Electrical Characterization and Modeling of High Frequency Arcs for Higher Voltage Aerospace Systems

Arcing in future high-voltage aerospace systems could occur more frequently and cause irreversible damage to electrical components and system structure, and increase the risk of fire. While arcs seen in low-voltage aerospace systems tend to be long-duration and low-energy events, higher-power but short-duration arcs may occur in high-voltage aerospace systems if they are readily detectable by system protection. This article investigates the characteristics of high current arc faults generated at the ac frequencies expected in future rotating machines used for higher voltage aerospace systems. As such, arcs with a peak current up to 4.6 kA are generated at frequencies in the range of 0.5–2 kHz using an underdamped RLC circuit, under pressures of 0.2–1 bar absolute. High-frequency arcs exhibit a similar characteristic to lower-frequency arcs. A reduction in pressure results in lower arc voltage and arc power. Arcing tests at atmospheric pressure may therefore represent a worst-case scenario and the development of a low-pressure test environment may not be necessary. A black box model is developed to provide good agreement with experimental arc voltage waveforms for different parameters investigated in this study. This is a generalized modeling approach to estimate high-frequency high-voltage arcing characteristics without recourse to experiment.


I. INTRODUCTION
D ECARBONIZATION is considered an essential pillar in creating a more sustainable environment as part of the European Green Deal [1].Direct emissions from the aviation sector are responsible for approximately 2% of global greenhouse gas emissions [2].There is an urgent need to develop aircraft with electrical systems operating at higher voltages to enable the power levels required in all-electric or hybrid electric propulsion systems [3].With the need for future aerospace electrical systems to be power-dense, there is a continued effort to increase the operating voltage of these systems.According to [4], future hybrid aircraft are expected to see an increase in the power demand up to 5 MW, which raises the operating system voltage to 1-3 kV.Self-contained networks, where generation, distribution, and transmission are achieved on-board give ac power generation an advantage with variable frequency systems going up to 2 kHz to reduce the weight/size of electrical machines [5].Previous work has shown that while the introduction of higher voltage power systems in aircraft enhances their efficiency, this has also introduced an increased probability of high-voltage faults that could lead to arcs and major failures in aircraft electrical systems [3].As with any electrical system, there is an expectation that faults will occasionally take place in insulation systems and arcs will develop as a result.Managing arcs that arise from electrical faults in aerospace electrical systems has previously been challenging given the lower operating voltage of the electrical system and low levels of fault current [5].This has resulted in aerospace cabling systems being designed to withstand the effects of sustained arcing due to wiring faults.
The majority of the arcing faults observed in aircraft have been attributed to being caused by insulation degradation and the subsequent short-circuit (accounted for more than half of the total failures in the period of 1980-1999) [3], [6].Given the voltage of these systems has been below Paschen's minimum, arcs are ignited when either an electrode gap is short-circuited by a physical connection (e.g., a wire rubbing against a metallic flange) or due to a conductive material traveling into the air gap between two conductors (e.g., contaminated water dripping onto cracked insulation).As arcs propagate on the cable surfaces or to adjacent circuits and conductors, they can cause severe damage to the component or the wider electrical system [7].
Previous research focused on understanding the characteristics of arcs in aircraft for 28 V dc and 115 V ac systems (as used on platforms such as the Boeing 737/Airbus A320).More recent work has extended this to consider the incremental voltage steps of 230 V ac / 540 V dc seen on systems such as the Boeing 787/Airbus A350.Significant work was carried out to investigate the nature of dc arcs in an aerospace environment at the time 540 V dc systems were introduced.In these dc systems, there is a specific challenge associated with current interruption due to the absence of a current zero.The results in [8], [9], [10], and [11] provide information on what is expected of an ac using rms values (e.g., arc voltage reducing at low pressure) but there is no prior work in the public domain that explores high-frequency ac arcs in an aerospace environment.In [8], dc arcs in the range of 7-300 A were shown to have a lower arc voltage as pressure reduces.The dissipated mean arc energy increased for higher currents and lower pressures which is not the result of a higher arc voltage per unit length but due to the arc elongation.Investigations in [9] and [10] for dc arcs at 540 V and a current range of 10-100 A, showed a non-linear increase of arc dissipated energy with system voltage and an unclear variation of energy as a function of pressure.
For previous ac arcs, investigations were mostly conducted on arc currents ranging from 10 to 350 A rms with system voltages under 500 V and frequencies up to 850 Hz [7], [12], [16].An increase in the operating frequency of ac arcs, from 360 to 850 Hz in [12] and [13] leads to a reduction in the current interruption capability and shortening of the "flat-shoulder" occurring at the current zero crossing.At a frequency of 850 Hz, it was found that the rate of change of current, di/dt is higher than at 360 Hz which weakens the insulating gas recovery process [13] and escalates the deterioration of cable insulation [14].
The continuous development of electric power systems on aircraft and the potential increase in the system voltage to 3 kV, as used the in E-fan X demonstrator [17], [18], is seen as a technical challenge to the safe operation of aircraft, especially with other evolutionary changes demanding optimized designs, improved efficiency, and higher power density.This is amplified by the presence of demanding mechanical and environmental conditions.On a power system level, this imposes a threat on the insulation systems and fault management.At lower voltages, the arc voltage is more likely to be significant in comparison to the system voltage and as a result, will lower the current flowing through a fault.In higher voltage systems where arc voltages become proportionally smaller than the system voltage, the fault current is increasingly determined by the system impedance and may increase significantly.This article presents experimental work carried out to examine the characteristics of ac arcs under pressures of 0.2-1 bar, frequencies of 0.5-2 kHz, and a peak arc current of up to 4.6 kA.The experimental investigations are to: 1) inform the development of a high-frequency aerospace arc model that can accurately evaluate different arc parameters without having to conduct a large volume of experimental work and 2) identify test techniques that could be used to qualify future higher voltage aerospace electrical systems.Arc energy was calculated based on the experimental data to examine the effects of various measurands including the arc length.A modified black box model has been developed that can provide good agreement with experimentally obtained arc parameters.The developed model in this work has wider implications in terms of assessing the impact of high-frequency arcs on highervoltage aerospace applications.

