In-Depth Simulation of Low-Voltage AC Arc-Fault and Saturated Transformer Fault Detection System

In this research, we focus on low-voltage arc-faults in AC systems. In our previous studies, we demonstrated that arc-faults in AC systems differ from those in DC systems because in an AC system the arc itself is not a gap-jumping electrical arc between two conductors but rather an advanced glowing connection state that occurs exclusively in copper-based connections. In the present study, we improved upon our AC arc-fault generation simulation in MATLAB, matching our previous findings. The arc-fault simulation in MATLAB replicated the exact waveform exhibited in an actual AC arc-fault environment. Therefore, we concluded that the phenomenon likely followed the mechanism we proposed in our previous research. We have also detected the phenomenon by using a method we devised in our previous research and refined it to match the mechanism derived from our present findings. The simulation results for our detection method revealed that to obtain the best detection accuracy, the magnetic core of the inductor/current transformer must have low coercivity and may not be saturated before the current waveform has shifted to another polarity. This detection method may yield a greater ratio of accuracy to manufacturing cost given that the main component does not include a high-frequency circuit analyzer.

In-Depth Simulation of Low-Voltage AC Arc-Fault and Saturated Transformer Fault Detection System Sittichai Wangwiwattana and Yoshikazu Koike Abstract-In this research, we focus on low-voltage arc-faults in AC systems.In our previous studies, we demonstrated that arc-faults in AC systems differ from those in DC systems because in an AC system the arc itself is not a gap-jumping electrical arc between two conductors but rather an advanced glowing connection state that occurs exclusively in copper-based connections.In the present study, we improved upon our AC arcfault generation simulation in MATLAB, matching our previous findings.The arc-fault simulation in MATLAB replicated the exact waveform exhibited in an actual AC arc-fault environment.Therefore, we concluded that the phenomenon likely followed the mechanism we proposed in our previous research.We have also detected the phenomenon by using a method we devised in our previous research and refined it to match the mechanism derived from our present findings.The simulation results for our detection method revealed that to obtain the best detection accuracy, the magnetic core of the inductor/current transformer must have low coercivity and may not be saturated before the current waveform has shifted to another polarity.This detection method may yield a greater ratio of accuracy to manufacturing cost given that the main component does not include a highfrequency circuit analyzer.Index Terms-Arc discharges, circuit simulation, contacts, electrical fault detection, magnetic cores, sparks, surface discharges, transformer cores.

