Research on earth surface potential distribution and amendment for soil resistivity horizontal hierarchical model in current inflow test.

1. Introduction

With the development of high-voltage direct current (HVDC), the increase of ground current exacerbates the problem of direct current (DC) bias in converter stations and substations remarkably (Calixto et al. 2010; Calixto, Nobre, and Alves 2015; Calixto et al. 2010). For instance, HVDC projects in Zhexi and Tianzhong caused the DC bias current of the nearby transformers to reach beyond the standard value in its debugging stage, which can threaten the operating safety of power grid when the DC bias current is seriously exceeded (Calixto et al. 2012; Dawalibi and Blattner 1984;He, Jiang, and Zhou 2007;Hao, Yu, and Zhang 2009). In this case, an accurate SRHHM is needed when selecting the site of the DC grounding to inhibit grounding electrode current which can effectively avoid DC bias.

At present, researchers mainly use the numerical calculation method to inverse the SRHHM (Liu, Cui, and Sun 2009;Liu,Yan, and Ma 2016; Lu, Wen, and Lan 2010). From the view of physics, the nature of inversion for soil parameters is the inverse problem of electromagnetic fields (Lu, Xiao, and Mao 2006). From the perspective of mathematics, the inversion of soil parameters in the N horizontal layer is the optimisation for 2N-1 variables, including soil resistivity of N layer and layer depth of N-1 soil layer. First, the apparent resistivity of different spacings between electrodes is measured by Wenner four-probe method. Then, the non-linear objective function is used to transform the solution problem of the soil parameters into the extreme value problem of the objective function. Finally, an optimisation method (Liu and Ma 2015; Jiangtao, Zhicheng, and Keji 2015; Ling, Jiangtao, and Xiaoku 2014; Ling, Bichuan, and Jiangtao 2015;Xu, Wen, and Shu 2004) is applied in the inversion for parameters of the soil resistivity layer model (Yongming, Xingmou, and Tao 2012;Yongjun,Qi, and Zhiyuan 2014; Zeng, Zhang, and Zhao 2009; Zhao, Liu, and Cheng 2010). However, the inversion algorithm is mainly based on theoretical calculations, and its results must be verified through experiments in practical project.

Therefore, some domestic researchers verify the SRHHM using the current inflow test, and the main way of which is to amend the model based on the ESP distribution. Currently, literature that uses the current inflow test to detect the SRHHM is rare. However, the effect of soil resistivity on ESP distribution in the single pole operation ofHVDC is similar to this work. Ji-ming Lu, etc. from Huazhong University of Science and Technology have analysed the effects of soil resistivity on ESP with multi-layer soil models. The results show that the ESP decreases rapidly near the ground electrode and the downward trend of which decreases with the increasing distance. The resistivity of the surface layer and high resistivity layer in the underground has a great influence on the ESP distribution (Zou, Yao, and He 2016). Zhiguo Hao, etc. from Xi'an Jiaotong University have established the two-layer and four-layer soil resistivity models through the ANSYS software. Their results show that the layered structure of soil resistivity do have a lot of impacts on the ESP distribution, and a more accurate calculation value can be obtained by using a multi-layer soil resistivity model (Zhang, Cai, and Wen 2014). Ling Ruan, etc. from Hubei State Grid Electric Power Research Institute have adopted the magnetotelluric method to measure the deep-layer soil resistivity and have got the DC grounding electrode resistance by comparing the 5-layer horizontal soil resistivity model to the 15-layer one. It turns out that only by taking the shallow soil resistivity instead of the actual one will cause obvious deviation of the ESP (Zhang, Xiang, and Chen 2014). In addition, Lianguang Liu etc. from North China Electric Power University also have established a multi-layer soil resistivity model. Their study findings show that the soil resistivity near the pole site has a great influence on the grounding electrode resistance and step voltage (Zhang, Zhou, and Zhong 2011).

Based on actual cases, this paper uses the ANSYS software to establish the SRHHM and explore the ESP distribution. Finally, this paper proposes a basic amendment method for the model whose validity is verified in actual project cases.

2. Actual current inflow test and simulation model

Current inflow test is a method to verify the accuracy of the SRHHM and to amend SRHHM by measuring the ESP distribution produced by the ground current. This test includes two parts: the actual current inflow test and the simulation fitting.

