Off-line location strategy for single-phase ground fault of distribution line

This paper adopts off-line location strategy of single-phase grounding fault of distribution lines, determines size and frequency of injected AC signal by analyzing distribution parameters of lines, and then develops portable small current signal source with adjustable frequency through power conversion control technology, and develops signal detector by analyzing noise correlation and adaptive morphological filtering. Then off-line location strategy is developed according to above two signal devices. Finally, it is verified that the strategy can accurately locate fault point of distribution line.


Introduction
At present, domestic distribution lines cover a wide area, long lines and many branches, and operating environment is complex and changeable.With the advancement of national policy orientation and urban construction, the growth rate of distribution network cable lines is close to 10%, which leads to a significant increase in the probability of failure [1][2][3][4] .According to statistics, 70% of faults in distribution system are caused directly or indirectly by single-phase grounding faults, which are often accompanied by overvoltage burnout or breakdown of equipment in stations.Therefore, it is urgent to diagnose and analyze the operating status of distribution network lines, and to accurately select and locate lines when a single-phase grounding fault occurs, so as to shorten the troubleshooting time [5][6] , reduce risk of largescale power outage, and improve service life of equipment in stations.
The off-line location strategy for single-phase grounding fault formulated in this paper can locate faulty node and solve the above problems [7] .The detailed process is described below.

Frequency modulation AC signal size and frequency analysis
The selection of frequency-modulated AC positioning signal is mainly to reduce influence of grounding transition resistance and branch line capacitance on positioning accuracy.Since injected signal of AC method is AC signal, it is bound to be affected by distributed capacitance and distributed inductance of distribution line, etc, so it needs to be studied and analyzed.

Distribution parameters
Considering uniform distribution of lines, line distribution capacitance C and distributed inductance L are used to reflect energy storage characteristics of electric field and magnetic field distributed in space around lines, respectively.Specific equation is shown in formula (1) : In equation, Dm is geometric mean distance, r is wire radius, and μr is relative magnetic permeability of conductor material.
By assigning values to above parameters, the value ranges of line distributed capacitance and distributed inductance can be obtained respectively.
Considering distributed inductance and distributed capacitance in general, ignoring line resistance and conductance, 30 km line equivalent circuit is obtained, as shown in figure 1.

Selection of injection signal size
When selecting AC signal frequency and injection energy, it is necessary to know line length and fault ground resistance, and these two key quantities are uncertain.Equivalent circuit of fault resistance and distributed capacitance is shown in figure 2. In actual project, current Ir of fault point is specified to be greater than distributed capacitance current Ic of flowing wire.In order to ensure that detector can recognize and distinguish Ir and Ic, the condition Ir≥Ic is taken, as shown in formula (3) : When current flowing into fault point reaches more than IA, positioning effect is ideal.Since fault resistance is in parallel with distributed capacitance, injected current is A 2I .The determination of injection current is related to performance of AC signal detector.Experimental data show that when current flowing into fault point reaches more than 70mA, positioning effect is ideal.In order for detector to distinguish fault current, maximum current flowing into distributed capacitor is 70mA.In actual positioning, injection current is selected as 100mA.

Determination of injection signal frequency
The off-line low-frequency AC location method is to inject AC signal into fault phase under off-line state of power failure, and then detect AC signal along line with hand-held AC signal detector.Therefore, it is very important to study relationship between distributed capacitor current of conductor and frequency.
Considering ZC>>ZL, line reactance is simplified by calculation as shown in formula (4) : It can be seen that line reactance is frequency independent.In addition, since distributed capacitor current is positively correlated with frequency of injected AC signal, in order to reduce distributed capacitor current, the frequency of injected current should be appropriately reduced, and it should be distinguished from power frequency.

Portable frequency-adjustable small current signal source
Based on research of SVPWM wave control technology, PID double closed-loop feedback control technology and high frequency switching power conversion technology, portable small current signal source with frequency modulation is developed [8] .
SPWM control technology mainly modulates width of a series of pulses to obtain required waveform equivalent.RMS current loop in PID current double closed-loop feedback control technology is outer loop, and RMS output current is controlled by PI regulator to ensure stable output of current, In addition, AC constant current power supply adopts high frequency switch to achieve power conversion, which takes advantage of low loss under IGBT high frequency switch mode to complete SPWM conversion and control, and achieve high power converter.
The schematic diagram of whole circuit of small current signal source is shown in figure 3. The main circuit of power supply adopts AC-DC-AC structure, including input soft start circuit, input rectifier, DC filter, H full bridge inverter, transformer isolation transformer and output filter circuit.AC-DC part is three-phase bridge rectifier.H full bridge inverter adopts IGBT as switching element, adopts SPWM technology to control inverter.After PWM wave output by inverter is filtered by LC filter circuit, inverter sinusoidal alternating current is output.Control circuit is mainly composed of signal generating unit, SPWM wave generating unit and so on.