II. EXPERIMENTAL SETUP AND DATA PROCESSING A. High Current Test Circuit
As shown in Fig. 1, the circuit consists of a capacitor bank (each capacitor being 1500 µF) charged with a dc power supply (125 kV, 30 mA, Glassman) through a 10 k charging resistor, R C .Resistors, R eq of 100 k are connected across each capacitor, C to ensure equal voltage distribution during charging and to act as bleed resistors after testing.A safety earth switch (monostable pneumatic control) is connected in series to a 1 k resistor, R dump, and connected in parallel to the capacitor bank to further facilitate the discharge of capacitors.Different combinations of L and C were used to emulate the prospective fault current and circuit frequencies.A bistable pneumatic switch was used to discharge the capacitor bank once it had reached the required charging voltage, V S .
Arc initiation was carried out using a fuse wire of 0.2 mm diameter connected between the copper electrodes in a vacuum vessel capable of operating at a range of pressures [Fig.1(b)].Fuse wires were used to recreate the arc initiation [11] to avoid incorporating an ac triggering source or developing complex moving contacts.The arc current and arc voltage were measured using a current transformer (Pearson model 4418, 0.001 V/A) and a differential voltage probe (Cal Test Electronics, CT4079-NA, 15 kV) respectively.The charging voltage across the capacitors was measured using a TENMA voltage probe and a multi-meter.
The arc behavior due to effects of circuit frequency (0.5-2 kHz), arc current (25%-100% of maximum current), electrode gap (2.5-40 mm), and pressure (0.2-1 bar) were investigated.In all the tested configurations, to ensure equipment is operated within its ratings, the arc current was calculated to not exceed 5 kA as in Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where f is the frequency in hertz, and R is the estimated circuit resistance in ohms with a V S of 0.65 kV across each capacitor.Frequencies in the kilohertz range are chosen to replicate high-speed operations aiming at lower inductance and smaller-size generators [19].Higher voltage systems operating at variable frequencies in the range of 360-800 Hz already exist in Boeing 787.Higher ranges were only tested such as in the E-Fan X demonstrator, which ran at 1500 Hz before it ended in 2020 [17].Details of inductor-capacitor combination examples used in this work alongside the tested charging voltages are depicted in Table I.
A stainless steel pressure vessel, rated up to 10 bar and with a volume of ∼158 L, was used to investigate the arc behavior under pressures of 1, 0.6, and 0.2 bar, which corresponds to conditions expected in a non-pressurized aircraft compartments at ground level, approximately 15 000 feet, as experienced by vertical take-offs/landings in flying taxis, and approximately 40 000 feet, which is the typical cruise altitude of commercial aircraft, respectively.The vessel was fitted with a support plate for the fuse wire with a variable gap between the two electrodes.For low-pressure tests, the vessel pressure was reduced to 0.2 and 0.6 bar via a vacuum compressor.The pressure was regularly checked using a plugin digital gauge to ensure no change in pressure.All pressure values indicated in this work are absolute.An identical procedure was repeated after each arc ignition.

