Lifetime extension of the high voltage asynchronous machine in relation to the voltage endurance test

The study aims to achieve a simple, reliable, and significant lifetime extension of the high-voltage asynchronous machine in relation to the voltage endurance test. To achieve this goal, the focus was on achieving longer-lasting and more stable insulation of the stator package of an asynchronous machine. Longer-lasting and more stable insulation of a stator is achieved by reinforcing the weak points on its prefabricated multiturn coils. These reinforcements were performed with standard insulating materials that are used for the production of the prefabricated multiturn coils (because there is no data regarding the long-term behavior of new materials that show some better properties in laboratories, but only during short-term tests). With such reinforced weak spots based on prefabricated models, they were made by the classical procedure with the use of standardized tools. To track the effects of the improvement of the insulation characteristics of a stator, an algorithm was developed based on the law of increasing probability and the determination of lifetime curves to the voltage endurance test. The lifetime curves were determined by the method of increasing voltage with the transformation of the obtained results to the corresponding results by the constant voltage method. The applied algorithm that was formed for this study, had been verified with statistical reliability of 95%. The combined measurement uncertainty of the measurement procedure was about 5%.


Introduction
The increased need for energy caused an increase in the voltage of the distribution network in urban areas to 20 kV. This led to the need for a transformer reduction of the power supply of asynchronous machines designed for a maximum voltage of 15 kV (which is not the case with synchronous machines that are designed for a maximum voltage of 24 kV) [1,2]. To reduce the costs of using asynchronous machines by connecting them directly to distribution networks, tests were carried out on the insulation of its stator. (it was found that 50% of failures of asynchronous machines are due to the breakdown of stator insulation) [3][4][5]. Since the stator of high-voltage machines is made of a multiturn coil, the stability of its insulation determines the condition of the stator insulation as a whole [6,7]. For this reason, a test of the interthread Lacquer-Glass-Glass-Lacquer (LGGL) insulation of the prefabricated multiturn coil was carried out (LGGL) [8,9].
The test results in the works showed that the LGGL interlayer insulation has the weakest points in the part of the multiturn coil, which are located outside the grooves of the stator of the electric machine. This is explained by the technological process of producing a multiturn coil. Bending occurs in the parts of the prefabricated multiturn coil that are outside the grooves of the stator (end-winding) of the electric machine during production. This multiple bending leads to cracking of the LGGL insulation and damage to the conductor, which is the cause of the weakening of the insulation in those areas. Tests on the influence of insulation stress due to temperature, oscillations, and humidity also show that the parts of the multiturn coil most susceptible to their influence are also the parts located outside the grooves of the stator [3,8]. These parts of the multiturn coil are the parts that age the fastest [7]. In related works, tests were carried out on the possibility of improving the insulation characteristics of the multiturn coil (and thus the insulation of the entire stator of the electric machine) by additionally insulating the ends of the multiturn coil. The obtained results showed that the additional insulation of the parts of the multiturn coil that is outside the grooves of the stator improves the insulating properties of the multiturn coil to a certain extent. Research has shown that temperature, oscillations, and humidity (in the same order of importance) contribute the most to the destruction of the multiturn coil [8]. It was also established that the destruction of the prefabricated multiturn coil occurs only after the insulation is broken/breached.
In the present study, the possibility of extending the life of the multiturn coil by changing the technological procedure of making the multiturn coil was considered. Experiments were conducted with 3 multiturn coil prototypes with improved characteristics. The prototypes were designed in the direction of reducing the intensity of the electric field in the interturn insulation, improving the insulation characteristics of the ends of the multiturn coil by reducing the temperature at the ends of the multiturn coil. The obtained results proved that with the changes made to the prototypes extend the operating life of the multiturn coil, and thus the insulation of the stator of the electric machine.