I. INTRODUCTION
S INCE its introduction, electricity has been both a key- stone of modern technologies and a hazard, necessitating caution in any activity harnessing its power.These hazards include electrocution and the risk of fire.Following the widespread adoption of electric household appliances, research and development has focused on technology that reduces the risks to property and human life.
The low-voltage AC arc-fault is one of the most perplexing phenomena studied by researchers in the field of electricity.Despite being one of the most destructive types of electrical hazards, its mechanism is not well understood [1].Lowvoltage AC arc-faults have been studied extensively by Shea and colleagues [2], [3], [4].Other researchers [5], [6], [7] have been able to reproduce its specific waveform and pattern in low-voltage phenomena, but none was able to identify its cause.A study by Martel [8]  The authors are with the Functional Control System, Shibaura Institute of Technology, Tokyo 135-8548, Japan (e-mail: nb19508@shibaura-it.ac.jp; koikey@shibaura-it.ac.jp).
Digital Object Identifier 10.1109/TCE.2023.3324637 underlying low-voltage arc-faults.However, as we will discuss in the next section, in a previous study, we concluded that their proposed mechanism shares similarities with observations but the actual cause behind the phenomenon is different.A study by Kim et al. [9] used a graphite electrode to generate a low-voltage arc-fault.The waveform is very similar, with a prominent current shoulder and a drop in voltage near the zero-crossing point.However, a glowing connection can itself create the same type of waveform in current and voltage.
Although the mechanism behind this phenomenon is not well understood, the behavior of the waveform is well documented and can be replicated easily [10].There are many methods for preventing arc-faults, including the arc-fault circuit interrupters (AFCI), which is a commonly used circuit that detects the high-frequency component of the phenomenon [11].However, according to a study by Engel et al. [12], AFCIs are prone to accidental tripping because some electrical appliances generate a waveform similar to that of a low-voltage arc-fault.This is not entirely surprising given that the method of detection is based only on a comparison of the problematic waveform.
In essence, the detection method does not directly examine the actual cause, only the symptom of it.For this reason, many researchers have attempted to devise an alternate method of detection.Most such work has focused on DC arc-fault detection [13], the arcing behavior and waveform of which differs from its AC counterpart.Many studies that aimed to detect AC arc-faults have used neural networks and computers with advanced computational capabilities [14], [15], [16], [17], [18], [19].Although their results have been promising, this approach is not feasible for smaller devices.According to the previously mentioned studies, low-voltage arc-faults have a specific pattern that differs for each type of material.Our own research [20], [21], [22], has revealed the pattern that occurs when one of the conductors is made from copper or a copper-based material.Specifically, there is a voltage drop when the arc occurs and a current shoulder is formed, as shown in Figure 1.
Conversely, when a conductor does not contain copper, it does not exhibit the arc-like phenomenon, but instead glows red from resistive heat as demonstrated by Shea and colleagues.We were able to fully replicate that phenomenon and we also revealed that the arcing state when a copper oxide bridge forms is temperature-determinant.At room temperature or lower, the oxide bridge does not exhibit an arc-like state when the circuit is energized.However, if we induce a resistive heating effect by heating the oxide bridge to around 500 Celsius, the oxide bridge will exhibit an arc-like state.We  have determined that a partial copper oxide bridge made from a semiconductor material [23] that behaves like a weak conductor at high temperatures would burn off and become an insulator.The copper around that area was continuously oxidized, thereby creating a loop in the conducting path and subsequently burned off.This process observed with the naked eye resembled an arc jump across the gap.From this, we concluded that the detection process used by many other researchers is unsuitable because the phenomenon they observed was not an arc-fault but rather an advanced stage of glowing connection that is unique to copper-based connections.
We have devised two main ways to detect such phenomena: voltage waveform detection [21] and current waveform detection [22].In our study on voltage waveform detection, when this type of glowing connection occurs, it produces a signature voltage drop at one point in the cycle.However, it is difficult to create a basic logic system that is capable of recognizing such a pattern because it can change depending on how size of the load using the power and how inductive or capacitive the load is, given that the phase shift between voltage and current can greatly impact the location where voltage drop occurs.We discovered that the voltage peak-to-peak values between the load line and the neutral line differed slightly where the neutral line produced a slightly lower voltage peak.This difference can be used to detect the glowing connection state but only at a very low power draw, which is not suitable for most operations.The conventional waveform-detection method uses a saturated current transformer to detect the current shoulder when these glowing phenomena occur in the system.Our work done is somewhat similar to a detection method that uses a Rogowski coil [24], [25] to detect changes in current flow.This device can detect the glowing phenomenon at low current with high accuracy.We were able to partially simulate that detection system, and we concluded that the glowing stage introduced a small variable resistance, which produced a peak-to-peak voltage that differed between the stage with Fig. 2. The current study is meant to support the previous claim in our theorized mechanism of action.Fig. 3.
A modified version of powerctsat by Sibille.The modification removed the shunt load from the current transformer to match the actual experiment conducted in our previous research.The load was not modified because it was required for the simulation.
the glowing phenomenon and the stage without it.However, this was only a preliminary simulation, and the simulated model did not take all the variables from the actual experiment because there was no data sheet, leaving much room for improvement.There was also a distinctive waveform pattern from the saturated current transformer that the simulation model was unable to replicate.
In the present study, we create a new simulation model that is as accurate as the actual experiment we conducted to test our hypothesis and reached a conclusion on low-voltage arcfaults in AC system [23].This paper also includes a more accurate version of the simulation model that is capable of replicating the irregularities and discrepancies, which was not possible with the previous model.

