# Life Prediction of Dry Reactor Sensor Based on Deep Neural Network

Authors: Hongbing Guo; Jianying Meng; Yue Yang; Lu Zheng; Xuan Liu; Ming Tan
Journal: Journal of Sensors
 (2022)

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## Abstract

In order to solve the problem of increasing the number and service life of a dry-type air core reactor and frequent interturn insulation faults, this paper proposes a life prediction method of a dry-type reactor sensor based on the deep neural network. On the basis of summarizing the research status of turn-to-turn insulation-related problems, this method studies the switching overvoltage generated in the process of breaking the dry-type air core reactor, the deterioration law of turn-to-turn insulation under the cumulative action of switching overvoltage, the influence of thermal aging on the Switching Overvoltage Withstand characteristics of turn-to-turn insulation, and the electrical aging life of turn-to-turn insulation under the power frequency overvoltage. Based on the deep neural network, the electrical aging life model of turn-to-turn insulation of the dry-type air core reactor under power frequency overvoltage is obtained. The results are as follows: with the increase of the applied voltage amplitude, the deterioration speed of the turn-to-turn insulation of the model sample accelerates. When the applied voltage amplitude reaches a certain value, the maximum discharge amount and pulse discharge power of the partial discharge pulse increase rapidly, and the image coincidence degree reaches 85%. The electric aging life curve of the modified interturn insulation model sample of the dry-type air core reactor has a high correlation with the measured aging life data, and the performance is more than 95%. The research results of this paper lay a practical foundation for further research on the deterioration mechanism of interturn insulation under the combined action of multiple factors and provide theoretical support for the risk and life assessment of the dry-type air core reactor.


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## Body

## 1. Introduction

As a basic industry related to the national economy and the people’s livelihood, the power industry is related to the overall situation of economic and social development. The economically developed load center is concentrated in the eastern coast, which is far away from the large-capacity hydropower units in the southwest and the large-capacity thermal power units in the north [1]. Objective conditions require the power system to have higher transmission efficiency and capacity, so as to realize economic, reasonable, safe, and reliable high-capacity and long-distance power transmission. Reactors are mainly divided into iron core reactors and dry-type air core reactors. Dry-type air core reactors have technical advantages such as unsaturated, high strength, light weight, low noise, and simple structure and are widely used in power systems (as shown in Figure 1). In the power system with a voltage level of 66 kV and below, the dry-type air core reactor accounts for more than 80%. By 2016, the market capacity of the dry-type air core reactor has reached 30 billion yuan. With the increase of the number of dry-type air core reactors put into operation and operation life, the failure rate also gradually increases [2, 3].Figure 1
A life prediction method and process of dry reactor sensor based on deep neural network.In the early fault analysis, the researchers believed that rain invasion caused the moisture on the outer surface of the encapsulated insulation of the dry-type air core reactor and surface discharge, resulting in uneven distribution of the electric field inside the insulation, partial discharge, continuous corrosion of insulation, and finally interturn insulation fault. According to the research results, relevant departments have taken a variety of preventive measures for outdoor dry-type air core reactors. The actual operation experience of the air core reactor shows that there are still frequent interturn insulation accidents. Studying the causes of the operating overvoltage of the dry-type air core reactor and the laws followed and the causes and development process of the interturn insulation fault under the conditions of operating overvoltage and power frequency overvoltage and understanding the failure mechanism of interturn insulation of the dry-type air core reactor can provide a theoretical basis for manufacturing enterprises to optimize the interturn insulation design of the dry-type air core reactor and improve the production process. It can also provide reference for the power operation department to improve the operation mode of the dry-type air core reactor, study various protective measures, and develop corresponding protective devices.


