Optimal Design of Grounding System Considering the ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005

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Optimal Design of Grounding System Considering the Influence of Seasonal Frozen Soil Layer Jinliang He, Senior Member, IEEE, Yanqing Gao, Student Member, IEEE, Rong Zeng, Member, IEEE, Weimin Sun, Jun Zou, and Zhicheng Guan

Abstract—Frozen soil leads to the change of the soil model. This would affect the safety of the grounding system. The design of the grounding system considering the seasonal frozen soil should be based on the full investigation of the actual maximum depth of the frozen soil and the actual layered soil models. The final design scheme of the grounding system should be determined synthetically from two phases–first, the grounding system is designed in the normal soil model and its safety is checked in the frozen soil model, second, it is designed in the frozen soil model and its safety is checked in the normal soil model. The influences of the frozen soils on the optimal design of grounding systems in homogeneous and double-layer soil models were systematically analyzed, and the respective design methodologies of the grounding systems were proposed. The influence of vertical electrodes on the design of the grounding system considering the seasonal frozen soil was discussed. The analyzed results state that the safety of grounding system can be sufficiently improved by vertical grounding electrodes added to the horizontal grounding grid. Index Terms—Frozen soil, grounding resistance, grounding system, optimal design, safety, step voltage, touch voltage, vertical grounding electrode.

I. INTRODUCTION

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HE GROUNDING system of the substation should ensure the safe and reliable operation of power systems, and guarantee a human being’s safety in the situation of grounding fault in the power system [1]. The safety of power apparatus in the substation can be reached by decreasing grounding resistance and grounding potential rise of substations; but the safety of people must be reached by equalizing the potential distribution on the ground surface and reducing step and touch voltages. How to equalize the potential distribution of the ground surface above the grounding system is very important, which is the key to ensure the safety of the grounding system for substations. The optimal design of grounding systems for substations can ensure the equalization of the potential distribution of the ground surface above the grounding system, and can obviously improve the safety of the grounding system [2]–[7]. Sverak [6] first proposed the idea of unequal span arrangement among all grounding conductors of the substation grounding system. Sun et al. discussed the optimal design of the grounding system in the nonuniform soil model [7].

The optimal design of the grounding system is based on the actual soil models. But the soil resistivity changes in different seasons. In the frozen season, the resistivity of the frozen soil increases to several to ten times that in normal season, which is measured in the range from 1000 to 15 000 m. The thickness of the frozen soil is about 1 to 2 m in North China, but can reach about 4 to 6 m in Northeast China. The frozen season would strongly affect the safety of the grounding system as discussed in [8]. The influence of seasonal factors on the safety of the grounding system was analyzed in detail in [8]. The frozen season would change the soil model, the homogeneous soil would become a two-layer soil in the frozen season, and a double-layer soil model would still be a double-layer soil model, or become a three-layer soil model. Perhaps a grounding system safely designed according to the normal soil model would not be safe in the frozen season. But the influence of the frozen soil on the optimal design of the grounding system has not been found in literature. The design methodology of grounding system considering the influence of the frozen soil was systematically analyzed by the numerical method with CDEGS software of SES Co. [9] in this paper. II. OPTIMAL DESIGN PRINCIPLE OF GROUNDING SYSTEM The so-called optimal design of grounding systems for substations is to suitably arrange the conductors of grounding systems to equalize the leakage current distribution and the potential of ground surface; this would ensure making all grounding conductors sufficiently utilized and to decrease step and touch voltages. As shown in Fig. 1, the grounding conductor arrangement with exponent regularity is obviously reasonable. This arrangement not only decreases potential gradient of the ground surface, but is also certified as a safe and economic design method. The key problem is how to determine the exponent regularity. As shown in Fig. 1, when the grounding conductors are arranged according to an exponent regularity, the conductor span decreases gradually from the center to the side of the grounding grid. The th conductor span from the center is to

Manuscript received May 6, 2003; revised September 13, 2003. Paper no. TPWRD-00222-2003. The authors are with the Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]; gaoyq@ mails.tsinghua.edu.cn; [email protected]; [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TPWRD.2004.835434

(1)

is defined as the compression ratio, which is constant, , if , then the grounding grid is designed of with an equal conductor span. If the conductor number ; if is grounding grid in one side is even, then . odd, then where

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Fig. 2.