II. METHODOLOGY
In this research we have created this flowchart as shown in Figure 2. of the merit and reasoning behind the study.
Our previous study [23] made use of the circuit model shown in Figure 3.The original model was modified from powerctsat from the online MATLAB library by Sibille [26].However, in our previous study, we were unable to completely simulate the actual AC arc-fault state using this model because the circuit did not contain the same type of load that we used in the actual experiment.The primary coil of the current transformer was connected to another type of load that worked only in this specific setup.
The variable of the core and its construction were also limited to this simulation.Therefore, for us to create the same model as in our previous study, we needed to recreate the simulation.The model shown in Figure 4 was created for this purpose.The parameters of all values were tailored to our actual experiment (Figure 5), which was our equivalent circuit.However, there were a few values that we were unable to determine, including the magnetic properties of the current transformer core and the precise glow resistance, which will be  The previous model, in which we applied a random number generator at the variable "R" to simulate the randomness of glowing resistance, was unsuitable.We realized that the glowing resistance was not simply a fluctuation of glow resistance, but that there was a pattern.The glow resistance was at its lowest when the glow/arcing state was at its most energetic, and the glow resistance was at its highest when the glow/arcing state was seemingly extinguished at every zero-crossing point of the current, as we observed in studies by us as well as other researchers.Hence, in our model we instead made use of a pattern-generator named the "Glow-resistance Generator," the resistance of which also depended on the amount of power that "RLoad" draws.In our previous research, we concluded that the glow resistance when the arc was extinguished was higher when less power was drawn by "RLoad".The higher the power that is needed in the circuit, the lower the glow resistance would be.In the actual experiment we conducted, at one point where the circuit draws a large amount of power, the arc-fault would simply become a glowing red-hot connection where the arcing phenomenon was no longer present.In the present study, the glowing resistance waveform in the generator is as shown in Figure 6.Because the zero-crossing point of our experiment occurs at every half period, the glow resistance Fig. 6.The Glow-resistance Generator creates a large amount of resistance at every interval where zero-crossing point occurs in the circuit.The resistance is then added by the White-noise Generator, which simulates parasitic resistance that changes according to temperature.spikes at every 10-ms interval for a frequency of 50 Hz.We also added the "White-noise Generator," with uniform noise generation.The noise generator has a very low resistance fluctuation in the micro-ohm range, to the simulation due to the glowing phenomenon of this type.The "White Noise" generator introduces a very small fluctuation in resistance in addition to the "Glow resistance Generator" when the temperature at the contact point changes rapidly.In the actual experiment, we were unable to measure the distribution of the resistance noise.In these cases, we have made use of many noises model in the simulator and the result are similar since the resistive noise is in micro-ohm level.We made use of uniform noise generation for this simulation case.
This simulation model simulates a low-voltage arc-fault, which is used for a comparison with the actual experiment that we conducted.The parameters are adjusted to be as accurate as the actual experiment.The power source is an AC electrical plug of 50 Hz and 100 V, which is isolated using an isolating transformer.This is done to protect the main fuse of the experiment room and to avoid any unwanted alarm from such an experiment.The type of load used in the circuit was a simple wire-wound resistor, with values of 12, 25, and 100 .The arc-fault gap is recreated by applying a mixture of copper oxides on one side of the contact and making the contact spark.Copper oxides are gathered by heating electrical copper contacts of the same type, which are acquired from the socket.The copper contact is then placed into an electric furnace and heated to 700 • C for 10 min to form a surface layer of copper oxide, after which the oxides are removed from the surface of the sample and crushed into fine powder.The contact spark creates a high temperature that fuses the copper oxide dust into a copper oxide bridge, which is the main area where low-voltage arc-faults occur.The electrical contact with an oxide bridge is then used as the break-make contact between two conductors, creating a spark.Once the spark is capable of sustaining itself without further assistance, the voltage and current waveform are recorded.
The simulation which included a saturable current transformer required hysteresis modeling.Figure 7 show all the parameter used in the simulation.The explanation of the parameter will be explained in Result and Discussion.

