A high-impedance fault detection scheme for DC aircrafts based on comb filter and second derivative of voltage

(cid:1) This article presents a fault detection scheme based on comb ﬁ lter and second derivative of voltage for DC Aircrafts. (cid:1) The proposed method is also without any communication link in methodology or implementation in the system. (cid:1) The scheme proved to work during different fault resistances from low to high resistances within an appropriate accuracy. (cid:1) This eliminates require of communication link, and moreover, it also distinguishes the high impedance faults and noises. (cid:1) The fault location scheme is tested by real-time setups


Introduction
Short-circuit protection in DC aircraft is currently a wide-attention research topic, with a particular focus on fault detection.Due to the weight limitations, the DC nature of the power system, and requiring fast FDD operation, the conventional breakers and fuses cannot offer adequate protection on fault events [1].Furthermore, short-circuit faults in electric aircraft are one of the main reasons for failures in operation, and even can have catastrophic consequences [2].For these reasons, it is an undeniable fact that employing an effective FDD is mandatory to detect and isolate faults quickly.Moreover, when a fault occurs through a high-value fault impedance, the current is often less than the threshold of the fuses; and detecting the small magnitude of fault current during HIFs is a challenging task for protection relays [3].If a HIF remains in the system for a long time, it results in repetitive current re-ignition and extinction [4].Traditional overcurrent fault detection techniques are well carried out in conventional power systems, however, unfortunately, the reliability of these methods is not assured in HIFs.In the case of DC aircraft systems, strict system operation requirements and special types of loads ask for a seamless and reliable protection system.Therefore, the detection of the HIFs is of significant importance to ensure the electrical safety of DC aircraft [5].
In recent years, a few fault detection methods are developed for different DC electrical systems, such as shipboards [6], DC microgrids [7], microgrid clusters [8], and DC distribution grids [9].However, the lack of comprehensive FDDs on DC aircraft is a challenge to the reliability of aircraft and requires more development.In Ref. [10], a fault detection method is suggested for DC aircraft by using temporary deviations of load circuit model coefficients and wiring parameters.In this method, different fault resistance values are analyzed, however, this technique suffers from high fault detection time.A low-cost fault detection method based on the acquisition of the current waveform is presented in Ref. [11].In this approach, the fault resistance is neglected, and furthermore, the fault is detected within 1,000 ms, which is unacceptable for the safety of DC aircraft.Another method is presented in Ref. [12] to detect arc faults in DC aircraft by optical spectrometry.This method detects faults in several milliseconds; however, it requires some additional equipment to be installed parallel with FDD, which increases the weight of the aircraft, and consequently, it makes higher fuel consumption and cost.
In DC systems, fault detection can be performed by different tools, such as wavelet transforms [13], artificial neural networks [14], machine learnings [15], and Hilbert-Huang transforms [16].However, due to the complexity of these methods, the total computational burden and operation time of the fault detection unit will be high.Therefore, in this paper, the second derivative of current is used as the core of FDD.The derivative of current has been used for different fault detection systems such as standalone [17], and grid-connected DC microgrids [18], which also show the high speed and low complexity of this technique.Furthermore, in this paper, the comb filter is used in series with the second derivative of fault current to add the capability of detecting HIFs in DC aircraft.The comb filter is implemented in Ref. [19] for wind turbine fault detection, and in Refs.[20,21] for transmission line fault detection.The results in Ref. [20] show the improvement capability of the comb filter on transient feature extractions of fault detection units.However, due to the differences between the practical systems, it should be noted that the existing studies only focused on power systems such as wind turbines and transmission lines, which have different limitations, requirements, and performances, as they operated in AC current with a lower rate of change of current and voltage.
To the best of the author's knowledge, the proposed scheme has the highest operation speed and lowest cost among the existing local fault detection systems for DC aircraft.The existing fault detection methods require both ends' data, and therefore, they suffer from noise and delay.Furthermore, the absence of a comprehensive and accurate fault detection method for HIFs in DC aircraft leads to an inaccurate performance of the existing methods during these types of faults.Consequently, in this research, a Comb filter and two-stage derivatives of voltage in one end of the faulty line in DC aircraft are used, and the application of the proposed method on different events is investigated through extensive simulations and real-time tests.The obtained results manifest the significance of the proposed novel scheme as there are few studies performed on the local fault detection of DC aircraft.
The aforementioned studies reveal that LIF and HIF detection in DC aircraft is still an unsolved challenge and requires more development.This lack of research, especially during HIFs, motivates to propose a fast fault detection method for these systems.Therefore, in this paper, an advanced fault detection approach based on a hybrid comb filter and second derivative of voltage in DC aircraft is proposed to detect both HIF and LIF within the lowest possible time.The proposed fast FDD detects the faults before damaging the freewheeling diodes of converters during the fault without requiring any communication links.The main contributions of the paper are summarized as follows: 1.The proposed fault detection scheme is developed using a Comb filter and the second derivative of voltage, as a novel method in a DC aircraft's protection system; 2. The proposed technique is applied to a DC aircraft as a new fault detection method; to the best of the authors' knowledge, the operation time of the proposed method is lower than the existing methods, which ensures the safety of the electrical system; The rest of this paper is organized as follows.The characteristics of faults in DC aircraft are investigated in Section 2. In Section 3, the fault detection scheme based on a hybrid comb filter and second derivative of voltage is proposed.The real-time test results of the proposed scheme are described in Section 4. Finally, the paper is concluded in Section 5.