Industrial production of prefabricated multiturn coils
Prefabricated multiturn coils, as independent components of the stator, could have different shapes, while their fundamental characteristics and technological manufacturing process remain very similar. In the experimental part of this research, prefabricated multiturn coils have been used. The shape of the prefabricated multiturn coil is a very common type used in engineering practice. The properties of the prefabricated multiturn coil and changes during the exploitation concerning the voltage endurance test of an asynchronous machine predominantly depend on the technological process of their production and the applied materials. When considering the possibility of an extension of prefabricated multiturn coils' lifetime, it is necessary to consider improvements in the process of their production rather than using new materials as the long-term behavior of the new materials is insufficiently known. The first step of production consists of wrapping a thin copper conductor with lacquer-glass-glass-lacquer insulating tape (two folded strips wound at an angle of 45º). Thereafter, an ellipsoidal structure is formed from the insulating thin copper conductor. The main insulation is then applied to the flat part of the ellipsoidal shape that will be placed in the slots of the stator package. The main purpose of the main insulation that is placed on the slot area of the coil is to provide mechanical strength in contact with the stator package where electrodynamic forces and mechanical vibrations occur. An important feature of the main insulation is that it should be homogeneous, compact, and should not contain air bubbles. After applying the main insulation, the ellipsoidal contour is pressed and bent to give it a final shape, which consists of two coil slots area and two so-called multiturn coil end winding. Figure 1 shows the drawing and two photographs of the end-winding of the prefabricated multiturn coil (the end-winding of the prefabricated part of the high-voltage asynchronous machine has suffered double and single bending stresses).
The end-winding of the prefabricated multiturn coil is insulated with a tape that is either porous or impregnated with resin (mica tape is most often used). The multiturn coil end-winding must be compact, as in this way resistance to moisture and mechanical stresses are achieved. Thereafter, the obtained prefabricated multiturn coil is once again insulated and the final shape is formed (Fig. 2). In Fig. 2a, the Roman numerals I and II are used to indicate the parts that suffered bending stress, called the end-winding of the prefabricated multiturn coil while the numeral III indicates the parts called the slot area of the coil (III) that did not suffer the stress caused by bending, during the formation of the prefabricated  Figure 2b shows a photo of the commercial prefabricated multiturn coil that was used. In addition, during the exploitation of the end-winding coil, vibrations cause abrasion of the insulation and damage to the copper conductor. These two phenomena increase the occurrence of partial discharge and insulation breakdown [7].
To fill the air space between the prefabricated multiturn coil (i.e., the main insulation) and the slot of the stator sheet-metal package, an impregnating agent is used. The impregnating agent is, most frequently, an impregnating resin because it does not contain solvents like varnishes (lacquers) do. The end-winding of the prefabricated multiturn coil is also impregnated and subsequently baked with a complete multiturn coil for polymerization.

Experiment
Different types of stresses (thermal, mechanical, voltage, humidity) and the aging of the prefabricated multiturn coils of high voltage asynchronous machines caused by those stresses, are evenly distributed across the multiturn coils due to symmetry [8][9][10]. This means that the examination of one multiturn coil from the aspect of parameters that affect aging, according to the law of the probability of increase, corresponded to the aging of the stator's insulation system [11].
Excluding the effects of standard exploitation and ambient conditions, a parameter that affects the aging of the multiturn coils is a partial discharge. Ultimate voltage aging, i.e., the end of life of the multiturn coil, happens with its breakdown. On the other hand, the test of aging over breakdown voltage is economically unprofitable and can be completely replaced by the test of partial discharge threshold because there is a unique linear physical relationship between the two quantities, expressed by a quantity called the coefficient of proportionality [12].
The idea of the experimental procedure was to make certain (not significant) modifications to the observed weak insulation points of commercially prefabricated multiturn coils, thus extending their lifetime. In addition to commercial multiturn coils, all the components from which the multiturn coil is made were available for the experiments, as well as all the necessary devices for making the prefabricated multiturn coils. Based on such available components and devices, prefabricated multiturn coils of the same shape as the multiturn coils illustrated in Fig. 2 (100 pieces) were produced with certain changes which, based on previous tests, were expected to extend the lifetime of the prefabricated multiturn coils, as well as the lifetime of the high voltage asynchronous machine itself. The number of 100 samples (pieces) provides 100 (or slightly less as a consequence of the application of Chauvenet's criterion) random variables for all examined commercial prefabricated multiturn coils and all prototypes. This number is sufficient for concluding since according to the t-test, 50 random variables are sufficient for statistical analysis [13].
