Fault Line Selection Method Considering Grounding Fault Angle for Distribution Network

Li Si-bo,Zhao Yu-lin*,Li Ji-chang,and Sui Tao

1 College of Electrical and Information,Northeast Agricultural University,Harbin 150030,China

2 Chenguang Pyroelectricity Limited Liability Company in Raohe,Shuangyashan 155700,Heilongjiang,China

Introduction

In China,the range of mid and low voltage distribution networks is from 10 to 66 kV,and these networks generally use small current grounding power systems (Tang et al.,2013;Zhao et al.,2010).In the system with its neutral point grounding via arc suppression coil,line selection for single-phase grounding fault has always been a difficult point in distribution network automation technology (Pang,2010).The reduction of zero-sequence current by inductive compensation after fault may lead numerous comparison methods based on the power frequency steady-state component to fail to work (Chen et al.,2007).As transient signal carries more fault information,using some analysis tools,such as wavelet transformation to detect fault in order to expand information has become a research hotspot in recent years (Gong,2009).Zhu (2011) from Changsha University of Science and Technology,carried out wavelet transform on transient zero-sequence current in every feeder,and then notarized the fault line by comparing the polarities of the modulus maximum.Zhao and Wang (2010),suggested to compare modulus maximum of each line transient characteristics after wavelet transformation.If the ratio of the largest one and the second largest one was greater than a certain threshold,it proved that the line with the largest one went wrong.After testifying that the frequency characteristic and oscillating component of zero-sequence power in fault line and those in sound feeders were different,Li and Shu (2013) from Kunming University of Science and Technology,synthetically analyzed oscillating component of one,two,four and six times power frequency signal to determine the fault line.

However,when grounding fault occurs near the zero point of the phase voltage,the fault transient component is small and lasts for an extremely short time.According to that,present methods of line selection based on wavelet are insufficient.In addition,the touch of overhead feeders with trees may lead to high-resistance faults,which can bring about missselection in actual operation (Shu and Zhu,2013).So,it is essential to improve the selection criterion of fault line with small fault angle to achieve selection without dead zone.In this paper,after the analysis of the transient process of the single-phase grounding fault in distribution network,the fault transient signal was decomposed into different frequency bands by the selected wavelet,according to different fault angles,corresponding frequency band which wavelet energy concentrated in was selected as characteristic band for line selection.This method could make the criterion more perfect.

Principles and Methods

Analysis of influence of different fault angles on transient zero-sequence current in singlephase grounding fault

In the distribution network with the neutral point via arc suppression coil grounding system,the equivalent transient circuit figure of the single-phase grounding fault is shown in Fig.1.

Fig.1 Equivalent circuit of system transient process

In Fig.1,u0was zero-sequence voltage,rLwas the resistance of arc suppression coil,L was the inductance of arc suppression coil,C was the sum of capacitance to earth in three-phase lines,L0was the sum of equivalent inductance of three-phase lines and transformer in current,R0was equivalent resistance in current.Transient grounding current idwas consisted of the transient capacitance current iCand transient inductance current iL.The characteristics of transient current was mainly dependent on the transient capacitance current during the incipient time (Dai and Zhang,2003).Transient process produced highfrequency free oscillation (Liu,2009),as inductance only allowed the direct current and prevented the alternating current,and as L was remarkably bigger than L0,the series branch of L and rLin Fig.1 can be ignored.The circuit consisted by u0,L0,R0,and C was available to get the differential equation of transient capacitance current.This equation was shown as the follow:

With the initial condition t=0,instantaneous expression for capacitance current after Laplace transform can be obtained as follow (Nian,2009):

In the formula above,Umwas the amplitude of phase voltage,Icmwas the amplitude of capacitance current,ωfwas the free oscillating component frequency of transient capacitance current,δ was attenuation coefficient,and τ was time constant.When fault occured at the phasevoltage peak,the free oscillating component of iChad the largest amplitude iC.os.max.At the point of t=Tf/4,the value of this maximum wasAccordingly,the largest amplitude of the transient free oscillating component was proportional to the ratio of the free oscillating frequency ωfand power frequency ω.In this case,the characteristics of transient zero-sequence current of all the lines mainly relied on iC,and the energy of iCconcentrated in the high frequency band within 300-1 500 Hz.

On the contrary,if fault occurred at the zero-crossing point of the phase voltage,the free oscillating component of iChad the smallest amplitude iC.os.min,and this minimum wasIn this condition,as the free oscillating component was equal to the amplitude of the capacitance current in power frequency,there was no obvious transient capacitance current components.The fundamental component occupied major part,so the energy was concentrated in 0-50 Hz.In this case,the transient inductance current should be taken into consideration,its expression was:

iLwas composed of direct-current component and fundamental component,and its oscillating frequency in transient process was equal to power frequency (Li,2011).

It could be concluded that both the frequency of iCand the frequency of iLconcentrated in the low frequency band during the zero-crossing point fault,as the transient zero-sequence current was the superposition of iCand iL,and its wavelet energy was also mainly situated at low frequency range.

