It is difficult to detect and extinguish direct current(DC)arc in power electronics systems,and the arc could easily lead to a fire and cause great damage to surrounding equipment.A DC arc generation simulation unit i...It is difficult to detect and extinguish direct current(DC)arc in power electronics systems,and the arc could easily lead to a fire and cause great damage to surrounding equipment.A DC arc generation simulation unit is established,in which DC series arcs are generated by dragging the moving electrode away from the fixed one with the help of the stepper motor.In addition,a ferrite rod antenna is used to receive the electromagnetic radiation signals induced by the arcs.Based on experiments using the unit,the general characteristics of DC arc,including the pulse characteristics of arc current and source output in corresponding time window,and the frequency-domain characteristics of arc current,are studied.With discussion on three detection methods,it is concluded that the variation of current and voltage of arc,the spectrum of the arc current during the discontinuous intervals and the radiating electromagnetic signal are all features that can be adopted for detecting DC series arc.Therefore,a synthetic judgment method is suggested for further study.展开更多
The load types in low-voltage distribution systems are diverse.Some loads have current signals that are similar to series fault arcs,making it difficult to effectively detect fault arcs during their occurrence and sus...The load types in low-voltage distribution systems are diverse.Some loads have current signals that are similar to series fault arcs,making it difficult to effectively detect fault arcs during their occurrence and sustained combustion,which can easily lead to serious electrical fire accidents.To address this issue,this paper establishes a fault arc prototype experimental platform,selects multiple commonly used loads for fault arc experiments,and collects data in both normal and fault states.By analyzing waveform characteristics and selecting fault discrimination feature indicators,corresponding feature values are extracted for qualitative analysis to explore changes in timefrequency characteristics of current before and after faults.Multiple features are then selected to form a multidimensional feature vector space to effectively reduce arc misjudgments and construct a fault discrimination feature database.Based on this,a fault arc hazard prediction model is built using random forests.The model’s multiple hyperparameters are simultaneously optimized through grid search,aiming tominimize node information entropy and complete model training,thereby enhancing model robustness and generalization ability.Through experimental verification,the proposed method accurately predicts and classifies fault arcs of different load types,with an average accuracy at least 1%higher than that of the commonly used fault predictionmethods compared in the paper.展开更多
Arc grounding faults occur frequently in the power grid with small resistance grounding neutral points.The existing arc fault identification technology only uses the fault line signal characteristics to set the identi...Arc grounding faults occur frequently in the power grid with small resistance grounding neutral points.The existing arc fault identification technology only uses the fault line signal characteristics to set the identification index,which leads to detection failure when the arc zero-off characteristic is short.To solve this problem,this paper presents an arc fault identification method by utilizing integrated signal characteristics of both the fault line and sound lines.Firstly,the waveform characteristics of the fault line and sound lines under an arc grounding fault are studied.After that,the convex hull,gradient product,and correlation coefficient index are used as the basic characteristic parameters to establish fault identification criteria.Then,the logistic regression algorithm is employed to deal with the reference samples,establish the machine discrimination model,and realize the discrimination of fault types.Finally,simulation test results and experimental results verify the accuracy of the proposed method.The comparison analysis shows that the proposed method has higher recognition accuracy,especially when the arc dissipation power is smaller than 2×10^(3) W,the zero-off period is not obvious.In conclusion,the proposed method expands the arc fault identification theory.展开更多
A reconstruction method using experimental arc fault data to improve the testing efficiency of protection devices is introduced. By establishing an arc-current database and employing collaborative control of data and ...A reconstruction method using experimental arc fault data to improve the testing efficiency of protection devices is introduced. By establishing an arc-current database and employing collaborative control of data and circuit feedback signals, the electronic load can be precisely regulated enabling arc fault currents to be reproduced in real-world circuits. To address the frequency mismatches caused by power frequency fluctuations, an adaptive correction control strategy is proposed to eliminate waveform distortions in the reconstructed arc current. Simulations and experiments confirmed the consistency between the arc data and reconstructed current signals, and the method’s feasibility was further validated by testing six arc-fault protection devices from different manufacturers.展开更多
