Optimal Detection and Identification of DC Series Arc in Power Distribution System on Shipboards

In this paper, a series arc was simulated under resistive load and motor load, which are mainly used in small ships, and the arc signal was analyzed using discrete wavelet transform. After calculating the correlation coefficient between the single arc pulse and the wavelet, Biorthogonal (bior) 3.1 was selected as the optimal mother wavelet, and the signal was analyzed using multiresolution analysis. From the results, arc signals were distributed in the detail components D2, D3, D4 and D5, corresponding to a frequency range of 19.5–312.5 kHz, with the optimal arc signal extracted based on these values. In addition, in order to distinguish between arc and normal conditions, signal energy was analyzed. By applying the magnitude and signal energy analysis method, the DC series arc generated in the power distribution system of a shipboard was identified.


Introduction
As reported by the Korea National Fire Data System, more than 500 cases of ship fires have occurred over the past five years. In 2019, about 33% of ship fires were caused by electrical faults, causing enormous financial losses and human injuries. Figure 1 shows occurrence rates of electrical fires between 2017 and 2019, and it can be seen that about 50% of electrical fires were caused by poor connections, partial disconnection and degraded or compressed insulation, all of which can be attributed to the series arc. In addition, more than 80% of these electrical fires occurred in the power distribution system of old shipboards docking at the port, as a result of the absence of crew members. Therefore, it was difficult to put out the fires immediately, and it was easy for fires to spread to other ships nearby, causing serious economic losses. For this reason, measures should be taken to prevent electrical fires on old small ships [1,2].
There is a lot of interest in the detection and analysis of DC series arcs for fire prevention. In particular, research is being actively conducted focusing on aircraft, houses and solar power facilities, but there is not enough research regarding the application to shipboards. In order to prevent electrical fire accidents caused by series arcs, much research is being actively conducted based on the Underwriters Laboratories (UL) 1699 and the International Electrotechnical Commission (IEC) 62606 [3][4][5][6][7]. To detect an AC series arc, the change of peak current was measured in the 1990s [8,9] and, afterward, various electrical parameters, such as the crest factor and the average value, were used to improve the accuracy of arc detection [10][11][12]. The most important feature for AC arc detection is a shoulder in the current waveform [13]. Compared with AC systems, however, DC arcs have no zero crossing points and shoulder. Therefore, it is not an easy task to distinguish a DC arc fault from normal conditions using existing AC arc fault detection techniques [14,15]. To detect a DC series arc, several studies, such as current entropy [16,17], electromagnetic radiation [18,19] and frequency spectrum [20], were conducted. The intrinsic behavior of the arc signal was analyzed by current entropy to distinguish between an arc fault and a normal condition [16]. This method has a lower sampling frequency and a short time to detect arc faults, but it is easy to influence an arc signal by a noise signal depending on the surrounding environment [17]. When an arc fault occurs, it is accompanied by electromagnetic radiation, light and noise. Recently, one of these, the magnitude of the electromagnetic radiation signal, was actively analyzed to identify the DC series arc. This method has an advantage for noncontact arc detection, but it is limited because it can only detect an arc fault at specific locations where a sensor is installed [18,19]. Besides, the arc current signals have various time-frequency characteristics depending on the different loads. The sum of optimal frequency spectrum was calculated based on fast Fourier transform (FFT) to differentiate an arc fault from a normal condition [20]. When the sum of spectrum values in the specific frequency range was over a specific value, arc faults were identified. This method identifies arc faults simply, but it may be unreliable depending on the load types because the specific frequency range and spectrum value may depend on the loads. For this reason, various methods for detection of DC series arcs are being studied to distinguish arc faults from normal conditions, and most of them involve complex and expensive devices [21,22]. In Korea, however, it is not practical to apply complex and expensive devices to old shipboards to prevent electrical fires caused by series arcs on shipboards. There is a lot of interest in the detection and analysis of DC series arcs for fire prevention. In particular, research is being actively conducted focusing on aircraft, houses and solar power facilities, but there is not enough research regarding the application to shipboards. In order to prevent electrical fire accidents caused by series arcs, much research is being actively conducted based on the Underwriters Laboratories (UL) 1699 and the International Electrotechnical Commission (IEC) 62606 [3][4][5][6][7]. To detect an AC series arc, the change of peak current was measured in the 1990s [8,9] and, afterward, various electrical parameters, such as the crest factor and the average value, were used to improve the accuracy of arc detection [10][11][12]. The most important feature for AC arc detection is a shoulder in the current waveform [13]. Compared with AC systems, however, DC arcs have no zero crossing points and shoulder. Therefore, it is not an easy task to distinguish a DC arc fault from normal conditions using existing AC arc fault detection techniques [14,15]. To detect a DC series arc, several studies, such as current entropy [16,17], electromagnetic radiation [18,19] and frequency spectrum [20], were conducted. The intrinsic behavior of the arc signal was analyzed by current entropy to distinguish between an arc fault and a normal condition [16]. This method has a lower sampling frequency and a short time to detect arc faults, but it is easy to influence an arc signal by a noise signal depending on the surrounding environment [17]. When an arc fault occurs, it is accompanied by electromagnetic radiation, light and noise. Recently, one of these, the magnitude of the electromagnetic radiation signal, was actively analyzed to identify the DC series arc. This method has an advantage for noncontact arc detection, but it is limited because it can only detect an arc fault at specific locations where a sensor is installed [18,19]. Besides, the arc current signals have various Therefore, in this paper, a study was conducted to prevent fires caused by DC series arcs in the power distribution system of shipboards. The optimal method for detection and identification of DC series arcs was proposed for power distribution systems on shipboards. A resistive load and motor load were used to simulate the power distribution system of old shipboards. The arc signal was analyzed by discrete wavelet transform (DWT) and multiresolution analysis (MRA) to confirm the optimal frequency band for arc detection. In addition, a method to compare arc signal energy with noise signal energy was proposed to distinguish between arc signals and noise signal.

