambient temperature in order to achieve accurate prediction is still in progress [6,7]. Artificial neural network simulation has been applied to existing diagnostic systems which depend on the chemical composition of gases evolved on transformer oil [8]. The simultaneous monitoring of different phenomena such as partial discharge and unsolved gases for the judgment of transformer insulation has also been carried out [9]. Artificial (accelerated) aging has also been studied in order to evaluate its effect on different properties of transformer oil mixtures [10]. However, monitoring and modeling of the effects of actual aging on the physical,
0378-7796/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 8 - 7 7 9 6 ( 9 8 ) 0 0 1 5 6 - 4
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chemical and electrical characteristics on continuously stressed transformer oils have scarcely been reported. The purpose of this study is to derive mathematical models for aging effects on the characteristics of transformer oil based on delayed-time monitoring of its physical, chemical and electrical properties. The main concern is to predict their change with service period. An individual model for each property has been deduced and a model for the breakdown voltage as a function of its water content, total acidity and service period has been derived for each transformer oil. A general model for the transformer oil breakdown voltage as a function of the previously mentioned properties has also been given by combining the results of the monitored transformer oils into that of a single equivalent transformer. The results showed good agreement between the predicted and measured values. The contribution of this study can be summarized in the following points: 1. Depending on the results of measurements of the physical, chemical and electrical properties for several large power transformers in the field for long periods of time (up to 8 years) the properties affecting the breakdown voltage have been revealed. 2. Models for these properties as a function of service period have been deduced and the adequacy of the models has been verified. 3. Two models for the breakdown voltage either as a function of service period or as function of the total acidity, water content and service period have been introduced. The latter can be used for management of transformer maintenance and economy of oil supply. 4. These models are adaptable which means that their parameters can be tuned to each transformer and also the model parameters can be improved with accumulation of the measurement results which achieves the best fit of the intermediate results and good prediction for short term. 5. The deduced models have been implemented for the prediction of transformer oil properties as a function of service period and prediction of breakdown voltage as a function of total acidity, water content and service period of transformer oil. Deviation of the measurements from the model would indicate the probability of a major disturbance in the transformer.
main criteria for the judgment of the transformer oil insulation quality. The tests include the determination of transformer oil breakdown voltage, total acidity, water content, viscosity, ash content and flash point. Periodical testing has been carried out for long period of time (about 8 years) and twelve large power transformers have been tested in the field. Monitoring of transformer oil properties had started after replenishing with fresh (new) oil or after purification of the ‘currently in use’ transformer oil.
2.1. Transformer oils The transformer oils are given the designations Tr. 1, Tr. 2…up to Tr. 12. Transformer oils from Tr. 1 to Tr. 9 and Tr. 12 are used and purified oils, while Tr. 10 and Tr. 11 are fresh (new) oils. The transformer oils Tr. 11 and Tr. 12 have been used as test cases of the introduced models.
2.2. Breakdown 6oltage Determination of breakdown voltage of each transformer oil sample has been carried out according to the IEC 156 testing procedure [11]. The apparatus used to carry out the tests is PGOS-3 BAUR with automatic voltage rising up to 75 kV. A schematic diagram of the electric circuit of the system is given in Fig. 1(a). Fig. 1(b) gives the main configuration and dimensions of the test cell. In the IEC 156 test the breakdown events are repeated six times, then the average of the breakdown voltage values is obtained and given as the breakdown voltage test result in kV. The rate of voltage rising is 2 kV/s and the electrodes have spherical shape of 13 mm diameter. The spacing is adjusted to be 2.5 mm. Testing starts with 3 min stand time and breakdown events are separated by intermediate stir time and stand time of 1 min each.
2.3. Total acidity Total acidity determination is a chemical neutralization process. The total acidity for a given oil sample has been determined according to the procedure given in IP 139/64 [12]. The total acidity is given as (mg KOH/g of oil).
2.4. Flash point 2. Experimentation The main feature of this study is the use of the internationally adopted testing procedures for the acceptance of transformer oils. These tests are specified by the International Electrotechnical Commission (IEC) and similar bodies and they are considered to be the
Flash point of the transformer oil sample has been determined by Pensky Martin open cup method [12]. It is the minimum temperature at which transformer oil will flash. Low values of flash point will cause the oil to flash inside the transformer by sparks due to tap changing etc.