The development of aircraft electrification can improve energy utilization efficiency and reduce the green gas emissions,which is the future trend.However,aircraft electrification would increase the probability of arc...The development of aircraft electrification can improve energy utilization efficiency and reduce the green gas emissions,which is the future trend.However,aircraft electrification would increase the probability of arc faults in the wire system.Arc can ignite the combustibles by the arc column or hot droplets,which has high fire risks.Arc faults have triggered several catastrophic aeronautical accidents in the past.Electrical fire safety is a top priority of aircraft in the future.An in-depth understanding of the arc fault ignition mechanism plays a crucial role in preventing arc fires and optimizing wire layout.This review article performs a comprehensive summary of relevant research concerning the fire risks of arc faults,the causes of arc faults in the wire system,and the ignition behaviors of arc faults.The main findings regarding the direct ignition of arc faults and ignition of hot droplets are emphasized.The arc ignition characteristics in existing research are firstly summarized,including the arc ignition experiment platforms and thermal hazard characteristics of arc faults.Additionally,the generation,impacting process,and ignition characteristics of hot droplets are then presented.Finally,the limitations in existing research about ignition characteristics of arc faults are also outlined,while identifying the future research needs of fires caused by arc faults.展开更多
Arc fault detection is desperately required in Solid State Power Controllers（SSPC） in addition to their fundamental functions because arcs will provoke growing harm and threat to aircraft safety. Experimental study ...Arc fault detection is desperately required in Solid State Power Controllers（SSPC） in addition to their fundamental functions because arcs will provoke growing harm and threat to aircraft safety. Experimental study has been done to obtain the faulted current data. In order to improve the detection speed and accuracy, two fast arc fault detection methods have been proposed in this paper with the analysis of only half cycle data. Both Fast Fourier Transform（FFT） and Wavelet Packets Decomposition（WPD） have been adopted to distinguish arc fault currents from normal operation currents. Analysis results show that Alternating Current（AC） arcs can be effectively and accurately detected with the proposed half cycle data based methods. Moreover,experimental verification results have also been provided.展开更多
It has been known that DC arc faults pose a hazard in power electronics systems. Due to the fault current is lower than normal current load, series arc is more difficult to be discovered than parallel arc. The traditi...It has been known that DC arc faults pose a hazard in power electronics systems. Due to the fault current is lower than normal current load, series arc is more difficult to be discovered than parallel arc. The traditional methods of DC series arc faults detection have some disadvantages, such as large computation, long delay and easier influence by interferences. In this paper, a novel method with multi-scale morphological filtering was utilized for the fault detection of DC series arc. Compared to the tradition method, the proposed method is more simple and efficient. It was verified that it was convenient for field application of on-line monitoring and diagnosis with a good ability to prevent misjudgments from the environment interference.展开更多
Outdated testing methods hinder the success rate of carbonized cable preparation in low-voltage arc fault tests,leading to incomplete tests and high failure rates.To address this issue,we finely categorized the prepar...Outdated testing methods hinder the success rate of carbonized cable preparation in low-voltage arc fault tests,leading to incomplete tests and high failure rates.To address this issue,we finely categorized the preparation results of carbonized cable specimens by analyzing the experimental phenomena during the carbonization process and assessing the impact of high-voltage energization time on the outcomes,presenting a process control strategy aimed at optimizing the preparation results of carbonized cable specimens.This method utilizes three periodic moving algorithms(root-mean-square,average,and shoulder percentage)to classify the cable specimens into four preparation categories:open-circuit carbonization,under-carbonization,short-circuit carbonization,and successful carbonization.The high-voltage energization time during carbonization or secondary carbonization was adjusted to optimize the preparation of the carbonized cables by considering different discrimination outcomes.Finally,the proposed method was tested on a purpose-built carbonized cable experimental platform,which confirmed its effectiveness in differentiating the preparation outcomes of the carbonized cable specimens and improving the success rate of the carbonized cable preparation.The proposed method has significant potential for application in low-voltage arc fault test systems.展开更多
We mainly study the detection of arc faults in the direct current (DC) system of lithium battery energystorage power station. Lithium battery DC systems are widely used, but traditional DC protection devices areunable...We mainly study the detection of arc faults in the direct current (DC) system of lithium battery energystorage power station. Lithium battery DC systems are widely used, but traditional DC protection devices areunable to achieve adequate protection of equipment and circuits. We build an experimental platform based onan energy storage power station with lithium batteries. Then, the data collection of normal current and arc-faultcurrent is completed under multiple conditions, and the waveforms of obvious and weak signals as the arc occursare presented. We analyze the principles and application range of several common spectrum-sensing methods andstudy the feasibility of applying them to the arc detection field. Finally, the covariance absolute value detectionalgorithm is selected, and the average value of the current is filtered out to make the algorithm adapt to the arcdetection field. The result shows that the detection probability in 500 sets of experimental data has reached 98%.展开更多
