The document describes an electro-thermal model for metal-oxide arresters (MOAs) that considers the interaction between temperature and resistive current. The model consists of an electric model and a thermal model. The electric model uses an artificial neural network trained on experimental voltage-current-temperature data to calculate current based on applied voltage and temperature. The thermal model uses a circuit to calculate temperature changes based on power loss from the electric model. An algorithm iterates between the models to simulate the electro-thermal characteristics over time. Experimental validation showed good agreement between simulated and experimental temperature-time profiles under different voltages.
Multi-Physics Analysis of a Refractory Metal ACOperated High Temperature Heat...SIMULIA
Electrically operated high temperature furnaces and reactors are used in many industrial manufacturing processes such as sintering or single crystal growth in order to allow for the required process conditions. In view of their outstanding characteristics refractory metals are ideally suited as materials for the resistive heating elements. Nevertheless, significant and lifetime- limiting irreversible deformations of these elements can be frequently observed which are assumed to be caused by a combination of temperature expansion, electromagnetic forces, and high temperature creep effects. In order to study this undesired behavior, a multi-physics model of a particular three-phase AC heating element of a sintering furnace is formulated and implemented within Abaqus. It accounts for the primary involved coupled physical mechanisms such as the harmonic electrical field problem, the thermal problem governed by Joule's law, thermal expansion, high temperature creep and harmonic forces caused by the electromagnetic field along with field dependent constitutive behavior. Since in general solving the fully coupled problem on a 3D domain is computationally demanding and Abaqus lacks functionality in the field of electromagnetism, a semi-analytical approach for consideration of time-harmonic electromagnetic forces within mechanical analysis is developed in the present work. The model implemented as a userdefined extension for Abaqus is computationally very attractive since it avoids discretization of the medium surrounding the heater. Furthermore, some aspects of modeling coupled physical problems of different characteristic time-scale are briefly discussed. Results from application of the model are in good qualitative agreement with in-situ observations and confirm the relevance of considering electromagnetic forces within analysis of high temperature furnaces.
Simulation and Results of Static Var Compensator for Electric Arc Furnace No ...ijtsrd
Electric arc furnace is unbalanced, nonlinear and time varying loads, which can cause many problems in the power system. Voltage variation problem is the major focus of the power system because the loads can vary anytime. Power quality issue has a very high attractive for power system engineers and try to solve these problems by several effective ways. In this thesis, Static Var Compensator SVC , thyristor controlled reactor compensation with thyristor switched capacitor TCR TSC type is designed and its performance is simulated in the case studies. This unique design of this device SVC is used for reactive power compensation for nonlinear loads such as electric arc furnace EAF in an industrial plant. Moreover, the SVC is more effectively enhance the voltage stability. Single tuned passive harmonic filter can reduce total harmonic distortion THD caused by thyristor controlled reactor of SVC. The installation site for this thesis is No. 1 Iron and Steel Mill, Pyin Oo Lwin. And then, data is taken from this Steel Mill. Simulation results will be provided by using MATLAB SIMULINK. Dr. Thet Mon Aye "Simulation and Results of Static Var Compensator for Electric Arc Furnace (No 1 Iron and Steel Mill, Pyin Oo Lwin, Myanmar)" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26613.pdfPaper URL: https://www.ijtsrd.com/engineering/electrical-engineering/26613/simulation-and-results-of-static-var-compensator-for-electric-arc-furnace-no-1-iron-and-steel-mill-pyin-oo-lwin-myanmar/dr-thet-mon-aye
Finite Element Method for Designing and Analysis of the Transformer – A Retro...idescitation
Finite Element Analysis (FEA) using Finite Element Method (FEM) was
developed over 70 years to solve the complex elasticity and structural analysis problem in
civil and aeronautical engineering. Application of FEA is being expanded to simulation in
electrical engineering also to solve the complex design problems. The circuit theory models
for designing transformers are not much accurate in determining the transformer
parameters such as winding impedance, leakage inductance, hot spot temperature etc. The
physical realization of these parameters is needed on a prototype unit. The finite element
method can play a vital role in deriving these parameters without any physical verification.
An effort has been made in this paper to show the effectiveness of finite element method in
determining the above said parameters while designing the transformers - both oil cooled as
well as dry type - for power and distribution sectors as well as to analyze and detect the
internal faults in the transformer.
Solar Module Modeling, Simulation And Validation Under Matlab / SimulinkIJERA Editor
Solar modules are systems which convert sunlight into electricity using the physics of semiconductors. Mathematical modeling of these systems uses weather data such as irradiance and temperature as inputs. It provides the current, voltage or power as outputs, which allows plot the characteristic giving the intensity I as a function of voltage V for photovoltaic cells. In this work, we have developed a model for a diode of a Photovoltaic module under the Matlab / Simulink environment. From this model, we have plotted the characteristic curves I-V and P-V of solar cell for different values of temperature and sunlight. The validation has been done by comparing the experimental curve with power from a solar panel HORONYA 20W type with that obtained by the model.
Designing and testing of metal oxide surge arrester for EHV lineRohit Khare
Surge arresters constitute an indispensable aid to insulation coordination in electrical power systems. There the voltages which may appear in an electrical power system are given in per-unit of the peak value of the highest continuous line-to-earth voltage, depending on the duration of their appearance. The voltage or overvoltage which can be reached without the use of arresters is a value of several p.u. If instead, one considers the curve of the withstand voltage of equipment insulation (here equipment means electrical devices such as power transformers) one notices that starting in the range of switching overvoltages, and especially for lightning over voltages, the equipment insulation cannot withstand the occurring dielectric stresses. At this point, the arresters intervene. When in operation, it is certain that the voltage that occurs at the terminal of the device - while maintaining an adequate safety margin - will stay below the withstand voltage. Arresters’ effect, therefore, involves lightning and switching over voltages.
The time axis is roughly divided into the range of lightning overvoltage (microseconds), switching overvoltages (milliseconds), temporary overvoltages (seconds) – which are commonly cited by the abbreviation "TOV" – and finally the temporally unlimited highest continuous system operation voltage.
Iron losses in ferromagnetic enclosures of gas-insulated transmission lines u...Power System Operation
The enclosure of AC gas-insulated transmission lines
(AC-GIL) is ordinarily made of aluminium. In HVDC
systems, it can be economically and technically
reasonable to manufacture the enclosure of GIL from
steel. To check the feasibility to operate such DC-GIL
even under AC the relevant losses in the steel enclosure
must be known.
The present paper compares three different methods to
determine the specific iron losses of steel when exposed
to magnetic fields with power frequencies. The iron
losses as a function of the magnetic field strength are
measured with a pipe sample in a coaxial conductor
arrangement, a pipe sample in a toroidal core test and
with relevant strips in an Epstein frame. The results
from the three test methods are found to be in close
agreement. By calculating the iron losses in a GIL with
steel enclosure the reduction of the transmission capacity
is estimated when changing from DC to AC operation.
Electrical discharge machining is basically a non-conventional material removal process which is widely used to produce dies, punches and moulds, finishing parts for aerospace and automotive industry, and surgical components. This process can be successfully employed to machine electrically conductive parts irrespective of their hardness, shape and toughness.
Multi-Physics Analysis of a Refractory Metal ACOperated High Temperature Heat...SIMULIA
Electrically operated high temperature furnaces and reactors are used in many industrial manufacturing processes such as sintering or single crystal growth in order to allow for the required process conditions. In view of their outstanding characteristics refractory metals are ideally suited as materials for the resistive heating elements. Nevertheless, significant and lifetime- limiting irreversible deformations of these elements can be frequently observed which are assumed to be caused by a combination of temperature expansion, electromagnetic forces, and high temperature creep effects. In order to study this undesired behavior, a multi-physics model of a particular three-phase AC heating element of a sintering furnace is formulated and implemented within Abaqus. It accounts for the primary involved coupled physical mechanisms such as the harmonic electrical field problem, the thermal problem governed by Joule's law, thermal expansion, high temperature creep and harmonic forces caused by the electromagnetic field along with field dependent constitutive behavior. Since in general solving the fully coupled problem on a 3D domain is computationally demanding and Abaqus lacks functionality in the field of electromagnetism, a semi-analytical approach for consideration of time-harmonic electromagnetic forces within mechanical analysis is developed in the present work. The model implemented as a userdefined extension for Abaqus is computationally very attractive since it avoids discretization of the medium surrounding the heater. Furthermore, some aspects of modeling coupled physical problems of different characteristic time-scale are briefly discussed. Results from application of the model are in good qualitative agreement with in-situ observations and confirm the relevance of considering electromagnetic forces within analysis of high temperature furnaces.