B. Data Processing
Current and voltage signals were recorded for arcs in underdamped circuits of decaying fault current magnitudes up to 4.6 kA and frequencies from 0.5 to 2 kHz.The arcs generated in this testing are self-extinguishing and behave as a non-linear resistive circuit element, which changes as a function of the injected current and the electrode gap.The arc duration is defined by the energy stored in the capacitor bank and the level of damping resulting from the resistance of the arc.While these circuits see a decrease in current every half cycle, it is important to note that this effect would likely not be seen in an aerospace electrical system where a more constant level of fault current is expected.Arcs were analyzed based on the current and voltage waveforms by calculating the associated arc resistance, conductance, power injected into the arc, and arc energy.The arc energy was calculated using the instantaneous integral of the arc power.For all experiments, unless otherwise stated, only the first half cycle was analyzed as it represents a realistic approximation of a practical ac system in which a constant value of arc current may flow.The analyzed data were processed using median filtering to reduce undesired noise whilst preserving the required waveform properties.

III. RESULTS AND DISCUSSION
A. Effect of Electrode Gap Fig. 2(a) and (b) shows the effect of varying electrode gaps on voltage and current characteristics for a 4.6 kA arc in a 1.5 kHz circuit.While the electrode gap does not equate to the actual arc length, it infers a minimum value of arc length and is likely to be a close approximation to the arc length in the first half cycle before the arc elongates further.As expected, the electric arc behaves as a non-linear resistive element.Fig. 2(a) shows an increase in arc voltage as the electrode gap is widened.The voltage increases, sub-linearly, by a factor of four, when the electrode gap was increased from 2.5 to 40 mm due to the higher voltage drop across the longer arc column (assuming every arc has a constant cross section).The average arc voltage is also changing and does not maintain a constant value due to the stochastic changes of the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.arc which involve changing length and temperature.At current zero, an arc voltage overshoot is sometimes observed, e.g., at 2 ms for 10 mm, which represents the sudden increase in arc resistance as the current reaches the zero crossing.The electrode voltage drop, V electrode , was estimated to be between 14.97-33 V for 4.6 kA arcs in the range of 1-2 kHz whereas for shorter gaps V electrode is not negligible.In [20], V electrode was reported to be 16.3 V irrespective of current magnitude or frequency whilst in [21] it was shown to be in the range of 20-40 V regardless of the gap length.It can be seen from Fig. 2(b) that the arc current recorded a small decrease of 4% within the first half cycle when the electrode gap was increased from 2.5 to 40 mm with a lower arc duration.The current flowing into the circuit, 4.6 kA, when compared with the value expected from theory, 4.75 kA, has a higher degree of damping as a result of the arc resistance.However, both waveforms remain a damped sinusoid with no change at the current zero.This is due to the arc presenting a higher resistance to the test circuit and thereby resulting in an increased rate of damping.It illustrates the challenge of delivering a highcurrent test circuit at higher frequencies for use in qualification tests of future aircraft electrical systems.The stored energy in capacitors must be considerably high if capacitor banks are used to support testing.