In resonant grounding systems,most single-phaseto-ground faults evolve from IAFs(Intermittent Arc Faults).Earlier detection of IAFs can facilitate fault avoidance.This work proposes a novel method based on machine lea...In resonant grounding systems,most single-phaseto-ground faults evolve from IAFs(Intermittent Arc Faults).Earlier detection of IAFs can facilitate fault avoidance.This work proposes a novel method based on machine learning for detecting IAFs in three steps.First,the feature of zero-sequence current is automatically extracted and selected by a newlydesigned FINET(“For IAFs,Neuron Elaboration Net”),instead of traditional feature selection based on time-frequency decomposition.Moreover,data of the zero-sequence current divided by different time windows are successively input into the trained FINET.A proposed PSF(principal-subordinate factor)analyses the results obtained from FINET to improve anti-interference in the mentioned IAF detection algorithm.Experiments using PSCAD/EMTDC software simulation data show the proposed method is feasible and highly adaptable.In addition,the detection result of on-site recorded data demonstrates the effectiveness of the proposed method in practical resonant grounding systems.展开更多
The behavior of fault arc in a high-speed switch （HSS） has been studied theoretically and experimentally. A simplified HSS setup is designed to support this work. A two-dimensional arc model is developed to analyze ...The behavior of fault arc in a high-speed switch （HSS） has been studied theoretically and experimentally. A simplified HSS setup is designed to support this work. A two-dimensional arc model is developed to analyze the characteristics of fault arc based on magnetic-hydrodynamic （MHD） theory. The advantage of such a model is that the thermal transfer coefficient can be determined by depending on the numerical method alone. The influence of net emission coefficients （NEC） radiation model and P1 model on fault arc is analyzed in detail. Results show that NEC model predicts more radiation energy and less pressure rise without the re-absorption effect considered. As a consequence, P1 model is more suitable to calculate the pressure rise caused by fault arc. Finally, the pressure rise during longer arcing time for different arc currents is predicted.展开更多
This paper investigates direct current(DC) arc fault detection in photovoltaic system. In order to avoid the risk of fire ignition caused by the arc fault in the photovoltaic power supply, it is urgent to detect the D...This paper investigates direct current(DC) arc fault detection in photovoltaic system. In order to avoid the risk of fire ignition caused by the arc fault in the photovoltaic power supply, it is urgent to detect the DC arc fault in the photovoltaic system. Once an arc fault is detected, the power supply should be cut off immediately. A lot of field experiments are carried out to obtain the data of arc fault current of the photovoltaic system under different current conditions. Cable length, arc gap, and the effects of different sensors are tested.These three conditions are the most significant features of this paper. Four characteristic variables from both the time domain and the frequency domain are extracted to identify the arc fault. Then the logistic regression method in the field of artificial intelligence and machine learning is originally used to analyze the experimental results of arc fault in the photovoltaic system. The function between the probability of the arc fault and the change of the characteristic variables is obtained. After validating 80 groups of experimental data under different conditions,the accuracy rate of the arc fault detection by this algorithm is proved to reach 100%.展开更多
This paper focuses on the simulation of a fault arc in a closed tank based on the magneto-hydrodynamic （MHD） method, in which a comparative study of three radiation models, including net emission coefficients （NEC...This paper focuses on the simulation of a fault arc in a closed tank based on the magneto-hydrodynamic （MHD） method, in which a comparative study of three radiation models, including net emission coefficients （NEC）, semi-empirical model based on NEC as well as the P1 model, is developed. The pressure rise calculated by the three radiation models are compared to the measured results. Particularly when the senti-empirical model is used, the effect of different boundary temperatures of the re-absorption layer in the semi-empirical model on pressure rise is concentrated on. The results show that the re-absorption effect in the low-temperature region affects radiation transfer of fault arcs evidently, and thus the internal pressure rise. Compared with the NEC model, P1 and the semi-empirical model with 0.7 〈 α 〈 0.83 are more suitable to calculate the pressure rise of the fault arc, where is an adjusted parameter involving the boundary temperature of the re-absorption region in the semi-empirical model.展开更多
基金Project supported by International Cooperation Project in Shaanxi Province of China(2012KW-01)
文摘It is difficult to detect and extinguish direct current(DC)arc in power electronics systems,and the arc could easily lead to a fire and cause great damage to surrounding equipment.A DC arc generation simulation unit is established,in which DC series arcs are generated by dragging the moving electrode away from the fixed one with the help of the stepper motor.In addition,a ferrite rod antenna is used to receive the electromagnetic radiation signals induced by the arcs.Based on experiments using the unit,the general characteristics of DC arc,including the pulse characteristics of arc current and source output in corresponding time window,and the frequency-domain characteristics of arc current,are studied.With discussion on three detection methods,it is concluded that the variation of current and voltage of arc,the spectrum of the arc current during the discontinuous intervals and the radiating electromagnetic signal are all features that can be adopted for detecting DC series arc.Therefore,a synthetic judgment method is suggested for further study.
