1.Introduction

An increasing number of electrical devices are being adopted in aviation industry with the development of More/All Electric Aircraft(MEA/AEA).However,traditional switches such as contactors,breakers and relays are bringing challenges for protections in aircraft electrical power systems due to their physical effects such as arc faults.Power electronic devices allow the combination of switching functions and protections into one device with digital microprocessors.1,2Solid State Power Controllers(SSPC),as shown in Fig.1,are among these new technologies and are being widely studied.These SSPCs are implied to realize ‘soft switching” and intelligent control of electrical loads onboard of aircraft.2In addition to achieving traditional functions like preventing electrical devices from being damaged by overloads or short circuits,SSPCs are free of mechanical wear with high reliability,lower power dissipation,and a new capability for remote control and monitoring.All these advantages make SSPC particularly suitable for aerospace applications.3

Fig.1 Application of SSPC in aircraft power system.

Damages caused by arcs on aircraft account for an increasingly large percentage of aviation security issues nowadays.An arc is an electrical breakdown of a gas that produces an ongoing plasma discharge,resulting from a current through normally nonconductive media,such as air.4The temperature of an arc is extremely high and usually rises to several thousand degrees centigrade in just a few microseconds.Such high temperature will melt insulation materials,cause fires easily and threaten the security of aircraft cables and equipment.Serious damages may occur when situations get worse.

Arcs can be divided into two types which are good arcs and bad arcs according to their forming mechanism.3A good arc is usually generated between the wire and the plug base when an electrical appliance is plugged into or removed from the electrical system.Good arcs are acceptable and there is no need to prevent them.A bad arc is also called an arc fault,which is induced by insulation aging or insulation damages.Moist atmosphere and electrical loose connection also contribute a lot in producing bad arcs.Bad arcs can be divided into two categories according to the location where they occur:series arcs and parallel arcs.5Series arcs are caused by loose connections or poor contacts,while parallel arcs usually result from short circuits between wires or between wires and electrical structures.

Although they themselves do not generate arcs when they are working,SSPC could not avoid other possible arcs which may occur at other places,like the aircraft cables.Thus,SSPCs are no longer satisfied with their current functions,which in fact is still a replacement of traditional protection devices and a higher requirement,namely,arc fault detection is put forward.Series arc faults are considered to be more dangerous due to the increase in the total load impedance and the fact that circuit breakers cannot respond timely to such a lowcurrent fault.5,6Thus,this paper focuses on series Alternating Current(AC)arc fault detection.The faulted half cycle data are reconstructed with the two proposed methods,and analyzed in frequency domain using Fast Fourier Transform(FFT)and Wavelet Packet Decomposition(WPD)respectively,to investigate the accuracy of the proposed two methods.

The remaining parts of this paper are as follows:Section 2 gives an introduction of SSPC.Section 3 illustrates the arc fault data generation mechanism.Section 4 provides the detection results of one cycle data,with FFT and WPD,in order to provide comparative studies with proposed methods.Section 5 presents application procedures of the two proposed methods with half cycle data,together with the detection results to show the pros and cons of each method.Hardware platform was constructed and experimental results are provided in Section 6.Section 7 concludes the whole paper and puts forward the work that needs to be done in the future.

2.Solid state power controllers

SSPCs are semiconductor devices that control electrical power supplied to a load.Fig.2 shows the fundamental block diagram of the AC SSPC.They perform supervisory and diagnostic functions in order to prevent overload conditions and short circuits.

A typical SSPC consists of the following parts:main power devices,driving circuit,signal conditioning circuit,shortcircuit protection circuit,and the CPU module.7This new intelligent switch is different from conventional switches like contactors and relays because it uses a static switching device(such as MOSFET,IGBT,or JFET)controlled by a microcontroller.This microcontroller directly measures the output current via a sensing resistor,and it also allows activating or deactivating the state of SSPC from a remote location.

SSPC turns circuits on or off according to the command from CPU and acts safely if the CPU is out of order.They can not only protect electric devices from short circuit and overloads,but also allow protecting power wires with the I2t curve within the short circuit limit to fully utilize the thickness of aircraft cables.Fig.3 shows several channels of SSPCs integrated into one PCB board.And several pieces of SSPC boards will realize the functional unit of Electrical Load Management Center(ELMC),as depicted in Fig.4.

In addition to those basic functions illustrated above,the arc fault detection is desperately required nowadays because it prevents potential damages,such as fires,caused by arcs in aircraft.However,searching for an algorithm to effectively detect arc faults is not easy because of the randomness and complexity characteristic of arc faults.Since audio,photic and thermal features are not practical to be adopted in aviation SSPC which ought to bear little size and light weight,the key point to differentiate normal operations from arc fault depends severely on the information contained in the output current waveform.This paper proposes two methods in frequency domain to detect arc faults with the analysis of only half cycle data.The implementation of arc detection does not change the fundamental block diagram as shown above but merely needs additional signal conditioning circuit and a segment of arc detection program in CPU.