It should be emphasized that, after the changes in the process of making commercially prefabricated multiturn coils, the procedure for obtaining an improved prototype was continued with the standard procedure. It should also be mentioned that the changes made for the formation of prototypes 1, 2, and 3 were additive, i.e., prototype 2 also contained changes made to prototype 1, and prototype 3. Prototype 3 also contained changes made to prototypes 1 and 2. Thereby, not only identical technological procedures but also the same insulating and conductive materials were used. This is important to point out because the chemical industry offers new materials with better properties, according to the results of laboratory tests for this application. However, there is no experience in their long-term operation, for which high-voltage asynchronous machines are produced. In addition, the experiments were performed with standard materials and with standard procedures for the production of prefabricated multiturn coils. The reason for such a procedure is due to the lack of experience with the long-term behavior of the prefabricated multiturn coils made using new materials. This does not exclude the use of new materials in the future.
To measure the threshold of partial discharge and the breakdown voltage a Professional instrument manufacturer HIOKI represented in Fig. 3a was used, equipped with appropriate software for these measurements. According to the manufacturer's instructions, measurements were performed at frequencies of 0.1 and 50 Hz. The obtained results did not Fig. 3 shows photos of elements of the measuring system: a instrument B2HV diagnostic; b measurement chamber; c commercial prefabricated multiturn coil at partial discharge threshold voltage recorded with a HikVision thermal imaging camera, partial discharge threshold recording obtained with an oscilloscope; d partial discharge threshold recording obtained with an oscilloscope differ statistically (although it was expected that measurements at 50 Hz would lead to irreversible changes in the coil insulation during the measurements). The presented results refer to measurements obtained with a frequency of 50 Hz. The IEC 60,270 standard was used to measure the partial discharge threshold voltage and the breakdown voltage for the voltage endurance test. The prefabricated multiturn coil zone in which the potential discharge appeared was determined by recording (in a dark space) with a thermal camera HikVision, Fig. 3c. In parallel with recording with a thermal camera, a partial discharge occurred and was recorded with an oscilloscope. The results were matched 100%.
The measurements were performed under strictly controlled laboratory conditions so the aging of the tested samples was exclusive due to stress. During the measurement of the partial discharge and the breakdown voltage, the measuring instruments were placed in the 100 dB protection cabin, Fig. 3b. The cabin was galvanically separated from the rest of the measurement system. The combined measurement uncertainty of the procedure was less than 5%. Measurement uncertainty type A is determined based on the second central moment of the statistical sample of measured quantities. Measurement uncertainty type B was determined factory and/or laboratory for each instrument, and combined measurement uncertainty was determined according to the instructions [14,15].
First measurements were performed on two statistical samples of one hundred values of random variables partial discharge threshold voltage, and breakdown voltage for the commercially prefabricated multiturn coil. As will be seen, the lifetime of the stator insulation has been proven to be dominated by a statistical sample of a random variable partial discharge threshold voltage. At the same time, the most accurate lifetime curves were obtained by measuring the breakdown voltage and breakdown time by constant voltage experiments. Having all this in mind only random variables of partial discharge threshold voltage and the ordered pair (breakdown voltage, breakdown time) were measured.
The statistical samples of 100 random variables ordered pair (breakdown voltage, breakdown time) of the commercially prefabricated multiturn coil and the prototypes 1, 2, and 3 were experimentally determined. The measurements were performed with increasing voltage, and then the obtained results were transformed into the results that would be obtained by the measurement with constant voltage (under the same conditions). The results obtained in this way made it possible to determine cumulative probability curves on the Weibull paper and duration curves with arbitrarily determined probability quantiles. However, the first step regarding mostly experimentally determined statistical samples was their statistical analysis to determine the cumulative probability and the lifetime curves.