Series Arc and Its Characteristics
Arc is defined as a luminous discharge of electricity across an insulating medium, usually accompanied by the partial volatilization of the electrodes [6,7,23]. Due to the current flow in the circuit and the high temperature, arc is one of the main causes of electrical fires. There are two types of arc, depending on the fault current path, as shown in Figure 2, namely series arc and Energies 2020, 13, 5973 3 of 16 parallel arc [24][25][26][27]. Parallel arcs occur in a short circuit and generate an arc current with high energy. On the other hand, series arcs occur at the connection in series with the load. The arc current is limited by the load and the arc impedance, which has a relatively lower energy. Therefore, conventional circuit breakers and fuses cannot operate to protect the distribution line. For this reason, it is more difficult to detect series arcs than parallel arcs.

Series Arc and Its Characteristics
Arc is defined as a luminous discharge of electricity across an insulating medium, usually accompanied by the partial volatilization of the electrodes [6,7,23]. Due to the current flow in the circuit and the high temperature, arc is one of the main causes of electrical fires. There are two types of arc, depending on the fault current path, as shown in Figure 2, namely series arc and parallel arc [24][25][26][27]. Parallel arcs occur in a short circuit and generate an arc current with high energy. On the other hand, series arcs occur at the connection in series with the load. The arc current is limited by the load and the arc impedance, which has a relatively lower energy. Therefore, conventional circuit breakers and fuses cannot operate to protect the distribution line. For this reason, it is more difficult to detect series arcs than parallel arcs. Series arcs under AC voltage is well studied, whereas little research has been carried out to study that under DC voltage. Figure 3 represents the typical current signal of the series arc under AC and DC 24 V. Under AC voltage, the arc extinguishes near the zero-crossing point due to insufficient voltage for sustaining the discharge. After the voltage recovers, the arc ignites again. Therefore, there is a shoulder in every half-cycle of the current signal. Rising edges are also present just after the shoulders, which is one of the main characteristics of the AC series arc. However, as shown in Figure  3b, only irregular, high-frequency components can be seen on the current waveform of the DC series arc. Series arcs under AC voltage is well studied, whereas little research has been carried out to study that under DC voltage. Figure 3 represents the typical current signal of the series arc under AC and DC 24 V. Under AC voltage, the arc extinguishes near the zero-crossing point due to insufficient voltage for sustaining the discharge. After the voltage recovers, the arc ignites again. Therefore, there is a shoulder in every half-cycle of the current signal. Rising edges are also present just after the shoulders, which is one of the main characteristics of the AC series arc. However, as shown in Figure 3b, only irregular, high-frequency components can be seen on the current waveform of the DC series arc.
Arc is defined as a luminous discharge of electricity across an insulating medium, usually accompanied by the partial volatilization of the electrodes [6,7,23]. Due to the current flow in the circuit and the high temperature, arc is one of the main causes of electrical fires. There are two types of arc, depending on the fault current path, as shown in Figure 2, namely series arc and parallel arc [24][25][26][27]. Parallel arcs occur in a short circuit and generate an arc current with high energy. On the other hand, series arcs occur at the connection in series with the load. The arc current is limited by the load and the arc impedance, which has a relatively lower energy. Therefore, conventional circuit breakers and fuses cannot operate to protect the distribution line. For this reason, it is more difficult to detect series arcs than parallel arcs. Series arcs under AC voltage is well studied, whereas little research has been carried out to study that under DC voltage. Figure 3 represents the typical current signal of the series arc under AC and DC 24 V. Under AC voltage, the arc extinguishes near the zero-crossing point due to insufficient voltage for sustaining the discharge. After the voltage recovers, the arc ignites again. Therefore, there is a shoulder in every half-cycle of the current signal. Rising edges are also present just after the shoulders, which is one of the main characteristics of the AC series arc. However, as shown in Figure  3b, only irregular, high-frequency components can be seen on the current waveform of the DC series arc.