坤二少爷冷着脸说：“不敢恭维，血光之灾吧！”又一笑，“过路之人，随便说说，老爷就当没听见罢——我真的要走了！”

Fig.2 Block diagram of AC SSPC.7

Fig.3 AC SSPC board.

Fig.4 Electrical load management center with pieces of AC SSPC boards.

3.ARC fault characteristics

The aviation AC SSPC arc fault is a non-linear and timevarying process,and extracting the eigenvalues or characteristic quantities of AC arc fault may take advantage of its voltage and current waveforms.Since the occurrence of arc is random,and in the aviation electrical power distribution systems,cables are often laid in a very small space,the arc fault voltage is not a good choice for monitoring.It’s almost impossible to measure the cable voltage everywhere,so the arc fault current is preferred to detect and diagnose arc fault in the circuit according to its variations.Fig.6 shows a typical AC arc fault current waveform in time domain.

旅游营销推广方面，应凸显地域特色，优化、整合文化传播媒介。出游前，目的地文化主要通过大众媒体、文学艺术作品等使游客产生旅游动机。这一阶段，文化传播媒介能够对游客的初始认知产生较大的影响，相关营销机构可以挖掘地方文化特色，提炼具有吸引力的旅游目的地形象，通过优化和整合各种亲近大众生活的传播渠道，如文学、艺术、历史和民俗等，进行推广宣传，达到更深远的营销效果。此外，在文化传播的内容上，一方面应该深入了解游客对旅游目的地具体的感知和兴趣点，强化这些重要概念的传播；另一方面可根据游客视角的文化认知网络，挖掘和激活地域文化中重要但游客不了解的概念，并通过建立概念之间的联系，丰富游客对地域文化的认知。

3.1.Volt-ampere characteristics of AC arc fault

In the circuits of AC SSPC,it is hard to establish stable criteria for arc fault detection due to the fact that physical parameters,such as voltage,current,and impedance,are varying during the fault.When the arc fault current passes through zerocrossing point,sufficient energy cannot be obtained from the power source to support the arc burning,and as a consequence,the temperature decreases,which results in faster exhausting of arcs.

When the current of the arc fault passes through the zerocrossing point,the burning of arcs weakens gradually,and the resistance of the arc increases subsequently(period O to A).Therefore,the arc fault current is approximately zero based on the analysis of Ohm’s Law.This period is called the ‘zero off time”of arc fault current in AC SSPC,also known as the‘ flat shoulder”.7The length of‘zero off time” is influenced by several factors,including voltage and current of the circuit,as well as the load characteristics(resistance,inductance,capacitance,etc.).Moreover,the length will also be re flected by the internal arc burning process within the arc gap.A typical volt-ampere characteristic curve of AC SSPC arc is shown in Fig.5,which is symmetrical with respect to the coordinate origin.8

3.2.Time domain characteristics of AC arc fault

The basic method for arc fault detection is to extract the fault feature vectors depending on the current and voltage waveform differences between the arc fault and normal conditions.This section discusses the general characteristics of AC arc fault from three aspects,namely volt-ampere characteristics,time domain characteristics, and frequency domain characteristics.

The voltage and current waveforms can be used to extract the eigenvalues or characteristic quantities of arc fault in aviation AC SSPC,which is actually a non-linear and time-varying process.Due to the limited space and complex environment in aircraft,it is not convenient to measure the cable voltage,and thus the arc fault current is preferred to detect and diagnose arc fault based on the analysis of its variations.Fig.6 shows a typical current and voltage waveform under arc fault in time domain.

It can be noticed that there will be ‘zero off dead zone” in every half cycle when arc fault occurs,which is also called ‘ flat shoulder”,and this characteristic can be used as features to extract arc current.The amplitude of the current waveform will decrease due to the presence of arc gap resistance.

这种色素沉积导致的黑缝，不仅跟我们平时的饮食习惯有关，还跟自身的牙齿结构有很大的关系。牙齿的窝沟点隙越深，就越不容易清洁到位，色素就越容易附着，从而出现黑缝。那么，我们该如何预防色素沉积而产生的黑缝呢？

3.3.Frequency domain characteristics of AC arc fault

A large percentage of harmonics will be contained in current waveform when arc fault occurs in AC SSPC,due to the randomness and nonlinearity of arc.The main frequency domain characteristics of arc fault in AC SSPC can be summarized as follows:

Fig.8 also shows the adopted circuit which generates arcs to imitate situations where an arc fault occurs during a flight.In this circuit,the AC power supply voltage is 115 V/400 Hz and the sensor resistor is 0.4 Ω.The signal is recorded using the HBM Genesis7t high-speed data acquisition system and the sampling rate is 200 kHz,which means that 500 points are sampled in each cycle.The adjustable load part consists of different load types,such as resistance,inductance,and capacitance.