B. Effects of Circuit Frequency and Pressure
This section investigates the change in the arc characteristics as a function of the circuit frequency, tested for pressures of 0.2 and 1 bar and a fixed electrode gap of 2.5 mm.The test frequencies were achieved by varying the inductance and capacitance values whilst maintaining an arc current of 2.4 and 4.6 kA.The values of the capacitors bank and the coilformed inductance used to produce the required frequencies are depicted in Table II.
Fig. 3 shows the effect of varying circuit frequency on the arc voltage waveform.The ambient pressure was also investigated to determine whether the change in frequency could cause an adverse effect in a low-pressure environment.From experiments, as the circuit frequency increases, the arc exhibits two main changes: 1) a slight decrease in the arc voltage amplitude and 2) a higher rate of change in voltage, dV /dt.The arc voltage slightly reduces for higher frequencies due to the lower inductance value in the test circuit being used, which introduces less damping and lower circuit resistance (Table II).As the pressure is reduced to 0.2 bar, there is a reduction in the arc voltage magnitude.This is due to the low mean electric field of the arc column at low pressure which increases the electrical conductivity for arc temperatures from 5000 to 12 000 K [8].At higher frequencies, the arc voltage difference between 0.2 and 1 bar reduces as observed between Fig. 3(a) and (c) for 1.5 and 0.5 kHz arcs, respectively.The waveform slopes in Fig. 3 represent dV /dt, which reduces with lower frequencies for both 0.2 and 1 bar.The difference in arc voltage remains but may be due to the burning of the fuse wire.The arc voltage magnitude, circuit arrangement, and parameters contribute to the nonlinearity of the arc voltage waveform seen in Fig. 3. Their combined effect disrupts the arc voltage curve and contributes to adding high harmonics to the signal [22].
Fig. 4 shows the arc voltage gradient of a 4.6 kA arc.For shorter electrode gaps, the channel resistance is lower, and the total arc voltage is dominated by the anode and cathode volt drops.This leads to a high-voltage gradient to maintain the arc across the electrode gap.As the electrode gap increases, the arc voltage gradient reduces and the arc voltage almost entirely falls across the arc channel leading to a relatively constant arc voltage and a less distorted square wave observed for longer electrode gaps (i.e., >40 mm in this study).This means that the relationship between the arc voltage and arc length can be approximated as directly proportional with longer electrode gaps, whilst it cannot be presented by a simple scalar for shorter electrode gaps.Unlike power system equipment such as the 15 kV switchgear and medium-voltage motor control centers (MCC), the compact designs of aircraft suggest that arc faults will be for shorter gap spacing between adjacent electrical systems.This makes the estimation of arc voltage for aircraft faults difficult due to the non-linear relationship between arc voltage and arc length at shorter electrode gaps.For results obtained at 0.2 bar pressure, the voltage gradient is generally lower than their counterparts at 1 bar regardless of the circuit frequency, as shown in Fig. 4.This may be a direct consequence of arc elongation at lower pressure.

C. V-I Characteristics of Electric Arcs
This section explores the V -I characteristics of arcs under pressures of 0.2 and 1 bar and across electrode gaps of 2.5 and 40 mm.Fig. 5 shows the flow of the first two cycles of a 4.6 kA Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
arc which form two hysteresis loops.Each loop in Fig. 5(a) illustrates the arc in terms of voltage-current relationship and the area of the loop.At every first cycle, before the arc is completely established, a noisy higher arc voltage peak is sometimes seen at arc initiation.The presence of fuse wire to ignite the arc and its vaporization could be responsible for this event as the wire burning changes the surrounding dynamic for the first few microseconds.For fuse wires stretched across electrode gaps, a high current density is required to vaporize the fuse wire.The rise in arc voltage corresponds to the sudden application of voltage leading to wire vaporization across the electrode gap.At this stage, the current starts to flow through the wire and subsequently through the arc with an upsurge due to the high current density and the arc voltage drops.As the current continues to increase, the arc voltage remains at a relatively constant value and independent of the arc current.Prior to arc extinguishing, the arc voltage starts to increase slowly until I arc is 0. At current zero, arc resistance, as opposed to arc conductance, is momentarily at a high value and results in a significant voltage drop across the electrode gap.The electrode gap is almost immediately under voltage stress and the current begins to flow in the opposite direction.Other cycles exhibit similar behavior but with a higher energy dissipation as the arc becomes cooler.
Fig. 5(b) shows the V -I characteristics of the same arc under low pressure.The loop area represents the integral of the product of voltage and current (i.e., arc power).Arcs under atmospheric pressure, Fig. 5(a), have larger loops which correspond to the slightly higher arc voltage leading to higher arc energy.A typical V -I hysteresis loop would have two matching half cycles.In this case, the changes associated with the arc voltage, arc current, and circuit damping resulted in the loop having a different shape every half cycle.A small reduction in the arc voltage can sometimes be observed as the arc progresses toward the peak current.This is normally counteracted by a voltage increase to maintain the arc as illustrated in Fig. 5(a) for the 2.5 mm electrode gap during the first cycle (i.e., t = 1 ms).