Weak signal anti-interference processing technology
Weak current signal detection technology through noise correlation analysis, the main research is how to improve signal-to-noise ratio to obtain the best noise cancellation signal under complex noise background, and then quickly identify and extract useful weak measurement current signal.
Noise correlation mainly measures degree of correlation or similarity between signals.Taking white noise as an example, its power spectral density function is constant in the whole frequency domain.For general white noise signal in distribution network fault signal, selection of sinusoidal or semi-circular structural elements can achieve better denoising effect.
Correlation function can be used to characterize the degree of correlation between signals, which is a function to measure the degree of correlation or similarity between signals.Signals are generally divided into two categories: energy signals and power signals.Correlation functions mainly include autocorrelation function and cross-correlation function, as shown in following formula (5) to (6) : The autocorrelation function of the energy signal is defined as: The autocorrelation function of the power signal is defined as: Mathematical morphology is built on basis of integral geometry and random set theory, and the analysis of various signals is carried out directly in time domain, which is more effective than various means of signal processing in frequency domain, and operation is relatively simple, which can greatly improve speed of signal processing.Basic operations include dilation and corrosion, which can be combined to form morphology open and morphology closed.The peak noise in signal can be reduced by selecting appropriate structural elements for open operation, and trough noise in signal can be reduced by closed operation.Morphological filter can be formed by concatenation of operations, which can better solve the problem of output deviation.
The distribution network fault signal is usually a one-dimensional signal, which is set as and defined as a structural element.The expansion and corrosion operations of the signal using the structural element are shown in formula ( 7 The open and closed operations of morphology can be obtained by combining the two basic operations of expansion and corrosion, as shown in formula (8): The peak noise in signal can be reduced by selecting the appropriate structural elements for open operation, while trough noise in signal can be reduced by close operation.An alternate filter can be obtained by performing two operations alternately.Alternate filter is often used for image smoothing and denoising.By alternating etching and swelling operations, it smooths details and edges in image and removes noise.As shown in formula (9): In order to quantitatively evaluate filtering effect of various filters, the root-mean-square error formula can be used to compare waveform changes before and after filtering, as shown in formula (10) below: The larger the value, the larger the difference between the compared signals.The concept of weight is introduced, and the weight proportion of the filtered signal in calculation results is continuously increased through adaptive weighting calculation, so as to obtain the best noise reduction signal.In addition to the combination of morphological operations, the shape and scale of structural elements also have a great influence on filtering effect.The common filter structure elements are straight line, oblique line, curve, triangle, semicircle and other shapes.Generally used in fault signal noise elimination effect of structure element shape including triangle, semicircle and sine and cosine shape.Common cosine, triangular, semicircular.

Research on off-line location technology of single-phase grounding fault
Considering that low-frequency AC signal is milliampere-level current, and current carrier is highvoltage power line, detection personnel can not get close to line, and accurate detection is very difficult.Based on above description of data characteristics of frequency modulation low current signal source and magnetic field detector, off-line location strategy for single-phase grounding fault of distribution line is proposed, as shown in figure 4.
Based on above research on data characteristics and functional performance of frequence-modulated low-current signal source and magnetic field detector, project proposes an off-line location strategy for single-phase grounding fault of distribution lines, as shown in figure 4. The portable frequencyadjustable offline positioning prototype device adopts AC frequency modulation signal positioning, injecting high-voltage 80Hz or 22Hz AC signal into fault line phase by phase, and signal will flow along route to fault point, and through fault point into the ground to form a loop.Only fault phase generates an AC signal to determine fault phase.When high-voltage 80Hz AC signal is injected into fault line, according to principle of electromagnetic induction, there must be a magnetic field with the same frequency as injected signal in fault section, and 80Hz signal detector detects magnetic field intensity.When high voltage 22Hz AC signal is injected into fault line, clamp ammeter is stuck on fault phase, and AC current value is displayed on 22Hz signal receiver.
First, find fault phase, inject high-voltage 80Hz AC signal phase by phase, and on-phase is fault phase.Inject high-voltage 80Hz AC signal into fault phase, 10-15 meters away from overhead line (measurement value of device is larger within this distance), handheld 80Hz signal detector and the line to keep vertical along the line, can use 1/2 method of step detection, when measurement value is greater than 100, detector will emit sound and light alarm, fault point is downstream.When measured value is less than 100, detector does not send an alarm signal, and fault point is upstream.When detector is vertically close to fault rod, measurement value is greater than 300, detector will issue an audible and visual alarm.When detector and fault rod are vertically away from fault rod about 15 meters, measurement value is less than 100, detector will not issue an alarm signal, so as to determine the point as fault point.
When there is interference in field electromagnetic environment, the line branch is long (or grounding transition resistance is large), and fault branch cannot be distinguished by 80Hz signal, the 22Hz AC signal is injected into fault line instead, and 22Hz is a low-frequency signal with strong anti-interference ability.Current clamp meter is stuck phase by phase on the branch phase of line, and only fault phase will generate AC signals.When current value displayed on signal receiver is consistent with output value on signal source, the fault branch is determined.Then change high-voltage 80Hz AC signal to find fault path.The fault location can be determined after several judgments.

Conclusions
This paper introduces off-line location strategy of single-phase grounding fault of distribution line, analyzes parameters and equivalent circuit of distribution line, and determines size and frequency of injected AC signal.Based on three control technologies, a portable frequency modulation small current signal source is developed.Finally, through analysis of noise correlation and adaptive morphological filtering, signal detector is developed and its working principle is expounded.Compared with previous offline positioning technology, this strategy can accurately find fault point.

Figure 3 .
Figure 3. Schematic diagram of basic principle of portable frequency-adjustable small current signal source.

Figure 1 .
Lossless transmission line equivalent circuit.