(2)High-frequency components will be contained in the current waveform due to the instantaneous change of the current at the end of ‘zero off dead zone” caused by arc fault.

Fig.5 Typical volt-ampere characteristic curve of AC arc.

Fig.6 Typical arc fault current and voltage waveforms of AC SSPC.

In addition to the above mentioned general characteristics of arc fault in time domain and frequency domain,the arc faults in aviation SSPC have their specific characteristics:

When a half-cycle data is collected,no matter it is the former half cycle or the latter half cycle,every time it is with a microprocessor or DSP.Then each half-cycle waveform is constructed into a new one-cycle waveform.If the targeted half cycle is normal,the new-constructed waveform is still a normal sinusoidal waveform.Otherwise,the new-constructed waveform is a distorted sinusoidal waveform.Finally,the problem is turned into analysis with one-cycle data which has already been illustrated before.

(2)The aviation arc fault voltage and current waveform is more complex due to the factors such as limited weight and space,greater electromagnetic interference,and complex working environment.

(3)The fundamental frequencies of aviation arc fault are higher than the territorial power system,which is 400 Hz for constant frequency aviation power system or 360–800 Hz for variable frequency aviation power system,while the frequency of territorial power system is 50 Hz or 60 Hz.

4.Related works

There are several reasons that will result in the occurrence of arc fault,namely the small cracks of the aviation cable surface caused by heat,cold or electromagnetic radiation,the chemical corrosion and the damage of the cables under repair.9A large amount of heat is released when an arc fault occurs,and it can ignite flammable items around,causing a fire or even explosion.It has been proved that the temperature caused by a 2–10 A arc current can be up to 2000–4000 °C,and a small arc current can even cause a fire.10

Recently,some scholars have proposed the idea of Arc Fault Detection(AFD)function integrated in SSPC.11,12On one hand,it can save space and reduce weight,and on the other hand,it is easier to manage the power distribution system intensively.Moreover,the reduction of the number of mechanical switching devices helps to improve the reliability of the power distribution system.

In Ref.11,arc fault detection function is divided into low impedance AFD and high impedance AFD,as shown in Fig.7.For low impedance arc,traditional mechanical fuses,relays and circuit breakers can realize the arc detection and protection function due to its low impedance and large arc current.However,for high impedance arc,the arc current is usually relatively small,and it cannot meet the operation conditions set by the traditional switches,so this study mainly focuses on the high impedance AFD.

Several publications are already available in the field of high impedance arc fault detection.13–18The study in Ref.13 uses three features of low-voltage series arc fault signals,namely the singularity,the uncertainty and the energy features as the input vector of improved multi-level BP neural network,and then the mapping relation between characteristic vector and series arc is established.In Ref.14,combined with the wavelet transform module maxima and multi-resolution analysis,the db3 wavelet function is used to extract the feature vector in each frequency band of both the normal and fault signals,and with the improved BP neural network,the fault is diagnosed by the mapping relationship between the feature vector and arc fault.The basic principle of AFD in Ref.15 is based on decomposing the samples by wavelet every 5-consecutive-cycle and obtaining the average value and standard deviation of high-frequency energy in each layer,and with these data,a wavelet neural network is constructed to detect serial arc faults of different kinds of load.Another study 16 illustrates that the signal energy of some sub-bands is useful information to re flect the serial arc fault patterns,and then,a Radial Basis Function Neural Network(RBFNN)is trained by using the data of signal energy obtained from discrete wavelet transform.

All the four approaches described above are based on wavelet transform,and the defect of using this method is that there is a large randomness in detecting characteristic parameters,and it is difficult to determine a threshold parameter to distinguish the arc with system normal operating events,such as load switching.Furthermore,because of the complexity of wavelet transform theory and its computation,it is difficult to achieve the algorithm,and the requirements for the CPU or controller are very high.17

It is worth mentioning that both studies in Refs.18,19 have achieved the on-line detection of arc fault.In 18,a detection algorithm utilizing time and time-frequency domain characteristics is proposed to differentiate between Direct Current(DC)arc fault and normal condition.While the study19describes a multi-algorithm detection architecture and shows how it is possible with this architecture to detect around 75 percent of arc faults occurring in a circuit.