The experimentally obtained results were treated as follows: 1-The rejection of all the doubtful results using Chauvenet's criterion. 2-The results obtained for one statistical sample were tested for belonging to a single sample using the U-test. 3-Using the graphical test, χ 2 -test (Chi-Square test), and Kolmogorov test, the affiliation of random variables of each statistical sample to the Normal distribution, Weibull distribution, exponential distribution, and double exponential distribution was tested. The distribution that was determined as the most probable (i.e., had the least statistical uncertainty) determined the parameters by the moment's method and by the maximum likelihood method. It should be emphasized that the chosen test distributions (other than the Normal distribution) were the extreme value distributions and were chosen as such due to the nature of the quantity under the test. Namely, insulation damage resembles an extremely weak point and according to that logic, a random variable related to insulation weakening belongs to extreme random variables. This point is confirmed by the fact that all measured random variables belonged to the Weibull distribution (which is the basis for all the other extreme value distributions).
It should be emphasized that all the prototypes, together with the commercially prefabricated multiturn coil, were subjected to an additional experiment. Namely, the commercially prefabricated multiturn coil and all the prototypes were tested at the same time on the standard etalon oscillator table at a frequency of 100 Hz for 250 h. These tests made sense to determine whether, after the changes that were made during the prototype construction, there was increased sensitivity of the prefabricated multiturn coil at the frequency to which it is exposed during exploitation. The only noticeable effect of oscillations occurred in the case of prototype 3, in which there was a reduction in the occurrence of partial discharge in zone I compared to zones II and III (Fig. 2). In the case of prototypes 1 and 2, no changes in the effect of oscillations were observed compared to commercial types.
An experiment was also performed to record the position of the corona formation at a partial discharge threshold voltage. This experiment was performed with 100 commercially prefabricated multiturn coils and with 100 prototypes 1, 2, and 3 each. This experiment was performed in a darkened room individually on each of the 100 commercially prefabricated multiturn coils and prototypes. For each of these types of multiturn coils, the location of the first partial discharge was recorded with the Hik Vision instrument with the addition of a sensitive trigger system and a fast camera. In this way, it was possible to reliably determine in which of the zones I, II, or III (Fig. 2) of the prefabricated multiturn coil or prototype the breakdown is initialized by detecting the partial discharge threshold voltage. This realization was needed to interpret the observed effects related to the extension of the lifetime of the prototypes.

Results and discussion
The comparison of statistical samples of 100 random variables unambiguously indicated that the results of the experiment for determining the statistical sample of a random variable ordered pair (breakdown voltage, breakdown time), obtained by the constant voltage method, should be used to determine the lifetime curve. In this paper, however, the method of experimental determination of the statistical sample of a random variable ordered pair (breakdown voltage, breakdown time) was performed using the method of increasing voltage. This was done for a purely practical reason even though the constant voltage method is superior to this goal (the scientific reasons would be, theoretically speaking, absolutely satisfied if the measurement was performed by the constant voltage method, but such an experiment would last for decades and, worst of all, would not give the accurate results due to natural aging of measuring samples which would further lead to the synergy of the two mechanisms of aging). The same procedure was used for the measurement of the partial discharge threshold voltage. The difference in the obtained results was within the extended combined measurement uncertainty. Such a result is completely satisfying for engineering practice. Figure 4 illustrates a cross-section of the multiturn coil with an extracted part showing the conductor edges. In the extracted part, the electric field was calculated (and drawn) Fig. 4 Cross-section of the slot area of the coil with an extracted part along the edge of the conductor (in which the electric field between the two conductors is calculated using the electric charge simulation method and drawn according to the standard); 1-Conductor, 2-Lacquerglass-glass-lacquer insulation, 3-Main insulation (U be -the value of breakdown voltage LGGL insulation in the edge part of the field; U bh -the value of breakdown voltage LGGL insulation in the homogeneous part of the field; U bh > U be )

Fig. 5
Cumulative curve of the statistical sample of 100 random variables breakdown voltage for both commercially prefabricated multiturn coils and prototype 1 (from left to right) by the electric charge simulation method. Figure 4 shows that the sharp edges of the conductor are significantly increasing the value of the electric field in the insulator between the conductors, which can lead to an earlier and more intense occurrence of a partial discharge. For this reason, the edges of the conductors of the prototype are rounded.