## 2. Literature Review

In the late 1950s, dry-type air core reactors were used to limit various kinds of overcurrent in the power system. At that time, most of the dry-type air core reactors produced by power equipment manufacturing enterprises used cable conductors as windings, cable insulation as turn-to-turn insulation, and cement castings as support. The mechanical strength of the cement reactor is large, but it has the disadvantages of low insulation level, poor heat dissipation, easy moisture absorption, and inconvenient installation and use, so it is not widely used [4]. With the continuous application of new materials and the progress of technology, some changes have taken place in the structure of the dry-type air core reactor in the early 1960s. In the 1970s, the Canadian Trend Electric Company (hereinafter referred to as the TE company) first developed a new type of dry-type air core power reactor which is now widely used. This new type of dry-type air core power reactor is quickly recognized by power system users for its unique structure and excellent electrical performance and gradually replaces the traditional oil-immersed iron core power reactor and the old air core power reactor in the power system and its power users. At present, the manufacturers of dry-type air core reactors mainly include the TE company in Canada, ABB company in Germany, Spezieketa company in Austria, and Haefly company in Switzerland. Among them, the TE company has the highest market share and the widest coverage. After years of development, although the design idea and structure of the dry-type air core reactor manufactured by the TE company have not been greatly improved, the application field of its products has been continuously expanded, and the voltage level of the products has been increasing. The maximum voltage level of the current limiting reactor has reached 765 kV, the maximum voltage level of the shunt reactor has reached 115 kV, and the maximum voltage level of the smoothing reactor has reached 500 kV [5, 6]. In the late 1970s, the power sector began to try to purchase new dry-type air core reactors produced by foreign power equipment manufacturing enterprises and apply them to the power system. Compared with the old domestic reactor at that time, the imported new dry-type air core reactor has obvious technical advantages. In 1985, the Beijing Power Equipment Group Company of the former Ministry of Water Resources and Electric Power signed a special technology transfer agreement on a line wave arrester (a new type of small dry air core power reactor) and its manufacturing equipment with the TE company of Canada. The power equipment manufacturing department began the production of this new type of dry air core power reactor. In the early 1990s, some reactor manufacturers began the localization of new dry-type air core reactors by cooperating with colleges and universities. The mid-1990s have been able to produce some different types of new dry-type air core power reactors with small capacity. At the beginning of the 21st century, with the vigorous construction of the power grid, the research and development of new dry-type air core reactors has made great progress [7].Based on the above background, aiming at the practical problem of the high turn-to-turn insulation failure rate of the dry-type air core reactor in the power grid, this study studies the operating overvoltage generated in the process of breaking the dry-type air core reactor via the circuit breaker, the failure mechanism of turn-to-turn insulation of the dry-type air core reactor under the cumulative action of operating overvoltage, the influence law and micromechanism of thermal aging on the Switching Overvoltage Withstand capacity of turn-to-turn insulation, and the deterioration mechanism of turn-to-turn insulation under power frequency overvoltage and electric aging life equation.