According to the US safety standards UL 1699 of Arc Fault Circuit Breaker(AFCB),for the 400 Hz aviation AC line,the circuit breaker needs to trip when the AFCB detects 8 halfcycle arc faults in 100 ms.19All the above references are based on the analysis of whole-cycle arc current waveforms,and they do not analyze the half-cycle arc fault incidents.Therefore,in this paper,we use frequency domain method to detect the aviation AC arc fault,and FFT and wavelets are adopted as the main tool.On the basis of the analysis of whole-cycle arc waveform,the half-cycle arc waveform is selected as the basic detection unit.Moreover,this paper proposes two improved halfcycle detection methods to realize more accurate and faster arc fault detection.

5.Fault data generation

The method used in the laboratory to emulate the generation of a series AC arc on aircraft is shown in Fig.8.The terminals of the two wires are loosely connected with a bolt and they can move up and down freely.An arc will be generated between the bolt and wire terminals by vibrating them when the current is flowing through the circuit.

Fig.7 Classification of arc fault detection methods.

(1)Both of the harmonic amplitude and the DC component of arc current vary greatly compared with normal operation current.

The normal operation current and arc fault current are shown in Fig.9.In order to better emulate the process that current signals are analyzed and calculated in a microprocessor,both of them are resampled from 500 points per cycle to 64 points per cycle to reduce computation burden.

Fig.9 Waveforms of normal current and series AC arc current.

Fig.8 Circuit to generate arcs.

Fig.9 shows one cycle(f=400 Hz,T=1/f=2.5 ms)waveform of normal operation current and the typical waveform of series AC arc fault current(plotted by MATLAB using data obtained from HBM Genesis7t).Obviously,the two waveforms differ from each other.What we need to do is selecting the feature vectors based on analysis results to distinguish the arc fault from normal operation.Totally,35 cycles of data were obtained for analysis in the following sections,among which 5 cycles are normal operation current waveforms,and 30 cycles are arc fault current waveforms.Those data was obtained under different voltage levels and various loads(resistive load,capacitive load,and inductive load)to make more generalized scenarios for testing the proposed methods.

而信号系统安全预评价处于城市轨道交通工程全生命周期的最前端，属于安全管理体系中最为重要的事前管理。因此更应从全局角度和源头出发，全面地实施安全隐患辨识和安全风险预估等安全管理活动。

6.Traditional analysis with one-cycle data

In order to better understand the improvements of the proposed method in this paper,one-cycle data analysis results with FFT and WPD are first provided in this section.

现在，他无论做什么，都只凭理智。他齐膝盖撕下了两截裤腿，用来裹脚。他总算还保住了那个白铁罐子。他打算先喝点热水，然后再开始向船走去，他已经料到这是一段可怕的路程。

6.1.FFT analysis

The Fourier Transform(FT)is a mathematical transformation employed to transform signals between time(or spatial)domain and frequency domain.To easily implement Fourier analysis in microprocessors for digital signals,Discrete Fourier Transform(DFT)is a necessity and the spectrum of an N-point sampled signal can be derived according to the following equation:

农业管理部门要定期派遣科技队伍下乡，组织开展定点宣传活动，通过养殖户专业培训、广播电视等宣传媒介和水产养殖示范基地建设等途径，向当地的水产养殖人员科普滥用药物的危害和水产动物病害预防方法，传播无公害水产养殖技术，并大力宣传关于食品安全的法律法规，引起养殖专业户的重视，传播科学的水产养殖方法。与此同时，建立专门的水产养殖示范基地，向养殖户展示无公害水产养殖技术和正确的药物使用方法，引导养殖户认识到新技术的先进性，自觉采用新技术和新方法。针对滥用药物造成不良影响的违法违规案件，要进行全面通报和典型教育，督促养殖户转变观念，改变技术，提高水产养殖的规范化水平。

In general,DFT requires a higher computation complexity especially when N is quite large.A fast Fourier transform(FFT)is an algorithm to compute the DFT and its inverse.FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse(mostly zero)factors.As a result,FFT is widely used for many applications in Engineering,science,and mathematics.7Concerning the real time execution requirement in arc fault analysis,FFT is first adopted in this paper to extract the features of fault current with one-cycle data.

Both the normal operation current and arc fault current are analyzed with FFT.MATLAB Toolbox is adopted,where FFT analysis is available with only a few statements by invoking the FFT function.

式中：η为干燥t时间后草果脱水量，%；M0为草果初始含水量，%；Mt为微波干燥t时间后草果含水量，%。

The selection of mother wavelet and decomposition level is very important to implement WPD for arc fault detection.21,22In this paper,db10(Daubechies)wavelet is chosen as the mother wavelet,and scale 9 is selected as the decomposition level.More detailed analysis and comparison can be found in Ref.8.