In the actual current inflow test, an inflow electrode is first buried at the site of the DC ground electrode. Meanwhile, an auxiliary electrode is buried a significant distance away from the inflow electrode. Then, DC power supply is loaded between the inflow electrode and the auxiliary electrode. Finally, the ESP distribution is measured on some certain paths under the DC load. Figure 1 shows the schematic diagram of Current Inflow Test.

The inflow electrode is generally a circle with the radius of 5 m using four insulated wires symmetrically connected to the electrode. The distance between the inflow electrode and the auxiliary electrode is set to 10 km, and the measuring path is mainly along the connection direction of the two electrodes from the inflow electrode to the zero potential point. Due to the high potential near the inflow electrode and the low potential near the zero potential point, the measuring points of ESP distribution are mainly concentrated near the inflow electrode.

In the simulation fitting, a preliminary SRHHM is initially determined on the basis of the measured resistivity. Then the ESP distribution is simulated and compared with the measured data in the actual current inflow test. Finally, the resistivity of each layer is amended to make the simulation results consistent with the test one. Yet until now, there exists no standard way for the amendment of the SRHHM in the current inflow test, which leads to certain blindness in the simulation fitting.

2.1. Actual current inflow test

This paper takes the related data from Hunan Substation Grounding Project as a case study, and all the measurement data derive from Wuhan NARI Limited Company, State Grid Electric Power Research Institute, Wuhan, China. The Wenner four-probe method and Magnetotelluric method are adopted to measure the soil resistivity in the shallow layer (0-1 000 m) and the deep layer (1 000 m-[infinity]), respectively, and the measured results are shown in Table 1. Furthermore, a preliminary SRHHM is achieved (Figure 2).

The inflow electrode in the actual current inflow test is a ring-shaped horizontal electrode with the diameter of 10 m which is made by round steel. Four insulated wires are used to symmetrically connect with the ring-shaped electrode and lead out to the ground. The electrode is buried in approximately 1 m in depth. The auxiliary electrode adopts 10 copper clad steel electrodes with the diameter of 38 mm. The circuit between the two electrodes is an insulated wire with a cross-sectional area of 4 [mm.sup.2] and a length of 10 km. The test uses DC power supply with the output voltage of550 V and output current of approximately 5 A. Figure 3 is the path of the actual current inflow test in Yi'an Chong electrode site.

During the test, a high internal resistance digital multi-metre and a pair of copper-copper sulphate electrodes are used to measure the ESP. In the measurement, one electrode is fixed at the potential reference point which is normally the inflow elec-trode itself or the soil right above the inflow electrode. The other electrode moves point by point radially along the direction from the inflow electrode to the zero potential point. The potential of each measuring point should correspond precisely with the distance and the inflow current. The ESP distribution obtained from the measurement data is shown in Table 2.

2.2. Simulation model

In this paper, the ANSYS software is used to establish the simulation model of the actual current inflow test, which belongs to the steady current field analysis.

The most difficult part of the simulation in this model is the large geometric size. The distance between the inflow electrode and the auxiliary electrode is 10 km in the above-mentioned current inflow test. The geometric size of the ground surface in the model must be larger than this distance. Considering the computational accuracy, the surface area takes a square of 40 kmx40 km. Depth direction is theoretically infinity while the simulation model takes twice of the four layers, that is, 180 km. Because the simulation model is symmetrical about the connection between the inflow electrode and the auxiliary electrode, the model can be simplified to 1/2 model and the geometry size can be reduced to 40 km x 20 km x180 km. Assuming that the average size of the mesh is 100 m x 100 m x 100 m, then the total number of elements should be 1.44 x [10.sup.8].The model with so many elements is difficult to calculate, and it is necessary to simplify the finite element model.

The current inflow test mainly focuses on the ESP distribution between the inflow electrode and the zero potential point, where the zero potential point is usually at the midpoint of the inflow electrode and the auxiliary electrode. Assuming that the auxiliary electrode is a thin-walled cylindrical electrode with the centre of the inflow electrode, and the radius of the distance between the inflow electrode and the auxiliary electrode, then the finite element model can be simplified as a two-dimensional axisymmetric model. The model is symmetrical about the central axis of the inflow electrode. The current injected into the inflow electrode and auxiliary electrode is set as 5 A and -5 A, respectively. The distance between the two electrodes is set as 10 km. The boundary conditions of the model are shown in Figure 4(b), and the material property of the model is shown in Table 1. With the same model and mesh size, the number of elements can be reduced to 3.6 x [10.sup.4]. Besides, the degree of freedom of the two-dimensional model is also reduced, making the calculation greatly simplified.