Simulation and Results of Static Var Compensator for Electric Arc Furnace No ...ijtsrd
Electric arc furnace is unbalanced, nonlinear and time varying loads, which can cause many problems in the power system. Voltage variation problem is the major focus of the power system because the loads can vary anytime. Power quality issue has a very high attractive for power system engineers and try to solve these problems by several effective ways. In this thesis, Static Var Compensator SVC , thyristor controlled reactor compensation with thyristor switched capacitor TCR TSC type is designed and its performance is simulated in the case studies. This unique design of this device SVC is used for reactive power compensation for nonlinear loads such as electric arc furnace EAF in an industrial plant. Moreover, the SVC is more effectively enhance the voltage stability. Single tuned passive harmonic filter can reduce total harmonic distortion THD caused by thyristor controlled reactor of SVC. The installation site for this thesis is No. 1 Iron and Steel Mill, Pyin Oo Lwin. And then, data is taken from this Steel Mill. Simulation results will be provided by using MATLAB SIMULINK. Dr. Thet Mon Aye "Simulation and Results of Static Var Compensator for Electric Arc Furnace (No 1 Iron and Steel Mill, Pyin Oo Lwin, Myanmar)" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26613.pdfPaper URL: https://www.ijtsrd.com/engineering/electrical-engineering/26613/simulation-and-results-of-static-var-compensator-for-electric-arc-furnace-no-1-iron-and-steel-mill-pyin-oo-lwin-myanmar/dr-thet-mon-aye
Finite Element Method for Designing and Analysis of the Transformer – A Retro...idescitation
Finite Element Analysis (FEA) using Finite Element Method (FEM) was
developed over 70 years to solve the complex elasticity and structural analysis problem in
civil and aeronautical engineering. Application of FEA is being expanded to simulation in
electrical engineering also to solve the complex design problems. The circuit theory models
for designing transformers are not much accurate in determining the transformer
parameters such as winding impedance, leakage inductance, hot spot temperature etc. The
physical realization of these parameters is needed on a prototype unit. The finite element
method can play a vital role in deriving these parameters without any physical verification.
An effort has been made in this paper to show the effectiveness of finite element method in
determining the above said parameters while designing the transformers - both oil cooled as
well as dry type - for power and distribution sectors as well as to analyze and detect the
internal faults in the transformer.
Solar Module Modeling, Simulation And Validation Under Matlab / SimulinkIJERA Editor
Solar modules are systems which convert sunlight into electricity using the physics of semiconductors. Mathematical modeling of these systems uses weather data such as irradiance and temperature as inputs. It provides the current, voltage or power as outputs, which allows plot the characteristic giving the intensity I as a function of voltage V for photovoltaic cells. In this work, we have developed a model for a diode of a Photovoltaic module under the Matlab / Simulink environment. From this model, we have plotted the characteristic curves I-V and P-V of solar cell for different values of temperature and sunlight. The validation has been done by comparing the experimental curve with power from a solar panel HORONYA 20W type with that obtained by the model.
Designing and testing of metal oxide surge arrester for EHV lineRohit Khare
Surge arresters constitute an indispensable aid to insulation coordination in electrical power systems. There the voltages which may appear in an electrical power system are given in per-unit of the peak value of the highest continuous line-to-earth voltage, depending on the duration of their appearance. The voltage or overvoltage which can be reached without the use of arresters is a value of several p.u. If instead, one considers the curve of the withstand voltage of equipment insulation (here equipment means electrical devices such as power transformers) one notices that starting in the range of switching overvoltages, and especially for lightning over voltages, the equipment insulation cannot withstand the occurring dielectric stresses. At this point, the arresters intervene. When in operation, it is certain that the voltage that occurs at the terminal of the device - while maintaining an adequate safety margin - will stay below the withstand voltage. Arresters’ effect, therefore, involves lightning and switching over voltages.
The time axis is roughly divided into the range of lightning overvoltage (microseconds), switching overvoltages (milliseconds), temporary overvoltages (seconds) – which are commonly cited by the abbreviation "TOV" – and finally the temporally unlimited highest continuous system operation voltage.
Iron losses in ferromagnetic enclosures of gas-insulated transmission lines u...Power System Operation
The enclosure of AC gas-insulated transmission lines
(AC-GIL) is ordinarily made of aluminium. In HVDC
systems, it can be economically and technically
reasonable to manufacture the enclosure of GIL from
steel. To check the feasibility to operate such DC-GIL
even under AC the relevant losses in the steel enclosure
must be known.
The present paper compares three different methods to
determine the specific iron losses of steel when exposed
to magnetic fields with power frequencies. The iron
losses as a function of the magnetic field strength are
measured with a pipe sample in a coaxial conductor
arrangement, a pipe sample in a toroidal core test and
with relevant strips in an Epstein frame. The results
from the three test methods are found to be in close
agreement. By calculating the iron losses in a GIL with
steel enclosure the reduction of the transmission capacity
is estimated when changing from DC to AC operation.
Electrical discharge machining is basically a non-conventional material removal process which is widely used to produce dies, punches and moulds, finishing parts for aerospace and automotive industry, and surgical components. This process can be successfully employed to machine electrically conductive parts irrespective of their hardness, shape and toughness.
Development of magnetic pulse crimping process for highdurability connection ...IJERA Editor
Generally, hand-operated and hydraulic compressors use crimping of connection terminals. However, this equipment often causes compressed defects because non-uniform pressure is applied in the circumferential direction of the terminal during crimping. A defective terminal often leads to fire in electric equipment due to overheating. Therefore, there is a need to develop a new crimping process for manufacturing highly durable terminals. MPC (magnetic pulse crimping) uses uniform electromagnetic pressure by a high magnetic field interaction between coil and terminal. This process uses only electromagnetic pressure for crimping, so the terminal can be crimped without physical contact, thereby producing a highly durable connection terminal. In this study, a MPC process was developed to fabricate a prototypical terminal. The result was compared with other crimping processes in terms of durability. The crimped part using MPC has a lower rising temperature and higher tensile strength than those using other crimping process. It is inferred from the experimental results that an optimal charging voltage exists in the MPC process
A Study of Thermal Behaviour of HTS Devices at Alternating Current IJECEIAES
The paper presents a study on thermal behavior of a coil made of a hightemperature supercon-ducting tape representing operation of a superconducting device (for example, a transformer). Based on the results of a physical experiment, a mathematical model of superconducting coil operation under short circuit conditions at the load side was developed. Regimes of overheating by variable short circuit currents were investigated. In this case, short circuit current amplitudes ex-ceeded a critical current of a superconductor, and coil parameters (e.g. an average nonlinearity parameter of a current-voltage characteristic, a superconductor length, and others) were varied. Permissible overheating for a coil with the possibility of its return into the superconducting state after emergency conditions in a dead-time period of automatic reclosing was considered. A crite-rion for return of a superconducting device into the superconducting state within a dead-time period of automatic reclosing has been obtained.
Development of magnetic pulse crimping process for highdurability connection ...IJERA Editor
Generally, hand-operated and hydraulic compressors use crimping of connection terminals. However, this equipment often causes compressed defects because non-uniform pressure is applied in the circumferential direction of the terminal during crimping. A defective terminal often leads to fire in electric equipment due to overheating. Therefore, there is a need to develop a new crimping process for manufacturing highly durable terminals. MPC (magnetic pulse crimping) uses uniform electromagnetic pressure by a high magnetic field interaction between coil and terminal. This process uses only electromagnetic pressure for crimping, so the terminal can be crimped without physical contact, thereby producing a highly durable connection terminal. In this study, a MPC process was developed to fabricate a prototypical terminal. The result was compared with other crimping processes in terms of durability. The crimped part using MPC has a lower rising temperature and higher tensile strength than those using other crimping process. It is inferred from the experimental results that an optimal charging voltage exists in the MPC process
Analysis of Voltage and Current Variations in Hybrid Power SystemIJRST Journal
In this paper, a detailed dynamic model and simulation of a solar cell/wind turbine/fuel cell hybrid power system is Developed using a novel topology to complement each other and to alleviate the effects of environmental variations. Comparing with the nuclear energy and thermal power, the renewable energy is inexhaustible and has non-pollution Characteristics. Here Ultra-capacitors are used in power applications requiring short duration peak power. The voltage variation at the output is found to be within the acceptable range. The output fluctuations of the wind turbine varying with wind speed and the solar cell varying with both environmental temperature and sun radiation are reduced using a fuel cell. Therefore, this system can tolerate the rapid changes in load and environmental conditions, and suppress the effects of these fluctuations on the equipment side voltage. The proposed system can be used for off-grid power generation in non interconnected areas or remote isolated communities. Modeling and simulations are conducted using MATLAB/Simulink software packages to verify the effectiveness of the proposed system. The results show that the proposed hybrid power system can tolerate the rapid changes in natural conditions and suppress the effects of these fluctuations on the voltage within the acceptable range.
This article describes the operational principles, construction and other features of the four most basic transducers viz. Strain Gauge, Potentiometer, Load Cell and LVDT. Also this article describes the characteristic features of different material transduction properties.