Fig. 1. Grounding grid scheme arranged with exponent rule.

If the side length of the grounding system is , and conductors are arranged in one side, then the central conductor span is is even is odd

(2) (3)

There are two central conductor spans if the conductor number of the grounding grid in one side is odd. According to the above definition, when the side length of the grounding grid and the conductor number are determined; if we select a compression ratio , the central conductor span can be calculated by (2) or (3), and the conductor span between any two grounding conductors in a side of the grounding grid can be calculated by (1), then the grounding grid can be designed. If a compression ratio is selected, only a fixed grounding grid structure can be determined. For a square grounding grid, only one compression ratio should be determined, but for the rectangle grounding grid, then two compression ratios should be determined. For the grounding system in a double-layer soil with the upper-layer’s resistivity of 200 m and the bottom-layer’s resistivity of 50 m and a size of 80 80 m , there are nine conductors in every side. The thickness of the upper-layer soil is 5 m. The grounding resistance step and touch voltages under the different compression ratio are calculated. The analyzed results state the relationship between the touch voltage, and the compression ratio has an obvious “U” shape as shown in Fig. 2. When the compression ratio is 0.79, the touch voltage reaches its minimum. We define the optimum compression ratio (OCR) as the compression ratio, where the touch voltage reaches its minimum if the grounding grid is designed under this compression ratio. The relationship between the grounding resistance and the touch voltage still has an obvious “U” shape. The grounding resistance reaches its minimum at the OCR of 0.79 too. But basically, the grounding resistance of the grounding system is mainly determined by the area of the grounding system, the influence of the compression ratio on the grounding resistance is

Influence of compression ratio on the touch voltage.

very small so the grounding resistance is not the deciding factor to determine the OCR. On the other hand, the relationship between the step voltage and the compression ratio does not have an obvious regularity, but it is still reaches its minimum at the OCR of 0.79. Ordinarily, the touch voltage is higher than the step voltage, but the limit of the touch voltage calculated by IEEE Std. 80-2000 [1] is smaller than the limit of the step voltage. When a granite layer is used on the ground surface of the substation, ordinarily the maximum step voltage on the ground surface is smaller than its limit. If the touch voltage is in the safe region, then the step voltage is in the safe region too. So the step voltage is not the deciding factor to determine the OCR too. Ordinarily, the touch voltage is difficult to satisfy its limit, so the touch voltage is the deciding factor to optimally design the grounding system and determine the OCR. In our analysis, the maximum grid current is assumed to be the same in the normal season and in the frozen season. This means the fault current division factor is the same in the normal season and in the frozen season. But, in fact, in the frozen season, the grounding resistances of the grounding grid of substation and the grounding devices of all transmission towers would increase, then the fault current division factor of the transmission line in the frozen season would change too, and is different from that in the normal season. This phenomenon should be considered in actual grounding grid design. III. OPTIMAL DESIGN OF GROUNDING SYSTEMS IN HOMOGENEOUS SOIL The analysis of this paper is based on that the size of the grounding grid is supposed as 100 100 m , its burial depth is 1.0 m, and the resistivity of the frozen soil is 2000 m as the maximum grid current is assumed to be 10 kA. There are 11 grounding conductors in every side. A. Influence of Seasonal Frozen Soil Layer on the Optimal Design of Grounding System As shown in Fig. 3, the resistivity of the homogeneous soil is supposed to be 200 m, the surface granite layer is used to improve the safety of substation; its resistivity is 15 000 m, and its thickness is 10 cm. If a grounding system is buried in the homogeneous soil, when the seasonal frozen soil layer is considered, then the optimal design of a grounding grid is an optimal problem of the grounding grid in a two-layer soil model.