Fire Cases on Shipboards
In Korea, the old shipboards are more vulnerable to fire accidents because the regular inspection of shipboards is performed once every five years. The fire accidents occur in power distribution

Fire Cases on Shipboards
In Korea, the old shipboards are more vulnerable to fire accidents because the regular inspection of shipboards is performed once every five years. The fire accidents occur in power distribution systems that have arc faults while the old shipboards are in operation. Fire accidents can also occur at a location connected to a battery because the engine shuts off, but the battery still supplies a DC power source while the shipboards are at anchor. The crew can take action to extinguish the fire at an early stage when the shipboards are in operation, but a serious fire accident can occur due to the absence of the crew when the shipboards are at anchor. Figure 4 shows the photograph and diagram of the power distribution system on shipboards. In general, a battery is used as the power supply to operate the engine. The engine runs to charge the battery and to power the navigation system, lighting system, power regulator and other equipment. In addition, the bilge and water alarm system installed in series with the battery generates an alarm at all the times and operates automatically with a drain pump to prevent the ship from sinking. When the shipboards are in operation, all of the components in the power distribution system are vulnerable to electrical fires caused by series arcs. However, since the crew is on duty and there are fire alarms, the fires can be put out immediately. On the other hand, when the shipboards are at anchor with the engine stopped, the alarm system and drainage pump that connect in series with the battery are exposed to arc risk, which, in consequence, causes electrical fires.

Fire Cases on Shipboards
In Korea, the old shipboards are more vulnerable to fire accidents because the regular inspection of shipboards is performed once every five years. The fire accidents occur in power distribution systems that have arc faults while the old shipboards are in operation. Fire accidents can also occur at a location connected to a battery because the engine shuts off, but the battery still supplies a DC power source while the shipboards are at anchor. The crew can take action to extinguish the fire at an early stage when the shipboards are in operation, but a serious fire accident can occur due to the absence of the crew when the shipboards are at anchor. Figure 4 shows the photograph and diagram of the power distribution system on shipboards. In general, a battery is used as the power supply to operate the engine. The engine runs to charge the battery and to power the navigation system, lighting system, power regulator and other equipment. In addition, the bilge and water alarm system installed in series with the battery generates an alarm at all the times and operates automatically with a drain pump to prevent the ship from sinking. When the shipboards are in operation, all of the components in the power distribution system are vulnerable to electrical fires caused by series arcs. However, since the crew is on duty and there are fire alarms, the fires can be put out immediately. On the other hand, when the shipboards are at anchor with the engine stopped, the alarm system and drainage pump that connect in series with the battery are exposed to arc risk, which, in consequence, causes electrical fires.   Figure 5 shows two cases of DC series arcs occurring in the power distribution system on old shipboards, which were investigated by the National Forensic Service. It was confirmed that these fire accidents occurred because of the combustibles adjacent to the arc hot spot. It was also shown that the series arc faults in the power distribution system occurred as a result of the partial disconnection between the cords and the loose connection between the cord and the terminal.  Figure 5 shows two cases of DC series arcs occurring in the power distribution system on old shipboards, which were investigated by the National Forensic Service. It was confirmed that these fire Energies 2020, 13, 5973 5 of 16 accidents occurred because of the combustibles adjacent to the arc hot spot. It was also shown that the series arc faults in the power distribution system occurred as a result of the partial disconnection between the cords and the loose connection between the cord and the terminal.  Figure 5 shows two cases of DC series arcs occurring in the power distribution system on old shipboards, which were investigated by the National Forensic Service. It was confirmed that these fire accidents occurred because of the combustibles adjacent to the arc hot spot. It was also shown that the series arc faults in the power distribution system occurred as a result of the partial disconnection between the cords and the loose connection between the cord and the terminal.