基金This work was funded by Beijing Key Laboratory of Distribution Transformer Energy-Saving Technology(China Electric Power Research Institute).
文摘The load types in low-voltage distribution systems are diverse.Some loads have current signals that are similar to series fault arcs,making it difficult to effectively detect fault arcs during their occurrence and sustained combustion,which can easily lead to serious electrical fire accidents.To address this issue,this paper establishes a fault arc prototype experimental platform,selects multiple commonly used loads for fault arc experiments,and collects data in both normal and fault states.By analyzing waveform characteristics and selecting fault discrimination feature indicators,corresponding feature values are extracted for qualitative analysis to explore changes in timefrequency characteristics of current before and after faults.Multiple features are then selected to form a multidimensional feature vector space to effectively reduce arc misjudgments and construct a fault discrimination feature database.Based on this,a fault arc hazard prediction model is built using random forests.The model’s multiple hyperparameters are simultaneously optimized through grid search,aiming tominimize node information entropy and complete model training,thereby enhancing model robustness and generalization ability.Through experimental verification,the proposed method accurately predicts and classifies fault arcs of different load types,with an average accuracy at least 1%higher than that of the commonly used fault predictionmethods compared in the paper.
基金This work was supported in part by the Natural Science Foundation of Henan Province,and the specific grant number is 232300420301。
文摘Arc grounding faults occur frequently in the power grid with small resistance grounding neutral points.The existing arc fault identification technology only uses the fault line signal characteristics to set the identification index,which leads to detection failure when the arc zero-off characteristic is short.To solve this problem,this paper presents an arc fault identification method by utilizing integrated signal characteristics of both the fault line and sound lines.Firstly,the waveform characteristics of the fault line and sound lines under an arc grounding fault are studied.After that,the convex hull,gradient product,and correlation coefficient index are used as the basic characteristic parameters to establish fault identification criteria.Then,the logistic regression algorithm is employed to deal with the reference samples,establish the machine discrimination model,and realize the discrimination of fault types.Finally,simulation test results and experimental results verify the accuracy of the proposed method.The comparison analysis shows that the proposed method has higher recognition accuracy,especially when the arc dissipation power is smaller than 2×10^(3) W,the zero-off period is not obvious.In conclusion,the proposed method expands the arc fault identification theory.
基金Supported by the National Natural Science Foundation of China(52277136)the University Production-Study Cooperation Project of the Science and Technology Department of Fujian(2021Y4002)the 2018 Funding Program for Leading Talents in Scientific and Technological Innovation of Fujian Province(038000387024).
文摘A reconstruction method using experimental arc fault data to improve the testing efficiency of protection devices is introduced. By establishing an arc-current database and employing collaborative control of data and circuit feedback signals, the electronic load can be precisely regulated enabling arc fault currents to be reproduced in real-world circuits. To address the frequency mismatches caused by power frequency fluctuations, an adaptive correction control strategy is proposed to eliminate waveform distortions in the reconstructed arc current. Simulations and experiments confirmed the consistency between the arc data and reconstructed current signals, and the method’s feasibility was further validated by testing six arc-fault protection devices from different manufacturers.
基金supported by the National Natural Science Foundation of China[Grant no.U2033206].