Figs.10 and 11 show the resampled points and spectrums of the two signals shown in Fig.9,respectively.The resampled points are marked with ‘o” and the 0th harmonic order stands for DC component(only DC component and the first to the 15th harmonics are listed although total 31 harmonics are available according to Shannon’s sampling theorem).

The following points are selected as feature vectors for recognition of arc faults:peak value,DC component,fundamental component,and Total Harmonic Distortion(THD).Result contrast between the normal current and the arc current is shown in Table 1.

A conclusion can be drawn from Table 1 that when a series AC arc fault occurs,both peak current and fundamental component decrease as a result of the increase in the circuit impedance caused by arc fault,while DC component increases from 0.13 A to 0.4 A and THD increases from lower than 2%to more than 21%compared with the normal current.

综上所述，增强MRI对结直肠癌患者发生淋巴结转移的检出率及诊断准确率较高，可有效显示结直肠癌MRI图像特征，为临床制定治疗方案提供影像学资料。

Fig.10 Resampled points and spectrum of normal current.

Fig.11 Resampled points and spectrum of arc current.

To better understand the features of the series AC arc,the FFT analysis is also applied to 5 cycles of normal operation current and 30 cycles of arc fault current,and then similar analysis processes,including resampling and FFT analysis,are carried out.

20 out of 30 arc faults can be detected if the THD threshold is set at 15%whereas this parameter is usually lower than 2%for normal current.Combination of other parameters may be helpful to recognize those arc faults that cannot be detected by only THD.

Other parameters in addition to the above four can also be selected as feature vectors to set the detection criteria.With the help of artificial intelligence such as artificial neural networks,it is supposed that the arc faults will be correctly classified with the input of feature vectors extracted through FFT analysis.

某城市轨道交通运营线路的部分区段钢轨电位限制装置频繁动作，某些车站的钢轨电位限制装置甚至出现1 d 内动作上百次的情况。在排除了设备等自身故障的可能性后，维修人员最终将故障原因锁定在了“杂散电流”上。该线路运营时间较长，伴随着设施设备绝缘的老化，杂散电流腐蚀情况亦日渐突出，单纯依靠“堵”的方式已不能有效控制杂散电流的增长趋势。但该线路在杂散电流腐蚀防护系统设计时，仅设置了相应的监测设备，未设计排流柜(见图1)。

Table 1 Result contrast between normal current and arc current.

Conditions Peak(A) DC component(A) Fundamental component(A) THD(%)Normal 9.3665 0.1340 9.1090 1.64 Arc 8.4121 0.3983 7.4284 21.21

6.2.Wavelet packets decomposition analysis

Moreover,the analysis results with Wavelet Packets Decomposition(WPD)are also provided in this paper to give a comparative study.The sum of energies contained in each of the decomposition scales is used as the vector to recognize the faults.

WPD analysis will divide the original signal into multiple levels based on the characteristics of the band-pass filters.20The details of transient behavior in high-frequency bands can be amplified with this method,which is a better feature that can be used to distinguish the faulted signals.

The definition of continuous wavelet transform for a given signal f(t)∈ L2(R)with respect to a mother wavelet ψ(t)is

where a is the continuous scale factor and b is the continuous translation factor.

For practical applications,the continuous wavelet transform must be discretized.The discretional formulas of continuous scale factor aoand continuous translation factor boareand the representation of discrete wavelet transform can be written as

利用SPSS 19.0统计软件分析数据，每个标本独立重复三次，所有细胞实验独立重复三次，计量数据以均数±标准差表示，若满足正态性和方差齐性，两样本均数比较采用独立t检验和配对t检验，相关性分析采用Spearman秩相关性分析，P<0.05为差异有统计学意义。

Wavelet packet decomposes the original signal into both low frequency approximations and high frequency details,determining the resolution of signal in different frequency bands adaptively.The process schematic diagram of WPD is shown in Fig.12.In the testing of dynamic power electronic rectifier devices,the energies of different frequency bands will reflect the characteristics of damaged components in the circuit.Thus,the energy distribution of the arc current in different decomposition scales is selected as the feature vectors to extract faults.

The specific implementation steps are as follows:

(1)Adopt WPD technique on output current when arc faults occur in power electronics,and extract the signal features on decomposition scale j from low frequency to high frequency,with a total number of 2j.

(2)Reconstruct the wavelet packet decomposition coefficient and extract each frequency band signal on decomposition scale j.

(3)Calculate the total energy in each band.The energy feature T is constructed as follows:

Fig.12 Sketch map of WPD process.

whereis the energy of wavelet packet decomposition coefficient Sj，nof node n on decomposition scale j.is the discrete amplitude value of Sj，n.