Wavelet Transform and Multiresolution Analysis
In previous studies, DC series arcs were only analyzed in the frequency domain by fast Fourier transform. In this paper, wavelet transform (WT) was used to analyze the current signal of DC series arcs in the time and frequency domains simultaneously. The Fourier transform analyzes a signal by

Wavelet Transform and Multiresolution Analysis
In previous studies, DC series arcs were only analyzed in the frequency domain by fast Fourier transform. In this paper, wavelet transform (WT) was used to analyze the current signal of DC series arcs in the time and frequency domains simultaneously. The Fourier transform analyzes a signal by decomposing the signal into a family of complex sinusoids. In WT, a given signal is decomposed using the mother wavelet, by which the signal can be represented by the dilated and translated versions of a selected mother wavelet. Typical mother wavelets include Coiflet (coif), Daubechies (db), Symlet (sym) and Biorthogonal (bior) wavelets. The family of dilated and translated wavelets are given by where Ψ(t) is the mother wavelet, a and b are the scale factor and shift factor, respectively. a is used to modify the amplitude and duration of the prototype mother wavelet, by which the energies of the dilated wavelets are the same. b is used to translate the modified mother wavelet in the time domain [28,29]. A mother wavelet with different values of a and b is shown in Figure 6a, and Figure 6b is the corresponding modified wavelet presented in the frequency domain. It can be seen from Figure 6 that when a wavelet has a smaller value of a, its amplitude is higher, time duration is shorter, frequency bandwidth is wider and central frequency is higher. On the other hand, when a wavelet has a larger value of a, its amplitude is lower, time duration is longer, frequency bandwidth is narrower and central frequency is lower. As a result, a given signal in the time domain can be analyzed by decomposing it using a mother wavelet in both the time and frequency domains simultaneously.
has a larger value of , its amplitude is lower, time duration is longer, frequency bandwidth is narrower and central frequency is lower. As a result, a given signal in the time domain can be analyzed by decomposing it using a mother wavelet in both the time and frequency domains simultaneously. Discrete wavelet transform based on multiresolution analysis was used to analyze the arc current signal [30][31][32][33][34]. In MRA, the given signal is decomposed by the mother wavelet into a specific Discrete wavelet transform based on multiresolution analysis was used to analyze the arc current signal [30][31][32][33][34]. In MRA, the given signal is decomposed by the mother wavelet into a specific level N with the corresponding low-pass filter (LPF) and high-pass filter (HPF). The signals passing the LPF generate a detail (D) component and those passing the HPF generate an approximation (A) component. By application of MRA, the input signal can be represented by the detail coefficients at each level (D1, D2, · · · , Dn) and the approximation coefficients at the highest level (An) [35][36][37]. Figure 7 shows an example of multiresolution analysis resolving the signals into three layers. The downsampling of signals was performed by an HPF and an LPF, appearing as a detail coefficient and an approximation coefficient. The approximation component (A1) was resolved into the detail coefficient (D2) and approximation coefficient (A2) using downsampling through the filter to the next layer. The downsampling of the approximation coefficient (A2) was then performed at the next layer, with the process continuing up to the maximum decomposition level [35][36][37][38][39][40][41].
downsampling of signals was performed by an HPF and an LPF, appearing as a detail coefficient and an approximation coefficient. The approximation component (A1) was resolved into the detail coefficient (D2) and approximation coefficient (A2) using downsampling through the filter to the next layer. The downsampling of the approximation coefficient (A2) was then performed at the next layer, with the process continuing up to the maximum decomposition level [35][36][37][38][39][40][41].  Figure 8 demonstrates the experimental setup. An arc generator and a load were connected in series with the 24 V DC mains. The arc generator was designed according to UL 1699 and IEC 62606 [6,7]. The electrodes consisted of carbon-copper wire that is specified in UL 1699 and cord-cord wire that causes fire accidents on shipboards. The starter motor used in shipboard power distribution systems and a resistive load were used. The current signal of the series arc was detected using a highfrequency current transformer (HFCT) (Pearson Electronics Inc., Palo Alto, CA, USA). The frequency range of the HFCT is 1-20 MHz. A digital storage oscilloscope (DSO) (YOKOGAWA, DL9140, Tokyo, Japan) and a data acquisition (DAQ) unit (National Instrument, USB-5133, Austin, TX, USA) were used for signal acquisition. The sampling rate and bandwidth of the DSO were 5 GS/s and 1 GHz. The sampling rate and bandwidth of the DAQ were 100 MS/s and 50 MHz, respectively.   Figure 8 demonstrates the experimental setup. An arc generator and a load were connected in series with the 24 V DC mains. The arc generator was designed according to UL 1699 and IEC 62606 [6,7]. The electrodes consisted of carbon-copper wire that is specified in UL 1699 and cord-cord wire that causes fire accidents on shipboards. The starter motor used in shipboard power distribution systems and a resistive load were used. The current signal of the series arc was detected using a highfrequency current transformer (HFCT) (Pearson Electronics Inc., Palo Alto, CA, USA). The frequency range of the HFCT is 1-20 MHz. A digital storage oscilloscope (DSO) (YOKOGAW (a)