## 3. Research Methods

### 3.1. Simulation of Starting Overvoltage System of Dry-Type Air Core Reactor

Different from other types of power equipment in the power system, the dry-type air core reactor, as a compensation device, needs to be switched frequently according to the change of the system reactive power. Due to the parameter characteristics of the dry-type air core reactor, high-frequency and high-amplitude exponential attenuation oscillation overvoltage occurs at both ends of the reactor during the switching operation. On the basis of summarizing the current research status of breaking the overvoltage simulation of the dry-type air core reactor and the theoretical analysis of the single-phase circuit, taking the 66 kV dry-type air core shunt reactor in an actual power grid as the prototype, the overvoltage generated in the process of breaking the reactor via the three-phase circuit breaker is studied. According to the rated parameters and structural parameters of the reactor and the rated parameters and working characteristics of the SF6 circuit breaker, the simulation model of the reactor and circuit breaker is established, and the three-phase simulation circuit is built according to the actual wiring. Combined with the typical waveform of on-off overvoltage, the influence law of random parameters such as cut-off value and action time difference on overvoltage is analyzed. The theoretical analysis model of the three-phase circuit breaker breaking the shunt reactor is built [8–10].The actual circuit breaker model involved in this study is LTB72.5/D1. Its working characteristics mainly include current cut-off value, high-frequency arc extinguishing capacity, and dielectric recovery characteristics. The current chopping is caused by the instability of arc combustion. If the circuit breaker can inhibit the arc discharge ionization, the unstable plasma will be interrupted and form a nonzero chopping. This current value is called the cut-off value. The cut-off value of the circuit breaker is determined by its own characteristics and external circuit parameters. There are differences and great dispersion during each disconnection. An SF6 circuit breaker with a rated voltage of 300 kV was used in the laboratory to disconnect a 275 kV-150 mVa reactor. It was detected that the chopping current of the circuit breaker was between 0 and ~30 A. Considering that the voltage level of the circuit breaker and reactor in this paper is small, the cut-off value is 0~13 A. When the current frequency is greater than a certain value, the circuit breaker cannot successfully extinguish the arc regardless of whether other conditions are met. The upper frequency limit of the current that can be extinguished by the circuit breaker is called the high-frequency arc extinguishing capacity of the circuit breaker. The high-frequency arc-extinguishing capacity of the LTB72.5/D1 SF6 circuit breaker is between 50 and ~300 A/μs, and 100 A/μs is taken in this paper [11].According to the actual action characteristics of the circuit breaker in the process of disconnecting the reactor, the model module is programmed. In the program, given the action timets of the circuit breaker, the chopper current value I0 and the specific value of the high-frequency arc-extinguishing capacity, the initial state of SW_TACS is closed, the time range of each simulation is 0, the value is 30 ms, and it is calculated every 10 ns. In the simulation, the model module automatically measures the source side voltage U1, load side voltage U2, and loop current i and outputs the switching state of the control SW_TACS. The workflow of the model module is shown in Figure 2.Figure 2
Workflow of model module.The reactor model is BKK-20000/66, and its rated parameters and structural parameters are shown in Table1.Table 1
Rated parameters of BKK-20000/66 dry-type air core reactor.
Rated voltage (kV)Rated capacity (kVA)Rated reactance (Ω)Installation height (m)38.112000072.64.13This paper studies the overvoltage of the reactor as a whole, and the overvoltage frequency is very high. The equivalent circuit represented by centralized parameters is shown in Figure3.Figure 3
Concentrated parameter equivalent circuit of reactor.In Figure3, L is the inductance of the reactor, RL is the equivalent parallel resistance representing the loss of the reactor, CZ is the equivalent capacitance of the interturn capacitance network, and Cg1 and Cg2 are the values of the stray capacitance of the reactor to the ground equivalent to the first and last ends, respectively [12, 13].