To verify the reasonableness of the simplified model, a three-dimensional model and a two-dimensional axisymmetric model with the geometry of 40 km x 20 km x 40 km are, respectively, established for the current inflow test. The finite element model is shown in Figure 4. In the three-dimensional model, the size of the minimum element is 5 m x 5 m x 10 m while the size of the maximum element is 100 m x 100 m x 1000 m, and the total number of elements is 176 000. In the two-dimensional model, the minimum mesh size is only 0.95 m x 0.5 m yet the total number of elements is 59 000. These two kinds of models are then simulated by the same computer. The simulation time needed of the two-dimensional axisymmetric model is much shorter than that of the three-dimensional model. The ESP distribution calculated by the two models is shown in Figure 5. It can be seen that the ESP curves of the two models are approximately the same in the interval between the inflow electrode and the zero potential point (0-5 000 m). However, because the meshes of the three-dimensional model are coarser, the ESP distribution is not very smooth and the calculation error is greater. In the interval between the auxiliary electrode and the zero potential point (5 000-10 000 m), the ESP distribution of the three-dimensional model is opposite to that of the first half. Since the potential of the two-dimensional axisymmetric model is obtained through the hypothesis that the auxiliary electrode is a thin-walled cylindrical electrode, the results of this interval do not make sense and can be disregarded. Based on the above analysis, the simplified two-dimensional axisymmetric model is used to simulate the current inflow test in this paper.

3. Effect of soil resistivity on earth surface potential distribution

Soil resistivity directly affects the ESP distribution around the inflow electrode. In order to find the amended method for SRHHM to better match the measured data with the current inflow test, the ESP distribution with different SRHHM is studied. The initial model comes from Hunan Substation Grounding Project. Based on the measurements, the soil is horizontally stratified with five layers and the soil resistivity and depth of each layer are shown in Figure 2. To analyse the effect of the soil resistivity of each layer on the ESP distribution, the soil resistivity of one layer is changed and that of the other layers stays the same.

3.1. Effect of soil resistivity of first layer on earth surface potential distribution

Keep the soil resistivity of the other layers unchanged and setthatofthe first layer as 0.01 * [[rho].sub.1] (2.4[OMEGA] * m), 0.1 * [[rho].sub.1] (2.4[OMEGA] * m), [[rho].sub.1] (2.40[OMEGA] * m), 10 * [[rho].sub.1] (2.400[OMEGA] * m), and 100 * [[rho].sub.1] (2.4000[OMEGA]*m), respectively. Figure 6 presents the effect of the soil resistivity of the first layer on the ESP distribution. The results show that the smaller the soil resistivity is, the smaller the maximum potential is. Having little effect on the ESP in the region farther than 500 m away from the inflow electrode, soil resistivity of the first layer is more influential in the region within 500 m. The maximum potential is always near the inflow electrode. At this point, the soil resistivity of the first layer will then have a great influence on it. For instance, the maximum potential of 0.01 * [[rho].sub.1] model is 0.01% of that of 100 * [[rho].sub.1] model. Based on this, it is suggested that the current inflow test should measure the maximum potential accurately, and the simplest and most effective approach is to select the inflow electrode as the potential reference point for measurement.

3.2. Effect of soil resistivity of second layer on earth surface potential distribution

Keep the soil resistivity ofthe other layers unchanged and setthatofthesecond layeras0.01 * [[rho].sub.2] (38.44[OMEGA] * m), 0.1 * [[rho].sub.2] (38.404[OMEGA] * m), [[rho].sub.2] (38.44[OMEGA] * m), 10 * [[rho].sub.2] (38.440[OMEGA] * m), 100 * [[rho].sub.2] (38.440[OMEGA] * m), respectively. Figure 7 presents the effect of soil resistivity of the second layer on ESP distribution. The results show that the soil resistivity of the second layer also has a certain impact on the maximum potential, but the effect is far less obvious than that of the first layer. For example, the maximum potential of 0.01 * [[rho].sub.2] model and 0.01 * [[rho].sub.3] (1748.10[OMEGA] * m), 100 * [[rho].sub.3] (17481000[OMEGA] * m) model is only of a difference of 6.36%. The soil resistivity of the second layer mainly affects ESP within the region of 3000 m.

