[b]0 Introduction[/b] Ground faults have the highest incidence rate in power distribution networks, and therefore, ground fault protection in power distribution networks has been a major concern for decades. When a ground fault occurs in a system, the fault signal contains important transient components. Traditional signal analysis methods such as FFT, Kalman filtering, minimum variance method, and finite impulse response filtering all have limitations. In addition, in the early stage of a ground fault, the grounding point is often accompanied by a large grounding resistance, and the harmonic current components may be very small. This will affect the sensitivity of the fault location device, resulting in a low correct operation rate of existing protection devices, which cannot meet the requirements of actual engineering. Therefore, it is necessary to select a signal processing method that is suitable for analyzing non-stationary signals and has a strong ability to process weak signals. Wavelet analysis [1,2] is an international cutting-edge field that has become increasingly popular in recent years. It is a new signal processing method developed on the basis of Fourier transform. It overcomes the shortcomings of Fourier transform in that it cannot perform time-frequency localization analysis of signals simultaneously. It can perform fine analysis of signals, especially sensitive to transient abrupt changes or changes in weak signals. This paper introduces wavelet transform into the detection of grounding faults in distribution networks. The wavelet in reference [3] is selected as the analysis function, and the wavelet coefficients after wavelet transform are used to construct the protection criterion. Through simulation (EMTP), it is proved that the criterion can improve the correct operation rate of the protection device and is beneficial to improving the operation performance of the device when grounded through high resistance. [b]1 Relevant theories of wavelet analysis [1, 2][/b] Let Ψ(t)∈L2() be the mother wavelet that satisfies the allowable condition. The mother wavelet generates a family of functions through translation and scaling, which is called the continuous wavelet: [img=284,34]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/09g01.gif[/img] where a is the scaling parameter; b is the translation parameter. For a signal f(t) ∈ L2 ([img=15,18]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/t05.gif[/img]), its continuous wavelet transform is: [img=320,34]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/09g02.gif[/img] In the formula, [img=18,18]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/t06.gif[/img] a,b(t) are the conjugates of Ψa,b(t). This paper selects the complex function [img=284,37]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/09g03.gif[/img] that satisfies the allowable condition for rapid decay in reference [4] as the mother wavelet, and implements it using a recursive algorithm after discretization. Let the signal be s(t), then the wavelet transform coefficients Ws,Ψ(kT,f) at time t=kT (f is the wavelet scale and T is the sampling interval) can be obtained by recursive formula (2) [3]. Ws,Ψ(kT,f)=T{δ1s[(k-1)T,f]+δ2s[(k-2)T,f]+δ3s[(k-3)T,f]+ δ4s[(k-4)T,f]+δ5s[(k-5)T,f]}-λ1Ws,Ψ[(k-1)T,f]-λ2Ws,Ψ[(k-2)T,f]- λ3Ws,Ψ[(k-3)T,f]-λ4Ws,Ψ[(k-4)T,f]-λ5Ws,Ψ[(k-5)T,f]- λ6Ws,Ψ[(k-6)T,f] (2) If A=e-fT(σ-iω0), where σ=2π/,ω0=2π then: [img=283,210]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/09g05.gif[/img] Figure 1 shows the waveform of the mother wavelet in the time domain and its amplitude-frequency characteristics. [img=258,170]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0901a.gif[/img][img=233,169]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0901b.gif[/img] (a) Waveform of the mother wavelet in the time domain (b) Amplitude-frequency characteristics of the mother wavelet Fig.1 Time domain waveform and Fourier transform of the wavelet 2 Specific Applications of Wavelet Transform When a ground fault occurs in a distribution network, its fault characteristics are mainly manifested in the zero-sequence voltage of the bus and the zero-sequence current of each outgoing line. This paper uses the selected wavelet basis to extract the fundamental wavelet coefficients of the zero-sequence voltage of the bus and the zero-sequence current of each outgoing line, thus forming a criterion. Let the wavelet coefficient of the fundamental zero-sequence voltage of the bus at time nT be Wus(nT), and the wavelet coefficient of the fundamental zero-sequence current of the j-th outgoing line be Wis,j(nT) (j is the outgoing line number, j=1,2,3,…; T is the sampling interval; n is a positive integer), then the line selection criterion is: [img=260,44]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/09g06.gif[/img] This criterion can realize the selection of multiple grounding lines. If one or more outgoing lines satisfy equation (3), the outgoing lines that satisfy the condition are all fault lines. If none of the outgoing lines satisfy equation (3), then it is a bus fault. Figure 2 is the equivalent system diagram of the zero-sequence fault component when a single-phase ground fault occurs in the distribution network. As can be seen from the figure, the Yj(nT) of the faulty line is larger than that of the healthy line, so only the setting value needs to be selected for line selection. The setting value Kzd,j for each outgoing line depends on the specific system. [img=248,116]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0902.gif[/img] Fig.2 Equivalent system diagram of zero-sequence fault components Fig.2 Zero-sequence network The protection criterion in this paper is theoretically not limited by the minimum sampling rate. However, since the wavelet criterion is a waveform criterion, if the sampling rate is too low, it may lead to the loss or reduction of the singularity of the characteristic signal when the fault occurs, which will seriously reduce the protection sensitivity or even fail to provide protection. A high sampling rate means that the waveform characteristics can be better preserved, but the requirements for hardware will also be increased. The appropriate sampling rate must be carefully considered, taking into account both hardware performance (including A/D chip conversion speed, RAM storage capacity, CPU computing speed, etc.) and better preservation of fault signal characteristics. This paper selects 2000 Hz as the sampling rate for fault detection. 