The prototype of the prefabricated multiturn coil with rounded edges was completed by the standard procedure and named prototype 1. In the following procedure, the relevant features of prototype 1 were compared with the commercially prefabricated multiturn coil, from the aspect of aging. Figure 5 shows the cumulative curves of a statistical sample of 100 random variables breakdown voltage for a commercially prefabricated multiturn coil and a prototype with rounded edges, i.e., prototype 1, on the Weibull probability paper. The cumulative curve shown in Fig. 6, for both the commercially prefabricated multiturn coil and prototype 1, belongs to the complex probabilities of the additive type. Table 1 shows the results obtained by thermal imaging observation and by simultaneous measurement of the partial discharge threshold voltage of a commercially prefabricated multiturn coil.
The complex probability shown in Fig. 5 consists of two Weibull probabilities (or even three if cumulative lines are considered with extremely little statistical uncertainty). This result is easy to explain based on Table 1, which shows the zone of partial discharge threshold occurrence. A huge number of breakdown threshold occurrences take place at the end winding (zone I) of prototype 1 and this number differs by less than 10% compared to a commercially prefabricated  multiturn coil. Based on that, it can be concluded that the appearance of the partial discharge threshold originates in the multiturn coil end winding due to the damage to the inter conductor insulation that is caused by the technological manufacturing process, and not due to the sharp edges of the conductors. The sharp edges of the conductor affect the value of the partial discharge threshold voltage of the multiturn coil, but in all its zones equally (meaning zones I, II, and III). This interpretation is unambiguously confirmed by the results given in Table 1 which are obtained by locating the place of occurrence of the partial discharge threshold. The main result of this part of the experiment is that in Fig. 6 a significant increase (about 20%) of the breakdown voltage for prototype 1 is observed. This change leads to an extension of the 63% lifetime curve that is obtained by the measuring method with increasing voltage and later transformed (reduced) to the measuring method with constant voltage by about 17%, Fig. 7 (the 63% lifetime curve was determined by the method given in the appendix). Continuation of the improvement of prototype 1 of the prefabricated multiturn coil was the double insulation of the conductors with rounded edges using lacquer-glassglass-lacquer insulation (to reduce partial discharge), i.e. the formation of prototype 2. After the formation of the prefabricated multiturn coil 2, a new statistical sample of 100 random variables breakdown voltage was recorded. A similar level of increase was obtained when determining the statistical sample value of the partial discharge threshold for prototype 2 in comparison to prototype 1. Figure 6 shows the cumulative curves of the statistical samples of random variables breakdown voltage for the commercially prefabricated multiturn coil and prototype 1 and prototype 2 on the Weibull probability paper.
Based on this result, it can be concluded that the reinforcement of lacquer-glass-glass-lacquer insulation does not significantly contribute to the extension of the lifetime of the prefabricated multiturn coil. The extension of the lifetime of prototype 2 compared to prototype 1 was within the limits of the combined measurement uncertainty.
Since the end winding of the prefabricated multiturn coil suffers significant mechanical stresses due to oscillations (and in practice also significant ambient stresses), to extend its lifetime (from the aspect of failure caused by partial discharges and voltage breakdowns) special attention is paid to the insulation of the multiturn coil end-winding. This was especially interesting also because, during the technological process, the multiturn coil end-winding suffers from double and single bending stresses. On that occasion, the lacquer-glass-glass-lacquer insulation becomes thinner and may crack, as already mentioned. For this reason, prototype 3 was made for which additions and improvements to the insulation were aimed at insulating the multiturn coil endwinding.