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2.5. Water content
3. Experimental results and discussion
The apparatus used for the determination of water content is automatic Karl Fischer Titration. The water content is given as particle per million (ppm) in the transformer oil. The testing procedure has been carried out according to IP 356/78 standards [13].
As mentioned previously the experiments which are described in Section 2 have been carried out on each transformer oil periodically. Table 1 shows the results of transformer oil Tr. 10. The values in this table represent a sample of the results obtained for each transformer oil with differences in the intervals of monitoring periods. The results of transformer oils Tr. 11 and Tr. 12 will be used for testing the introduced models as will be explained in Section 4.
2.6. Ash content In the determination of ash content, any ash forming materials are considered to be undesirable impurities or contaminants. The procedure used to evaluate the ash content of an oil sample is given in [14].
2.7. Transformer oil 6iscosity Transformer oil viscosity affects the cooling efficiency of the transformer and hence its temperature rise which in turn affects the oil oxidation and acidity. The heat generated inside the transformer oil accelerates the chemical processes occurring inside it [15]. The testing procedure is given in [16].
3.1. Transformer oil breakdown 6oltage Transformer oil breakdown voltages as a function of their service periods are given in Fig. 2. The first point of each transformer oil result represents the beginning of the monitoring period. From this figure it can be seen that the breakdown voltage of transformer oil starts with a high value and then decreases with the course of time. For the purified transformer oils the initial breakdown voltages are relatively high when
Fig. 1. (a) A schematic diagram of the apparatus used for the determination of transformer oil breakdown voltage, (b) the configuration and main dimensions of the test cell.
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Table 1 The physical, chemical and electrical properties of transformer oil Tr. 10 Time (months)
BDV (kV)
Water content (ppm)
Total acidity (mg KOH/g oil)
Flash point (°C)
Ash content
Viscosity engler
0 12 24 36 48 60 72 78 84
52 54 48 46 42 36 36 34 32
19 21 26 28 32 42 39 40 42
0.001 0.001 0.001 0.030 0.048 0.060 0.080 0.090 0.096
154 154 154 154 154 154 154 154 154
Nil Nil Nil Nil Nil Nil Nil Nil Nil
1.59 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6
compared with that of the fresh (new) transformer oil. This may be due to purification. However, for all cases the breakdown voltages are still higher than the acceptable value specified by the IEC standards (between 30 and 50 kV) [11]. As found in literature, experiments confirmed that filtration and careful drying of the insulating liquid both could increase the breakdown voltage [17]. Abundant experimental evidence [18 – 20] showed that the dielectric strength of transformer oil with uniform fields drops sharply with a slight increase of moisture content, after which the dielectric strength becomes insensitive to any further increase in the moisture [21].The initial rates by which the breakdown voltages of purified transformer oils decrease are higher than that of fresh (new) oil. This may be due to the fact that a high initial breakdown voltage resulted from the large number of purification cycles which makes the transformer oil dry. In fact the presence of moisture has a drastic effect on the breakdown voltage of meticulously dried liquids [22]. The service periods after which the breakdown voltages of the considered transformer oils violate the IEC acceptable level are given in Table 2. The indicated service periods are the periods at which the first violation of the standard acceptable value of the property occurs. Two asterisks (**) indicates that violation has occurred before and has been recorded at this value, and three asterisks (***) means that violation hasn’t been recorded until this point. From Table 2 it can be seen that there is no correlation between the initial value of the breakdown voltage and the service period taken to violate the IEC acceptable level. This means that there are some other properties which are also time-dependent and may have great influence on the behavior of transformer oil breakdown voltage with the service period. These properties will have a great impact on the proposed models for the breakdown voltage. As the initial water content of most of the transformer oils is low this indicates that purification makes the transformer oils meticulously dry and this increases their water absorption from the atmosphere. The rate at which the breakdown voltages decrease between 50 and 30 kV is approximately the
same for all transformer oils. This may be due to the fact that the water contents in the transformer oils have reached the values after which the breakdown voltages become insensitive to further increase in water content. Further decrease in the breakdown voltage with low rate of increase of water content and high rate of increase of total acidity as shown at the end of monitoring periods in Figs. 3 and 4, respectively, may be due to the increase in transformer oil temperature and the probability of gas formation due to water evaporation, as will be discussed in the following subsections.