举目时时似故园，乡心自动向谁言。白云晓湿寒山寺，红叶夜飞明月村。震泽风帆归橘岸，钱塘水府抵城根。羡师了达无牵束，竹径生苔掩竹门。

The extracted features in Eq.(4)are used to distinguish arc fault.Through the simulation results,it is noticed that there is a significant increase in the sum of energies under arc faults,and a higher accuracy is thus obtained with WPD method.The results show that 25 out of 30 arc faults can be recognized through WPD analysis.

7.Proposed analysis method with half-cycle analysis

Although analysis with one-cycle data seems simple and appropriate,a more effective method is still needed.The SSPC shall turn off when an arc event which consists of a certain number of arc faults is con firmed.During one cycle time,there may be none,one,or two arc faults.However,one cycle analysis takes the whole period data as the basic detection unit,and it is difficult to say how many arc faults occur during one cycle.Therefore,the half-cycle waveform is supposed to act as the basic detection unit and an arc event could thus be con firmed earlier to lessen arc harm.It is easy to figure out that half-cycle analysis takes only half of the time that one-cycle analysis needs to con firm an arc event in ideal situations.

30 cycles of arc fault current waveforms which are comprised of 23 normal halves and 37 arc halves,are used.So the effectiveness of proposed methods is determined by how many arc faults that can be detected from the 37 arc halves and how many normal halves that are not regarded as arcs mistakenly.

7.1.Direct FFT and WPD analysis

The first method that we can think of immediately is to directly apply FFT or WPD to half-cycle data analysis,as shown in Fig.13.However,this method is not acceptable because there is no apparent difference between normal and arc halves any more from respective spectrums.In total,only 14 arcs out of 37 are detected.Spectrums of arc halves do not differ a lot from those of normal halves because even a half cycle of normal current contains a large number of harmonic components,just like an arc half.The analysis results with WPD on halfcycle data are,similar with FFT,also with lower accuracy.The predefined feature vectors no longer work with halfcycle data.

Step 1.Take a symmetry of the sampled half-cycle data on x-axis.

(1)The aviation arc fault duration is shorter because of the better insulation cables,and thus it is more difficult in order to detect the occurrence of arc fault.

Fig.13 Spectrums of normal half and arc half waveform with FFT.

7.2.Proposed preprocessing method one-anti-translational

The following steps show how to construct a new antitranslational one-cycle data,as can be noticed from Fig.14:

Step 1.Take a symmetry of the sampled half-cycle data on x-axis.

Step 2.Shift these data by N/2 points to construct new halfcycle data.

Step 3.Combine the sampled half-cycle data and the constructed half-cycle data to get new anti-translational onecycle data.

This proposed method can also be expressed with the following equation:

where

Aone-cycle=a[1]-a[N](N is a power of 2,here N=64)

Asampled=a[1]-a[N/2](sampled)

Aconstructed=a[N/2+1]-a[N](constructed)

Fig.14 Half-cycle data analysis with method one.

The veri fication results using MATLAB show that 26 out of 37 arc halves could be detected with this method and no normal half is detected mistakenly.Because of the symmetry of the constructed waveforms,as shown in Fig.14,there is no DC and even order harmonic components both of which could have acted as elements of feature vectors in the spectrums.

7.3.Proposed preprocessing method two-anti-symmetrical

The following steps show how to construct new antisymmetrical one-cycle data with the original half-cycle data,as indicated from Fig.15:

In order to better differentiate arc halves from normal halves,this paper proposed two waveform constructive methods.To be more precise,the original half-cycle current waveform is still chosen as the basic detection unit,but each halfcycle waveform has to be constructed to form a one-cycle waveform based on certain principles which will be described in the following.

2）硼肥。 基肥可亩施硼肥 150～250 g，每 2～3年施1次；喷施可在花期和幼果期用0.3%硼砂，促进花粉管延伸，以利于授粉受精，促进幼果对钙的吸收。

Step 2.Take a symmetry of these data on y-axis(at the point N/2)to construct new half-cycle data.

Step 3.Combine the sampled half cycle and the constructed half cycle to get a new anti-symmetrical one-cycle data.

This method can also be expressed in Eq.(6):

where

Awhole=a[1]-a[N](N is a power of 2,here N=64)

Aformer=a[1]～a[N/2](sampled)

Alatter=a[N/2+1]～a[N](constructed)

Fig.15 Half-cycle analysis with method two.

The verification results using MATLAB show that 33 out of 37 arc halves could be detected with this method and no normal half is detected mistakenly.Because of the symmetry of the constructed waveforms,as shown in Fig.15,there is no DC component which could have acted as an element of feature vectors in the spectrums.