文摘The development of aircraft electrification can improve energy utilization efficiency and reduce the green gas emissions,which is the future trend.However,aircraft electrification would increase the probability of arc faults in the wire system.Arc can ignite the combustibles by the arc column or hot droplets,which has high fire risks.Arc faults have triggered several catastrophic aeronautical accidents in the past.Electrical fire safety is a top priority of aircraft in the future.An in-depth understanding of the arc fault ignition mechanism plays a crucial role in preventing arc fires and optimizing wire layout.This review article performs a comprehensive summary of relevant research concerning the fire risks of arc faults,the causes of arc faults in the wire system,and the ignition behaviors of arc faults.The main findings regarding the direct ignition of arc faults and ignition of hot droplets are emphasized.The arc ignition characteristics in existing research are firstly summarized,including the arc ignition experiment platforms and thermal hazard characteristics of arc faults.Additionally,the generation,impacting process,and ignition characteristics of hot droplets are then presented.Finally,the limitations in existing research about ignition characteristics of arc faults are also outlined,while identifying the future research needs of fires caused by arc faults.
基金co-supported by the National Natural Science Foundation of China(Nos.51407144 and 51777169)the Aviation Research Funds(No.20164053029)+1 种基金the Fundamental Research Funds for the Central Universities(Nos.3102017ZY027 and 3102017GX08001)the Young Elite Scientist Sponsorship Program by CAST
文摘Arc fault detection is desperately required in Solid State Power Controllers（SSPC） in addition to their fundamental functions because arcs will provoke growing harm and threat to aircraft safety. Experimental study has been done to obtain the faulted current data. In order to improve the detection speed and accuracy, two fast arc fault detection methods have been proposed in this paper with the analysis of only half cycle data. Both Fast Fourier Transform（FFT） and Wavelet Packets Decomposition（WPD） have been adopted to distinguish arc fault currents from normal operation currents. Analysis results show that Alternating Current（AC） arcs can be effectively and accurately detected with the proposed half cycle data based methods. Moreover,experimental verification results have also been provided.
文摘It has been known that DC arc faults pose a hazard in power electronics systems. Due to the fault current is lower than normal current load, series arc is more difficult to be discovered than parallel arc. The traditional methods of DC series arc faults detection have some disadvantages, such as large computation, long delay and easier influence by interferences. In this paper, a novel method with multi-scale morphological filtering was utilized for the fault detection of DC series arc. Compared to the tradition method, the proposed method is more simple and efficient. It was verified that it was convenient for field application of on-line monitoring and diagnosis with a good ability to prevent misjudgments from the environment interference.
基金Supported by the National Natural Science Foundation of China(52277136)the University Production-Study Cooperation Project of Science and Technology Department of Fujian Province(2021Y4002)+1 种基金the 2018 Funding Program for Leading Talents in Scientific and Technological Innovation of Fujian(038000387024)Natural Science Foundation of Fujian Province(2020J05170).
文摘Outdated testing methods hinder the success rate of carbonized cable preparation in low-voltage arc fault tests,leading to incomplete tests and high failure rates.To address this issue,we finely categorized the preparation results of carbonized cable specimens by analyzing the experimental phenomena during the carbonization process and assessing the impact of high-voltage energization time on the outcomes,presenting a process control strategy aimed at optimizing the preparation results of carbonized cable specimens.This method utilizes three periodic moving algorithms(root-mean-square,average,and shoulder percentage)to classify the cable specimens into four preparation categories:open-circuit carbonization,under-carbonization,short-circuit carbonization,and successful carbonization.The high-voltage energization time during carbonization or secondary carbonization was adjusted to optimize the preparation of the carbonized cables by considering different discrimination outcomes.Finally,the proposed method was tested on a purpose-built carbonized cable experimental platform,which confirmed its effectiveness in differentiating the preparation outcomes of the carbonized cable specimens and improving the success rate of the carbonized cable preparation.The proposed method has significant potential for application in low-voltage arc fault test systems.
文摘We mainly study the detection of arc faults in the direct current (DC) system of lithium battery energystorage power station. Lithium battery DC systems are widely used, but traditional DC protection devices areunable to achieve adequate protection of equipment and circuits. We build an experimental platform based onan energy storage power station with lithium batteries. Then, the data collection of normal current and arc-faultcurrent is completed under multiple conditions, and the waveforms of obvious and weak signals as the arc occursare presented. We analyze the principles and application range of several common spectrum-sensing methods andstudy the feasibility of applying them to the arc detection field. Finally, the covariance absolute value detectionalgorithm is selected, and the average value of the current is filtered out to make the algorithm adapt to the arcdetection field. The result shows that the detection probability in 500 sets of experimental data has reached 98%.