HE et al.: OPTIMAL DESIGN OF GROUNDING SYSTEM CONSIDERING THE INFLUENCE OF SEASONAL FROZEN SOIL LAYER

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Fig. 3. Soil model of the grounding system in a homogeneous soil considering the seasonal frozen soil. Fig. 6. Influence of the thickness of the seasonal frozen soil on the grounding resistance of the grounding grid in homogeneous soil with the optimum design.

Fig. 4. Influence of the thickness of the seasonal frozen soil on the OCR of the grounding grid in homogeneous soil.

Fig. 5. Influence of the thickness of the seasonal frozen soil on the touch voltage of the grounding grid in homogeneous soil with the optimum design.

The analyzed relationship between the OCR and the thickness of the frozen soil is shown in Fig. 4. When the thickness of the frozen soil is smaller than the burial depth of the grounding system, the OCR increases very quickly, because the frozen soil with high resistivity can inhibit the fault current dispersing into the soil above the grounding grid, and can equalize the potential distribution. When the thickness of the frozen soil exceeds the burial depth of the grounding system (1.0 m), the OCR jumps to a small value, because the grounding system is buried from the normal soil to the frozen soil. Then with the increment of the frozen soil thickness, the OCR increases quickly, because the frozen soil inhibits the fault current dispersing into soil from the grounding conductors; this would lead to the increment of the OCR. With the increment of the frozen soil thickness, the respective maximum touch voltage is shown in Fig. 5 when the grounding system is arranged in the optimum design considering the influence of the frozen soil layer. When the thickness of the frozen soil is smaller than the burial depth of the grounding grid, it increases slightly with the increment of the thickness of the frozen

soil because the frozen soil inhibits the fault current dispersing into soil. But when the thickness of the frozen soil exceeds the burial depth of the grounding grid, it does not have a jump as the OCR shown in Fig. 1. It increases very quickly with the increment of the frozen soil thickness. When the thickness of the frozen soil is 1.5 m, the maximum touch voltage is 5.13 times that without considering the frozen soil. So, if there is a short-circuit fault in the frozen season, the grounding system is not safe. The grounding resistance is another safe index of the grounding system. When the grounding system is arranged in the optimum design, with the increment of the frozen soil thickness, the respective grounding resistance of the grounding grid is illustrated in Fig. 6. When the thickness of the frozen soil is smaller than the burial depth of the grounding grid, it increases slightly with the increment of the thickness of the frozen soil. But when the thickness of the frozen soil exceeds the burial depth of the grounding grid, it increases very quickly with the increment of the frozen soil thickness. When the depth of the frozen soil is 1.5 m, the grounding resistance is 1.74 times that without considering the frozen soil. B. Discussion on the Design Rule of the Optimum Design of Grounding Grid in Homogeneous Soil The optimal design of the grounding system buried in a homogeneous soil with or without the frozen soil layer can be easily analyzed, but the actual grounding system can only be built according to a fixed design; this design perhaps is obtained from the normal soil model, or from the frozen soil model. So we must discuss the rule of the optimum design of the grounding system, and determine whether the grounding system is safer according to which soil model–the normal soil model or the frozen soil model. Then, the actual grounding system would be built according to the optimum design in this determined soil model. 1) First, the grounding system is designed according to the normal soil model. The OCR is 0.5 and the respective maximum touch voltage is 1330 V. In the frozen season, when the thickness of the frozen soil is 0.5 or 1.5 m, then the calculated maximum touch voltage is 1416 or 7798 V, respectively, which increases 6.5% or 4.86 times. If the grounding system is designed according to the normal soil model, in frozen season, when the thickness of the frozen soil is smaller than the burial depth of the grounding grid, the maximum touch voltage increases slightly; but when

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TABLE I ANALYSIS RESULTS OF OPTIMAL DESIGN FOR GROUNDING SYSTEM IN TWO-LAYER SOIL WITH SEASONAL FROZEN SOIL LAYER

Fig. 7. Grounding system in double-layer soil with the seasonal frozen soil layer.