60 half cycles(37 arc halves and 23 normal halves)of data are tested by both methods.Both methods are able to treat normal halves without mistake.As for arc halves,Method Two(33 out of 37)is more effective than Method One(26 out of 37).Of course,detection results rely much on the threshold value of parameters of interest.In addition,both of the two methods lose some feature parameters and are critical about the computation ability of CPU.

However,Method One is easier to accomplish in a microprocessor than Method Two.Method One is OK as long as N points represent a whole period,regardless of where the first point is.As to Method Two,the first point must be located at the zero-crossing point of the signal.The reason is that a sinusoidal waveform is both axis-symmetric and centro-symmetric.All of this can be proved as follows:

For Method One,we assume that the sampled current waveform equation is

Then take a symmetry of y on x-axis and we get

Then shift y by N/2 to construct new half-cycle data and we get

So the new constructed one-cycle data can be obtained by combining y1 with y2,and can be expressed as follows:

This means that wherever the first point is,constructing new one-cycle data with Method One is always available.

For Method Two,we assume that the sampled waveform equation is

Then take a symmetry of the sampled half-cycle data on xaxis and we get

Then take a symmetry of these data on y-axis(at the point N/2),namely x=a+π,to construct a new half-cycle data and we get

To make sure that y1and y2always constitute a one-cycle waveform,there should always be

So

The calculation results show that the sampling interval should either be[a，a+ π)or[a+ π，a+2π)when using Method Two which also means that the first point must be located at the zero-crossing point of the signal.

The arc fault detection results with the proposed two methods with half original data,and the results of traditional onecycle data analysis are summarized in the following table.As can be noticed,the proposed reconstruction methods with half-cycle data show significant accuracy improvements,especially Method Two(see Table 2).

8.Experimental verification

Fig.16 shows the XE164FN development board used for arc fault detection algorithm veri fication,a product of Infineon Corporation.The development board is used to focus on the main concern eliminating other possible problems caused by peripheral circuits.Current signal is collected via the sensing resistor.The sampling rate in AD is set to make sure that each cycle datum consists of 64 points.The detection algorithm is programmed in CPU.Fig.17 shows the laboratory setup of the experiment.The voltage source is set at 115 V/400 Hz,which is commonly used in aircraft.The adjustable load is set at 23 Ω to make sure that the normal current is 5 A.Since series arc faults are considered to be more dangerous,as stated before in the paper,the experimental verification results with series AC arc faults are provided.

Figs.18 and 19 show the experimental result,and signals are still recorded by HBM Genesis7t.ChA1,ChA2 and ChA3 are three channels to display the waveforms of points of interest.ChA1 is the driving signal of the MOSFET.ChA2 is the detection result.We can see that a pulse is generated by CPU when an arc half waveform is detected and ChA3 is the recorded current waveform.The MOSFET is shut off when a certain number of arc halves are detected(in our case,the number is set to be 8 according to international standards).It can be noticed that the driving signal turns to 0(ChA1)when the maximum number of the accounted faults is reached,which means that the series arc fault is successfully detected with the proposed methods.Considering that a 64-point FFT computation may be an intolerable burden for CPU,a less-point calculation with high speed but low accuracy might be a better choice to ensure that the detection process is executed in real time.Of course,this strongly depends on the performance of the controller.

9.Summary and conclusions

This paper proposes two fast arc fault detection methods for AC SSPCs based on half-cycle data analysis.The proposedmethod is based on frequency domain analysis with FFT and WPD.Current data under both normal and arc conditions have been collected and analyzed.Experimental results show that series AC arc faults can be effectively detected with the obtained features through FFT analysis.

Table 2 Comparative study of different methods.

Method Onecycle data Method one antitrans(half cycle)Method two antisymm(half cycle)FFT 20/30,66.7%49/60,81.7% 56/60,93.3%WPD 25/30,83.3%54/60,90.0% 58/60,96.7%

Fig.16 Infineon XE164FN development board.

Fig.17 Setup of AC arc detection experiment.

Fig.18 Experimental result of arc detection for AC SSPC with FFT(resistive load).

Fig.19 Experimental result of arc detection for AC SSPC with Wavelet(inductive load).

However,more work has to be done in the future.For example,SSPC should be able to detect arc faults in a variable-frequency aircraft electrical power system since variable-frequency power supply will be adopted for next generation aircraft.In addition,artificial intelligence is widely used for automatic classification of fault types and it may provide a new way for AC arc detection.

Acknowledgements

This work was co-supported by the National Natural Science Foundation of China(Nos.51407144 and 51777169),the Aviation Research Funds(No.20164053029),the Fundamental Research Funds for the Central Universities (Nos.3102017ZY027 and 3102017GX08001),and the Young Elite Scientist Sponsorship Program by CAST.