Development of a Thermoelectric Micro generation based on Seebeck EffectIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
The Application of Artificial Intelligence Techniques for Modeling and Simula...MohammadMomani26
Abstract— This paper accurately models photovoltaic (PV) arrays based on genetic and Cuckoo Optimization algorithms. These algorithms are used to obtain the parameters of the array model based on a PV cell datasheet information. In this work, a comparison between the two-diode model and the single-diode model is presented. The adopted model is implemented on simulation platforms using MATLAB 2020a environment and it is designed to be of use to power electronics specialists. The mathematical analysis of the model is presented in detail where different cases of different temperature and solar irradiance are adopted. The model was tested and validated with experimental data. Validation and comparison data are taken from the Mutah university PV power plant. The results show that the two-diode model is more accurate than the single diode model, Cuckoo optimization algorithm handles the problem with low iterations and better fitness value as compared with the genetic algorithm. The work in paper is useful for power electronics designers and researchers who need an effective and more accurate way to model and simulate photovoltaic arrays.
Mathematical modeling, simulation and validation of photovoltaic cellseSAT Journals
Abstract In this paper, an analysis has been done on the effect of varying physical and environmental factors on the I-V (current voltage characteristics) of a photovoltaic cell using Matlab-Simulink. A standalone model has been created based on the mathematical relations between various parameters in photovoltaic cells made up of a single diode, a series resistance, and a shunt resistance. To validate the developed model, the values from I-V characteristics of this model have been compared with the experimental results. In addition, simulations have been done for I-V characteristics for different temperature and resistance values. The results obtained are analyzed and presented in this paper. Keywords: Solar cell, Modeling, Matlab-simulink
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Development of magnetic pulse crimping process for highdurability connection ...IJERA Editor
Generally, hand-operated and hydraulic compressors use crimping of connection terminals. However, this equipment often causes compressed defects because non-uniform pressure is applied in the circumferential direction of the terminal during crimping. A defective terminal often leads to fire in electric equipment due to overheating. Therefore, there is a need to develop a new crimping process for manufacturing highly durable terminals. MPC (magnetic pulse crimping) uses uniform electromagnetic pressure by a high magnetic field interaction between coil and terminal. This process uses only electromagnetic pressure for crimping, so the terminal can be crimped without physical contact, thereby producing a highly durable connection terminal. In this study, a MPC process was developed to fabricate a prototypical terminal. The result was compared with other crimping processes in terms of durability. The crimped part using MPC has a lower rising temperature and higher tensile strength than those using other crimping process. It is inferred from the experimental results that an optimal charging voltage exists in the MPC process
A Study of Thermal Behaviour of HTS Devices at Alternating Current IJECEIAES
The paper presents a study on thermal behavior of a coil made of a hightemperature supercon-ducting tape representing operation of a superconducting device (for example, a transformer). Based on the results of a physical experiment, a mathematical model of superconducting coil operation under short circuit conditions at the load side was developed. Regimes of overheating by variable short circuit currents were investigated. In this case, short circuit current amplitudes ex-ceeded a critical current of a superconductor, and coil parameters (e.g. an average nonlinearity parameter of a current-voltage characteristic, a superconductor length, and others) were varied. Permissible overheating for a coil with the possibility of its return into the superconducting state after emergency conditions in a dead-time period of automatic reclosing was considered. A crite-rion for return of a superconducting device into the superconducting state within a dead-time period of automatic reclosing has been obtained.
Development of magnetic pulse crimping process for highdurability connection ...IJERA Editor
Generally, hand-operated and hydraulic compressors use crimping of connection terminals. However, this equipment often causes compressed defects because non-uniform pressure is applied in the circumferential direction of the terminal during crimping. A defective terminal often leads to fire in electric equipment due to overheating. Therefore, there is a need to develop a new crimping process for manufacturing highly durable terminals. MPC (magnetic pulse crimping) uses uniform electromagnetic pressure by a high magnetic field interaction between coil and terminal. This process uses only electromagnetic pressure for crimping, so the terminal can be crimped without physical contact, thereby producing a highly durable connection terminal. In this study, a MPC process was developed to fabricate a prototypical terminal. The result was compared with other crimping processes in terms of durability. The crimped part using MPC has a lower rising temperature and higher tensile strength than those using other crimping process. It is inferred from the experimental results that an optimal charging voltage exists in the MPC process
Analysis of Voltage and Current Variations in Hybrid Power SystemIJRST Journal
In this paper, a detailed dynamic model and simulation of a solar cell/wind turbine/fuel cell hybrid power system is Developed using a novel topology to complement each other and to alleviate the effects of environmental variations. Comparing with the nuclear energy and thermal power, the renewable energy is inexhaustible and has non-pollution Characteristics. Here Ultra-capacitors are used in power applications requiring short duration peak power. The voltage variation at the output is found to be within the acceptable range. The output fluctuations of the wind turbine varying with wind speed and the solar cell varying with both environmental temperature and sun radiation are reduced using a fuel cell. Therefore, this system can tolerate the rapid changes in load and environmental conditions, and suppress the effects of these fluctuations on the equipment side voltage. The proposed system can be used for off-grid power generation in non interconnected areas or remote isolated communities. Modeling and simulations are conducted using MATLAB/Simulink software packages to verify the effectiveness of the proposed system. The results show that the proposed hybrid power system can tolerate the rapid changes in natural conditions and suppress the effects of these fluctuations on the voltage within the acceptable range.
This article describes the operational principles, construction and other features of the four most basic transducers viz. Strain Gauge, Potentiometer, Load Cell and LVDT. Also this article describes the characteristic features of different material transduction properties.
Development of a Thermoelectric Micro generation based on Seebeck EffectIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
The Application of Artificial Intelligence Techniques for Modeling and Simula...MohammadMomani26
Abstract— This paper accurately models photovoltaic (PV) arrays based on genetic and Cuckoo Optimization algorithms. These algorithms are used to obtain the parameters of the array model based on a PV cell datasheet information. In this work, a comparison between the two-diode model and the single-diode model is presented. The adopted model is implemented on simulation platforms using MATLAB 2020a environment and it is designed to be of use to power electronics specialists. The mathematical analysis of the model is presented in detail where different cases of different temperature and solar irradiance are adopted. The model was tested and validated with experimental data. Validation and comparison data are taken from the Mutah university PV power plant. The results show that the two-diode model is more accurate than the single diode model, Cuckoo optimization algorithm handles the problem with low iterations and better fitness value as compared with the genetic algorithm. The work in paper is useful for power electronics designers and researchers who need an effective and more accurate way to model and simulate photovoltaic arrays.
Mathematical modeling, simulation and validation of photovoltaic cellseSAT Journals
Abstract In this paper, an analysis has been done on the effect of varying physical and environmental factors on the I-V (current voltage characteristics) of a photovoltaic cell using Matlab-Simulink. A standalone model has been created based on the mathematical relations between various parameters in photovoltaic cells made up of a single diode, a series resistance, and a shunt resistance. To validate the developed model, the values from I-V characteristics of this model have been compared with the experimental results. In addition, simulations have been done for I-V characteristics for different temperature and resistance values. The results obtained are analyzed and presented in this paper. Keywords: Solar cell, Modeling, Matlab-simulink
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
energies-11-01610.pdf
1. energies
Article
Electro-Thermal Modeling of Metal-Oxide Arrester
under Power Frequency Applied Voltages
Jiazheng Lu, Pengkang Xie * ID
, Zhen Fang and Jianping Hu
State Key Laboratory of Disaster Prevention & Reduction for Power Grid Transmission & Distribution
Equipment, State Grid Hunan Electric Power Corporation Disaster Prevention & Reduction Center,
Changsha 410007, China; lujz1969@163.com (J.L.); policy@139.com (Z.F.); hujianping81016@sina.com (J.H.)
* Correspondence: xiepengkang@zju.edu.cn
Received: 30 May 2018; Accepted: 14 June 2018; Published: 20 June 2018
Abstract: Metal-oxide arresters (MOAs) are used to absorb the electrical energy resulting from
overvoltages in power systems. However, temperature rises caused by the absorbed energy can lead
to the electrothermal failure of MOAs. Therefore, it is necessary to analyze the electric and thermal
characteristics of MOAs. In this paper, in order to study the electric and thermal characteristics of
MOAs under power frequency voltage, an improved electrothermal model of an MOA is presented.
The proposed electrothermal model can be divided into an electric model and a thermal model.
In the electric model, based on the conventional MOA electric circuit, the effect of temperature on the
voltage–current (V–I) characteristics of an MOA has been obtained. Using temperature and applied
voltage as input data, the current flows through the MOA can be calculated using the artificial
neural network (ANN) method. In the thermal model, the thermal circuit of a MOA has been built.
The varistor power loss obtained from the electric model is used as input data, and the temperature
of the zinc oxide varistors can be calculated. Therefore, compared with the existing MOA models,
the interaction of leakage current and temperature can be considered in the proposed model. Finally,
experimental validations have been done, and the electrothermal characteristics of an MOA have
been studied by simulation and experimental methods. The electrothermal model proposed in this
paper can assist with the prediction of the electric and thermal characteristics of MOAs.