Selection of the Optimal Mother Wavelet
For a mother wavelet, the phase and frequency should keep a linear relationship so that the time delay due to frequency is constant, to ensure that the arc signal is not distorted during decomposition or overlapping after signal reconstruction [42,43]. For evaluating the similarity between the arc signal pulse and the mother, the correlation coefficient is used, which is defined as where ( ) is the single arc pulse and is its mean value and ( ) is the wavelet function and is the average value. The value of is between 0 and 1. A larger value means a greater similarity between the arc pulse and mother wavelet. Thus, the optimal wavelet should have the maximum correlation coefficient with the DC arc signal. It can be seen from the definition above, the single arc pulse and the wavelet should have the same length for calculating the correlation coefficient. However, since arc signals are commonly captured with a high sampling rate and the wavelet has a relatively short length, it is hard to ensure the same length for the two signals. Therefore, the following normalization procedures before calculating the correlation coefficient are necessary [44].
1. Set the maximum magnitudes of the arc signal ( ) and the mother wavelet function ( ) to 1 by dividing the peak value; 2. Count the lengths of the arc signal and the mother wavelet, assuming the values to be and , respectively; 3. Resample the mother wavelet with a time interval of / , by which the two signals have the same length; 4. Detect the times of ( ) and ( ) at their maximum points and shift ( ) according to the time difference so that the maximum points are at the same time.
The result of the correlation coefficient calculation between the arc current pulse in the resistive load with a cord-cord fault and the mother wavelet is shown in Figure 9. The bior 3.1 wavelet exhibited the highest similarity with the arc current pulse. Further analysis of the arc current pulses in other loads with different faults is shown in Table 1. The optimal mother wavelet for analyzing the arc current pulse at different loads with different faults was consistently bior 3.1. Therefore, the bior 3.1 wavelet was selected as the optimal mother wavelet for analyzing the DC series arc in this work.