D. Arc Energy Calculations
Sections III-A-III-C explored a range of parameters that impact arc behavior in future higher voltage aerospace electrisystems, which in return affect the accumulative arc energy.This section presents the arc energy calculations associated with different arcs.The arc energy is an important parameter in evaluating the hazards associated with arc faults.It results in erosion of metallic electrodes; significant levels of heat transfer and pressure increase that all constitute potential hazards to nearby systems/structures or personnel.In [23], it was mentioned that over 50% of the arc energy is responsible for melting and vaporizing metal and insulation, whilst the remaining arc energy is transferred to the arc column contributing to the processes of conduction, convection, or radiation.The accumulative arc energy of a 4.6 kA peak arc current during the first cycle at atmospheric pressure is shown in Fig. 6.During (A), the arc energy is relatively low, and the arc is not yet sustained.As the current increases, the energy Fig. 6.Variation of arc energy as an ac arc current sustains a 4.6 kA arc at 1 bar in a 1 kHz circuit across an electrode gap of 2.5 mm.Fig. 7. Arc energy accumulation for a 4.6 kA arc across an electrode gap of 2.5 mm, tested for pressures of 0.2, 0.6, and 1 bar.supplied to the arc increases and the arc temperature is at its highest corresponding to the peak current (B).Hence, the majority of arc energy transfer occurs during the middle of half cycles.The rise of energy during these time durations contributes to pressure changes within the vessel.For this test, the vessel volume is sufficiently large, so the pressure change is negligible.The energy continues to accumulate and momentarily saturates at (C) where the current passing through the arc channel is 0. The arc energy will continue to increase until the end of the half cycle as shown in Fig. 6.Fig. 7 illustrates the energy variation during the entire duration of the arc at different pressures.The arc voltage at lower pressures (i.e., 0.2 bar) reduces resulting in lower arc energy, which does not reflect the worst-case scenario.The arc at 1 bar produces a higher magnitude of arc energy than the arcs at 0.6 and 0.2 bar.Similar results were observed in the repeated experiments.While our work showed that a reduction in pressure reduces arc voltage per length, the work in [8] showed that arc elongation could then result in overall higher arc energy.

A. Model Theory: Hypothesis and Equations
In Section III, it was shown that high-current and highfrequency arcs behave as non-linear resistive elements in which the arc resistance is directly affected by circuit parameters.This behavior can be explained by a set of time-varying differential equations where the arc conductance varies as a function of arc current, voltage, and other arc parameters.There is limited literature published on the modeling of highfrequency and high-current arcs.This is somewhat expected as the current maximum operating frequency is 400-800 Hz for application in more-electric aircraft and high current arcs at 50/60 Hz are widely investigated for circuit breaker applications.The underlying challenge with modeling future higher voltage aerospace electrical systems is the lack of knowledge on the relationship between the arc voltage with parameters such as frequency, pressure, and electrode gap.Figs. 6 and 7 in Section III showed that the arc energy increases non-linearly with the electrode gap.Unlike longer gaps, short arcs cannot be simply represented by (2) as the arc voltage drop at the electrode cannot be neglected.Based on the experimentally obtained results, for electrode gaps between 2.5-100 mm, the arc energy increase can be represented by a natural logarithmic equation.Hence, the effect of arc elongation in an ac arc can be incorporated by scaling the arc model equation with the correct arc length function where B is the arc voltage gradient, and L is the arc length.