Keywords: Metal-oxide arresters; electrothermal model; temperature; leakage current; power loss
1. Introduction
Metal-oxide arresters (MOAs) are electric equipment that are used in the power systems for
protection against overvoltages [1,2]. When a MOA is subjected to an electric system operating voltage,
its resistance is high enough that the leakage resistive current can be neglected. However, due to
the highly non-linear voltage–current (V–I) characteristics, when the MOA is subjected to temporary
overvoltages or transient surges, the equivalent resistance become much smaller, and the resistive
dynamic behavior is predominant [3–6]. Due to these non-linear V–I characteristics and excellent
current/energy absorption capabilities, MOAs are widely used in the electrical power systems [1–6].
For an MOA, zinc oxide (ZnO) varistors are the core components, and the V–I characteristics of ZnO
varistors show temperature dependence under power frequency-applied voltages [7–11]. What’s more,
when an AC voltage is applied to a MOA, the resistive current flowing through the ZnO varistors can
cause power loss, which may lead to temperature rise or thermal failure of the MOA [12–15]. Thus,
in order to improve the thermal stability of MOAs, it is of great significance to study the interaction of
MOAs’ temperature and power loss characteristics under power frequency overvoltages.
In order to study the interaction of the electric and thermal characteristics of MOAs, it is necessary
to develop their electrothermal models. Electric models of MOAs were proposed to provide tools
Energies 2018, 11, 1610; doi:10.3390/en11061610 www.mdpi.com/journal/energies
2. Energies 2018, 11, 1610 2 of 13
for studies of insulation coordination, optimal location, and so on by Schmidt, Vita and Kim [16–18].
These models, which have considered the non-linear V–I characteristics of ZnO varistors, can be used
under different applied voltages (power frequency [16], switching [17], lightning [18], etc.). However,
the electric models proposed by Schmidt, Vita and Kim [16–18] have not considered the temperature
effects on the V–I characteristics of MOAs. The electric characteristics of surge arresters were studied
by He [19], and the electric failure modes of MOAs caused by thermal reasons were investigated [20].
The V–I characteristics of MOAs have been expressed as a function of temperature by Petit [21].
The influence of temperature on the resistive current of MOAs was studied by He, Bartkowiak and
Petit [19–21], but the power loss and temperature rise caused by the resistive current have not been
studied. In order to study the thermal characteristics of MOAs, methods have been suggested for
power loss and temperature performance prediction [22–27]. The thermal characteristics of MOAs
have been studied experimentally [22], and an analytical method for the performance prediction of
MOAs was proposed by Lat [23]. Finite element methods were applied to calculate temperature
and power loss [24–26], the thermal stability of MOAs with different structures was compared [24],
the effects of the thermal failure on the microstructure of ZnO varistors were analyzed [25], and the
pollution degree of MOA has also been considered when calculating the temperature rise of MOA [26].
Seyyedbarzegar [27] built a thermal balance diagram, and it has been confirmed that the power loss
caused by the leakage current is dependent on the applied voltage, temperature, and V–I characteristics
of the varistors.
In view of the existing studies, it can be known that when the resistive leakage current increases,
the power loss and temperature of the ZnO varistors rise [22–27], which consequently increases the
resistive leakage current in the ZnO varistors [19–21]. This process continues cumulatively, leading to
thermal instability and associated catastrophic effects. Using the existing simulation models mentioned
above, it is not possible to identify the interaction of leakage current and MOA temperature at the
same time. Therefore, in this paper, an electrothermal model is proposed. Compared with the existing
studies, the electrothermal model proposed in this paper has considered the interaction of resistive
current and the temperature rise of MOA; thus, it can simulate the electric and thermal characteristics
at the same time. This paper is organized as follows:
• Firstly, the conventional electric model of an MOA is introduced; based on the conventional
model, the diagram and calculation algorithm of the electrothermal model is proposed.
• Secondly, in order to build the electric part of the electrothermal model, experiments were
carried out to obtain the voltage–current–temperature (V–I–T) characteristics of the tested ZnO
varistors. According to the experimental results, the electric model of the tested ZnO varistors
considering the temperature effects is built using the artificial neural network (ANN) method.
Using temperature and applied voltage as input data, the leakage current flowing through the
varistors can be obtained, and the electric part of the electrothermal model has been validated
through experimental results.
• Thirdly, a thermal resistance circuit model is introduced to build the thermal part of the model.
Using power loss and ambient temperature as input data, the temperature of the MOA is
calculated, which is used as the input data of the electric model. By doing so, the electrothermal
model can be obtained combining the electric and thermal model built above. Compared with the
existing studies, the interaction between the resistive leakage current and the temperature rise of
ZnO varistors has been considered in this paper, and the electric and thermal characteristics can
be simulated at the same time.
• Finally, experiments were carried out to validate the simulation model, and its electric and thermal
characteristics have been studied. Compared with the existing studies, the relationship between
arrester temperature and time under different applied voltages is studied, and the experimental
and simulated results show good agreement with each other.
3. Energies 2018, 11, 1610 3 of 13
2. Diagram and Calculation Algorithm of Electrothermal Model
Conventional Electric Model Review
According to Section 1, MOAs have temperature-dependent non-linear V-I characteristics.
Under power frequency voltage, the current flowing through the ZnO varistor can be divided into
resistive and capacitive components. Therefore, the conventional circuit models of ZnO varistors
and MOAs are built and shown in Figure 1 [18]. In this conventional model, five ZnO varistors are
contained in the MOA; R, R1 to R5 represent the resistances of each varistor. C, C1 to C5 represent
the stray capacitance of each varistor. CFF is the capacitance between the upper and lower flanges,
CFUSi (i = 1, 2, 3) are the upper flange stray capacitances with spacers and aluminum sheets, and CFDSi
(i = 1, 2, 3, 4) are the stray capacitances among the lower flange and spacers and aluminum sheets.
Energies 2018, 11, x FOR PEER REVIEW 3 of 13
2. Diagram and Calculation Algorithm of Electrothermal Model
Conventional Electric Model Review
According to Section 1, MOAs have temperature-dependent non-linear V-I characteristics.
Under power frequency voltage, the current flowing through the ZnO varistor can be divided into
resistive and capacitive components. Therefore, the conventional circuit models of ZnO varistors
and MOAs are built and shown in Figure 1 [18]. In this conventional model, five ZnO varistors are
contained in the MOA; R, R1 to R5 represent the resistances of each varistor. C, C1 to C5 represent the
stray capacitance of each varistor. CFF is the capacitance between the upper and lower flanges, CFUSi
(i = 1, 2, 3) are the upper flange stray capacitances with spacers and aluminum sheets, and CFDSi (i = 1,
2, 3, 4) are the stray capacitances among the lower flange and spacers and aluminum sheets.
(a)
1
C
2
C
3
C
4
C
1
R
2
R
3
R
4
R
U
1
FDS
C
2
FDS
C
3
FDS
C
1
FUS
C 2
FUS
C
FF
C
5
C
5
R
3
FUS
C
4
FDS
C
(b)
Figure 1. Conventional circuit model for ZnO varistor and metal-oxide arrester (MOA): (a) varistor
model; (b) MOA model.
In the conventional model shown in Figure 1, R1 to R5 are only dependent on the V–I
characteristics of the ZnO varistors, and the power loss and temperature effects on the V–I
characteristics of MOAs are not considered. So, the electric model in Figure 1 can only be used to
calculate the electric characteristics of MOAs under specific temperature. Based on the electric model
in Figure 1, an electrothermal model of ZnO varistors is proposed in Figure 2, where P is the power
loss, Te is the varistor temperature, and Ta is the ambient temperature. As shown in Figure 2, the
Figure 1. Conventional circuit model for ZnO varistor and metal-oxide arrester (MOA): (a) varistor
model; (b) MOA model.
In the conventional model shown in Figure 1, R1 to R5 are only dependent on the V–I characteristics
of the ZnO varistors, and the power loss and temperature effects on the V–I characteristics of MOAs are
not considered. So, the electric model in Figure 1 can only be used to calculate the electric characteristics
of MOAs under specific temperature. Based on the electric model in Figure 1, an electrothermal model
4. Energies 2018, 11, 1610 4 of 13
of ZnO varistors is proposed in Figure 2, where P is the power loss, Te is the varistor temperature,
and Ta is the ambient temperature. As shown in Figure 2, the electrothermal model can be divided
into an electric part and a thermal part. In the electric part, using the applied voltage and varistor
temperature as input data, the temperature-dependent V–I characteristics can be estimated by an
artificial neural network (ANN). The power loss and electric characteristics (applied voltage, leakage
current) can be obtained as output data of the electric model. In the thermal model, a thermal circuit of
an MOA has been built. Based on the power loss of the ZnO varistors and the ambient temperature
as input data, the temperature of the varistors can be obtained as the output of the thermal model.