### 3.2. Electrical Aging Life Evaluation System of Turn-to-Turn Insulation under Power Frequency Overvoltage

Under the action of a single electric field, when the applied voltage is lower than the initial partial discharge voltage, the solid insulating material can work for decades without electrical aging, which mainly occurs after partial discharge. It is difficult to make solid insulating materials uniform and dense with their processing technology. Air gap or impurities lead to electric field distortion. When the applied voltage meets the conditions, it will lead to partial discharge. Under normal working conditions, the turn-to-turn insulation voltage of the dry-type air core reactor is very low, which is not enough to induce partial discharge. However, in the whole life cycle, the turn-to-turn insulation of the reactor bears a variety of overvoltages, such as switching overvoltage and local turn-to-turn power frequency voltage rise caused by moisture on the envelope surface, which may lead to partial discharge. In this paper, the electrical aging life equation of turn-to-turn insulation of the dry-type air core reactor under power frequency overvoltage is studied. The initial partial discharge voltage and power frequency breakdown voltage of the interturn insulation model sample of the nonaged dry air core reactor are measured to provide a reference for the determination of the aging voltage value. The constant power frequency voltage method and stepped power frequency voltage method are used to carry out the accelerated electrical aging test of model samples under power frequency overvoltage [14].The electric aging test platform is composed of the console, regulated power supply, voltage regulator, protective resistor, and capacitor voltage divider. The experimental circuit adds a regulated power supply on the basis of the traditional power frequency high-voltage test power supply to eliminate the influence of the power grid voltage fluctuation in the aging process to the greatest extent. The rated voltage of the test transformer is 100 kV and the rated capacity is 10 kVa.Common accelerated electrical aging methods include the constant voltage method, step voltage method, and sequential voltage method. The constant voltage method is the earliest and most widely used. In recent years, some scholars have used the step voltage method to carry out the electrical aging test of XLPE, polypropylene, and polyimide films and achieved good test results. In this paper, the step voltage method and constant voltage method are used for the accelerated electrical aging test. The test results of the two methods can confirm each other. The application process of the two voltages is shown in Figure4: Figure 4(a) is the step voltage method,U1~Umis the voltage of each stage,∆ukk=1~m−1is the boost value,trkk=1~m−1is the boost time,T1~Tm−1is the duration of the previous stage of withstand voltage,Tmis the duration of the last stage of withstand voltage, andmis the step-up stage; Figure 4(b) is the constant voltage method, which is continuously boosted to the test voltage and maintained until the test object breaks down [15, 16].Figure 4
Electric aging pressurization method.


## 3.1. Simulation of Starting Overvoltage System of Dry-Type Air Core Reactor

Different from other types of power equipment in the power system, the dry-type air core reactor, as a compensation device, needs to be switched frequently according to the change of the system reactive power. Due to the parameter characteristics of the dry-type air core reactor, high-frequency and high-amplitude exponential attenuation oscillation overvoltage occurs at both ends of the reactor during the switching operation. On the basis of summarizing the current research status of breaking the overvoltage simulation of the dry-type air core reactor and the theoretical analysis of the single-phase circuit, taking the 66 kV dry-type air core shunt reactor in an actual power grid as the prototype, the overvoltage generated in the process of breaking the reactor via the three-phase circuit breaker is studied. According to the rated parameters and structural parameters of the reactor and the rated parameters and working characteristics of the SF6 circuit breaker, the simulation model of the reactor and circuit breaker is established, and the three-phase simulation circuit is built according to the actual wiring. Combined with the typical waveform of on-off overvoltage, the influence law of random parameters such as cut-off value and action time difference on overvoltage is analyzed. The theoretical analysis model of the three-phase circuit breaker breaking the shunt reactor is built [8–10].The actual circuit breaker model involved in this study is LTB72.5/D1. Its working characteristics mainly include current cut-off value, high-frequency arc extinguishing capacity, and dielectric recovery characteristics. The current chopping is caused by the instability of arc combustion. If the circuit breaker can inhibit the arc discharge ionization, the unstable plasma will be interrupted and form a nonzero chopping. This current value is called the cut-off value. The cut-off value of the circuit breaker is determined by its own characteristics and external circuit parameters. There are differences and great dispersion during each disconnection. An SF6 circuit breaker with a rated voltage of 300 kV was used in the laboratory to disconnect a 275 kV-150 mVa reactor. It was detected that the chopping current of the circuit breaker was between 0 and ~30 A. Considering that the voltage level of the circuit breaker and reactor in this paper is small, the cut-off value is 0~13 A. When the current frequency is greater than a certain value, the circuit breaker cannot successfully extinguish the arc regardless of whether other conditions are met. The upper frequency limit of the current that can be extinguished by the circuit breaker is called the high-frequency arc extinguishing capacity of the circuit breaker. The high-frequency arc-extinguishing capacity of the LTB72.5/D1 SF6 circuit breaker is between 50 and ~300 A/μs, and 100 A/μs is taken in this paper [11].According to the actual action characteristics of the circuit breaker in the process of disconnecting the reactor, the model module is programmed. In the program, given the action timets of the circuit breaker, the chopper current value I0 and the specific value of the high-frequency arc-extinguishing capacity, the initial state of SW_TACS is closed, the time range of each simulation is 0, the value is 30 ms, and it is calculated every 10 ns. In the simulation, the model module automatically measures the source side voltage U1, load side voltage U2, and loop current i and outputs the switching state of the control SW_TACS. The workflow of the model module is shown in Figure 2.Figure 2
Workflow of model module.The reactor model is BKK-20000/66, and its rated parameters and structural parameters are shown in Table1.Table 1
Rated parameters of BKK-20000/66 dry-type air core reactor.
Rated voltage (kV)Rated capacity (kVA)Rated reactance (Ω)Installation height (m)38.112000072.64.13This paper studies the overvoltage of the reactor as a whole, and the overvoltage frequency is very high. The equivalent circuit represented by centralized parameters is shown in Figure3.Figure 3
Concentrated parameter equivalent circuit of reactor.In Figure3, L is the inductance of the reactor, RL is the equivalent parallel resistance representing the loss of the reactor, CZ is the equivalent capacitance of the interturn capacitance network, and Cg1 and Cg2 are the values of the stray capacitance of the reactor to the ground equivalent to the first and last ends, respectively [12, 13].