Selection of the Optimal Mother Wavelet
For a mother wavelet, the phase and frequency should keep a linear relationship so that the time delay due to frequency is constant, to ensure that the arc signal is not distorted during decomposition or overlapping after signal reconstruction [42,43]. For evaluating the similarity between the arc signal pulse and the mother, the correlation coefficient γ is used, which is defined as where X(i) is the single arc pulse and X is its mean value and Y(i) is the wavelet function and Y is the average value. The value of γ is between 0 and 1. A larger γ value means a greater similarity between the arc pulse and mother wavelet. Thus, the optimal wavelet should have the maximum correlation coefficient with the DC arc signal. It can be seen from the definition above, the single arc pulse and the wavelet should have the same length for calculating the correlation coefficient. However, since arc signals are commonly captured with a high sampling rate and the wavelet has a relatively short length, it is hard to ensure the same length for the two signals. Therefore, the following normalization procedures before calculating the correlation coefficient are necessary [44].

1.
Set the maximum magnitudes of the arc signal X(i) and the mother wavelet function Y(i) to 1 by dividing the peak value; 2.
Count the lengths of the arc signal and the mother wavelet, assuming the values to be j and k, respectively; 3.
Resample the mother wavelet with a time interval of j/k, by which the two signals have the same length; 4.
Detect the times of X(i) and Y(i) at their maximum points and shift Y(i) according to the time difference so that the maximum points are at the same time.
The result of the correlation coefficient calculation between the arc current pulse in the resistive load with a cord-cord fault and the mother wavelet is shown in Figure 9. The bior 3.1 wavelet exhibited the highest similarity with the arc current pulse. Further analysis of the arc current pulses in other loads with different faults is shown in Table 1. The optimal mother wavelet for analyzing the arc current pulse at different loads with different faults was consistently bior 3.1. Therefore, the bior 3.1 wavelet was selected as the optimal mother wavelet for analyzing the DC series arc in this work.

Arc Signal Decomposition
After the selection of the optimal mother wavelet, a frequency band of the arc current signal was analyzed by applying discrete wavelet transform using MRA. The sampling rate of the data acquisition unit was set at 1.25 MS/s, and the highest frequency of the detected current signal was 625 kHz. The corresponding frequency bands of each component are listed in Table 2, which verifies that the MRA interprets the decomposed components into a series of independent frequency bands by applying the downsampling method. In Table 2, components D1-D8 and A8 are shown as the final results of the MRA analysis, whereas A1-A7 are the intermediate processes.

Arc Signal Decomposition
After the selection of the optimal mother wavelet, a frequency band of the arc current signal was analyzed by applying discrete wavelet transform using MRA. The sampling rate of the data acquisition unit was set at 1.25 MS/s, and the highest frequency of the detected current signal was 625 kHz. The corresponding frequency bands of each component are listed in Table 2, which verifies that the MRA interprets the decomposed components into a series of independent frequency bands by applying the downsampling method. In Table 2, components D1-D8 and A8 are shown as the final results of the MRA analysis, whereas A1-A7 are the intermediate processes.  Figure 10 shows the decomposition of the signal using multiresolution analysis and mother wavelet bior 3.1. The current signals were measured under both normal and arc conditions, such as cord-cord and carbon-copper. As seen in Figure 10, the top signal is the original arc current measured using a wideband current transformer, the bottom signals present the detail components D1 to D8 and the approximation component A8. Figure 10a shows the decomposition of current signals under normal conditions. The high-frequency noise signal was confirmed to appear in the detail components D6 to D8 and the approximation component A8. As seen in Figure 10b,c, the detail components D2 to D5 were related to the arc occurrence and could be used to identify the arc phenomenon. Based on these results, the detail components D2 to D5 were selected as the optimal frequency band to analyze the arc signal and were therefore used for signal reconstruction. Figure 11 shows the comparison of the normal and arc conditions after reconstruction using the detail components D2 to D5, thereby allowing identification of the arc fault.
Energies 2020, 13, x FOR PEER REVIEW 10 of 17  Figure 10 shows the decomposition of the signal using multiresolution analysis and mother wavelet bior 3.1. The current signals were measured under both normal and arc conditions, such as cord-cord and carbon-copper. As seen in Figure 10, the top signal is the original arc current measured using a wideband current transformer, the bottom signals present the detail components D1 to D8 and the approximation component A8. Figure 10a shows the decomposition of current signals under normal conditions. The high-frequency noise signal was confirmed to appear in the detail components D6 to D8 and the approximation component A8. As seen in Figure 10b,c, the detail components D2 to D5 were related to the arc occurrence and could be used to identify the arc phenomenon. Based on these results, the detail components D2 to D5 were selected as the optimal frequency band to analyze the arc signal and were therefore used for signal reconstruction. Figure 11 shows the comparison of the normal and arc conditions after reconstruction using the detail components D2 to D5, thereby allowing identification of the arc fault.