The temperature of the arresters is used as the input data of the electric part of the model consequently.
Replacing the ZnO varistor model in Figure 1b with that in Figure 2, the electrothermal model of MOA
can be obtained.
Energies 2018, 11, x FOR PEER REVIEW 4 of 13
electrothermal model can be divided into an electric part and a thermal part. In the electric part,
using the applied voltage and varistor temperature as input data, the temperature-dependent V–I
characteristics can be estimated by an artificial neural network (ANN). The power loss and electric
characteristics (applied voltage, leakage current) can be obtained as output data of the electric model.
In the thermal model, a thermal circuit of an MOA has been built. Based on the power loss of the
ZnO varistors and the ambient temperature as input data, the temperature of the varistors can be
obtained as the output of the thermal model. The temperature of the arresters is used as the input
data of the electric part of the model consequently. Replacing the ZnO varistor model in Figure 1b
with that in Figure 2, the electrothermal model of MOA can be obtained.
,
U I
R
P
Ta
Te
C
U
Figure 2. Diagram of the electrothermal MOA model.
In order to solve the electrothermal model in Figure 2, a calculation algorithm is proposed in
Figure 3. The calculation process of the algorithm contains three steps:
1. Firstly, the V–I characteristics of ZnO varistors are measured under different temperatures
experimentally. Using the applied voltage and varistor temperature as input data and the
measured leakage current as output data, an artificial neural network is trained; thus, the V–I–
T characteristics of the tested ZnO varistors can be obtained using the ANN method. The
power losses of the varistors are calculated in order to be used in the thermal model.
2. Secondly, an equivalent thermal circuit of MOA is built; using the ambient temperature, power
loss, and MOA temperature at time t as input data, the temperature changes of the MOA can
be obtained, and the MOA temperature at the next time-step (t + Δt) is calculated as the output
data of the thermal model.
3. Finally, according to the last two steps, setting an ambient temperature, initial MOA
temperature, and applied voltage, the electrothermal characteristics at different times can be
calculated. If the difference between the electrothermal characteristics of two adjacent time
steps is smaller than a threshold value, the electrothermal state reaches a steady state. Once the
simulation time reaches the end, or the electrothermal simulation reaches a steady state, the
simulation process reaches the end.
Figure 2. Diagram of the electrothermal MOA model.
In order to solve the electrothermal model in Figure 2, a calculation algorithm is proposed in
Figure 3. The calculation process of the algorithm contains three steps:
1. Firstly, the V–I characteristics of ZnO varistors are measured under different temperatures
experimentally. Using the applied voltage and varistor temperature as input data and the
measured leakage current as output data, an artificial neural network is trained; thus, the V–I–T
characteristics of the tested ZnO varistors can be obtained using the ANN method. The power
losses of the varistors are calculated in order to be used in the thermal model.
2. Secondly, an equivalent thermal circuit of MOA is built; using the ambient temperature, power
loss, and MOA temperature at time t as input data, the temperature changes of the MOA can be
obtained, and the MOA temperature at the next time-step (t + ∆t) is calculated as the output data
of the thermal model.
3. Finally, according to the last two steps, setting an ambient temperature, initial MOA temperature,
and applied voltage, the electrothermal characteristics at different times can be calculated. If the
difference between the electrothermal characteristics of two adjacent time steps is smaller than a
threshold value, the electrothermal state reaches a steady state. Once the simulation time reaches
the end, or the electrothermal simulation reaches a steady state, the simulation process reaches
the end.
5. Energies 2018, 11, 1610 5 of 13
Energies 2018, 11, x FOR PEER REVIEW 5 of 13
t t t
= +Δ t t t
= +Δ
Figure 3. Calculation diagram for electrothermal characteristics’ estimation.
3. Electric Model Considering Temperature Effects
According to Section 2, the electrothermal model in this paper can be divided into an electric
part and a thermal part. In this section, the electric model is proposed. The V–I characteristics of the
tested varistors at different temperatures are obtained through experiments. The ANN method is
applied to simulate the temperature effects on V–I characteristics, and the simulated results show
good agreement with the experimental ones.
3.1. Experimental Setup, Test Species, and Procedures
An experimental setup for the measurement of V–I–T characteristics under a power
frequency-applied voltage is shown in Figure 4. As shown in Figure 4a, the experimental circuit
mainly includes a high voltage transformer, an oven, a high voltage probe, and a data acquisition
system. The high voltage transformer has an adjustable voltage between 0–10 kV. In the oven, there
is a thermal sensor, a temperature controller, and a heater; it is possible to increase the temperature
over 200 ± 3 °C in the oven. The data acquisition system includes a digital oscilloscope, back-to-back
connected Zener diodes Zd for overvoltage protection, and a 470-Ω shunt resistor Rsh for leakage
current measurements. The leakage current and applied voltage can be captured using a digital
oscilloscope in the data acquisition system. The experimental setup in Figure 4 can be used to
obtain the V–I characteristics of the ZnO varistors under different temperatures.
Figure 3. Calculation diagram for electrothermal characteristics’ estimation.
3. Electric Model Considering Temperature Effects
According to Section 2, the electrothermal model in this paper can be divided into an electric
part and a thermal part. In this section, the electric model is proposed. The V–I characteristics of the
tested varistors at different temperatures are obtained through experiments. The ANN method is
applied to simulate the temperature effects on V–I characteristics, and the simulated results show good
agreement with the experimental ones.
3.1. Experimental Setup, Test Species, and Procedures
An experimental setup for the measurement of V–I–T characteristics under a power
frequency-applied voltage is shown in Figure 4. As shown in Figure 4a, the experimental circuit
mainly includes a high voltage transformer, an oven, a high voltage probe, and a data acquisition
system. The high voltage transformer has an adjustable voltage between 0–10 kV. In the oven, there
is a thermal sensor, a temperature controller, and a heater; it is possible to increase the temperature
over 200 ± 3 ◦C in the oven. The data acquisition system includes a digital oscilloscope, back-to-back
connected Zener diodes Zd for overvoltage protection, and a 470-Ω shunt resistor Rsh for leakage
current measurements. The leakage current and applied voltage can be captured using a digital
oscilloscope in the data acquisition system. The experimental setup in Figure 4 can be used to obtain
the V–I characteristics of the ZnO varistors under different temperatures.
6. Energies 2018, 11, 1610 6 of 13
Energies 2018, 11, x FOR PEER REVIEW 6 of 13
sh
R d
Z
(a)
(b)
Figure 4. Experimental setup for voltage–current–temperature (V–I–T) characteristics measurement:
(a) experimental circuit; (b) test species and oven.
Studied MOA and varistors are shown in Figure 4b. The MOA structure includes ZnO
varistors, silicon rubber housing, and metal plates. Varistors, which have been removed from the
studied MOA, were tested to obtain the V–I–T characteristics under a power frequency voltage.
Firstly, the varistors were placed in the oven; then, voltage and current were measured. During the
tests, the oven temperature was fixed at ambient temperature (20 °C), and the required parameters
were then measured under different applied voltages. In order to measure the leakage current and
V–I characteristics under different temperatures, the oven temperature was fixed at a new value,
and this process was repeated continuously until all of the required values have been obtained. In
this paper, virgin arresters and ZnO varistors are used, and the degradation effects are not
considered.
3.2. ANN Modeling of V–I Characteristic Considering Temperature Effects
Temperature increments change the V–I characteristics, leading to different leakage current
waveforms and amplitudes at a constant applied voltage. Therefore, it is necessary to model the
MOA as a temperature-dependent element.
In this paper, the MOA temperature-dependent electrical model under power frequency
voltages has been simulated based on the non-linear resistor’s V–I characteristic estimation. An
artificial neural network (ANN) has been used to estimate the temperature effects on V–I
Figure 4. Experimental setup for voltage–current–temperature (V–I–T) characteristics measurement:
(a) experimental circuit; (b) test species and oven.
Studied MOA and varistors are shown in Figure 4b. The MOA structure includes ZnO varistors,
silicon rubber housing, and metal plates. Varistors, which have been removed from the studied
MOA, were tested to obtain the V–I–T characteristics under a power frequency voltage. Firstly,
the varistors were placed in the oven; then, voltage and current were measured. During the tests,
the oven temperature was fixed at ambient temperature (20 ◦C), and the required parameters were
then measured under different applied voltages. In order to measure the leakage current and V–I
characteristics under different temperatures, the oven temperature was fixed at a new value, and this
process was repeated continuously until all of the required values have been obtained. In this paper,
virgin arresters and ZnO varistors are used, and the degradation effects are not considered.
3.2. ANN Modeling of V–I Characteristic Considering Temperature Effects
Temperature increments change the V–I characteristics, leading to different leakage current
waveforms and amplitudes at a constant applied voltage. Therefore, it is necessary to model the MOA
as a temperature-dependent element.