3.2. Water content Transformer oil is hygroscopic and tends to absorb water from the atmosphere. Minute quantities of moisture are always present in insulating (transformer) oil of commercial purity [21]. Water is generated in the transformer oil by absorption from the atmosphere or by oxidation. The initial values of water content in the transformer oils and the time to violate the IEC limits are given in Table 2. The IEC limits the water content in the transformer oil to between 15–30 ppm [23]. As indicated for the transformer oil breakdown voltages there is no correlation between the initial water content and the time to violate the IEC limits. This may indicate that water content interacts with (or depends
Fig. 2. Transformer oil breakdown voltages as functions of service periods.
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Table 2 Time to violate IEC standard limits for the transformer oil breakdown voltage, water content and total acidity Property
Breakdown voltage
Water content
Transformer
Initial BDV (kV) Time to violate IEC (months)
Initial water content (ppm)
Time to violate IEC (months)
Initial total acidity (mg KOH/g oil)
Time to violate IEC (months)
Tr.1 (Pur.*) Tr. 2 (Pur.) Tr.3 (Pur.) Tr. 4 (Pur.) Tr. 5 (Pur.) Tr. 6 (Pur.) Tr. 7 (Pur.) Tr. 8 (Pur.) Tr. 9 (Pur.) Tr.10 (new)
74 70 75 80 78 71 73 72 63 52
8 10 8 11 16 16 17 27 30 19
**13 **12 **5 **15 **12 **8 **27 **5 **5 **48
0.006 0.01 0.128 0.016 0.064 0.008 0.014 0.096 0.03 0.001
**7 **36 0 **15 0 **44 **34 0 0 **48
**19 **48 ***44 **33 **45 **53 ***46 **53 ***55 ***84
Total acidity
* : Purified. ** : Violation occurred before this period. *** : Violation not recorded.
on) other properties. Fresh (new) transformer oil Tr. 10 has the longest service period to violate the IEC limits in spite of its relatively high water content when compared with that of other transformer oils. The results of water content for the transformer oils as a function of service periods are given in Fig. 3. The figure shows that water content increases in the transformer oil with the increase in service period. The initial rate of water increase is high then it decreases after the water content reaches a certain value. As mentioned previously water appears in the transformer oil as a result of the oxidation process. Some of the oxidation products do inhibit the reaction which thus stabilizes with time [22] and hence limits the water formation in transformer oil. This may explain the decrease in the rate of increase of water content after its initial high value. Transformer oil-bases affect their tendency to absorb water from the atmosphere. Transformer oils with nephthenic base tend to absorb a higher amount of water than those with paraffinic base. For each transformer oil, this may produce a different initial rate of increase of water content. The slight decrease in water content at the end of the monitoring period may be due to the increase in the total acidity which increases the transformer oil temperature and the evaporation of water from the transformer oil. Also the high increase of transformer oil temperature may decompose the oil and generate gases [8]. This may indicate that there is some interdependence or mutual interaction between water content and total acidity.
present originally in the crude transformer oil and not be completely eliminated during distillation [22]. Table 2 shows that the initial total acidity of new transformer oil is the lowest among all the considered transformer oils. Therefore it has the largest time to violate the standard acceptable level which specifies the total acidity to be less than 0.03 mg KOH/g oil [23]. The most important observation is that the rate of increase of water content in transformer oil decreases when the rate of increase of total acidity is high. This can be seen clearly at the end of monitoring periods. This may be due to evaporation of water from transformer oil by the rise in its temperature which increases the concentration of acids. Total acidity increases the temperature of transformer oil. In general, the service period after which the total acidity violates the standard specification limits depends on the initial values of the total acidity. However, for the first two transformer oils a noticeable difference is obtained between the initial total acidity, for transformer oils Tr. 1 (0.006 mg KOH/g oil, B 7 months) and Tr. 2 (0.01 mg KOH/g
3.3. Total acidity Fig. 4 shows the dependence of the total acidity of the transformer oils on service periods. In fact acids could result from the refining processes or they could be
Fig. 3. Dependence of transformer oil water content on the service periods.