3. Case Simulation and Line Selection Result Analysis In the research process of this paper, a large number of simulations were conducted on actual 10 kV systems with different neutral grounding methods using EMTP. Specific simulations were performed under various grounding methods, including grounding through transition resistors, busbar grounding, and self-extinguishing arc discharge. Many factors were considered during the simulation, such as changing the R/X of the outgoing line, changing the phase angle of the power supply, changing the number of outgoing line loops and the distance between long and short lines, changing the grounding resistance and grounding location, changing the load weight and asymmetry (implemented using a constant current source). In addition, the effects of asynchronous closing of parallel capacitors and the switching on/off of outgoing lines on line selection protection were also considered. The performance of the criteria in this paper is explained below only for the neutral point grounded through an arc suppression coil system. The system wiring diagram is shown in Figure 3. The line parameters are as follows: line length l1=28.708 km, l2=34.304 km, l3=44.988 km, l4=37.000 km; positive sequence impedance Z1=(0.17+j0.38) Ω/km, positive sequence capacity b1=3.045 μS/km, zero sequence impedance Z0=(0.23+j1.72) Ω/km, zero sequence capacity b0=1.884 μS/km; system short-circuit power is 1096 MVA; short-circuit voltages of transformer SFSZ8-31500/110 are uk1-2=10.5%, uk1-3=17.5%, uk2-3=6.5%. [img=309,245]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0903.gif[/img] Fig.3 Simulation example of a small current grounding system network 3.1 Single-phase grounding fault detection Figs.4 to 7 show the detection of grounding faults, self-extinguishing arc faults, and busbar grounding faults at t=0 s when phase A of line L4 is 6 km away from the busbar via transition resistors of 10 Ω and 20 kΩ, respectively. [img=275,171]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0904.gif[/img] Fig. 4 Earth-fault through 10 Ω on A-phase in line L4 [img=263,163]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0905.gif[/img] Fig. 5 Earth-fault through 20 kΩ on A-phase in line L4 [img=257,171]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0906.gif[/img] Fig. 6 Arcing-grounded fault on A-phase in line L4 [img=259,165]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0907.gif[/img] Fig. 7 Earth-fault in A-phase bus As shown in Figures 4-7, when a fault occurs on line L4, the Yj(nT) of line L4 (j=4) is the largest, and much larger than that of other outgoing lines (j=1,2,3). However, when a bus ground fault occurs, the Yj(nT) of all outgoing lines is very small. Therefore, after selecting a threshold value, the faulty line can be accurately detected. In addition, Figures 4 and 5 also show that the criterion in this paper is less affected by the transition resistance, which can improve the reliability of fault detection when grounded through high resistance. If the threshold value is selected as 0.0002, the fault can be correctly detected after the 10th sampling point (i.e., 1/4 cycle). 3.2 Two-phase ground fault detection Figures 8-10 show the fault detection situations when the L4 outgoing line AB phase short circuit grounding, L4 line A and B phases are grounded through transition resistance at different points, and L4 line A and L3 line B phases are grounded through transition resistance, respectively. [img=257,171]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0908.gif[/img] Fig. 8 Earth-fault between A-phase and B-phase in line L4 [img=261,170]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0909.gif[/img] Fig. 9 Earth-fault through resistance on A-phase and B-phase at different points in line L4 [img=257,165]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dlxtzdh/dlxtzdh99/dlxt9913/image13/0910.gif[/img] Fig.10 Earth-fault through resistance on A-phase in line L4 and on B-phase in line L3. For phase-to-phase grounding faults, the fault phase current increases, and overcurrent protection can trip. However, in the cases shown in Fig.9 and Fig.10, the phase current changes little, and the fault cannot be cleared by overcurrent protection. But in this case, the criterion in this paper can accurately detect the fault line, and the correct judgment time is about 1/4 cycle after the fault occurs on the outgoing line. 4 Conclusion Because the algorithm in this paper is implemented using a recursive algorithm, its advantage compared with the full-cycle Fourier method is that it is not constrained by the analysis window and can realize multi-point comparison. When a ground fault occurs, whether it is a line fault or a bus fault, the criteria in this paper can be accurately distinguished. In addition, it is less affected by the transition resistance, which can improve the operation performance of the protection when grounded through high resistance. [b]References[/b] [1] Qin Qianqing, Yang Zongkai. Practical Wavelet Analysis. Xi'an: Xi'an University of Electronic Science and Technology Press, 1995 [2] Zhao Songnian, Xiong Xiaoyun. Wavelet Transform and Wavelet Analysis. Beijing: Electronic Industry Press, 1996 [3] Zhang Chuanli. Research on Microcomputer Protection of Transformers: Doctoral Dissertation. Beijing: Tsinghua University, 1998 [4] CHAARI O, MEUNIER M, BROUAYE F. Wavelets: A New Tool for the Resonant Grounded Power Distribution Systems Relaying. IEEE Trans on Power Delivery, 1996, 11(3)