DC aircraft power system
Generally, aircrafts, such as the more electric DC aircraft, are largely equipped with different electrical components, such as wirings, converters, generators, and batteries.A simulation model of a DC aircraft, as shown in Fig. 1 is developed and used in this paper.The power supply system consists of two variable frequency starter generators (SG1 and SG2), an ESS as an auxiliary power unit, and different AC/DC and DC/DC converters (C1-C4).The main busbar of the power supply system is AE270 VDC, the secondary bus is AE28 VDC, converted by DC/DC converters to share the power demand of multiple loads [22].

LIF characteristics in DC aircrafts
After a fault in the DC aircraft, the DC link capacitors between cables and power electronic converters inject a high-rise current into the fault point.Immediately after the fault, capacitors will start the discharge state, and the current waveform of this stage, from real-time simulations, is depicted in Fig. 2, where the fault current magnitude could reach approximately 10 times the nominal current.The DC-link capacitor discharge current can be determined by [23]: As presented in Fig. 2, during the high-rise state of the current, the voltage of the faulty section will drop dramatically.Consequently, the voltage of the capacitor can be obtained by: Therefore, by subtracting Eqs. ( 1) and ( 2), the voltage of the capacitor is determined by: where Thus, the full discharge time of the capacitors, i.e., reaching the V C (t) ¼ 0 which is the end of the capacitor discharge state, is calculated by: Due to the low value of C in DC aircrafts, which causes a higher amount of ω, according to Eq. ( 5), the time of voltage collapse is much less than the AC systems, therefore, based on the transient characteristic of the system, the fault should be detected quickly within the capacitor discharge state to avoid voltage collapse in the DC aircraft.

HIF characteristics in DC aircrafts
When an energized wire approaches close to another wire or ground through a high resistance path, an HIF will occur.The fault current is low during HIFs, then, detecting this small magnitude current is a challenging task for today's FDDs.If the HIF remains in the system for a long time, it results in repetitive extinction and re-ignition in the cabling system of aircraft [24].The HIFs have very complex characteristics with highly nonlinear behavior.During HIFs, first, the fault current rises to the maximum value; then, the nonlinearity stage is started until the fault is isolated.The model of HIFs in DC aircraft has been considered rarely in designing a fault detection scheme.The model of [25] is utilized in this paper to accurately model the characteristic of HIFs.The HIF current waveform can be determined by Therefore, by determining R from Eq. ( 6) Eq. ( 7) is based on laboratory observations, and the constant value of m is determined by experimental tests for different HIFs in different situations.The variation of the root means square of HIF resistance by changing different values of arc constant, m, is depicted in Fig. 3(a).Therefore, by changing the arc constant, the accurate value of resistance can be selected.Voltage waveform during a HIF can be defined by using Eq. ( 6).By multiplying the two sides of Eq. ( 6) by R, the following equation can be extracted: The voltage waveform Eq. ( 8), also defines the fluctuation behavior of voltage during a HIF.The sensitivity analysis of Eq. ( 8), depicted in Fig. 3(b), shows a high dependency of system's voltage during HIF on the variation of fault resistance.Therefore, it is a proper feature to be used for fault detection schemes.As shown in Fig. 3(b), the severe voltage variations, due to variation of HIF resistance, will happen with lower resistances, and with very high fault resistances, the voltage will not change, which causes the fault detection more challenging.
The fault current of the designed model is represented in Fig. 4. As depicted in Fig. 4, the HIF current has repetitive behavior with a small value of magnitude.In this paper, the HIF in dc aircraft is modeled by a nonlinear resistor using Eq.(7).