In this paper, the MOA temperature-dependent electrical model under power frequency voltages
has been simulated based on the non-linear resistor’s V–I characteristic estimation. An artificial neural
7. Energies 2018, 11, 1610 7 of 13
network (ANN) has been used to estimate the temperature effects on V–I characteristics [28]. As shown
in Figure 5, the artificial network consists of an input layer, a hidden layer, and an output layer.
The applied voltage and varistor temperature are used as the ANN input data, the node number of the
hidden layer is chosen as 10, and the resistance can be obtained as output data.
According to the ANN method, the relationship between the output layer and input layer can be
given as Equation (1), where:
Y = w2 f (w1X + b1) + b2 (1)
In Equation (1), X is the input vector, Y is the output vector, and w1, w2 and b1, b2 are the connective
weights and bias in the hidden layer and output layer, respectively. f (·) is the non-linear activation
function in the hidden layer, as shown in Equation (2).
f (x) =
1 − ex
1 + e−x
(2)
Energies 2018, 11, x FOR PEER REVIEW 7 of 13
characteristics [28]. As shown in Figure 5, the artificial network consists of an input layer, a hidden
layer, and an output layer. The applied voltage and varistor temperature are used as the ANN input
data, the node number of the hidden layer is chosen as 10, and the resistance can be obtained as
output data.
According to the ANN method, the relationship between the output layer and input layer can
be given as Equation (1), where:
2 1 1 2
( )
Y w f w X b b
= + + (1)
In Equation (1), X is the input vector, Y is the output vector, and w1, w2 and b1, b2 are the
connective weights and bias in the hidden layer and output layer, respectively. f (·) is the non-linear
activation function in the hidden layer, as shown in Equation (2).
1
( )
1
x
x
e
f x
e−
−
=
+
(2)
e
T
U
I
Figure 5. Diagram of the artificial neural network (ANN) algorithm.
The back-propagation algorithm is applied to determine the connective weights and bias in
Equation (1). At the output layer, the error function is defined as in Equation (3), where RO is the
expected output and Rx is the actual output:
2
1
( )
q
O x
o
E R R
=
= −
(3)
In order to obtain the minimum value of the error function in Equation (3), a gradient descent
algorithm is employed to adjust the weights w1 and w2 in the ANN model. The weight-adjusting
formula is shown as Equation (4), where η is the learning rate, α is the momentum factor, and n is the
interaction number:
( )
( 1) ( ) ( ) [ ( ) ( 1)]
( )
ij ij ij ij
ij
E n
W n W n w n w n
w n
η α
∂
+ = + ⋅ − + − −
∂
(4)
Using Equations (1)–(4), the connective weights and bias can be calculated through the
experimental data obtained in Section 3.1. Thus, the mapping between the input and output data of
the ANN model can be obtained.
3.3. Capacitive Component Model of Leakage Current
An accurate parameter extraction of the capacitive components is also very important for the
electrothermal model of the MOA. It is confirmed by Bargigia, Spack-Leigsnering, Lundquist and
Figure 5. Diagram of the artificial neural network (ANN) algorithm.
The back-propagation algorithm is applied to determine the connective weights and bias in
Equation (1). At the output layer, the error function is defined as in Equation (3), where RO is the
expected output and Rx is the actual output:
E =
q
∑
o=1
(RO − Rx)2
(3)
In order to obtain the minimum value of the error function in Equation (3), a gradient descent
algorithm is employed to adjust the weights w1 and w2 in the ANN model. The weight-adjusting
formula is shown as Equation (4), where η is the learning rate, α is the momentum factor, and n is the
interaction number:
Wij(n + 1) = Wij(n) + η · (−
∂E(n)
∂wij(n)
) + α[wij(n) − wij(n − 1)] (4)
Using Equations (1)–(4), the connective weights and bias can be calculated through the
experimental data obtained in Section 3.1. Thus, the mapping between the input and output data of
the ANN model can be obtained.
3.3. Capacitive Component Model of Leakage Current
An accurate parameter extraction of the capacitive components is also very important for the
electrothermal model of the MOA. It is confirmed by Bargigia, Spack-Leigsnering, Lundquist and
8. Energies 2018, 11, 1610 8 of 13
Seyyedbarzegar [12–15] that the stray capacitance is independent of applied voltage and temperature.
In this paper, finite element methods are used to calculate the stray capacitances in ANSOFT Maxwell
software (V16 software, ANSYS company, Pittsburgh, PA, USA). The two-dimensional (2D) simulation
model is built in Figure 6. In the computation stage, for example, a 1-V voltage is applied to a single
element i, and the voltage of the other elements is set to 0 V. Evaluating the electric charge induced in
the other elements, the capacitance between element i and element j can be calculated in Equation (5),
where Qij is the electric charge induced between element i and j, and V is the voltage applied on
element i.
Cij =
Qij
V
(5)
Energies 2018, 11, x FOR PEER REVIEW 8 of 13
Seyyedbarzegar [12–15] that the stray capacitance is independent of applied voltage and
temperature. In this paper, finite element methods are used to calculate the stray capacitances in
ANSOFT Maxwell software (V16 software, ANSYS company, Pittsburgh, PA, USA). The
two-dimensional (2D) simulation model is built in Figure 6. In the computation stage, for example,
a 1-V voltage is applied to a single element i, and the voltage of the other elements is set to 0 V.
Evaluating the electric charge induced in the other elements, the capacitance between element i and
element j can be calculated in Equation (5), where Qij is the electric charge induced between element
i and j, and V is the voltage applied on element i.
ij
ij
Q
C
V
= (5)
Figure 6. Finite element simulation model of MOA.
3.4. Experimental Validation of the ANN Model
In order to validate the electric model of the MOA, the simulated V–I characteristics of the
varistor at different temperatures are compared with the experimental results. As shown in Figure 7,
for a constant temperature, 50 points on the V–I curve are measured, 42 points are used to build the
ANN model, and eight points are used to validate the calculated results of the ANN model. From
Figure 7, it can be confirmed that the simulated V–I–T characteristics obtained from the ANN
model are in good agreement with the experimental results. It can also be seen that, under power
frequency voltage, with an increasing varistor temperature, the equivalent varistor resistance
become smaller.
Figure 7. Comparison of V–I–T characteristics between simulated and experimental results.
Figure 6. Finite element simulation model of MOA.
3.4. Experimental Validation of the ANN Model
In order to validate the electric model of the MOA, the simulated V–I characteristics of the varistor
at different temperatures are compared with the experimental results. As shown in Figure 7, for a
constant temperature, 50 points on the V–I curve are measured, 42 points are used to build the ANN
model, and eight points are used to validate the calculated results of the ANN model. From Figure 7,
it can be confirmed that the simulated V–I–T characteristics obtained from the ANN model are in good
agreement with the experimental results. It can also be seen that, under power frequency voltage,
with an increasing varistor temperature, the equivalent varistor resistance become smaller.
Energies 2018, 11, x FOR PEER REVIEW 8 of 13
Seyyedbarzegar [12–15] that the stray capacitance is independent of applied voltage and
temperature. In this paper, finite element methods are used to calculate the stray capacitances in
ANSOFT Maxwell software (V16 software, ANSYS company, Pittsburgh, PA, USA). The
two-dimensional (2D) simulation model is built in Figure 6. In the computation stage, for example,
a 1-V voltage is applied to a single element i, and the voltage of the other elements is set to 0 V.
Evaluating the electric charge induced in the other elements, the capacitance between element i and
element j can be calculated in Equation (5), where Qij is the electric charge induced between element
i and j, and V is the voltage applied on element i.
ij
ij
Q
C
V
= (5)
Figure 6. Finite element simulation model of MOA.
3.4. Experimental Validation of the ANN Model
In order to validate the electric model of the MOA, the simulated V–I characteristics of the
varistor at different temperatures are compared with the experimental results. As shown in Figure 7,
for a constant temperature, 50 points on the V–I curve are measured, 42 points are used to build the
ANN model, and eight points are used to validate the calculated results of the ANN model. From
Figure 7, it can be confirmed that the simulated V–I–T characteristics obtained from the ANN
model are in good agreement with the experimental results. It can also be seen that, under power
frequency voltage, with an increasing varistor temperature, the equivalent varistor resistance
become smaller.
Figure 7. Comparison of V–I–T characteristics between simulated and experimental results.
Figure 7. Comparison of V–I–T characteristics between simulated and experimental results.
9. Energies 2018, 11, 1610 9 of 13
4. Thermal Model
In this paper, a thermal circuit is introduced to calculate the arrester temperature [22,23]. As shown
in Figure 8, P is the power loss obtained from the electric model, Ta is the ambient temperature, Te is
the varistor temperature, THI is the temperature of the inner surface of the arrester housing, TH is the
temperature of the polymer housing, RCHO is the thermal resistor between the varistor and housing,
REHR and REHCV are the radiation and conduction thermal resistances between the ZnO varistors and
housing, RHACV and RHAR are the conduction and radiation thermal resistance between the housing
and ambient, and CE and CH are the thermal capacitance of the ZnO varistor and housing.