III. RESULT AND DISCUSSION
The data collected from the actual experiment in our previous study was compared with the MATLAB simulation  results.The voltage and current waveform patterns were very similar.However, there was a small discrepancy in the voltage peak between the two main sets of data.The actual experiment voltage peak in all cases was lower than that in the simulated data.This was because the oscilloscope we used in the experiment was connected to the ground of the power supply.To obtain the same voltage level and more accurate results without noise, the oscilloscope needs to be in a floating configuration.However, such a configuration is an extreme hazard to the operator and thus was not used in the experiment.The slightly distorted voltage waveform still retains much of the pattern reported by other researchers; therefore, there should not be problem when the data are According to the comparison results we obtained, the lowvoltage arc-fault behavior and its specific waveform that is generated when one of the contacts is made from copper is due to the fluctuation of the resistance value near the zerocrossing point of the current, which causes the iconic "current shoulder."This type of shoulder is not present in other types of glowing connections and arc-faults when copper materials are not present in the contact.We hypothesize that the copper oxide bridge that was formed before the initial spark occurred and sustained the arc-fault state was the main cause of the observed phenomenon.It is well known that copper oxides are a semiconductor material in which conductivity increases with temperature.The arc-fault when copper is present in the contact material causes a rapid fluctuation in temperature.The most energetic phase of the arc-fault is when the voltage and the current are at their highest point and the least energetic phases is at the zero-crossing point of the current.This may result in a stage where the resistance is at its highest when it is in the least energetic phase, and conversely, it is at its lowest when it is in its most energetic stage.The simulation demonstrated that the rapid change in resistance was the main cause of its iconic voltage and current waveform.However, according to the simulation, the higher the power draw of the load, the higher the contact resistance when the arcing state occurs in its least energetic phase.This raised the question of whether a high amount of power would create a large spark and a higher temperature glow compared with a lower power draw.In this case the contact surface where copper oxides are present should maintain a higher temperature when the current is passing through the zero-crossing point in which the copper oxide bridge should have higher electrical conductivity at a high temperature compared with a lower-temperature bridge.It is hypothesized that the rapid formation of copper oxidesespecially cuprous oxide, which is the semiconductor part of the copper oxides bridge-is formed through oxidation with oxygen in the air.However, when the formation of the oxide occurs at a high temperature, it is likely that cuprous oxide will rapidly form cupric oxide, which is an electrical insulator.Because of the microscopic nature of the formation and its timeframe, it is not possible for us to study this further with the experimental apparatus.However, from the data we obtained, we can conclude that in a low-voltage AC system, when any arc-fault of a copper-based connection occurs, if the power drawn is low, there will always be a current shoulder that can be used as the basis for a detection system.Using the new simulation model, we were able to improve the detection model we developed in our previous study [23].In that study, we were able replicate the waveform that we obtained from the current transformer.However, the type of current transformer that is required for use in this type of application is not well understood.The waveform we obtained from the actual experiment is shown in Figure 11.In that figure, the peak has a jagged top edge.In our previous study, we were not able to explain the cause of this jagged edge when an arc-fault was present in the system.
We were only able to explain a replicate that a small increase in resistance value within the circuit can reduce the voltage peak of the current transformer.The present simulation model revealed that the jagged edge is caused by the zerocrossing point of the current.Because of the change in the magnetic flux within the current transformer, the transformer expends its energy when the current value stagnates, which created a large spike before it regained its magnetic energy (Figure 12).Therefore, the "saturated current transformer" method is most reliable when the power draw is low, that is, where the current shoulder is at its most prominent and should be able to be picked up by the current transformer.We performed another simulation, as shown in Figure 13, and the results were as we hypothesized.To make use of such a system, the magnetic core within the current transformer must be the main factor in the detection accuracy.The magnetic core must have an exceptionally low coercivity compared with a regular inductor core and high saturation level.Low coercivity means that the magnetic flux within the core can change immediately once the magnetic field that drives the core changes as shown in the following formula where we used Jiles-Atherton Hysteresis Model which we included Magnetizing equation ( 1) is for when the core is charging the magnetic field, Demagnetizing equation ( 2) for when the core in undergoing demagnetization and lastly, Magnetization curve equation (3).
B is the magnetic flux density (in Tesla) β is Rate of magnetization change.
H is magnetic field strength.μo is magnetic constant of the core.α is magnetic coupling properties of the material M is magnetization of the core.M is saturation magnetization.Hc is the coercive field strength of the material.As with (1) and ( 2), the magnetization change depend on Magnetization of the core which denoted in (3).If Hc as low as it can be, this would result in that core is susceptible to changes in magnetization.If there is a reverse of magnetic field causes by current.The core would also lose its magnetization quickly which would ideally create the shoulder we have mentioned In this case, change in the magnetic field in our system caused by the current shoulder, as explained earlier.A high saturation level means that the magnetic core should still be in a charging phase when the current shoulder phenomenon occurs.If the core becomes saturated before the phenomenon occurs, the method will not be able to detect the arc-fault reliably because there will be no abrupt change in the magnetic flux while the core is charging its magnetic field.The results of the simulation testing this claim is shown in Figure 14.