Proposed FDD
The proposed FDD consists of two derivative blocks, a comb filter, and two LPFs, as shown in Fig. 5.In the proposed scheme, the measured voltage signals are filtered by first LPF to remove all the unwanted frequency components consisting of the noise of measurement devices, or high-power demand in electronic devices during landing or take off, to get an accurate result and to avoid false triggering.As the derivative block can increase the noises, the second LPF is implemented after the derivative block to filter the high-frequency noises.Therefore, both LPFs should be designed to only filter the noises, which typically have a high-frequency characteristic.The current during fault will also have high-frequency content, however, obviously, such frequencies are lower than those of noises.Therefore, the cut-off frequency is selected for a fault event with the highest frequency, fault resistance equal to zero, and close to the measurement sensors.In this work, the cut-off frequency of LPF is selected as 400 Hz.
Moreover, due to the nature of sensors, the accuracy of current and voltage sensors can be influenced by drift, unwanted offsets, and noise.Due to the utilization of LPF, the proposed method is immune to noises; the unwanted offsets are removed by the first derivative, and the sensor drift is removed by the second derivative.Therefore, the proposed method works efficiently during different errors in the sensor.Furthermore, it only requires one sensor, and the need for voltage sensor is eliminated, which decreases the impact of sensor error on the operation of the fault detection method.The proposed FDD based on the derivative of fault waveform will provide the capability of differentiation of the DC aircraft system faults to isolate the fault within the lowest operation time.This is achieved by the appropriate setting of the threshold.An HIF like a cable insulation discharge may be difficult to identify because of the low value of fault current, or it may also be a challenge to distinguish faults and large load variations only based on di/dt.Moreover, the accurate classification of faults is difficult during load changes.
To enhance the effectiveness of the proposed method during HIFs, a comb filter is combined with dV/dt, as shown in Fig. 5.The concept of a comb filter is a filter that adds a delayed version of the original signal to itself.The general structure of the comb filter can be determined by [21]: Note that the scaling factor for the feedforward, α, usually should not exceed 1, since that would cause the output of the filter to increase steadily as a greater and greater signal is fed forward.The scaling factor, α, represents the increasing level of the delayed input signal, dV/dt, and output, y, and therefore it demonstrates the impact of previous samples on the output.Therefore, having the low value of scaling factor makes the output only dependent on the current samples, and high value of α makes the impact of delayed samples close to the current sample values.
Therefore, in this work, α is selected as 0.5, which accelerates the value of dV/dt in faulty events.In the proposed method, the input of the comb filter is the output of dV/dt block.Thus, Eq. ( 9) can be rewritten as: Consequently, the FDS value will be used for detecting the fault.The next step in the detection of the fault is selecting a suitable value of the threshold for FDS.Fig. 6 depicts different zones for the DC aircraft fault characterization based on different system events such as HIF, LIF, and load variation.Therefore, the value of FDS is calculated for a case with the highest load change, which typically happens during takeoff, and a 20% higher FDS is selected as the threshold of FDS.Accurate distinguishing between faults and load variations is difficult due to the overlapping zones only based on the dV/dt.However, due to the utilization of a comb filter in the proposed method, the overlapping zones will be narrower than dV/dt-based methods.One solution for the selection of the FDS threshold value, FDS th , is based on the highest value of load variation in the DC aircraft.Therefore, the maximum value of load variation is selected as the FDS threshold, and higher values of FDS will be categorized as a fault event.The overall procedure of the proposed FDD scheme is shown in Fig. 7, which includes three stages, Stage 1: monitoring the voltage waveform at the FDD location; Stage 2: applying the fault detection technique for the voltage signals; Stage 3: sending the tripping signal to fault interruption units.In this paper, real-time digital simulations are performed by using an OPAL-RT real-time simulator.