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66
cantly over the considered monitoring periods. This indicates that the flash point has little or approximately negligible dependence on the service periods of the transformer oils and hence its effect on transformer oil aging can be neglected for the practical service periods of the transformer oils. Therefore this property will be excluded from the proposed model.
3.5. Viscosity
Fig. 4. Transformer oil total acidity as function of service periods.
oil, B 36 months) and the periods to violate the standard acceptable level. This may be due to the effect of purification cycles on the concentration and balance of additives such as oxidation inhibitors and hence their effect on the thermal stability of transformer oil. The purification cycles of transformer oil Tr. 1 and Tr. 2 are 50 and 40 cycles, respectively. As indicated in the literature the course of the aging process may be different for various types of oil. Addition of inhibitor may play a decisive role [24]. Also the rate of dissipation of oxidation inhibitors affects the aging of transformer oils.
3.4. Flash point From IEC specifications the minimum value of flash point should not be less than 145°C [23]. Table 3 shows the measured values of the flash points. This table indicates that the flash point does not change signifi-
Table 3 shows the variation of transformer oil viscosity’s for different periods of time. This table indicates that the changes in transformer oil viscosity are negligibly small and it can be excluded from the modeling of the transformer oil breakdown voltage as a function of its physical properties.
3.6. Ash content Table 3 shows that ash content has not been formed in the transformer oil for relatively large observation periods. Therefore the exclusion of ash content from the model of breakdown voltage is justified and will not introduce error in the model.
3.7. Transformer oil properties considered in the models From the previous subsections it has been found that transformer oil breakdown voltage, total acidity and water content are functions of the service period while ash content, viscosity and flash points are approximately constant for different and long service periods. The discussion of the results indicated that transformer
Table 3 The variation of the transformer oil ash content, viscosity and flash point with service period Transformer oils
Ash content
Viscosity
Flash point (°C)
Tr. 1
Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months) Nil (up to months)
43
1.6 (up to 43 months)
150 (up to 43 months)
48
1.55(up to 48 months)
155 (up to 48 months)
41
1.7 (for 6 months, then 1.72 for 41 months)
148 (up to 41 months)
39
1.59 (for 15 months, then 1.6 up to 39 months)
144 (up to 39 months)
48
1.6 (up to 48 months)
155 (up to 48 months)
56
1.72 (for 44 months, then 1.7 up to 56 months)
150 (up to 56 months)
46 53
1.6 (for 39 months, then 1.7 for 6 months and 1.65 for 46 months) 1.55 (up to 53 months)
149 (for 39 months then 150 up to 46 months) 150 (up to 53 months)
55
1.6 (up to 55 months)
152 (up to 55 months)
84
1.59 (for 12 months, 1.5 for 12 months, then 1.6 up to 84 months)
154 (up to 84 months)
Tr. 2 Tr. 3 Tr. 4 Tr. 5 Tr. 6 Tr. 7 Tr. 8 Tr. 9 Tr. 10
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Table 4 Sample of breakdown voltage, water content and total acidity of transformer oils as functions of service period Transformer oils
Prop.*
A0
A1
A2
Pred.**
Exp.***
% Error
Tr.7
BDV W.C. T.A.
53.8572 17.7673 −0.004777
−0.2116 0.3659 0.000579
−0.0007 −0.0008 0.0000081
30.1479 43.55 0.10660
30 44 0.1
0.5 1.04 6.2
Tr.8
BDV W.C. T.A.
64.6567 30.3308 00.0976
−0.8861 −0.073 −0.00114448
0.0047 0.0138 0.000046
29.74 69.52 0.1777
28 65 0.16
5.85 6.50 9.9
Tr.12
BDV W.C. T.A.
62.688 22.7055 0.0337499
−0.7809 −0.1167 −0.0002222
0.0065 0.0073 0.0000283
39.29 43.0 0.13219
36 45 0.12
8.4 4.0 9.2
* Property. ** Predicted. *** Experimental.
oil breakdown voltage is strongly dependent on its total acidity, water content and service period. Also there is a mutual dependence and interaction between total acidity and water content. Therefore it can be concluded that a model for the breakdown voltage that incorporates total acidity, water content and service period will be comprehensive and this represents a justified conclusion from this study.