the thickness of the frozen soil exceeds the burial depth of the grounding grid, the maximum touch voltage increases sharply, the grounding system would be not safe. 2) Second, the grounding grid is designed according to the soil model in the frozen season. When the thickness of the seasonal frozen soil is 0.5 m, the analyzed OCR is 0.54, and the respective maximum touch voltage is 1305 V. If the grounding system is designed according to the frozen soil model, but in normal season, the maximum touch voltage is 1377 V, which increases 5.5%. The safety of the grounding grid would decrease slightly in normal season. When the thickness of the frozen soil is 1.5 m, the analyzed OCR is 0.76, and the respective maximum touch voltage is 6817 V. If the grounding system is designed according to the frozen soil model, but in normal season, the maximum touch voltage is 1612 V, which decreases 76.4%. So the safety of the grounding system would be improved in the normal season. Now we synthesize the analysis results in (1) and (2) for the design of the grounding system in homogeneous soil, if the thickness of the seasonal frozen soil is smaller than the burial depth of the grounding grid, regardless of whether the grounding system is designed according to the soil model in normal season or the soil model in the frozen season, its safety decreases in the respective frozen season or normal season, but if about 10% of the safe margin is considered in design, then the grounding system would be safe in all seasons. But when the thickness of the frozen soil exceeds the burial depth of the grounding system, then the grounding system should be designed according to the frozen soil model. IV. OPTIMAL DESIGN IN DOUBLE-LAYER SOIL A. Influence of Frozen Soil Layer on the Optimal Design of Grounding System The supposed double-layer soil model is that the resistivities of two soil layers are 100 and 500 m. The parameters of the grounding grid are the same presented above. As shown in Fig. 7, for a grounding system in a double-layer soil, when the thickness of the frozen soil is smaller than the thickness of the upper-layer soil, the optimal design of a grounding system is an optimal problem of the grounding system in a three-layer soil model. When the thickness of the frozen soil is larger than the thickness of the upper-layer soil, then the optimal design of a grounding system is still an optimal problem of the grounding system in a two-layer soil model. The thicknesses of the frozen soil and upper-layer soil were changed; the analyzed OCRs in different thickness of seasonal frozen soil layer are shown in

Fig. 8. Relationship between the thickness of the seasonal frozen soil and the optimum compression ratio of the grounding grid in double-layer soil.

Table I and the respective touch voltage and grounding resistance of the grounding system with the optimum design are shown in Table I too. The relationship between the thickness of frozen soil and the optimum compression ratio of grounding grid in a double-layer soil is shown in Fig. 8. Four different double-layer soil models were considered in this analysis. The respective maximum touch voltage and grounding resistance of the grounding grids at the optimum design are illustrated in Figs. 9 and 10. As shown in Fig. 8, if the soil resistivity (100 m) of the upper soil layer is lower than that (500 m) of the bottom soil layer, and the thickness of the upper soil layer exceeds the burial depth of the grounding grid, in this case it is 10 m, when the thickness of the frozen soil is smaller than the burial depth of the grounding grid, the OCR increases slowly with the increment of the thickness of the frozen soil. When it is larger than the burial depth of the grounding grid, the OCR increases quickly because the grid current is more difficult to leak into the soil with the increment of frozen soil.


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the burial depth of the grounding grid. When the thickness of the frozen soil exceeds the burial depth of the grounding grid, the grounding resistance increases very quickly, but when the thickness of the frozen soil exceeds about 1.2 m, then the grounding resistance increases slowly. B. Discussion on the Optimum Design Rule of the Grounding Grid in Double-Layer Soil

Fig. 9. Influence of the thickness of the seasonal frozen soil on the touch voltage of the grounding grid in double-layer soil with the optimum design.

Fig. 10. Influence of the thickness of the seasonal frozen soil on the grounding resistance of grounding grid in double-layer soil with the optimum design.