## 3.2. Electrical Aging Life Evaluation System of Turn-to-Turn Insulation under Power Frequency Overvoltage

Under the action of a single electric field, when the applied voltage is lower than the initial partial discharge voltage, the solid insulating material can work for decades without electrical aging, which mainly occurs after partial discharge. It is difficult to make solid insulating materials uniform and dense with their processing technology. Air gap or impurities lead to electric field distortion. When the applied voltage meets the conditions, it will lead to partial discharge. Under normal working conditions, the turn-to-turn insulation voltage of the dry-type air core reactor is very low, which is not enough to induce partial discharge. However, in the whole life cycle, the turn-to-turn insulation of the reactor bears a variety of overvoltages, such as switching overvoltage and local turn-to-turn power frequency voltage rise caused by moisture on the envelope surface, which may lead to partial discharge. In this paper, the electrical aging life equation of turn-to-turn insulation of the dry-type air core reactor under power frequency overvoltage is studied. The initial partial discharge voltage and power frequency breakdown voltage of the interturn insulation model sample of the nonaged dry air core reactor are measured to provide a reference for the determination of the aging voltage value. The constant power frequency voltage method and stepped power frequency voltage method are used to carry out the accelerated electrical aging test of model samples under power frequency overvoltage [14].The electric aging test platform is composed of the console, regulated power supply, voltage regulator, protective resistor, and capacitor voltage divider. The experimental circuit adds a regulated power supply on the basis of the traditional power frequency high-voltage test power supply to eliminate the influence of the power grid voltage fluctuation in the aging process to the greatest extent. The rated voltage of the test transformer is 100 kV and the rated capacity is 10 kVa.Common accelerated electrical aging methods include the constant voltage method, step voltage method, and sequential voltage method. The constant voltage method is the earliest and most widely used. In recent years, some scholars have used the step voltage method to carry out the electrical aging test of XLPE, polypropylene, and polyimide films and achieved good test results. In this paper, the step voltage method and constant voltage method are used for the accelerated electrical aging test. The test results of the two methods can confirm each other. The application process of the two voltages is shown in Figure4: Figure 4(a) is the step voltage method,U1~Umis the voltage of each stage,∆ukk=1~m−1is the boost value,trkk=1~m−1is the boost time,T1~Tm−1is the duration of the previous stage of withstand voltage,Tmis the duration of the last stage of withstand voltage, andmis the step-up stage; Figure 4(b) is the constant voltage method, which is continuously boosted to the test voltage and maintained until the test object breaks down [15, 16].Figure 4
Electric aging pressurization method.