Based on the above analysis,we could get different corresponding criteria for fault aiming at different angles of the phase voltage in line selection.

Wavelet transformation and multi-resolution analysis

Wavelet transformation is an effective time-frequency analysis tool.It has band-pass filtering property,and adapts to small scale fluctuation in signal.Its flexible scale makes itself highly capable to distinguish mutational signal,so it can detect the instantaneous and singular component in unsteady signal effectively and show the starting time and duration length simultaneously.As a result,it is wildly used for the analysis of transient fault signal in power system.

Expression of discrete wavelet transformation of any function f(t) is:

After sampling the signal according to the sampling theorem,we could get the signal frequency band within –π-+π.The positive part would be decomposed into low frequency band within 0-π/2 and high frequency band within π/2-π by ideal low-pass filter H0and high-pass filter H1,respectively.Since the bandwidth of each part was decreased into half,a half of sampling rate would not cause the loss of information.After each decomposition,the low frequency part could be decomposed again.The process above was called the multi-resolution decomposition on original signal x(n).

In the multi-resolution analysis,two-scale equations of the essential characteristic of scaling function φ(t) and wavelet function ψ(t) were (Peng,2003):

In the equations above,h0(k) and h1(k) standed for filter coefficient.

Recursion expressions of discrete approximation coefficient aj(k) and dj(k) were:

Line selection method based on wavelet energy

Original signal x(n) could be regarded as the sum of low frequency part xL(n) within 0-50 Hz and high frequency part xH(n).We chose the right spectrum for the wavelet coefficients as needed,and then calculated the wavelet energy.ELstanded for low frequency wavelet energy,which was the sum of square of wavelet coefficient of low frequency component.EHstanded for the high frequency wavelet energy as the same way.Transient capacitance current with higher frequency in fault zero-sequence current took up different proportions,which was why the transient zero-sequence current was different with different fault angles.By comparing ELor EH within the corresponding frequency band of each line,the distinction between the fault line and normal lines could be easily highlighted,and the accuracy of line selection increased accordingly.The selection steps of wavelet and the implementation steps of algorithm were shown as follows.

DbN wavelet is generally used in fault line selection.Its trait is shown as follows: with the increase of coefficient N,its regularity and locality in frequency domain rise as well,however,its compactly support in time domain gets longer,and the locality in time domain decreases.Combining frequency domain and time domain,db8 wavelet was used to execute this function.Spectrum was determined by sampling frequency and decomposition level.The increase of decomposition layers made the band narrow,and the sensitivity of criterion might decrease due to the reduction of sampling points.On the other hand,fewer decomposition layers led to a wider band in which some interference might mix into the useful information,which also reduced the reliability.To get a precise result,we chose five as the number of decomposition layers.

After fault occurred in the system,the zero-sequence voltage in bus increased.If its instantaneous value exceeded the threshold value,the fault line selection device could start immediately,and the zero-sequence current value 2 ms before and after the fault in each feeder would be recorded,and then the signal would be decomposed into five layers by db8 wavelet.Because the transient characteristic of zerosequence current was mainly determined by transient capacitance current and its energy mainly concentrated in the band within 300-1 500 Hz,5 kHz sampling frequency could meet the requirement.When the fault occurred near the zero-crossing point of the phase voltage,namely,the fault angle α＜αset,the wavelet energy within the low frequency was selected for comparison.In other cases,high frequency energy was used in the comparison.The value of αsetwas set as 30°.The coefficient below 156 Hz in level a5 was used for calculation of low-frequency wavelet energy,and the coefficient within 625-1 250 Hz in level d3 was used for calculation of high-frequency wavelet energy.Firstly,gathered all of the wavelet energy and recorded the number of the feeder with the maximum of wavelet energy,and then compared the maximum with the sum of wavelet energy of all the other feeders.Finally,if the maximum was bigger,the feeder with this maximum was just the defective one,and if the disparity between each wavelet energy was not significant,we could tell that the fault occurred in bus.With this method,we examined fault angle firstly,and then chose single frequency band for the extraction of coefficient and the calculation of wavelet energy.It effectively simplifies the calculation and improves the speed of calculation.The process is shown in Fig.2.

Results

Simulation model

MATLAB/simulink module was used as the simulation platform for the system of single-phase grounding fault in distribution network.To guarantee the accuracy of the experiment,we made use of the data from Harbin Substation.The level of the main transformer was 220 kV/66 kV and the capacity was 180 MVA.Its high-voltage side was connected with the ground directly.However,its low-voltage side was connected with the ground via arc suppression coil by turning on the switch,on the contrary,there was no compensation after turning off the switch.Six feeders of the substation were taken as representative,and the lengths of them were as follows: 2.03 km,4.53 km,8.28 km,10.41 km,14.74 km and 19.07 km,and the parameters of these overhead lines were as follows: r1=0.43 Ω • km-1,l1=0.36 mH • km-1,c1=9.94 nF • km-1,r0=0.74 Ω • km-1,l0=1.27 mH • km-1,c0=6.62 nF • km-1.The equivalent load in each line was in the mode of neutral point grounding.The simulation model of this system is shown in Fig.3.