4. Modeling technique In this section modeling of the results has been carried out as follows: 1. Modeling of the service period dependent properties namely breakdown voltage, total acidity and water content as a function of the service period. 2. Modeling of the breakdown voltage of each transformer oil as a function of its total acidity, water content and service period. 3. Combining the results of breakdown voltage, water content, total acidity and service period for all the monitored transformer oils into that of a single equivalent transformer and modeling of these results as indicated in item (ii). This will be called the general model. The model parameters can be modified by the consecutive measurement results of the studied transformer oils. Also the general model will be used to predict the properties of other transformer oils whose measurement results have either been considered or not, in the derivation of the model. Applying different modeling techniques and the measurement results to model transformer oil breakdown voltage, total acidity and water content as a function of service period concluded that the polynomial regression should be applied. For modeling the breakdown voltage as a function of its water content, total acidity and service period, a multiple linear regression model
should be used. The least squares technique is implemented for the derivation of these models [25–27]. The least squares estimation technique is usually reliable and is unlikely to be the source of significant error [6].
4.1. Modeling of transformer oil breakdown 6oltage, total acidity and water content as function of ser6ice period The results of each transformer oil which are shown in Figs. 2 and 3, and Fig. 4 are modeled using the least squares technique [25–27]. The general model for transformer oil breakdown voltage, water content or total acidity as a function of its service period has the following form: Y(x)=A0 + A1x+ A2x 2 + A3x 3 + ...
+ Anx n
(1)
where: Y(x) is the dependent variable (i.e. breakdown voltage, total acidity or water content) A0, A1, A2, A3,... and An are the model constants which are required to be determined, and x is the service period. The method for computing the constants A0, A1, A2, A3,... and An is given in [25–27]. A sample of modeling results of transformer oils Tr. 8, Tr. 10 and Tr. 12 are given in Table 4. In this table the constants (A0, A1, and A2) for the model for each transformer oil property are given. The models are used to predict these properties, using their corresponding constants, after a service period of three months of the last measurements given in Figs. 2–4 to be compared with measurement results which are obtained at that time. The breakdown voltage predicted by Eq. (1) will be given the designation Pred. (1). The absolute percentage errors between the measured and predicted values are also given in the table. Some of the results showed good agreement between the measured and predicted values while others showed some deviations. From the view point of modeling these differences can be reduced by different methods [25] among them is the increase of measurement
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‘R 2’ has been computed by the following equation [25,26]:
data which can be accomplished by reducing the service period between consecutive measurements and it can easily be carried out. However, from the experimental results it has been found that the deviation occurs when there is an abrupt change of the property with time which may indicate a certain disturbance in the transformer itself.
n
(3) where Yexp. is the experimental values of Y, Ymodel is the computed value of Y, Yav. is the average value of Y, and Y is the property which is required to be modeled (in this case the breakdown voltage.) The value ‘R 2’, for a model implies that ‘R 2’% of the sample variation is attributable to, or explained by one or more of the variables. Thus ‘R 2’ tells how well the model fits the data and thereby represents a measure of the adequacy of the overall model. Another test is the ‘F’ test. The values of ‘F’ are computed according to the following equation [25,26]:
4.2. Modeling of transformer oil breakdown 6oltage as a function of its water content, total acidity and ser6ice period From the previous section it has been concluded that the breakdown voltage of a transformer oil is mainly dependent on its water content, total acidity and service period. Therefore the authors proposed that the breakdown voltage of a transformer oil can be modeled by a multiple linear regression model [25 – 27] having the following form: F(x1, x2, x3)=B0 +B1x1 +B2x2 +B3x3
,
R 2 = 1− % (Yexp. − Ymodel)2 % (Yexp. − Yav.)2
F=
(2)
(R 2/k) ((1−R )/[n − (k+ 1)])
(4)
2
where n is the number of data points, k is the number of parameters (coefficients of the variable) of the model, and R 2 is computed by Eq. (3). The values of ‘F’ are computed and compared with the critical values of the ‘F’ distribution fa.(y1, y2) [25,26]. Where y1 and y2 are the degrees of freedom in the numerator (k) and denominator (n− k−1), respectively, and a is the level of significance. When the value of ‘F’ is greater than fa (y1, y2) this indicates that the multiple linear regression model is useful to predict the breakdown voltage of the transformer oils. The measured and predicted values for the breakdown voltages are also included in Table 5. The prediction of the breakdown voltage has been carried out by two differ-
where: F(x1, x2, x3) is the transformer oil breakdown voltage (kV), x1, is the transformer oil water content (ppm), x2 is the transformer oil total acidity (mg KOH/ g oil), x3 is the transformer oil service period (months), and B0, B1, B2 and B3 are the model constants.The constants B0, B1, B2 and B3 are determined by the least squares technique [25 – 27]. The model constants for some of the transformer oils are given in Table 5. The modeling method has been carried out for different numbers of measurements, and samples of the constants for each number of points used in the models are indicated in the table. To assess the utility of the hypothesized model the coefficient of determination
Table 5 Sample of the results obtained for model constants, ‘F’ test, and values of measured and predicted values for breakdown voltages Prop.