3.3. Effect of soil resistivity of third layer on earth surface potential distribution

Keep the soil resistivity of the other layers unchanged and set that of the third layer as 0.01 * [[rho].sub.3] (1748.10[OMEGA] * m), 100 * [[rho].sub.3] (17481000[OMEGA] * m), respectively. Figure 8 presents the effect of the soil resistivity of the third layer on ESP distribution. Although the soil resistivity of the third layer has little effect on the absolute value of the potential, the relative difference of the ESP is large at the far end of the inflow electrode (L > 4 000 m). The potential of 0.01 * [[rho].sub.3] model at 4 000 m is only 75% of that of the 100 * [[rho].sub.3] model. Apparently, with the increase of depth, the effect of soil resistivity on ESP distribution continues to wane. The simulation result shows that the soil resistivity of the fourth and fifth layers cannot be taken into consideration.

4. Amendments for soil resistivity horizontal hierarchical model

Through a large number of simulation analysis, the following basic rules are summarised. First, the surface (within the depth range of approximately 0 ~ 0.1 * Lzf) soil resistivity has a great impact on the maximum ESP, and the relation between the soil resistivity and the maximum ESP is approximately linear. Second, the sublayer (within the depth range of approximately 0.1 * Lzf ~ Lzf) soil resistivity mainly affects the ESP within the region of L < 0.6 * Lzf. Third, the middle-layer (within the depth range of approximately Lzf ~ 5 * Lzf) soil resistivity has a certain effectonthe ESPinthe regionof 0.8 * Lzf <L <Lzf. Fourth, the deep-layer (within the depth range of approximately 5 * Lzf ~ [infinity]) soil resistivity almost has no effect on the ESP.

Based on the aforementioned rules, some basic ideas about how to amend SRHHM is proposed. First, make the calculated maximum ESP consistent with the measured one by the current inflow test through amending the surface soil resistivity. Then, make the calculated potential distribution curve in accordance with that obtained by the current inflow test as far as possible by amending the sub-layer soil resistivity. Finally, if the relative difference of the ESP in the region of 0.8 * Lzf <L <Lzf is larger than needed, the mid-layer soil resistivity can be adjusted but there is no need to make amendments for the deep-layer soil resistivity.

Figure 9 shows the ESP distribution in Yi'an Chong electrode site. It can be observed that the calculated maximum ESP is higher and the decay rate of the calculated ESP near the inflow electrode is relatively slower. Based on the foregoing basic ideas, the surface soil resistivity should be reduced due to the higher maximum ESP. In addition, the sub-layer and middle-layer soil resistivity also need to be amended to make the decay curve substantially consistent with the measured results. Meanwhile, considering that the surface soil resistivity has the greatest impact on ESP distribution and the depth range of the existing first layer is relatively uncertain, so the first layer is divided into two layers in accordance with the upper interface and under interface mentioned in Table 1.Itis ensured that the equivalent soil resistivity of the two layers is not quite different from the initial first layer. Table 3 shows the SRHHM before and after the amendment. Figure 9 also shows the amended ESP distribution in Yi'an Chong electrode site. The results show that the amended data can better fit the measured ESP distribution.

5. Conclusion

In response to the problems existing in the amendment for the soil resistivity horizontal hierarchical model, a two-dimensional axisymmetric finite element model is built in this paper. Combining with the engineering cases, the conclusions may be drawn as follows:

(1) Surface (within the depth range of approximately 0 ~ 0.1 * Lzf) soil resistivity has a large impact on the surface maximum potential, and it is approximately proportional to the surface maximum potential within a certain range. Therefore, the surface soil resistivity must be noted when amending a soil resistivity horizontal hierarchical model, and it can be divided into several layers if possible.

(2) Deep-layer (within the depth range of approximately 5 * Lzf ~ [infinity]) soil resistivity almost has no effect on the Earth surface potential, so the current inflow test can not amend the soil resistivity in this area.