Energies 2018, 11, x FOR PEER REVIEW 9 of 13
4. Thermal Model
In this paper, a thermal circuit is introduced to calculate the arrester temperature [22,23]. As
shown in Figure 8, P is the power loss obtained from the electric model, Ta is the ambient
temperature, Te is the varistor temperature, THI is the temperature of the inner surface of the
arrester housing, TH is the temperature of the polymer housing, RCHO is the thermal resistor between
the varistor and housing, REHR and REHCV are the radiation and conduction thermal resistances
between the ZnO varistors and housing, RHACV and RHAR are the conduction and radiation thermal
resistance between the housing and ambient, and CE and CH are the thermal capacitance of the ZnO
varistor and housing.
Figure 8. Thermal model of MOA.
In Figure 8, the input to the thermal circuit is the power loss obtained from the electric model.
It is assumed that the initial temperature of the varistors and housing is the same with the fixed
ambient temperature, and that the difference between the temperatures of the varistors can be
neglected [22,23]. According to the equations given by Lat [22,23], once the structure and thermal
parameters of the MOA are known, the thermal resistance and capacitance at different times in
Figure 8 can be calculated. Therefore, in this paper, the temperature variations are obtained by
solving the thermal circuit in Figure 8.
5. Experimental Validations
In order to validate the proposed electrothermal model, experimental data has been carried out
using the experimental setup in Figure 5. Power frequency voltages were applied on the tested
MOA, and the temperature and leakage current flowing through the MOA was measured.
Under normal working conditions, the phase voltage applied on each 10 kV MOA is about 5.8
kV. When the arrester temperature is 24.7 °C, the applied voltage, leakage current, and thermal
picture photographed by a high-quality thermal camera is shown in Figure 9. As shown in the
figure, the leakage current is in sinusoidal waveform, and the amplitude of the leakage current is
about 1 mA. The capacitive current is much larger than the resistive current, and the difference
between the temperatures of the varistors in the MOA can be neglected. Seen from Figure 9b, it can
be seen that the simulated leakage current can effectively reflect the experimental results.
Due to switching or power system faults, the power frequency overvoltages applied on the
MOA can be much higher than operation voltage. In order to monitor these conditions, a 17.4-kV
AC overvoltage was applied on the arrester. The voltage applied on the MOA and the leakage
current flowing through the varistors are shown in Figure 10a, while the thermal picture
photographed by high quality thermal camera is shown in Figure 10b. As shown in Figure 10, when
the arrester temperature is 27.9 °C and the applied voltage is 17.4 kV, the leakage current amplitude
is about 40 mA. From Figure 10, it can also be seen that the simulated current curve can effectively
reflect the amplitude of the experimental results.
CHO
R
HACV
R
HAR
R
P
Ta
E
T
H
T a
T
HI
T
E
C
EHCV
R
EHR
R
H
C
Figure 8. Thermal model of MOA.
In Figure 8, the input to the thermal circuit is the power loss obtained from the electric model. It is
assumed that the initial temperature of the varistors and housing is the same with the fixed ambient
temperature, and that the difference between the temperatures of the varistors can be neglected [22,23].
According to the equations given by Lat [22,23], once the structure and thermal parameters of the
MOA are known, the thermal resistance and capacitance at different times in Figure 8 can be calculated.
Therefore, in this paper, the temperature variations are obtained by solving the thermal circuit in
Figure 8.
5. Experimental Validations
In order to validate the proposed electrothermal model, experimental data has been carried out
using the experimental setup in Figure 5. Power frequency voltages were applied on the tested MOA,
and the temperature and leakage current flowing through the MOA was measured.
Under normal working conditions, the phase voltage applied on each 10 kV MOA is about
5.8 kV. When the arrester temperature is 24.7 ◦C, the applied voltage, leakage current, and thermal
picture photographed by a high-quality thermal camera is shown in Figure 9. As shown in the figure,
the leakage current is in sinusoidal waveform, and the amplitude of the leakage current is about
1 mA. The capacitive current is much larger than the resistive current, and the difference between the
temperatures of the varistors in the MOA can be neglected. Seen from Figure 9b, it can be seen that the
simulated leakage current can effectively reflect the experimental results.
Due to switching or power system faults, the power frequency overvoltages applied on the
MOA can be much higher than operation voltage. In order to monitor these conditions, a 17.4-kV AC
overvoltage was applied on the arrester. The voltage applied on the MOA and the leakage current
flowing through the varistors are shown in Figure 10a, while the thermal picture photographed
by high quality thermal camera is shown in Figure 10b. As shown in Figure 10, when the arrester
temperature is 27.9 ◦C and the applied voltage is 17.4 kV, the leakage current amplitude is about
10. Energies 2018, 11, 1610 10 of 13
40 mA. From Figure 10, it can also be seen that the simulated current curve can effectively reflect the
amplitude of the experimental results.
Energies 2018, 11, x FOR PEER REVIEW 10 of 13
(a) (b)
Figure 9. Electrothermal characteristics of MOA under the applied voltage of 5.8 kV. (a) Voltage and
current time curves; (b) thermal picture.
(a) (b)
Figure 10. Electrothermal characteristics of MOA under the applied voltage of 17.4 kV. (a) Voltage
and current time curves/courses; (b) thermal picture.
The frequency spectra of the leakage current in Figures 9 and 10 are shown in Figure 11. As
shown in Figure 11a, under normal working conditions, the applied voltage is in the linear section
of the V–I characteristics curve, and the harmonics of the leakage current are so small that they can
be neglected. When the applied voltage reaches the non-linear section, as shown in Figure 11b, the
amplitudes and odd harmonics of the leakage current increase greatly.
When the ambient temperature is 23 °C, under different overvoltages, the amplitude variations
of current and temperature with time are shown in Figure 12, from which it can be seen that when
the applied voltage is smaller than 17.4 kV, the arrester temperature is kept stable. When the
applied voltage is larger than 17.4 kV, the power loss of the arrester is larger than the heat
dissipation, the varistor resistance decreases, and the leakage current increases, leading to an
electrothermal failure of MOAs.
Figure 9. Electrothermal characteristics of MOA under the applied voltage of 5.8 kV. (a) Voltage and
current time curves; (b) thermal picture.
Energies 2018, 11, x FOR PEER REVIEW 10 of 13
(a) (b)
Figure 9. Electrothermal characteristics of MOA under the applied voltage of 5.8 kV. (a) Voltage and
current time curves; (b) thermal picture.
(a) (b)
Figure 10. Electrothermal characteristics of MOA under the applied voltage of 17.4 kV. (a) Voltage
and current time curves/courses; (b) thermal picture.
The frequency spectra of the leakage current in Figures 9 and 10 are shown in Figure 11. As
shown in Figure 11a, under normal working conditions, the applied voltage is in the linear section
of the V–I characteristics curve, and the harmonics of the leakage current are so small that they can
be neglected. When the applied voltage reaches the non-linear section, as shown in Figure 11b, the
amplitudes and odd harmonics of the leakage current increase greatly.
When the ambient temperature is 23 °C, under different overvoltages, the amplitude variations
of current and temperature with time are shown in Figure 12, from which it can be seen that when
the applied voltage is smaller than 17.4 kV, the arrester temperature is kept stable. When the
applied voltage is larger than 17.4 kV, the power loss of the arrester is larger than the heat
dissipation, the varistor resistance decreases, and the leakage current increases, leading to an
electrothermal failure of MOAs.
Figure 10. Electrothermal characteristics of MOA under the applied voltage of 17.4 kV. (a) Voltage and
current time curves/courses; (b) thermal picture.
The frequency spectra of the leakage current in Figures 9 and 10 are shown in Figure 11. As shown
in Figure 11a, under normal working conditions, the applied voltage is in the linear section of the V–I
characteristics curve, and the harmonics of the leakage current are so small that they can be neglected.
When the applied voltage reaches the non-linear section, as shown in Figure 11b, the amplitudes and
odd harmonics of the leakage current increase greatly.
When the ambient temperature is 23 ◦C, under different overvoltages, the amplitude variations
of current and temperature with time are shown in Figure 12, from which it can be seen that when
the applied voltage is smaller than 17.4 kV, the arrester temperature is kept stable. When the applied
voltage is larger than 17.4 kV, the power loss of the arrester is larger than the heat dissipation,
the varistor resistance decreases, and the leakage current increases, leading to an electrothermal
failure of MOAs.
11. Energies 2018, 11, 1610 11 of 13
Energies 2018, 11, x FOR PEER REVIEW 11 of 13
(a) (b)
Figure 11. Frequency spectra of the leakage current. (a) U = 5.8 kV; (b) U = 17.4 kV.