First of all, in the phase of formation of the prefabricated multiturn coils in the future zones I and II (i.e. future endwindings), 6 conductors of the same shape and parallel to the Fig. 8 Modified multiturn coil end winding structure of prototype 3: a prototype drawing; b photos of prototype 3; c photos of prototype 3 in the construction phase main conductor were added (3 on each side of the main conductor). The thickness of the added conductors was 10% of the thickness of the main conductor. The added conductors were galvanic connected with the main conductor to the top of the future zone I and the end of future zone II. The galvanic connection of the added conductors was done by hard soldering. After hard soldering, the places of galvanic connections are polished to a high gloss. After the galvanic connection, the additional conductors are insulated with the double lacquerglass-glass-lacquer (the insulation of the same thickness as the main conductor where the insulation of the connection position of the main conductor and the additional conductors is especially strengthened). Further shaping and isolation of the prefabricated multiturn coils were completed as previously described. The installation of prototype 3 did not require any changes to the stator package. Figure 8 shows the end-winding of prototype 3 (a-prototype drawing, b-photos of prototype 3, c-photos of prototype 3 in the construction phase).
Thereafter, the five-fold conductor was pressed. Certainly, this operation was performed in zones I and II of the conductors and was not an easy task to perform in the given conditions. The technological process was continued in a standard way. After obtaining the final shape, the endwinding of prototype 3 is additionally insulated with a porous Fig. 9 Breakdown cumulative curve of the statistical sample of 100 random variables breakdown voltage for the commercially prefabricated multiturn coil and prototypes 1, prototype 2, and prototype 3 (from left to right) strip that is made of natural fibers and mica, impregnated with resin, and additionally exposed to high temperatures to achieve the polymerization of the resin. Subsequently, prototype 3 was finalized by the standard procedure. With prototype 3, 100 random variables' breakdown voltage were measured (by increasing voltage method transforming the results to those that would be obtained by the constant voltage method). Figure 9 illustrates the cumulative curves of the statistical sample of the random variable breakdown voltage for commercially prefabricated multiturn coil, prototype 1, prototype 2, and prototype 3 on the Weibull probability paper. Figure 9 shows that prototype 3 has a higher breakdown voltage value of about 35% compared to the commercially prefabricated multiturn coil. This result can be explained by the fact that the cumulative distribution of the random variable breakdown voltage is no longer a combined additive type. Namely, the finishing touches to the end-winding of the prototype approximately equalized the partial discharge threshold voltage (and thus the breakdown voltage) in zones I, II, and III, as shown in Table 2. At the same time, this equalized the value of the breakdown voltage along with the entire prototype and eliminated all the weak points of the insulation of the end-winding of prototype 3. This proves that the described constructive changes during the formation of prototype 3 achieved homogenization of the entire prefabricated multiturn coil insulation. The consequence of the homogenization of the insulation of prototype 3 is the extension of its service lifetime by 35% compared to the commercial prefabricated multiturn coil in relation to the voltage endurance test, which is inferred from Fig. 7. Figure 10 shows the 63% lifetime curve of the commercially prefabricated multiturn coil, prototype 1, prototype 2, and prototype 3.

Conclusion
By comparing the obtained values of the partial discharge threshold and the lifetime for commercially prefabricated multiturn coils and prototypes 1, 2, and 3, it can be concluded that prototype 3 is by far the best. Prototype 1 had a significant increase in the partial discharge threshold and the extension of the lifetime. Interestingly, the reinforcement of the inter conductor insulation does not give any noticeable improvements (prototype 2). It is shown that the reinforcement of the inter conductor insulation has no significant effect on the slot area of the prefabricated multiturn coil, unlike the effect in the zone of the end-winding of the prefabricated multiturn coil. Namely, it has been observed that increasing the number of lacquer-glass-glass-lacquer inter conductor layers does not contribute to improving the insulation characteristics of prefabricated stator multiturn coils of high-voltage asynchronous machines, and neither contributes to the extension of the lifetime. Accordingly, we can conclude that the technological process of double and single bending during the formation of the end-winding of the prefabricated multiturn coil creates approximately the same number of damages to the lacquer-glass-glass-lacquer insulation. Naturally, if the number of insulation layers was to increase significantly (20-30), there would certainly be a significant reduction in the partial discharge threshold voltage (which has been confirmed experimentally). However, at the same time, there would be a significant change in the dimensions of the highvoltage asynchronous machine, which could not be justified by the reduction of the partial discharge threshold voltage.