## 4. Result Analysis

### 4.1. Effective Power Frequency Constant Voltage Electrical Aging Test

Conduct electrical aging test under 6 kV~13 kV constant power frequency voltage. For 12 samples under each voltage, remove the maximum and minimum values of the test data to obtain 80 effective data. The variation trend of pulse maximum discharge and pulse discharge power with voltage was measured. The application mode of voltage is the step-by-step boost, and the duration of the step-by-step voltage is 720 s. The specific step-by-step boost mode is consistent with the step-by-step boost process [17, 18]. The partial discharge parameters of 12 model samples were measured, and the maximum and minimum values of the test data were removed to obtain 10 effective test data. In order to prevent the current overshoot caused by accidental breakdown from damaging the partial discharge measuring instrument in the process of partial discharge parameter measurement, only the partial discharge parameters with a voltage amplitude less than 4.5 kV are measured.The electrical aging test data of 140 effective power frequency constant voltage at 14 voltage levels are obtained. Based on the differential idea, when the voltage amplitude changes little, the electric aging life equation should follow the inverse power formula. In order to determine that the aging voltage amplitude will affect the value of the withstand voltage life indexN, the constant voltage electrical aging test data in different voltage amplitude ranges are analyzed, and the values of index N and constant C are shown in Table 2.Table 2
N and C values calculated from constant piezoelectric aging data corresponding to different voltage ranges.
Voltage range (kV)6~106~116~126~136~14N value2.733.043.4344.21C value2.74E74.92E71.02E82.94E84.32E8Voltage range (kV)6~157~168~179~1810~19N value4.385.346.317.157.94C value5.89E85.4E95.57E105.48E114.67E12Voltage range (kV)11~1912~1913~1914~1915~19N value8.358.668.9610.1910.56C value1.62E134.09E131.02E143.66E151.26E16It can be seen from Table2 that no matter whether the number of aging life data increases or decreases, as long as the electrical aging life data obtained under the high-amplitude voltage used for parameter estimation of inverse power life model increases, the parameter estimation values of the withstand voltage life index n and constant C increase [19].Calculate the average value of 10 effective data of the maximum partial discharge pulse and pulse discharge power of the model sample under each aging voltage amplitude and obtain the variation law of the partial discharge parameters of the interturn insulation model sample with the aging voltage amplitude, as shown in Figure5.Figure 5
Variation trend of partial discharge parameters with voltage.As can be seen from Figure5, when the applied voltage amplitude is low, the maximum pulse discharge amount and pulse discharge power amplitude of partial discharge of the model sample are very small. After the applied voltage amplitude reaches a certain value, the maximum pulse discharge amount and pulse discharge power of the partial discharge pulse increase rapidly. The maximum pulse discharge generally represents the partial discharge of large-scale defects in the insulation. Therefore, the variation trend of the maximum pulse discharge with the applied voltage amplitude proves that the size of air gap defects with partial discharge increases with the increase of the applied voltage amplitude. The pulse discharge power of partial discharge comprehensively represents the instantaneous value of the pulse discharge frequency, pulse discharge quantity, and applied voltage amplitude and represents the amount of energy released in the process of partial discharge. The greater the energy, the faster the insulation deterioration rate. Therefore, the variation trend of the partial discharge pulse power with the applied voltage amplitude shows that the deterioration rate of the turn-to-turn insulation of the model sample increases with the increase of the applied voltage amplitude [20–23].