Real-time simulation results and discussions
The effectiveness of the proposed scheme is verified by real-time simulations on different scenarios.The structure of the under-study DC aircraft is the same as Fig. 1.The FDDs are installed at converter locations, as the measurements are located at the converters, and to use the  converter interruption capabilities for de-energizing the faulty point, and at the terminal of other DC components, which are not equipped with converters, in association with an SSCB.In this section, the details of fault characteristics in different events, LIFs and HIFs, are introduced.The proposed method is constructed in real-time OPAL-RT in which simulations are conducted using MATLAB/Simulink through the OPAL RT-Lab interface.Furthermore, it should be noted that all currents, voltages, and FDS values in simulation results are scaled in p.u. to provide a better comparison between them.

LIF
An LIF with fault resistance of 0.1 Ω, at t ¼ 0.5 s is created at C1.The corresponding voltage drop in C1 and FDS signals of C1, C2, C3, and C4 are presented in Fig. 8(a).It can be observed that the determined FDS value of C1 is higher than other converters, and the trip signal is sent to the C1 when the FDS exceeds the FDS th of C1, which is 0.2, after 3 ms of the fault event.By considering the tripping operation of C1, the fault current through C1 is also shown in Fig. 8(b), which shows the proper and fast operation of FDD.
In the second scenario, an LIF with fault resistance of 0.25 Ω, at t ¼ 0.5 s is created at the left aileron and elevator, and the results are shown in Fig. 9.As observed in Fig. 9, the fault is detected within 8 ms, and only SSCB1 is operating to de-energize the faulty component.The fault current, flowing through SSCB1, is shown in Fig. 9, where it can be seen that the fault is isolated before the freewheeling diode stage to ensure the safety of the whole DC aircraft electrical system.

HIF
The detection of HIFs is the focus of this paper.As mentioned before, due to the low fault current magnitude, it was a challenge to detect this type of fault.The impact of a HIF with fault resistance of 3 Ω at t ¼ 0.5 s at the DC load side is considered to validate the performance of the proposed scheme, and the results are shown in Fig. 10.In this case, as shown in Fig. 10(a), the variations in voltage and current, compared to LIFs, are not large, and it causes the difficulties of the fault detection by traditional methods.As shown in Fig. 10(b), the FDS exceeds the threshold after 22 ms and sends the trip signal to SSCB 4. It should be noted that due to the lower fault current magnitude during HIFs, a longer operation time of FDDs is also acceptable, however, to ensure the safety of the DC aircraft system, the proposed method detects and isolate the faulty section within the lowest possible time, as shown in Table 1.The performance of the proposed method for higher values of fault resistances is shown in

Load change
The performance of the proposed FDD is investigated for a step-change in load M2, which causes a 5% sudden voltage drop as shown in Fig. 12.It can be seen in Fig. 12 that the value of FDS does not exceed the FDS th, and therefore, any unnecessary trip signal from FDD is avoided.

Selectivity of the proposed method
The selectivity of the fault detection method means that the closest FDD should send the trip signal to interrupters before other FDDs to ensure that only the faulty point will be isolated.Therefore, the selectivity of the proposed method is evaluated for a fault at C2, and FDS curves of all converters are shown in Fig. 13.It can be observed that only the responsible FDD will operate.Moreover, the rise-time of the FDS curve for FDD of C2 is much higher than other FDDs, which proves the lower operation time of closer FDD.
The operation time of the proposed method under different fault resistances is presented in Table 1.Based on these results, it can be concluded that the proposed fault detection technique effectively detects different fault events in a DC aircraft, and this will help the isolation of the faulty point in a minimum time bound.