B. New Model Development and Implementation: Based on a Modified Mayr Model
The instantaneous arc conductance for ac arcs can be calculated by the arc current and voltage at a given time.According to [24], the arc conductance can be calculated using the Mayr-based (3) with two parameters: time constant, τ and cooling power, P out .The cooling power constant depends on two fitting parameters, C I and P o defined in (4).Both fitting values along with the arc time constant can be estimated as reported in [24] 1 where u is the arc voltage, i is the arc current, τ is the time constant, p is the gas pressure, and C I and P o are the fitting parameters.
In Section IV-A, it was explained that the arc energy varies non-linearly with the electrode gap, which can be represented by a natural logarithmic function.To incorporate the arc length effect into the model, the cooling power constant is scaled by the natural logarithmic function of the electrode gap [(5)].The arc model was integrated into the circuit shown in Fig. 1 using Simulink to replicate a similar arc discharge testing setup.In this model, it is assumed that the arc length is equal to the electrode gap.Although this assumption is not reflective of the physical nature of a high current short-duration arc, given their capability of varying drastically from the electrode gap, it still gives a good estimation of the arc voltage for the tested conditions.P 0 and C 1 are estimated from the comparison of the simulated and experimental arc voltage waveforms to calculate the lowest rms value as the worst-case scenario.Both parameters, P 0 and C 1 , are then multiplied by the logarithmic relationship between the arc energy and arc length where P out is the cooling power in watt, i is the arc current in ampere, l is the electrode gap in millimeters, and P o and C 1 are the model parameters.Fig. 8 shows the comparison of the arc model waveforms to the experimental results for a 4.6 kA in a 1 kHz circuit as a function of two electrode gaps: 5 and 100 mm under atmospheric pressure.A peak is observed during the first microseconds due to the action of the fuse wire, which is resembled by the model by virtue of the initial arc conductance, g(0).Those peaks are present at each current-zero crossing to model the high resistance when the current is in a low region.In the high current regions, for the 2.5-100 mm range, the modeled waveforms yield good agreement with the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.experimental results for up to 100 mm.Model results deviate from experimental at current-zero and near the current-zero crossing as the interruption region is not considered in this model.
Table III shows the and experimental results for a 4.6 kA at 1 kHz under 1, 0.6, and 0.2 bar.Based on (5), the modified model is in good agreement with the experimental results for 1 bar (Fig. 8).As the pressure reduces, satisfactory results are observed for 2.5 mm.At 40 mm, a significant difference is seen between the results of the modeled arc [( 5)] and the experimental data.This is because (5) does not account for pressure variation and only assumes the arc voltage change is directly associated with the logarithmic function of the electrode gap.
Equation (6), a modified version of (5), estimates the cooling power as a function of the electrode gap and air pressure which then feeds into the estimation of arc voltage.This modification improves the applicability of the new arc model to include arc simulations at aeronautical conditions.Simulation results and comparisons of ( 5) and ( 6) are shown in Fig. 9.It illustrates good agreement with the experimental data where the reduction in pressure reduces the cooling power leading to a slow exponential reduction in the average arc voltage across the electrode gap where p is the air pressure in bar absolute, and P 0 and C 1 are equal to 10 −4 W•mm −1 and 20 W•bar•A −1 •mm −1 , respectively.