### 4.2. Modification of Electric Aging Inverse Power Life Model

Under the condition of partial discharge, the electrical aging life data of the turn-to-turn insulation model sample of the dry-type air core reactor does not follow the inverse power life model. With the increase of the aging voltage amplitude, the values of parametersN and C in the inverse power model increase, in order to obtain a more accurate empirical formula of electrical aging life under the partial discharge condition, so as to estimate the electrical aging life of the turn-to-turn insulation of dry-type air core reactor under lower voltage. Take the voltage amplitude corresponding to the estimated values of each group of N and C parameters in Table 2 as the average value of the voltage within the range and obtain the effective data of 15 groups of unknown parameters N and C varying with the voltage amplitude. The empirical formulas of N and C affected by the voltage amplitude u are formulas (1) and (2), respectively:
(1)N=−10.1+8.51e0.0518U,(2)lnC=13.9+0.017U2.54.Substituting equations (1) and (2) into their logarithmic form, the modified empirical formula of electric aging life is the following equation:
(3)lnL=13.9+0.017U2.54+10.1−8.51e0.0518UlnU.The curve corresponding to equation (3) and the measured electric aging life data points (average value of 5 samples) of model samples under electric aging voltage amplitudes of 4.5 kV, 6.5 kV, 8.5 kV, 10.5 kV, 12.5KV, 14.5 kV, and 16.5 kV are drawn in Figure 6.Figure 6
Comparison between electric aging life curve and measured data.It can be seen that the electrical aging life curve of the modified interturn insulation model sample of the dry-type air core reactor has a high correlation with the measured aging life data, which can reach more than 95%. Therefore, the new empirical formula of electrical aging life can accurately reflect the electrical aging law of the turn-to-turn insulation model sample of the dry-type air core reactor under the action of power frequency overvoltage [24, 25].


## 4.1. Effective Power Frequency Constant Voltage Electrical Aging Test

Conduct electrical aging test under 6 kV~13 kV constant power frequency voltage. For 12 samples under each voltage, remove the maximum and minimum values of the test data to obtain 80 effective data. The variation trend of pulse maximum discharge and pulse discharge power with voltage was measured. The application mode of voltage is the step-by-step boost, and the duration of the step-by-step voltage is 720 s. The specific step-by-step boost mode is consistent with the step-by-step boost process [17, 18]. The partial discharge parameters of 12 model samples were measured, and the maximum and minimum values of the test data were removed to obtain 10 effective test data. In order to prevent the current overshoot caused by accidental breakdown from damaging the partial discharge measuring instrument in the process of partial discharge parameter measurement, only the partial discharge parameters with a voltage amplitude less than 4.5 kV are measured.The electrical aging test data of 140 effective power frequency constant voltage at 14 voltage levels are obtained. Based on the differential idea, when the voltage amplitude changes little, the electric aging life equation should follow the inverse power formula. In order to determine that the aging voltage amplitude will affect the value of the withstand voltage life indexN, the constant voltage electrical aging test data in different voltage amplitude ranges are analyzed, and the values of index N and constant C are shown in Table 2.Table 2
N and C values calculated from constant piezoelectric aging data corresponding to different voltage ranges.
Voltage range (kV)6~106~116~126~136~14N value2.733.043.4344.21C value2.74E74.92E71.02E82.94E84.32E8Voltage range (kV)6~157~168~179~1810~19N value4.385.346.317.157.94C value5.89E85.4E95.57E105.48E114.67E12Voltage range (kV)11~1912~1913~1914~1915~19N value8.358.668.9610.1910.56C value1.62E134.09E131.02E143.66E151.26E16It can be seen from Table2 that no matter whether the number of aging life data increases or decreases, as long as the electrical aging life data obtained under the high-amplitude voltage used for parameter estimation of inverse power life model increases, the parameter estimation values of the withstand voltage life index n and constant C increase [19].Calculate the average value of 10 effective data of the maximum partial discharge pulse and pulse discharge power of the model sample under each aging voltage amplitude and obtain the variation law of the partial discharge parameters of the interturn insulation model sample with the aging voltage amplitude, as shown in Figure5.Figure 5
Variation trend of partial discharge parameters with voltage.As can be seen from Figure5, when the applied voltage amplitude is low, the maximum pulse discharge amount and pulse discharge power amplitude of partial discharge of the model sample are very small. After the applied voltage amplitude reaches a certain value, the maximum pulse discharge amount and pulse discharge power of the partial discharge pulse increase rapidly. The maximum pulse discharge generally represents the partial discharge of large-scale defects in the insulation. Therefore, the variation trend of the maximum pulse discharge with the applied voltage amplitude proves that the size of air gap defects with partial discharge increases with the increase of the applied voltage amplitude. The pulse discharge power of partial discharge comprehensively represents the instantaneous value of the pulse discharge frequency, pulse discharge quantity, and applied voltage amplitude and represents the amount of energy released in the process of partial discharge. The greater the energy, the faster the insulation deterioration rate. Therefore, the variation trend of the partial discharge pulse power with the applied voltage amplitude shows that the deterioration rate of the turn-to-turn insulation of the model sample increases with the increase of the applied voltage amplitude [20–23].