B0 B1 B2 B3 R2 F f0.05 (y1, y2) BDV* pred. (1) BDV** pred. (2) BDV*** pred. (3) Exp.****
Transformer oils Transformer oil Tr. 2 7 points 6 points
Transformer oil Tr. 3 7 points 6 points
Transformer oil Tr. 4 7 Points 6 points
Transformer oil Tr. 5 7 points 6 points
76.0886 −0.7453 145.126 −0.5065 0.9974 383.62 9.28 30.6245 26.6311
97.591 −0.8181 −135.69 0.3423 0.96322 26.1887 9.28 34.3236 30.2332
79.6419 −0.6538 −39.485 −0.2725 0.8899 8.0826 9.28 28.2725 24.73
80.4663 −0.6227 −88.577 −0.2364 0.88509 5.13513 19.16 28.6322 26.9922
69.4156 −0.8403 308.009 −0.5802 0.97496 38.9393 9.28 28.8046 29.7329
40.655 −0.5594 709.480 −1.2239 0.98981 64.757 19.16 28.528 30.6177
75.8226 −0.7324 152.693 −0.5295 0.997554 271.8872 19.16 29.72 31.2578
194.638 0.1298 −951.91 0.5722 0.9705 21.932 19.16 33.1611 33.7376
30.5510
30.
35.1149
33.5763
27.642
26.5387
28.444
32.3488
26
31.5
31
32
28
28
27
28
* Pred. (1), Eq. (1): Y(x) = A0+A1x+A2x2. ** Pred. (2), Eq. (2), F(x1, x2, x3)= B0+B1x1+B2x2+B3x3; where, x1, x2 and x3 are measured values. *** Pred. (3), Eq. (2), F(x1, x2, x3)= B0+B1x1+B2x2+B3x3; where, x1, x2 and x3 are predicted values. **** Experimental value.
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Table 6 Results of testing of the general model for the transformer oil breakdown voltage Transformer oil
Service period (x3) (months)
Water content (ppm)
Total acidity (mg KOH/g Breakdown voltage oil) (measured)
Breakdown voltage (predicted)
Tr. 11
0 24 60 72 96 108 120
16 20 28 29 32 40 51
0.03 0.032 0.04 0.048 0.06 0.064 0.08
64 57 48 46 39 36 36
67.0238 60.2073 48.5039 45.8992 39.9065 31.9825 21.873
Tr. 12
0 11 23 35
18 20 23 31
0.06 0.06 0.064 0.08
63 59 56 48
65.7161 62.5949 58.3155 50.4733
ent methods. The first one depends on the substitution of the measured values of the water content, total acidity at the desired service period in the multiple linear regression model. These predicted values will be given the designation Pred. (2). In the second method the values of total acidity and water content are predicted first from their individual models as a function of service period, Eq. (1) using their corresponding constants, and then these values are substituted in the breakdown voltage multiple linear regression model. The predicted values in this case have been given the designation Pred. (3). Table 5 shows some of the predicted and measured values of the transformer oil breakdown voltages. Predicted values of the individual transformer oil model as function of its service period agree with those obtained from the measurements. Also the substitution of the predicted values of water content, total acidity and service period of a given transformer in its multiple linear regression model gives values approximately the same as those of the individual model and the experimental results. From Table 5 it can seen that the predicted and measured values are in good agreement. This may support the conclusion inferred from the previous section which considered the breakdown voltage as a function of the total acidity, water content and service period. Also the table justifies the applicability and validity of the proposed model.