(a) (b)
Figure 12. Amplitudes’ variation of temperature and leakage current with time. (a) Temperature; (b)
leakage current.
6. Discussions
The simulated and measured results in Section 5 can be explained as follows.
Under normal working conditions, when the applied voltage is 5.8 kV, the capacitive
component of the leakage current is dominate, the leakage current is in sinusoidal waveform, and
the harmonics of leakage current can be neglected. Under power frequency overvoltage, when the
applied voltage reaches the non-linear section of the V–I curve, the leakage current increases
rapidly, and the resistive component of the leakage current is dominate. The frequency spectra
show that the odds harmonics of the leakage current become much higher under power frequency
overvoltage.
Under the ambient temperature of 23 °C, when the power frequency overvoltage is smaller
than 18 kV, the power loss caused by the leakage current is equal to the heat emitted into the
ambient; thus, the temperature of the MOA remains stable when the applied voltage is smaller than
18 kV. When the applied voltage increases continuously, the heat created by the leakage current is
larger than the emitted heat, leading to an exponentially increasing MOA temperature. This
increases the leakage current in the ZnO varistors, and finally leads to the thermal failure of the
MOA.
According to the above discussion, it is suggested that the critical voltage between the small
current and non-linear regions should be designed to be higher than the max power frequency
voltages in the power system; thus, the electrothermal failure of the MOA can be avoided under
power frequency overvoltages.
Amplitude
(mA)
Figure 11. Frequency spectra of the leakage current. (a) U = 5.8 kV; (b) U = 17.4 kV.
Energies 2018, 11, x FOR PEER REVIEW 11 of 13
(a) (b)
Figure 11. Frequency spectra of the leakage current. (a) U = 5.8 kV; (b) U = 17.4 kV.
(a) (b)
Figure 12. Amplitudes’ variation of temperature and leakage current with time. (a) Temperature; (b)
leakage current.
6. Discussions
The simulated and measured results in Section 5 can be explained as follows.
Under normal working conditions, when the applied voltage is 5.8 kV, the capacitive
component of the leakage current is dominate, the leakage current is in sinusoidal waveform, and
the harmonics of leakage current can be neglected. Under power frequency overvoltage, when the
applied voltage reaches the non-linear section of the V–I curve, the leakage current increases
rapidly, and the resistive component of the leakage current is dominate. The frequency spectra
show that the odds harmonics of the leakage current become much higher under power frequency
overvoltage.
Under the ambient temperature of 23 °C, when the power frequency overvoltage is smaller
than 18 kV, the power loss caused by the leakage current is equal to the heat emitted into the
ambient; thus, the temperature of the MOA remains stable when the applied voltage is smaller than
18 kV. When the applied voltage increases continuously, the heat created by the leakage current is
larger than the emitted heat, leading to an exponentially increasing MOA temperature. This
increases the leakage current in the ZnO varistors, and finally leads to the thermal failure of the
MOA.
According to the above discussion, it is suggested that the critical voltage between the small
current and non-linear regions should be designed to be higher than the max power frequency
voltages in the power system; thus, the electrothermal failure of the MOA can be avoided under
power frequency overvoltages.
Amplitude
(mA)
Figure 12. Amplitudes’ variation of temperature and leakage current with time. (a) Temperature;
(b) leakage current.
6. Discussions
The simulated and measured results in Section 5 can be explained as follows.
Under normal working conditions, when the applied voltage is 5.8 kV, the capacitive component
of the leakage current is dominate, the leakage current is in sinusoidal waveform, and the harmonics
of leakage current can be neglected. Under power frequency overvoltage, when the applied voltage
reaches the non-linear section of the V–I curve, the leakage current increases rapidly, and the resistive
component of the leakage current is dominate. The frequency spectra show that the odds harmonics of
the leakage current become much higher under power frequency overvoltage.
Under the ambient temperature of 23 ◦C, when the power frequency overvoltage is smaller than
18 kV, the power loss caused by the leakage current is equal to the heat emitted into the ambient; thus,
the temperature of the MOA remains stable when the applied voltage is smaller than 18 kV. When
the applied voltage increases continuously, the heat created by the leakage current is larger than the
emitted heat, leading to an exponentially increasing MOA temperature. This increases the leakage
current in the ZnO varistors, and finally leads to the thermal failure of the MOA.
According to the above discussion, it is suggested that the critical voltage between the small
current and non-linear regions should be designed to be higher than the max power frequency voltages
in the power system; thus, the electrothermal failure of the MOA can be avoided under power
frequency overvoltages.
12. Energies 2018, 11, 1610 12 of 13
7. Conclusions
In this paper, an electrothermal model of a MOA has been proposed. It has considered the
interaction between the leakage current and the temperature rise of the MOA. Using applied voltage,
ambient temperature, and initial temperature as input data, the temperature and leakage current of a
MOA at any time can be calculated. Experimental validations have been done, and the experimental
and simulated results show good agreement with each other.
The electrothermal models in this paper can be used to predict not only the voltage and leakage
current, but also the temperature characteristics of a MOA. It is also suggested that the critical voltage
between the small current and non-linear regions should be designed to be higher than the max power
frequency voltages in the power system to avoid the electrothermal failure of MOAs. The studies in
this paper can assist with the design and type selection of MOAs in the power system.
Author Contributions: P.X. carried out the experiments, analyzed the test results, and wrote this paper. J.L. gave
input to the analysis of test results. J.H. and Z.F. carried out the experimental set up.
Funding: This research was funded by State Grid Corporation of China Science and Technology Program, grant
number [5216AF160005].
Acknowledgments: The authors gratefully acknowledge the contributions of all members of the external
insulation research team in State Grid Hunan Electric Power Corporation for their work on this paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. Gu, S.Q.; Chen, W.J.; He, J.L.; Shen, H.B.; Zhang, S. Development of Surge Arresters with Series Gap
Against Lightning Breakage of Covered Conductors on Distribution Lines. IEEE Trans. Power Deliv. 2007, 4,
2191–2198. [CrossRef]
2. Toshihiro, T.; Jun, T.; Shigemitsu, O. Energy Absorption Capacity of a 500 kV Surge Arrester for Direct and
Multiple Lightning Strokes. IEEE Trans. Dielectr. Electr. Insul. 2015, 2, 916–924. [CrossRef]
3. Brito, V.S.; Lira, G.R.S.; Costa, E.G.; Maia, M.J.A. A Wide-Range Model for Metal-Oxide Surge Arrester.
IEEE Trans. Power Deliv. 2018, 1, 102–109. [CrossRef]
4. Tominaga, S.; Azumi, K.; Shibuya, Y.; Imataki, M.; Fujiwara, Y.; Nishida, S. Protective Performance of Metal
Oxide Surge Arrester Based on the Dynamic V-I Characteristics. IEEE Trans. Power Apparatus Syst. 1979, 6,
1860–1871. [CrossRef]
5. Magro, M.C.; Giannettoni, M.; Pinceti, P. Validation of ZnO surge arresters model for overvoltage studies.
IEEE Trans. Power Deliv. 2004, 4, 1692–1695. [CrossRef]
6. Nigol, O. Methods for analyzing the performance of gapless metal oxide surge arresters. IEEE Trans. Power
Deliv. 1992, 3, 1256–1264. [CrossRef]
7. Li, S.T.; He, J.Q.; Lin, J.J.; Wang, H.; Liu, W.F.; Liao, Y.L. Electrical-Thermal Failure of Metal-Oxide Arrester
by Successive Impulses. IEEE Trans. Power Deliv. 2016, 6, 2538–2545. [CrossRef]
8. He, J.Q.; Lin, J.; Liu, W.Q.; Wang, H.; Liao, Y.; Li, S.T. Structure-Dominated Failure of Surge Arresters by
Successive Impulses. IEEE Trans. Power Deliv. 2017, 4, 1907–1913. [CrossRef]
9. Christodoulou, C.; Vita, V.; Perantzakis, G.; Ekonomou, L.; Milushev, G. Adjusting the Parameters of Metal
Oxide Gapless Surge Arresters’ Equivalent Circuits Using the Harmony Search Method. Energies 2017,
10, 2168. [CrossRef]
10. Tuczek, M.N.; Hinrichsen, V. Recent Experimental Findings on the Single and Multi-Impulse Energy
Handling Capability of Metal-Oxide Varistors for Use in High-Voltage Surge Arresters. IEEE Trans. Power
Deliv. 2014, 5, 2197–2205. [CrossRef]
11. Stojanovi, Z.N.; Stojkovi, Z.M. Evaluation of MOSA condition using leakage current method. Electr. Power
Energy Syst. 2013, 52, 87–95. [CrossRef]
12. Bargigia, A.; De, N.; Pigini, A. Comparison of Different Test Method to Assess the Thermal Stresses of Metal
Oxid Surge Arrester under Pollution Condition. IEEE Trans. Power Deliv. 1993, 1, 146–155. [CrossRef]