As shown in Fig. 8, for the case that the thickness of upper soil layer is 0.8 m, and its resistivity (100 m) is still smaller than that (500 m) of the bottom soil layer, when the thickness of the frozen soil is smaller than the burial depth of the grounding grid, the OCR increases with the increment of the frozen soil thickness; when it exceeds the burial depth of the grounding grid, the OCR jumps to a small value, the reason is similar to the case of homogeneous soil discussed above, then the OCR increases with the increment of the frozen soil thickness because the frozen soil layer with high resistivity (2000 m) prevents the fault current from dispersing into the bottom soil layer with low resistivity (500 m) from the grounding grid. If the soil resistivity (500 m) of the upper soil layer is higher than that (100 m) of the bottom soil layer, the OCR increases with the thickness of the frozen soil. But if the thickness of the upper-layer soil is smaller than the burial depth of the grounding system, when the thickness of the frozen soil is smaller than the burial depth of the grounding grid, the OCR increases slowly with the increment of the thickness of the frozen soil; when it is larger than the burial depth of the grounding grid, the OCR increases quickly. Analyzing Fig. 9, when the thickness of the seasonal frozen soil is in the range from 0 to 0.6 m, the respective maximum touch voltage on the ground surface above the grounding grid with the optimum design decreases slightly and then increases very slowly. When the thickness of the frozen soil exceeds the burial depth of the grounding system, the maximum touch voltage increases quickly, but when the thickness of the frozen soil exceeds about 1.2 m, then the maximum touch voltage increases slowly. From Fig. 10, we observed that the grounding resistances of the grounding grids with the optimum design in all four cases increases very slowly with the increment of the frozen soil’s thickness when the thickness of the frozen soil is smaller than

Only the case that the resistivity (100 m) of the upper-layer soil is smaller than that (500 m) of the bottom-layer soil is discussed. First, the grounding grid is designed without considering the frozen soil according to the soil model in normal season. If the thickness of the upper-layer soil is 10 m, the analyzed OCR is 0.28 and the respective maximum touch voltage is 896.5 V. Then, the safety of the grounding system at the optimum design according to the normal soil model should be checked according to the respective soil model in the frozen season. In the frozen season, when the thickness of the frozen soil is 0.5 or 1.5 m, then the calculated maximum touch voltage is 781 or 7871 V, respectively, which decreases 12.9%, or increases 7.77 times. So if the grounding grid is designed according to the soil model in the normal season and satisfies the safe demands of IEEE Std. 80 [1], then in the frozen season, if the thickness of the seasonal frozen soil is smaller than the burial depth of the grounding grid, the grounding grid is more safe; but when it exceeds the burial depth of the grounding grid, the maximum touch voltage increases 7.77 times and the grounding grid is not safe. For the case when the thickness of the upper-layer soil is 0.8 m, which is smaller than the burial depth of the grounding grid, the analyzed OCR is 0.36 and the respective maximum touch voltage is 3307 V. When the grounding grid is arranged at the optimum design according to the normal soil model in the frozen season, when the thickness of the frozen soil is 0.5 or 1.5 m, then the calculated maximum touch voltage is 3735 or 10 520 V, respectively, which increases 12.9%, or 2.18 times. So in the case when the resistivity of the upper-layer soil is small and its thickness is smaller than the burial depth of the grounding grid, if we assumed the grounding grid is designed according to the normal soil model and reaches the safe demands, the grounding grid would not be safe in frozen season. When the thickness of the frozen soil is smaller than the burial depth, the maximum touch voltage increases slightly. If we consider about 15% safe margin, then the grounding grid is safe in the frozen season; but when the thickness of the frozen soil exceeds the burial depth, the maximum touch voltage increases too much and the grounding system is not safe. Second, the grounding grid is designed according to the soil model in the frozen season. For the case that the thickness of the upper-layer soil is 10 m, when the thickness of the frozen soil is 0.5 m, the analyzed OCR is 0.28, and the respective maximum touch voltage at the optimum design is 781 V, but in normal season, the maximum touch voltage is 896.5 V, which increases 14.9%. When the thickness of the frozen soil is 1.5 m, the analyzed OCR is 0.53 and the respective maximum touch voltage at the optimum design is 6386.6 V, but in normal season, the maximum touch voltage is 1068 V, which decreases 83.3%.