基金sponsored by the National Natural Science Foundation of China (No.51677030).
文摘In resonant grounding systems,most single-phaseto-ground faults evolve from IAFs(Intermittent Arc Faults).Earlier detection of IAFs can facilitate fault avoidance.This work proposes a novel method based on machine learning for detecting IAFs in three steps.First,the feature of zero-sequence current is automatically extracted and selected by a newlydesigned FINET(“For IAFs,Neuron Elaboration Net”),instead of traditional feature selection based on time-frequency decomposition.Moreover,data of the zero-sequence current divided by different time windows are successively input into the trained FINET.A proposed PSF(principal-subordinate factor)analyses the results obtained from FINET to improve anti-interference in the mentioned IAF detection algorithm.Experiments using PSCAD/EMTDC software simulation data show the proposed method is feasible and highly adaptable.In addition,the detection result of on-site recorded data demonstrates the effectiveness of the proposed method in practical resonant grounding systems.
基金supported by National Key Basic Research Program of China(973 Program)(No.2015CB251001)National Natural Science Foundation of China(Nos.51221005,51177124,51377128,51323012)+1 种基金the Science and Technology Project Funds of the Grid State Corporation SGSNKYOOKJJS1501564Shaanxi Province Natural Science Foundation of China(No.2013JM-7010)
文摘The behavior of fault arc in a high-speed switch （HSS） has been studied theoretically and experimentally. A simplified HSS setup is designed to support this work. A two-dimensional arc model is developed to analyze the characteristics of fault arc based on magnetic-hydrodynamic （MHD） theory. The advantage of such a model is that the thermal transfer coefficient can be determined by depending on the numerical method alone. The influence of net emission coefficients （NEC） radiation model and P1 model on fault arc is analyzed in detail. Results show that NEC model predicts more radiation energy and less pressure rise without the re-absorption effect considered. As a consequence, P1 model is more suitable to calculate the pressure rise caused by fault arc. Finally, the pressure rise during longer arcing time for different arc currents is predicted.
文摘This paper investigates direct current(DC) arc fault detection in photovoltaic system. In order to avoid the risk of fire ignition caused by the arc fault in the photovoltaic power supply, it is urgent to detect the DC arc fault in the photovoltaic system. Once an arc fault is detected, the power supply should be cut off immediately. A lot of field experiments are carried out to obtain the data of arc fault current of the photovoltaic system under different current conditions. Cable length, arc gap, and the effects of different sensors are tested.These three conditions are the most significant features of this paper. Four characteristic variables from both the time domain and the frequency domain are extracted to identify the arc fault. Then the logistic regression method in the field of artificial intelligence and machine learning is originally used to analyze the experimental results of arc fault in the photovoltaic system. The function between the probability of the arc fault and the change of the characteristic variables is obtained. After validating 80 groups of experimental data under different conditions,the accuracy rate of the arc fault detection by this algorithm is proved to reach 100%.
基金supported by National Key Basic Research Program of China(973 Program)(No.2015CB251002)National Natural Science Foundation of China(Nos.51221005,51177124)+2 种基金the Fundamental Research Funds for the Central Universitiesthe Program for New Century Excellent Talents in UniversityShaanxi Province Natural Science Foundation of China(No.2013JM-7010)
文摘This paper focuses on the simulation of a fault arc in a closed tank based on the magneto-hydrodynamic （MHD） method, in which a comparative study of three radiation models, including net emission coefficients （NEC）, semi-empirical model based on NEC as well as the P1 model, is developed. The pressure rise calculated by the three radiation models are compared to the measured results. Particularly when the senti-empirical model is used, the effect of different boundary temperatures of the re-absorption layer in the semi-empirical model on pressure rise is concentrated on. The results show that the re-absorption effect in the low-temperature region affects radiation transfer of fault arcs evidently, and thus the internal pressure rise. Compared with the NEC model, P1 and the semi-empirical model with 0.7 〈 α 〈 0.83 are more suitable to calculate the pressure rise of the fault arc, where is an adjusted parameter involving the boundary temperature of the re-absorption region in the semi-empirical model.