Identification of DC Series Arc
The flowchart of the DC series arc identification is shown in Figure 12. The HFCT was used to detect the current of the power distribution system on shipboards. The signal was then decomposed by MRA and detail components D2-D5 were used for signal reconstruction. Two criteria were used to distinguish the arc condition and the normal condition, namely the signal magnitude and the signal energy. The signal energy of a given signal s(t) is defined as where K and i are the signal record length and a variable of length, respectively. Specifically, if the magnitude of the extracted signal ( ) is three times greater than the normal signal ( ), and the signal energy of the extracted signal ( ) is five times greater than the normal signal ( ), arc is considered to occur.

Identification of DC Series Arc
The flowchart of the DC series arc identification is shown in Figure 12. The HFCT was used to detect the current of the power distribution system on shipboards. The signal was then decomposed by MRA and detail components D2-D5 were used for signal reconstruction. Two criteria were used to distinguish the arc condition and the normal condition, namely the signal magnitude and the signal energy. The signal energy of a given signal s(t) is defined as where K and i are the signal record length and a variable of length, respectively. Specifically, if the magnitude of the extracted signal (I i ) is three times greater than the normal signal (I o ), and the signal energy of the extracted signal (E i ) is five times greater than the normal signal (E o ), arc is considered to occur. Figure 13 shows the power spectrum of the extracted signal. The signal energies of the normal and arc conditions in the cord-cord are 1.42 and 120.11, respectively, and 1.42 and 8.80 in the carbon-copper, respectively. Therefore, the signal energy can be used to distinguish the normal and arc conditions.  Figure 13 shows the power spectrum of the extracted signal. The signal energies of the normal and arc conditions in the cord-cord are 1.42 and 120.11, respectively, and 1.42 and 8.80 in the carboncopper, respectively. Therefore, the signal energy can be used to distinguish the normal and arc conditions.   Figure 13 shows the power spectrum of the extracted signal. The signal energies of the normal and arc conditions in the cord-cord are 1.42 and 120.11, respectively, and 1.42 and 8.80 in the carboncopper, respectively. Therefore, the signal energy can be used to distinguish the normal and arc conditions.

Conclusions
DC series arc is one of the main causes of electrical fires in the power distribution system of a shipboard, however, there is no effective method for detecting and identifying the arc on shipboards. In this paper, an experiment setup was configured to simulate a DC series arc on shipboards, which mainly consisted of an arc generator, resistive load and motor load. The arc current signal was

Conclusions
DC series arc is one of the main causes of electrical fires in the power distribution system of a shipboard, however, there is no effective method for detecting and identifying the arc on shipboards. In this paper, an experiment setup was configured to simulate a DC series arc on shipboards, which mainly consisted of an arc generator, resistive load and motor load. The arc current signal was detected by a HFCT and was analyzed by DWT. The correlation coefficient between single arc pulses and wavelets was calculated and compared, by which the optimal mother wavelet bior 3.1 was selected. By decomposing the arc signal using MRA, it was verified that the detail components D2-D5 were related to arc occurrence, and they were therefore used for signal reconstruction. In addition, a DC arc identification method was proposed based on the signal magnitude and the signal energy, by which arc occurrence could be predicted. The results from this paper are expected to be applied in the power distribution system of a shipboard to avoid potential electrical fires. Compared with other existing methods, the arc identification proposed in this paper has optimal frequency components to detect arc faults and specific values for the signal magnitude and the signal energy to identify arc conditions and normal conditions on a shipboard. However, the proposed method was verified under a restricted condition and it is therefore necessary to verify its performance for arc detection by applying it to various types of shipboards. Future work will pay attention to the development of a DC series arc detector for shipboards, which is composed of an HFCT and a microcontrol unit embedded in the proposed method.