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Fig. 11. Influence of the thickness of the seasonal frozen soil on the optimum compression ratio of the grounding system with vertical grounding electrodes in homogeneous soil.

For the case that the thickness of the upper-layer soil is 0.8 m, when the thickness of the frozen soil is 0.5 m, the analyzed OCR is 0.47, and the respective maximum touch voltage is 3167 V, but in the normal season, the maximum touch voltage is 1006 V, which decreases 68.2%. When the thickness of the frozen soil is 1.5 m, the analyzed OCR is 0.58, and the respective maximum touch voltage at the optimum design is 8239 V, but in normal season, the maximum touch voltage is 1119 V, which decreases 86.4%. So for the case when the resistivity of upper-layer soil is smaller than that of bottom-layer soil, synthesizing the analysis results in the grounding grid being designed according to the soil model in frozen season and in normal season if the grounding system is buried in the top-layer soil, when the thickness of the frozen soil is smaller than the burial depth of the grounding grid, the grounding grid should be designed according to the normal soil model; but when the thickness of the seasonal frozen soil exceeds the burial depth of the grounding grid, then the grounding grid should be designed according to the frozen soil model with the largest thickness of the frozen soil. If the grounding system is buried in the bottom-layer soil, the grounding grid should be designed according to the frozen soil model with the largest thickness of the frozen soil. If the designed grounding system satisfies the safe demands of IEEE Std. 80-2000 [1], then in the other season, the grounding system is still safe. For the case that the resistivity of the upper-layer soil is higher than that of the bottom-layer soil, or other multilayer soil models, the design regularity of the grounding system considering the frozen soil can be obtained according to the same analysis above. V. INFLUENCE OF VERTICAL GROUNDING ELECTRODES ON THE OPTIMAL DESIGN IN HOMOGENEOUS SOIL A. Influence of Frozen Soil Layer on the Optimal Design of Grounding System If four vertical grounding electrodes with a length of 60 m are added on the four corners of the grounding gird, the grounding system is buried in a homogeneous soil with a resistivity of 200 m. In this case, the relationship between the analyzed OCR and the thickness of the frozen soil is shown in Fig. 11. When the thickness of the frozen soil is smaller than the burial depth of the grounding grid, the OCR increases with the increment of the thickness of the seasonal frozen soil, but when the


Fig. 12. Influence of the thickness of the seasonal frozen soil on the touch voltage of the grounding system with vertical grounding electrodes in homogeneous soil with the optimum design.

Fig. 13. Influence of the thickness of the seasonal frozen soil on the grounding resistance of the grounding system with vertical grounding electrodes in homogeneous soil with the optimum design.

thickness of the seasonal frozen soil reaches 0.5 m, then the OCR is kept unchanged. When its thickness exceeds the burial depth of the grounding grid, the OCR suddenly jumps to a small value and then the OCR increases quickly with the increment of the frozen soil thickness. As shown in Fig. 11, the OCR of the grounding system with vertical grounding electrodes changes in a similar regularity with that of the grounding grid without vertical grounding electrodes as shown in Fig. 4, but the value of OCR increases about 0.25. This means that the grounding grid is arranged more uniformly when the vertical grounding electrodes are added because these vertical grounding electrodes disperse a portion of fault current into soil. With the increment of the frozen soil thickness, the respective maximum touch voltage is shown in Fig. 12 when the grounding system is arranged at the optimum design. When the thickness of the frozen soil is smaller than the burial depth of the grounding grid, it increases slightly with the increment of the thickness of the frozen soil; this is different from the regularity of the grounding system without a vertical grounding electrode which lightly decreases as shown in Fig. 5. But when the thickness of the frozen soil exceeds the burial depth of the grounding grid, it increases quickly with the increment of the frozen soil thickness. When the depth of the frozen soil is 1.5 m, the maximum touch voltage is 3077 V, but the respective value without the vertical grounding electrode is 687 V. The changing regularity of the grounding resistance with vertical grounding electrodes is shown in Fig. 13. Compared to that without a vertical grounding electrode as shown in Fig. 6, the grounding resistances with vertical grounding electrodes significantly decreases.


