INTRODUCTION
Most of mediumvoltage distribution network lines in China are overhead lines and more than 80% of faults originate from the singlephase short circuit fault (Hanninen and Lehtonen, 1998). When singlephase earth fault occurred in small current grounding system, line voltage remains symmetrical and does not affect the normal use of electricity users. However, the nonfault phasetoground voltage would be increased to the times the original. Under the special condition, the grounding capacitive current might cause the fault point across, produce instantaneous over voltage, lead to the insulation breakdown and it is likely to be expanded to 2phase or 3phase short circuit which could greatly decrease the safety and reliability of distribution network.
Years of research by many experts at home and abroad, the location method based on the differences among used signal is mainly divided into the active method and passive method. Passive method, as the primary research method, includes impedance method (MoraFlorez et al., 2008), traveling wave method (Tao, 2012) and the steady zerosequence reactive power direction method (Zhang et al., 2008). But each method has limitations in practical application: Impedance method is likely to be influenced by many factors such as circuit and system operation mode and has a relatively simple application; traveling wave method is not suitable for distribution lines which are of complicated structure and many branches; the steady zerosequence reactive power direction method is not applicable to neutral grounded though arc suppression coil. In recent years, some scholars have tried to adopt mathematical analysis tool to fault location in small current grounding system, such as the wavelet transform (Pang et al., 2007) and mathematical morphology (Ren et al., 2008). Because of the weakness fault current, unstable arc when the ground fault occurs and the limitations of the methods used, the lack of theoretical basis, the small current grounding fault location has not been effectively resolved.
In this study, by means of calculating the maximum value of the correlation coefficient, improving the correlation coefficient and threshold based on the correlation analysis theory, this method has eliminated the calculation error due to asynchronous data acquisition from feeder terminal unit and easily solved the key technology problem of the field application. A large number of ATP simulations demonstrate that, this adaptive correlation analysis method has raised the accuracy of the fault location and meet the practical requirements to a great extent which is immune to various neutral point operation modes, different fault inception angles and different grounding resistance.
MATERIALS AND METHODS
The previously published studies on the correlation coefficient may not be suitable for fault location because of its disadvantages of the algorithm. The characteristics of transient zeromode power was briefly introduced here when singlephase earth fault occurred in small current grounding system. Then the adaptive location algorithm is proposed based on the correlation coefficient.
Description of the characteristics of transient zeromode power: Since the threephase system is influenced by the electromagnetic coupling between phases, mutual inductance and distributed capacitance, it is necessary to adopt Karrenbaur transform (Yan et al., 2014) to threephase system which can be changed as a noncoupling modular field for the suppose of calculating the zero mode power. When the neutral noneffectual grounded system is in fault, the system will generate transient zeromode signal and produce a virtual voltage source in the fault point (Wang et al., 2012), as shown in Fig. 1. Tian et al. (2010), stated that owing to the influence from the voltage source to the fault line, the transient zeromode power signal from fault point to the bus bar terminal flows from N to M which has a low resonant frequency and a large signal amplitude and it is equal to the sum of other healthy lines’ transient zeromode power; the transient zeromode power signal from the fault point to the load terminal flows from P to Q which has a high resonant frequency and a small signal amplitude.

Fig. 1:  Equivalent circuit of zeromode network 

Fig. 2(ac): 
Zeromode powers (a) M and N, (b) N and P and (c) P and Q in healthy section and faulty section, waveform 
From Fig. 2, when singlephase ground fault occurs in the NP section, the two ipsilateral adjacent detecting points have small power amplitudedifferences, consistent initial polarity and high waveform similarity, while the differences of the amplitude between the two detection points on both sides of the fault point is large and the initial polarity is opposite with a low waveform similarity.
Method of location algorithm based on correlation coefficient of transient zeromode power
Initial scheme of fault location: The correlation analysis theory is selected to reflect the characteristics of the transient zeromode power (Tian et al., 2011). Zeromode power of every two adjacent detection points in the fault line is expected to be used as a sample signal to calculate the correlation coefficient; therefore, the correlation coefficient equation is as follows:
where, p_{01} (n) and p_{02} (n) are, respectively transient zeromode power of the adjacent two detection points; n is the sampling sequence and n = 0 indicates that the fault occurs; N1 is the length of data window of power. In general, threshold value of the correlation coefficient σ is 0.7 or 0.8. If ρ<σ, it is decided as the fault section; if ρ<σ, it is decided as the healthy section (Tian et al., 2011).