(3) Basic ideas of amendments for soil resistivity horizontal hierarchical model are presented. First, amend the surface soil resistivity to make the calculated maximum Earth surface potential consistent with that measured by the current inflow test. Then, make the earth surface potential distribution curve in accordance with the current inflow test curve as far as possible through amending the sub-layer soil resistivity. If the earth surface potential relative differences is larger than needed in the region of 0.8 * Lzf <L <Lzf, the mid-resistivity soil resistivity is adjusted. No amendments will be made to the deep-layer soil resistivity.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant number 51507092) and Research Fund for Excellent Dissertation of China Three Gorges University (Grant number 2018SSPY060). The authors thank Bairong Song from School of Foreign Languages, China Three Gorges University for her language translating work and Alan Treworgy from Lewiston, Maine, USA, for his language revision advice.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by the National Natural Science Foundation of China [Grant number 51507092]; Research Fund for Excellent Dissertation of China Three Gorges University [Grant number 2018SSPY060]

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Li Qiu (a,b), Liyang Huang (a), Yao Xiao (c), Pan Su (a), Jie Yang (d), Bin Peng (e), Qi Xiong (a,b), Xiwu Zhao (f) and Changzheng Deng (a)

(a) College of Electrical Engineering & New Energy, China Three Gorges University, Yichang, China; (b) Hubei Key Laboratory of Cascaded Hydropower Stations Operation & Control, China Three Gorges University, Yichang, China; (c) Changchun Electric Supply Company, Changchun, China; (d) State Grid Electric Power Research Institute, Wuhan NARI Limited Company, Wuhan, China; (e) State Grid Hunan Maintenance Company, Changsha, China; (f) State Grid Shangrao Power Supply Company, Shangrao, China

CONTACT Pan Su [??] 2992528544@qq.com [??] College o( Electrical Engineering & New Energy, China Tnree Gorges Unwersrty, Yichang, China

ARTICLE HISTORY

Accepted 28 April 2018

KEYWORDS

Current inflow test; earth surface potential; soil resistivity horizontal hierarchical model; finite element analysis

https://doi.org/10.1080/1448837X.2018.1473010
```Table 1. The preliminary measurement data of the soil resistivity in
Yi'an Chong electrode site.

Depth of each soil layer
Upper interface              Under interface
Range (km)     Average (km)   Range (km)      Average
(km)

First layer   Earth surface  Earth surface   0.158-0.274     0.214
Second layer   0.158~0.274    0.214          1.945-3.561     2.568
Third layer    1.945-3.561    2.568         36.004-54.001   46.60
Fourth layer  36.004~54.001  46.60          90.000-91.994   90.668
Fifth layer   90.000-91.994  90.668         [infinity]     [infinity]

Average         Average resistivity
thickness (km)  ([OMEGA].m)

First layer     0.214               240
Second layer    2.354             3 844
Third layer    44.032           174 810
Fourth layer   44.068            35 428
Fifth layer   [infinity]          7 965

Table 2. Earth surface potential measurement data in Yi'anchong pole
site.

Disthance L (m)      6         7         8         9         10

Potential U (V)     22.32      19.67     17.61     16.09     14.8
Disthance L (m)     20         30        50        70       100
Potential U (V)     10.4        8.97      7.34      6.84      6.01
Disthance L (m)    200        300       500       700     1 000
Potential U (V)      4.2        3.22      2.04      1.73      1.24
Disthance L (m)  2 000      3 000     4 000     5 000
Potential U (V)      0.81       0.19      0.06     0

Disthance L (m)     15

Potential U (V)     11.75
Disthance L (m)    150
Potential U (V)      4.96
Disthance L (m)  1 500
Potential U (V)      0.88
Disthance L (m)
Potential U (V)

Table 3. Soil resistivity horizontal hierarchical model before and
after the amendment.

Depth of each          Soil resistivity
soil layer (km)         ([OMEGA]*m)
Preliminary   Amended     Preliminary    Amended
model         model       model          model

First Layer   0.214       158              240          130
274                           500
Second        2.568         2.568        3 844        4 228
Layer
Third        46.60         46.60       174 810      174 810
Layer
Fourth       90.668        90.668       35 428       35 428
Layer
Fifth        [infinity]    [infinity]    7 965        7 965
Layer
```
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