References

1.Izquierdo D,Barrado A,Fernandez C,Sanz M,Lazaro A.SSPC active control strategy by optimal trajectory of the current for onboard system applications.IEEE Trans Indust Electron 2013;60(11):5195–205.

2.Barrado A,Izquierdo D,Sanz M,Raga C,Lazaro A.Behavioural modeling of solid state power controllers(SSPC)for distributed power systems Twenty-fourth annual IEEE applied power electronics conference and exposition;2009 Feb 15–19.Washington,D.C.Piscataway:IEEE Press;2017.p.1692–7.

3.Andrea J,Zirn O,Bournat M.Principle of arc fault detection for solid state power controllerIEEE 58th Holm conference on electrical contacts(Holm).Piscataway:IEEE Press;2012.p.1–6.

4.Choi JH,Kim SH,Yoo DS,Kim K-H.A diagnostic method of simultaneous open-switch faults in inverter-fed linear induction motor drive for reliability enhancement.IEEE Trans Indust Electron 2015;62(7):4065–77.

5.Yao X,Herrera L,Ji S,Zou K,Wang J.Characteristic study and time-domain discrete-wavelet-transform based hybrid detection of series DC arc faults.IEEE Trans Power Electron 2014;29(6):3103–15.

6.Li WL,Zhang XB,Li HM.Design of star-connected autotransformer based 24-pulse rectifier and its application in the more electric aircraft.Eur Power Electron Drives J 2014;24(1):37–44.

7.Liu WJ,Zhang XB,Ji RP,Dong YJ,Li WL.Arc fault detection for AC SSPC in MEA with HHT and ANNIEEE international conference on aircraft utility systems.Beijing.Piscataway:IEEE Press;2016.p.7–12.

8.Li W,Monti A,Ponci F.Fault detection and classi fication in medium voltage DC shipboard power systems with wavelets and artificial neural networks.IEEE Trans Instrum Measur 2014;63(11):2651–65.

9.Li W,Liang L,Liu W,Wu X.State of charge estimation of lithium ion batteries using a discrete time nonlinear observer.IEEE Trans Indust Electron 2017;64(11):8557–65.

10.Gregory GD,Kon Wong,Dvorak RF.More about arc-fault circuit interrupters38th IAS annual meeting on conference record of the industry applications conference;2003 Oct 12–16.Salt Lake City,UT.Piscataway:IEEE Press;2003.p.1306–13.

11.Qi Pan,Jovanovic Slavisa,Lezama Jinmi,Schweitzer Patrick.Discrete wavelet transform optimal parameters estimation for arc fault detection in low-voltage residential power networks.Electric Power Syst Res 2017;143:130–9.

12.Liu G,Cao YN,Liu Y,et al.A survey on arc fault detection and wire fault location for aircraft wiring systems.Am J Gastroenterol 2009;1(1):903–14.

13.Li W,Ferdowsi M,Stevic M,Monti A.Co-simulation for smart grid communications.IEEE Trans Indust Inform 2014;10(4):2374–84.

14.Hosseinabadi HZ,Nazari B,Amirfattahi R,Mirdamadi HR,Sadri AR.Wavelet network approach for structural damage identification using guided ultrasonic waves.IEEE Trans Instrum Measur 2014;63(7):1680–92.

15.Banerjee S,Mitra M.Application of cross wavelet transform for ECG pattern analysis and classification.IEEE Trans Instrum Measur 2014;63(2):326–33.

16.Wu CJ,Liu YW.Smart detection technology of serial arc fault on low-voltage indoor power lines.Int J Electr Power Energy Syst 2015;69:391–8.

17.Jovanovic Slavisa,Chahid Abderrazak,Lezama Jinmi,Schweitzer Patrick.Shunt active power filter-based approach for arc fault detection.Electric Power Syst Res 2016;141:11–21.

18.Yao X,Herrera L,Ji SC,Zou K,Wang J.Characteristic study and time-domain discrete-wavelet-transform based hybrid detection of series DC arc faults.IEEE Trans Power Electron 2014;29(6):3103–15.

19.Hamid Mortazavi S,Moravej Zahra,Shahrtash Mohammad.A hybrid method for arcing faults detection in large distribution networks.Int J Electr Power Energy Syst 2018;94:141–50.

20.UL 1699,Arc-Fault Circuit Interrupters,United States:UL Standard Destination;2006.

21.Deng F,Zeng XJ,Pan LL.Research on multi-terminal traveling wave fault location method in complicated networks based on cloud computing platform.Prot Control Modern Power Syst 2017;2(4):12–8.

22.Li Y,He L,Liu F,Li CB,Cao YJ,Shahidehpour M.Flexible voltage control strategy considering distributed energy storages for DCdistributionnet work.IEEE Trans Smart Grid2017;PP(99),1–1.