Results of typical cases

Case 1.To test the effectiveness of the algorithm in the case of the fault near zero-crossing point of the phase voltage,the fault angle was set as 10°.A fault with high grounding resistance in the end of the line was chosen in order to test the reliability of algorithm more precisely.Line 3 was set as the fault one,the grounding resistance Rfwas 2 000 Ω,and the compensation degree was over-compensation by 10%.After the simulation,the figure of the waveform for zero-sequence current in each feeder was shown in Fig.4a.The program carried out wavelet transform on these zero-sequence currents,and then used the wavelet coefficient to calculate the low-frequency wavelet energy.Finally,we could get the result shown in Fig.4b,in which,the wavelet energy in feeder 3 was significantly higher than that in other feeders.So the result of this case was accurate.

Fig.2 Algorithm flow chart

Fig.3 Simulation model

Fig.4 Transient zero-sequence current waveform of each feeder and transient low-frequency wavelet energy of each feeder under a feeder fault

Case 2.To test the accuracy of the algorithm for the fault in bus,we set the single-phase grounding fault in bus,took 200 Ω as the value of the fault resistance,set over-compensation by 8% as the compensation degree,and decreased the fault angle to 0°.The program took sample of the initial sequence of these six zero-sequence currents,and then carried out wavelet transform on them and calculated the wavelet energy.Because the fault occured at the zero-crossing point,the program chose the low-frequency energy to calculate and compare.The result is shown in Fig.5.

Fig.5 Transient low-frequency wavelet energy of each feeder under bus fault

Case 3.Because the intermittent arc grounding fault occupies a certain proportion in actual operations,the test of this algorithm for arc fault is needed.The dynamic characteristic of arc is complex.However,the mode of the turning on and turning off switch repeatedly was used in this experiment to simulate the arc.We set the arc grounding fault in feeder 6,6 km far away from the bus.The arc fault had usually occurred at the peak of phase-voltage,so the grounding angle was set as 90°,and the compensation degree was over-compensation by 6%.The wavelet energy of each feeder is shown in Fig.6.

Fig.6 Transient high-frequency wavelet energy of each feeder under arc fault

Discussion

Typical case simulation results

As the fault angles were less than 30°,case 1 and case 2 were both under the condition of small angle fault.The transient zero-sequence current in each feeder mainly depended on low frequency component,so the calculation of the wavelet energy in low band was needed correspondingly.In case 1,the result of lowfrequency wavelet energy after wavelet transformation in every feeder is shown in Fig.4b,and it could be seen that the wavelet energy of feeder 3 was not only obviously bigger than those in other lines but also bigger than the sum of them,so line 3 was the fault feeder.This result was consistent with the given condition,so the line selection was accurate.Due to the high grounding resistance,the fault current was very small and below 5 A.There was no remarkable disparity between the fault one and others.But the disparity was significantly widened after the calculation of the wavelet energy and the comparison of the maximum,which improved the reliability of line selection.In Fig.5,although the wavelet energy of feeder 6 was the biggest one,its value was not far more than the sum of others.Compared with the figure of case 1,it could be seen that there was a significant difference between this type of fault and the fault in a feeder.Through the analysis above,the bus fault could be ensured,which was consistent with the given settings.So the line selection result proved out to be accurate.In Fig.6 of case 3,the high frequency wavelet energy in feeder 6 was greater than the sum of those in the other feeders,which indicated that line 6 was the fault one.This result showed that the algorithm was also applicable to the arc grounding fault and the big angle fault.

Adaptability

There is interference from the outside or the system itself during the process of signal transmission,so the anti-interference ability is needed in line selection algorithm.The adaptability of algorithm can be verified by the experiment in which some white noise is added to initial signal.We could set the signal-tonoise ratio of the white noise as 20 db.The simulation results could prove that the line selection method was also effective and feasible under the condition of noise interference.A large number of simulation experiments with different fault angles and different compensation degrees had been done,under the ordinary situation and the situation with noise,all of the results were right.Some representative data are picked out and listed in Table 1.

Table1 Line selection results

Conclusions

For the single-phase grounding fault in small current grounding power system,after dissecting the characteristic of transient zero-sequence current,it could be concluded that if the fault occurred at the zero-crossing point of phase voltage,the frequency band which the energy of fault signal concentrated in was different from other conditions.According to different fault angles,different characteristic frequency bands were chosen for the wavelet transformation and the calculation of wavelet energy,which improved the line selection criterion of small fault angle and achieved selection method without dead zone.With this method,there was no need to compare the amplitude and polarity of the current in each feeder,so the calculation was simplified.It was not only applied to the system in the mode of the lowvoltage side grounding via arc suppression coil,but also could be used in the ungrounding system.Besides that,it could meet the demand of the arc fault and had antiinterference ability.With the parameters,such as the fault resistance,the fault angle and the compensation degree changed,all of the simulation experiments in MATLAB/simulink platform proved out that the results of this line selection method were correct and effective.

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