Comparison and discussion
To better demonstrate the effectiveness of the proposed scheme, this technique is compared with those of Ref. [15], and Refs.[26][27][28][29] in terms of different criteria such as additional equipment requirement, HIF detection function, and detection time as presented in Table 2.
A DC fault detection by using machine learning is suggested in Ref. [15], and the faults are detected by using current and voltage data at one side of the line.However, the impact of fault resistance is neglected, and the faults with zero resistance are detected within 84 ms, which cannot guarantee the safety of components.In Ref. [26], a fault detection method based on sensitivity analysis of fault current is suggested for different fault resistance values.This method does not require additional components; however, it has a limitation on selecting the appropriate value of the threshold.The method introduced in Ref. [27] uses the neural network to detect the fault in a DC aircraft.This technique uses different training data on different fault conditions to provide a more accurate fault detection technique, however, in practical situations, it is difficult to provide a wide range of data for fault cases, and it also has a high fault detection time without the capability of detecting HIFs.In Ref. [28], a machine learning-based fault detection method is presented and implemented in different operating voltages.However, it has a high fault detection time without the HIF functionality.Furthermore, the requirement of a high sampling rate sensor for this method increases the complexity of sensors and packet dropout probability.An intelligent three-tie switch is presented in Ref. [29] to detect HIF.However, this method requires a communication link, and the fault detection time is too high.Therefore, this method is not suitable for DC aircraft applications.
The extensive analysis and comparisons presented in this paper prove that the proposed scheme has a lower fault detection time than the other fault detection schemes, and it provides the capability of HIF detection, within 30 ms, ensuring the safety of DC aircraft during both LIFs and HIFs for faults up to 5 Ω, without any additional equipment, and only by using voltage sensor with a low sampling rate of 20 kHz.It can be implemented by low-cost sensors and has a lower rate of data losses.
The proposed fault detection scheme is validated by testing different scenarios and disturbances on a DC aircraft through simulation and experimental studies.The results demonstrate that the developed fault detection scheme is fast and effective to detect faults in different locations and components of a DC aircraft with resistances up to 5 Ω within 30 ms.This range of fault resistance is categorized as HIF, which is difficult, or impossible to detect by existing methods.Moreover, the operation time of 30 ms, as presented in Table 2, guarantees the safety of the whole DC system during faults.In addition, as shown in Fig. 12, the proposed fault detection scheme distinguishes between overloads and fault events, to avoid nuisance tripping in overload events.Furthermore,   the implementation of the proposed fault detection scheme is communication-less, therefore, in addition to the lower cost compared to communication-based methods, issues such as delay and noise of communication links do not exist in this protection system.
The computational complexity of the proposed method is measured by CPU time and memory.A computer with 3-GHz i7-Core CPU, 8.0-GB RAM is used for the implementation of the proposed method on simulation, and the computations for the analysis of fault signals by OPAL-RT require less than 1 ms, and memory of around 10 MB.The complexity of Comb-based methods has been evaluated in Ref. [30].It has been shown that the Comb filters are a class of low-complexity filters especially useful for multistage decimation processes.

Conclusion
Designing a fast and reliable fault detection technique for DC aircraft is the main task to guarantee seamless power flow during faults.In this paper, an FDD is proposed to detect both LIFs and HIFs in DC aircraft and to ensure the safety of the electrical system.After a fault event in DC aircraft, the proposed scheme effectively detects the faults before reaching the peak value of fault current to ensure the safety of power electronic-based components.The effectiveness of the proposed method is validated by real-time simulations, and it is found that the proposed FDD requires a maximum of 30 ms to clear HIFs.It is also demonstrated that the proposed scheme can easily distinguish between the overload conditions and HIFs and avoid sending trip signals during overloads.

Fig. 2 .
Fig. 2. Current and voltage waveforms during fault in DC aircrafts.

Fig. 6 .
Fig. 6.Classification of DC aircraft events based on FDS values.

Fig. 9 .
Fig. 9. Voltage and current for an LIF with fault resistance of 0.25 Ω, at t ¼ 0.5 s, created at left aileron and elevator and isolated after 8 ms.

Fig. 10 .
Fig. 10.Results for a HIF with fault resistance of 3 Ω is at t ¼ 0.5 s at DC load side.(a) Current and voltage waveforms.(b) FDS.

Fig. 11 .
In this case, 4 different HIF scenarios with different fault resistances are applied in different fault locations, and the FDS proves the speed and accuracy of fault detection in different conditions.The fault resistances of HIF 1 , HIF 2 , HIF 3 , and HIF 4 are 5 Ω, 4.3 Ω, 4 Ω, and 3.3 Ω, respectively.

Fig. 11 .
Fig. 11.Performance of the proposed FDD under different HIF scenarios.
This paper proposes a fault detection scheme for low and high impedance faults up to 5 Ω.HIFs, which cause very low fault currents, have been considered limitedly in previous one-ended fault detection methods for DC systems; 4. The proposed fault detection scheme only uses the voltage measured at one end of the line.Therefore, it is more immune to noise compared to communication-based methods.

Table 1
Operation time of proposed method under different fault resistances.

Table 2
Comparison of existing and proposed schemes.