However, the change in the structure of the conduction system of the multiturn coil end winding and the introduction of additional (independent, inter conductor insulation) caused a significant extension of the lifetime of prototype 3. This can be explained by the damage that occurs during the formation of the multiturn coils. Such an explanation is confirmed by the fact that subsequent reinforcements of the multiturn coil end winding significantly reduce the partial discharge threshold voltage and prolongs the lifetime.
The synergistic effect of temperature, oscillations, and humidity (if there are no atypical stresses) is responsible for the destruction of the multiturn coil. The destruction of the multiturn coil occurs when a partial discharge and a breakthrough occur somewhere on the multiturn coil. After that, the delamination of the sandwich structure of the multiturn coil occurs due to the long-term effect of temperature, oscillations, and electrodynamic forces. Moisture and heated air penetrate the stratified layers of the prefabricated multiturn coil damaged in this way and lead to the splitting of the sandwich structure of the multiturn coil [8]. Based on this description of the synergy of the stress of the multiturn coil with temperature, oscillations, and moisture, it can be concluded that the initiation of the delamination of the multiturn coil comes with the appearance of a partial breakdown and a breakdown of the insulation. In this sense, it can be concluded that by delaying the occurrence of partial discharge and the breakdown of the multiturn coil insulation, its destruction is delayed. This means that prototype 3 would have a repeated effect on the long life of the multiturn coil even in conditions of increased temperature, amplitude of oscillations, and humidity.
The obtained results also show that the weakest zone of the prefabricated stator multiturn coil is its ends (end-winding), i.e., both multiturn coil end windings (in Fig. 2 marked by I and II). It happens because the technological process in these zones causes bending and damage to the insulation, and thus the electric field between the conductor stops being homogeneous. In addition, as the end windings of the prefabricated multiturn coil are outside the slots of the stator package, it is more exposed to mechanical and ambient stresses. The general conclusion would certainly be that by improving construction and by better insulation of the multiturn coil end windings, as performed on prototype 3 (or similar) of the stator prefabricated multiturn coils, it would be possible to increase the lifetime of high voltage asynchronous machines. It is important to emphasize that the changes made during the production of prototypes did not cause the slightest change in the aging mechanism of the obtained prototypes concerning the commercially prefabricated multiturn coil, which is concluded based on the linearity of the lifetime curves for commercially prefabricated multiturn coil and all tested prototypes.
The empirical distribution of the statistical distribution breakdown time (Fig. 11a) was obtained based on the updated analysis. It is emphasized and physically explained that the obtained random variables are best described by the Weibull distribution (the Weibull distribution fits the random variables obtained by the constant voltage experiment): The lifetime characteristic, which is another name for the breakdown voltage/breakdown time diagram, is constructed using arbitrarily selected quantiles of the specified distribution. Experience has shown that the diagram forms a line on a double exponential scale, Fig. 11b. In the case when confidence intervals are known for the given quintiles, they will be transferred to the lifetime characteristics. For each quantile p of the breakdown time, the lifetime characteristic is described as: u dp k dp t −1/r dp (2) where the k dp constant is determined by the geometry of the structure, while r is the exponent of the lifetime which depends exclusively on the insulating material. Deviation from the shape of the lifetime line indicates that the aging mechanism of the insulating material is changing.
By adopting the Weibull distribution, analogous to Eq. (1), and for the random variable breakdown voltage U d with a fixed breakdown time t d1 , it follows that for the same breakdown probability F(t d ; u d1 ) F(u d ; t d1 ) : Based on Eq. (2) (law of lifetime), assuming that the exponent r is identical for all quantiles, a relation is obtained for the same dependence and the value: Based on Eqs. (4a) and (4b), a relation is obtained between Weibull exponents for breakdown time δ t , breakdown voltage δ u , and lifetime exponent r: It should be emphasized that the given relationship is correct only if both variables U d and T d belong to the Weibull distribution, Fig. 1c, which has been repeatedly emphasized and physically explained. It should be emphasized that