C. Model Applicability Validation
The modified arc model was compared with experimental and modeling work on ac arcs in the air under atmospheric pressure from previous research at a range of applications including power and high frequency, high current, and high voltage.The results, which validate the applicability of our model to a wide range of applications, are shown as follows.
1) High Current, Low Voltage, and Power Frequency: According to Wu et al. [25], low voltage ac arcs of short durations can be modeled as shown in (7).This model was proven applicable for single-phase arc currents in the range of 3-100 kA.According to (7), for an electrode gap of 60 mm at a rated voltage of 50 V, the estimated arc voltage is 82.28 V.By incorporating our model, ( 6), in a representative ac system on Simulink, an average arc voltage of 81.82 V is obtained.For a 100 mm electrode gap, (7)  aeronautical conditions for arc currents up to 5 kA, frequencies in the range of 0.5-2 kHz, and electrode gaps between 2.5-40 mm under pressures of 0.2, 0.6, and 1 bar.The main conclusions of this work are as follows.
1) Generalized modeling approach without recourse to experiment-arc current and arc voltage waveforms obtained at 1, 0.6, and 0.2 bar were analyzed and fed into an arc model that defines the relationship between the electrode gap and the arc cooling power through a natural logarithmic function.Good agreement between experimental and simulated results is achieved for electrode gaps up to 100 mm and frequencies between 1-2 kHz.The initial modified model showed deviation at longer gaps and lower pressures.A further improved model was developed that was able to correlate the change in pressure to the arc cooling power.This generalized modeling approach can be used to predict energy levels for a given fault current and fault duration, which could eliminate the need to develop complex experimental setups to reproduce arc faults under challenging conditions.2) Testing methodology for arc hazards under aeronautical conditions-pressure variability, setup versatility, and high-power generation are three important aspects of the designed setup.Tests carried out at atmospheric pressure represent the worst-case scenario for arc duration up to 11 ms.For arcs tested under 1, 0.6, and 0.2 bar, atmospheric arcs produced the highest energy.Representative tests under a low-pressure environment may be unnecessary for the specified test conditions to assess arc hazards.The setup is applicable for tests of other applications including at power frequencies and higher voltages.3) Electrical characterization of high frequency and high current arcs-the analysis of the arc voltage and current waveforms showed that higher frequency arcs display a slightly lower average arc voltage due to the lower inductance used to produce the frequency.Consequently, lower arc energy is produced due to corresponding changes in the circuit impedance of the test setup.The effect of higher frequencies on the voltage gradient is minimal for longer electrode gaps.In general, lower voltage gradients were captured for tests undertaken at lower frequencies.Arc energy is found to be higher with longer gaps but not necessarily higher per unit length due to the potential arc elongation that could occur at lower pressures.

Fig. 1 .
Fig. 1.(a) Schematic of the high current test circuit and (b) arc vacuum chamber with the arc electrodes.

Fig. 2 .
Fig. 2. Variation in (a) arc voltage and (b) arc current of a 4.6 kA arc across electrode gaps of 2.5-40 mm in a 1.5 kHz circuit under atmospheric pressure.

Fig. 3 .
Fig.3.Arc voltage at circuit frequency of (a) 1.5, (b) 1, and (c) 0.5 kHz with 2.4 kA current peak tested for a 2.5 mm electrode gap and under pressures of 0.2 and 1 bar (dashed lines: average arc voltage calculated based on the first half cycle).

Fig. 4 .
Fig. 4. Arc voltage gradient of a 4.6 kA arc as a function of electrode gaps for 1, 1.5, and 2 kHz (marker: experimental data and solid line: fitting curves).

Fig. 5 .
Fig. 5. V characteristics of the first two cycles of 4.6 kA arcs in a 1 kHz circuit for 2.5-and 40-mm electrode gaps at (a) 1 and (b) 0.2 bar (clockwise change).

Fig. 9 .
Fig. 9. Time-varying simulated arc voltage waveforms of a 4.6 kA arc under 1 kHz for (a) 0.2 and (b) 0.6 bar, tested for a 40 mm electrode gap.

TABLE II CAPACITOR
AND INDUCTOR COMBINATIONS USED TO INVESTIGATE THE FREQUENCY EFFECT

TABLE III COMPARISON
OF THE EXPERIMENTAL ARC VOLTAGE VALUES AND THE MODEL RESULTS FOR 2.5 AND 40 mm UNDER 1, 0.6, AND 0.2 BAR ABS yields 75.58 V, which contradicts the increase in arc voltage as a response to longer electrode gaps.On the other hand, our model yields 92.34 V which is representative of the expected arc voltage The latter has shown that for 850 Hz, an average arc voltage is estimated at 43.94 V with no significant difference for 3.6 and 8.3 kHz.Equation (6) has shown a satisfactory estimate of 32.36 V.V. CONCLUSIONA high-frequency test setup was developed to investigate the behavior of ac arcs in a pressure vessel.The underdamped test circuit assessed the arc performance characteristics under Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.