The initial scheme of locating algorithm based on the correlation coefficient of transient zeromode power has the following disadvantages by Eq. 1.
The extracted power signal must be synchronized but there exists time error between each measuring device.
The imperfect correlation coefficient criterion might not determine fault point accurately, without taking consideration of the situation when correlation coefficient is negative, i.e., when ρ is negative and ρ<σ, as the ground fault occurs, it is prone to misjudgment.
Ignoring the certain distribution system where the downstream line of fault point is long and the situation that the difference of amplitude and resonant frequency of transient zeromode power on both sides of fault point is small. Hence, it is needed to improve the correlation coefficient equation and the improving measures are as follows.
Synchronous signal processing: In order to avoid time error caused by the two detection points, it is necessary to adopt bidirectional waveform translation method to obtain the maximum correlation coefficient; correspondingly, the computational equation of the maximum correlation coefficient is as follows:
where, n_{0} is the translation point number of the largest correlation coefficient; f is the sampling frequency of signal; Δt is time error caused by the master station of distribution network, n_{0} ∈ [f.Δt, f.Δt+1, ..., 0, 1, ..., f.Δt]. By means of bidirectional movement, calculating the maximum value of the correlation coefficient can effectively solve the asynchronous signal problem caused by the inconsistent initial time of the signal acquisition of transient zeromode power. With regard to the two signals that have different starting time and similar waveforms, one characteristic signal should be regarded as the reference signal and the other should be translated point by point. Calculating correlation coefficient for different translation points and the larger the correlation coefficient value is, the better overlap of two waveforms have, with the smaller difference of initial time. The two signals can be regarded as synchronization when value of the correlation coefficient is the largest. As for the similarity of the two signals is very low, by means of bidirectional movement, the maximum correlation coefficient is almost close to zero which meets the principle of relative positioning as usual.
Correction of correlation coefficient and threshold: A reliable and effective correlation coefficient fault criterion should widen the gap between the fault section and the healthy fault section, reduce the correlation coefficient effectively. In order to reflect similarity of zeromode power waveform more precisely, the amplitude of zeromode power can be taken into consideration. With the introduction of the amplitude, the correlation coefficient calculation result is prone to be greatly improved and the improved equation is as follows:
In this equation, amplitude difference of zeromode power measurement is very small for the two ipsilateral adjacent detecting points (generally, ρ_{max}>0.9); therefore, measurement about the sum of the amplitude has tiny differences within the time sequence of samples. While the amplitude difference of zeromode power measurement varies widely for the two adjacent detection points on both sides (generally, 1≤ρ_{max}≤0.2), therefore, measurement about the sum of the amplitude has big differences within the time sequence of samples. Even in the distribution system whose downstream of the fault point has a long line and in the special situation of high waveform similarity of the two sides of the detecting point, it’s verified by experience that the introduction of zeromode power amplitude can still effectively decrease the correlation coefficient of the adjacent two detection points.
The threshold can be adaptively set according to the correlation coefficient of each section in the fault lines and the equation is as follows:
where, σ_{ij} is the correlation coefficient of each section, N is the total number of fault line sections. If σ_{ij}≥σ_{T}, it is decided as the healthy section; otherwise, it is decided as the fault section. The value of the correlation coefficient threshold σ_{T} is based on σ_{th}, the rules are as follows:
• 
If σ_{th}<0.2, then σ_{T} = 0.2 
• 
If 0.2≤σ_{th}≤0.6, then σ_{T} = σ_{th} 
• 
If σ_{th}>0.6, then σ_{T} = 0.6 
RESULTS AND DISCUSSION
Experiment results and analysis: The small current grounding system model simulation, analysis and comparison location algorithm was proposed above.