The model constants C1, C2and C3 are obtained by combining the results of measurements (breakdown voltages, total acidity and service period) of the transformers from Tr. 1 to Tr. 10 and by manipulating them as those of an equivalent transformer. Table 6 shows the measured total acidity, water content and breakdown voltage as functions of service periods of the transformer oils Tr. 11 and Tr. 12 which are fresh (new) and used (purified) oils, respectively. The results from these transformer oils are not used in the derivation of the model. From this table it can be seen that there is a good agreement between the measured and predicted values which justifies the applicability and validity of the proposed model. Table 7 shows the breakdown voltage for different transformer oils whose measurement results are used for the derivation of the model. The table shows the service period and the breakdown voltage which is measured at this time as the first and second values (between brackets), respectively. In general there is a good agreement between the measured and predicted values. There is a difference between the predicted and measured values for some transformer oils against the service period. By inspecting the behavior of these transformer oils it has been found that there is an abrupt increase in the total acidity or water content
4.3. General model for the breakdown 6oltage as a function of water content, total acidity and ser6ice period
Table 7 Sample of the experimental and the general model predicted results Tr. 2
(x3, Exp. BDV) Pred. BDV
(0, 70) 71.42
(45, 32) 31.07
(48, 26) 26.14
The model is obtained by combining the results of measurements of the transformers into that of a single equivalent transformer. The model has the following mathematical form:
Tr. 4
(x3, Exp. BDV) Pred. BDV
(27, 34) 36.62
(39, 28) 28.24
(42, 26) 27.1
Tr. 5
(x3, Exp. BVD) Pred. BDV
(24, 41) 38.61
(45, 28) 27.92
(51, 28) 26.4
Fg (x1, x2, x3)=C0 + C1x1 +C2x2 +C3x3
Tr. 8
(x3, Exp. BDV) Pred. BDV
(5, 52) 52.32
(35, 41) 43.94
(53, 28) 24
Tr. 10
(x3, Exp. BDV) Pred. BDV
(60, 36) 38.06
(78, 34) 36.92
(87, 30) 32.53
(5)
where Fg is the breakdown voltage (kV), x1, x2, and x3 are those defined in Eq. (2), and C1, C2 and C3 are constants computed by the least squares technique.
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between two successive points during the course of measurements. This deviation continues for some time until the property takes a smooth course of variation with time. This abrupt increase indicates a certain disturbance in the transformer. This depicts another applicability of the model which gives an indication of the occurrence of a disturbance in the transformer under service conditions. This model can be valuable to electric power companies whose transmission and distribution networks are spread over large areas with different climatic and loading conditions by depending on the measurements for samples of the transformers in each location and deducing a general model for their transformer oil properties.
[3]
[4]
[5]
[6]
[7]
5. Conclusions Experimental studies and modeling of the effects of aging on the transformer oil properties have been carried out by monitoring large number of transformers in the field by internationally adopted testing methods and for long periods of time, up to 8 years. The following conclusions are inferred: 1. The transformer oil breakdown voltage, water content and total acidity are continuously deteriorating with extended service periods while the values of flash point, viscosity and ash content are approximately constant. 2. Mathematical models for the transformer oil breakdown voltage, total acidity and water content as a function of service period have been introduced, their adequacy has been proved and their applicability for the prediction of these properties has been justified. 3. A mathematical model for the breakdown voltage of transformer oil as a function of its water content, total acidity and service period has been given. The application of this model for the prediction of the breakdown voltage using the measured and predicted values of its water content and total acidity at a given service period illustrated its validity. 4. A general model for the transformer oil breakdown voltage as a function of its water content, total acidity and service period has been deduced by using the testing results of a group of transformers as those of an equivalent transformer. Predicting the breakdown voltage for transformer oils whose measured properties either have been used or not in the derivation of the model proved the model to be accurate.
[8]
[9]
[10]
[11]
[12] [13] [14] [15]
[16] [17]
[18] [19]
[20] [21]
[22] [23]
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