## 4.2. Modification of Electric Aging Inverse Power Life Model

Under the condition of partial discharge, the electrical aging life data of the turn-to-turn insulation model sample of the dry-type air core reactor does not follow the inverse power life model. With the increase of the aging voltage amplitude, the values of parametersN and C in the inverse power model increase, in order to obtain a more accurate empirical formula of electrical aging life under the partial discharge condition, so as to estimate the electrical aging life of the turn-to-turn insulation of dry-type air core reactor under lower voltage. Take the voltage amplitude corresponding to the estimated values of each group of N and C parameters in Table 2 as the average value of the voltage within the range and obtain the effective data of 15 groups of unknown parameters N and C varying with the voltage amplitude. The empirical formulas of N and C affected by the voltage amplitude u are formulas (1) and (2), respectively:
(1)N=−10.1+8.51e0.0518U,(2)lnC=13.9+0.017U2.54.Substituting equations (1) and (2) into their logarithmic form, the modified empirical formula of electric aging life is the following equation:
(3)lnL=13.9+0.017U2.54+10.1−8.51e0.0518UlnU.The curve corresponding to equation (3) and the measured electric aging life data points (average value of 5 samples) of model samples under electric aging voltage amplitudes of 4.5 kV, 6.5 kV, 8.5 kV, 10.5 kV, 12.5KV, 14.5 kV, and 16.5 kV are drawn in Figure 6.Figure 6
Comparison between electric aging life curve and measured data.It can be seen that the electrical aging life curve of the modified interturn insulation model sample of the dry-type air core reactor has a high correlation with the measured aging life data, which can reach more than 95%. Therefore, the new empirical formula of electrical aging life can accurately reflect the electrical aging law of the turn-to-turn insulation model sample of the dry-type air core reactor under the action of power frequency overvoltage [24, 25].


## 5. Conclusion

With the increase of the number and service life of the dry-type air core reactor, turn-to-turn insulation faults occur frequently. This paper summarizes the research status of turn-to-turn insulation. Focusing on the failure mechanism of turn-to-turn insulation of the dry-type air core reactor under overvoltage, this paper mainly studies the switching overvoltage generated in the process of disconnecting the dry-type air core reactor, the deterioration law of turn-to-turn insulation under the cumulative action of switching overvoltage, the influence of thermal aging on the Switching Overvoltage Withstand characteristics of turn-to-turn insulation, and the electrical aging life of turn-to-turn insulation under power frequency overvoltage. The main work and conclusions of this paper are as follows:(1)
This paper studies the influence of thermal aging on the Switching Overvoltage Withstand characteristics of turn-to-turn insulation of the dry-type air core reactor. The results show that thermal aging will not reduce the breakdown voltage, partial discharge, and other parameters of the dry-type air core reactor. With the deepening of thermal aging, the mechanical properties of the polyester film decrease, which leads to the exponential decline of the cumulative action times of the model sample to withstand the operating overvoltage(2)
This paper carried out the accelerated electrical aging life test of interturn insulation model samples and established the mathematical model of the electrical aging life. The results show that when there is partial discharge under power frequency overvoltage, the electrical aging life of turn-to-turn insulation of the dry-type air core reactor does not follow the inverse power model, and the withstand voltage life indexn and constant C increase with the increase of the test voltage. The modified electric aging life equation can more accurately predict the interturn insulation life of the dry-type air core reactor under the condition of partial discharge



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*Source: 6982950-2022-06-25.xml*