IV. CONCLUSION
The results from our new MATLAB simulation model have elucidated the mechanism underlying the low-voltage arc-fault in AC.The phenomenon is not a true arc jump between two conductors but rather a glowing connection behavior resulting from the combination of copper oxides and oxidizing Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
atmosphere, which causes variable contact resistance.This kind of resistance in the system can increase to a very high level at specific intervals of the power frequency, thereby creating the illusion of an arc-like state.This simulation confirmed that copper may not be the best material to use at a contact point because of its inherent fire-hazard risk, even at a very low power usage.The detection method for this phenomenon that we have tested experimentally in our previous study has been verified by the present simulation.By utilizing an open-circuit current transformer, we were able to detect the glowing connection reliably at a low voltage and low power application.However, as the simulation results showed, not all types of current transformers can be used in this type of application.In our previous study, we were able to determine that the lower the rating of the current transformer, the better it is at detection.According to the present simulation results, the property that dictates the detection accuracy is the B-H hysteresis loop.Meanwhile, the coercivity and retentivity of the magnetic core should be as low as possible in magnetic flux retention, whereas the saturation flux should be as high as possible.At present, it is unknown whether a material suitable for the design criteria of this application exists.Therefore, further research should be conducted on the construction of the magnetic core and its.

Fig. 1 .
Fig.1.Low-voltage AC arc-fault with a 100-W load.Voltage drops near the location where the current is distorted.However, the current shoulder is not necessarily at the zero-crossing point but can form near it.

Fig. 4 .
Fig. 4.New simulation model, which is mostly accurate to the actual experiment.A few of the variables were unknown, including the magnetizing specification of the current transformers.

Fig. 5 .
Fig. 5. Physical experiment setup to that in the experiment conducted in our previous paper.The main load switches from a load of around 100 to 12 .The oxide bridge is the arcing gap denoted as the resistor.Due to the apparatus and instruments being in different locations to prevent vibration induced by the isolating transformer, a complete setup in one picture is unavailable.

Fig. 7 .
Fig. 7. Hysteresis parameters used in the current transformer within the simulation model.

Fig. 8 .
Fig. 8.Comparison of experiment and MATLAB simulation.The load value was 100 .

Fig. 9 .
Fig. 9. Comparison of experiment and MATLAB simulation.The load value was 25 .

Fig. 10 .
Fig. 10.Comparison of experiment and MATLAB simulation.The load value was 12 .

Fig. 11 .
Fig. 11.Output from a saturated current transformer when an arc-fault is present in the system.The load used in this experiment was 25 .

Fig. 12 .
Fig. 12. Relation between voltage in the current output of the transformer and the current in the circuit.The transformer quickly saturated once the polarity shifted.

Fig. 13 .
Fig. 13.The jagged edge in the actual experiment was caused by the current shoulder of the phenomenon.The simulation load value was 100 .

Fig. 14 .
Fig. 14.Comparison between states with and without arc-faults.The simulation load values were 5 .The case with arc-faults has a very shallow current distortion.However, the peak value from the current transformer does not differ.
deduced the mechanism Manuscript received 12 June 2023; revised 2 September 2023; accepted 30 September 2023.Date of publication 16 October 2023; date of current version 26 April 2024.(Corresponding author: Sittichai Wangwiwattana.) c 2023 The Authors.This work is licensed under a Creative Commons Attribution 4.0 License.
For more information, see https://creativecommons.org/licenses/by/4.0/Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.