Small current grounding system model: Utilizing the model built by ATP with small current to ground system to verify the validity of the method in this study and it was shown in Fig. 3. The line is composed of six lines L_{1}∼L_{6} and the length of them are 20, 15, 24, 8, 16 and 30 km, respectively. The fault occurs on the 10 km position of the line 1, four detection devices of A, B, C and D are installed at the 8.5, 9.5, 10.5 and 11.5 km, respectively. Distributed parameter model was adopted to simulate the practical lines (Zhang et al., 2007) and the positive sequence impedance is: z_{1} = 0.17+j0.38 Ω km^{1}; positivesequence conductance to ground is: b_{1} = 3.045 μs km^{1}; zerosequence impedance is z_{1} = 0.23+j1.72 Ω km^{1}; zerosequence conductance to ground is b_{1} = 1.884 μs km^{1}. Line equivalent load impedance of No. 1 and No. 3 is Z_{L} = 400+j120 Ω. The transformer is in the shape of Y/Y_{0} connection and rated capacity of the transformer is 40 MVA; primary voltage is 220 kV; secondary voltage is 35 kV; noload losses 35.63 kV; inductance is 0.183 Ω; steadystate magnetizing current is 0.672 A; main magnetic flux is 202.2 wb; magnetizing impedance is 400 kΩ; a winding leakage impedance is 0.4 Ω; secondary winding leakage impedance is 0.006 Ω. As more than 80% fault originate from the singlephase short circuit fault, it is necessary to take the simulation of Aphase to ground fault for an example. According to the model built by ATP, the capacitive current is larger than 20 A and the arc suppression coil should be added to this system.

Fig. 3:  Model of small current grounding system 

Fig. 4:  Waveform of transient zero mode power of data window selected 
The sampling frequency is 10^{6} Hz and the data window length of oneforth of power frequency cycle (5 msec) is selected to simulate. The basic condition of the simulation are as follows: Inception phaseangle is 0° and the grounding fault occurs in the NP section; grounding resistance is 5 Ω; the detuning is 8%; the simulation step is set as 1 μsec; the singlephase short circuit time is 0.01 sec; the time of termination is 0.1 sec. The waveform of transient zero mode power in 5 msec is shown in Fig. 4.
The data acquired by the simulation is processed by MATLAB and then calculates that the original correlation coefficients ρ_{mn} = 0.9990, ρ_{np} = 0.1083, ρ_{pq} = 0.9425, the amended correlation coefficients σ_{mn} = 0.9980, σ_{np} = 0.1379, σ_{pq} = 0.8951 and the threshold σ_{T} = 0.5851. Therefore, it’s determined that the fault section is in the NP section and the positioning result is correct.
Now on the condition of given different transition resistance and the initial phase angles of voltage are 0°, 30°, 60° and 90°, calculating the correlation coefficients before and after the correction and the results are shown in Table 1.
Analysis of algorithm results compared to previously published studies: According to Tian et al. (2011), the correlation analysis theory taking advantage of the transient zeromode power is selected to locate the fault section, however, there are some errors applied to various neutral point operation modes. The reasons are as follows.
In Table 1, the correlation coefficient of transient zeromode power such as ρ_{mn} and ρ_{pq} is positive and all larger than 0.9, while the correlation coefficient of transient zeromode power between the two adjacent detection points on both sides such as ρ_{np} is negative, or positive in some cases. If the criterion threshold is taken as 0.7, under the initial phase angle of 30°, ρ_{mn}and ρ_{pq} are both greater than 0.7, besides, ρ_{np} is less than 0.7, so the fault section can be determined accurately. However, the correlation coefficient of the fault section (NP) under 30°, 60°, 90° is positive or negative but ρ_{np} is larger than 0.7 sometimes, at this time, the fault section can be misjudged. When the transition resistance is 200 Ω in Table 1, the value of ρ_{np} varies from 0.79240.4627 which makes significant differences between the two adjacent detection points on both sides, further widens the gap between the fault section and the healthy fault section. Meanwhile, the threshold is adaptively set as 0.6000 according to each section of faulty line No. 1. ρ_{np} before correction is 0.7924 when σ_{T} is taken as 0.7, so the previous studies published above can not effectively determine the fault section.
Based on the above analysis, it’s possible to misjudge the fault section by the previous studies published above in various neutral grounding systems from the data of Table 1. After the synchronization of signal processing, the improvement of the correlation coefficient and the threshold, this method can improve the accuracy of fault section location for not only different inception phase angles but also various transition resistances.
CONCLUSION
In this study, a novel fault location method of small current grounding is proposed on the basis of adaptive correlation analysis and the method has modified the original correlation coefficient and threshold of the transient zeromode power signals on both sides of the detection point. A large number of simulation experiments show that the method could be applied extensively, hardly be affected by the structure of the system and the neutral point grounding mode and can effectively adjust the fault criterion by using DA system which greatly improves the correct rate of location and lays a good foundation for the research and practical application of fault location in small current grounding system.
ACKNOWLEDGMENTS
The project is supported by The National Natural Science Foundation of China (No. 51374072) and The Science and Technology Research Projects of Heilongjiang Province Educational Committee, China (No. 12531062).