B. Discussion on the Optimal Design Rule for Grounding System With Vertical Grounding Electrode in Homogeneous Soil 1) First, the grounding system is designed without considering the frozen soil, the OCR is 0.75 and the respective maximum touch voltage is 584 V. In the frozen season, when the thickness of the frozen soil is 0.5 or 1.5 m, then the calculated maximum touch voltage is 610 or 3134 V, respectively, which increases 4.4%, or 4.4 times. 2) Second, the grounding grid is designed according to the soil model in the frozen season. When the thickness of the frozen soil is 0.5 m, the analyzed OCR is 0.78, and the respective maximum touch voltage is 572 V, but in the normal season, the maximum touch voltage is 592 V, which increases 3.4%. When the thickness of the frozen soil is 1.5 m, the analyzed OCR is 0.78, and the respective maximum touch voltage is 3077 V, but in the normal season, the maximum touch voltage is 592 V, which decreases 80.8%. Now we synthesize the analysis results in (1) and (2) for the design of grounding system with vertical grounding electrodes in homogeneous soil if the thickness of the frozen soil is smaller than the burial depth of the grounding system, regardless of whether the grounding system is designed according to the normal season soil model or the frozen soil model, its safety decreases in the respective frozen season or normal season, but if about 5% of the safe margin is considered in design, then the grounding system would be safe in all seasons. But when the thickness of the frozen soil exceeds the burial depth of the grounding system, then the grounding system should be designed according to the frozen soil model.

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TABLE II ANALYZED RESULTS OF GROUNDING SYSTEMS WITH VERTICAL GROUNDING ELECTRODES IN A DOUBLE-LAYER SOIL MODEL

2) The resistivity of the upper-layer soil (500 m) is higher than that (100 m) of the bottom-layer soil and the OCR is kept unchanged with the increment of the seasonal frozen soil thickness, so the vertical grounding electrodes can eliminate the influence of the frozen soil on the grounding system design. If the thickness of the frozen soil is smaller than the burial depth of the grounding system, the maximum touch voltage at the optimum design increases slightly with the increment of the frozen soil thickness; when the thickness of the frozen soil exceeds the burial depth of the grounding system, then the maximum touch voltage at the optimum design increases with the increment of the frozen soil thickness. If the vertical grounding electrodes contact the bottom soil layer with low resistivity, the maximum touch voltage and grounding resistance decreases highly.

VI. INFLUENCE OF VERTICAL GROUNDING ELECTRODES ON THE OPTIMAL DESIGN IN A DOUBLE-LAYER SOIL A. Influence of Frozen Soil Layer on the Optimal Design of the Grounding System

B. Discussion on the Optimal Design Rule for Grounding System With Vertical Grounding Electrode

The double-layer soil model is assumed that as the resistivity of two soil layers is 100 m and 500 m, the thickness of the upper-layers soil is 40 m. Four vertical grounding electrodes are added in the four corners of the grounding grid. The analyzed results are shown in Table II. Analyzing the results in Table II, the following conclusions can be determined for the optimal design of the grounding system in a double-layer soil model with frozen soil layer. 1) The resistivity of the upper-layer soil (100 m) is smaller than that (500 m) of the bottom-layer soil, regardless of whether the vertical grounding electrodes touch the bottom soil layer, the OCR increases with the increment of the frozen soil thickness. If the thickness of the frozen soil is smaller than the burial depth of the grounding system, the maximum touch voltage at the optimum design decreases slightly with the increment of the frozen soil thickness; when the thickness of the frozen soil exceeds the burial depth of the grounding system, then the maximum touch voltage at the optimum design increases.

Now we discuss the case that the resistivity of the upperlayer soil is 100 m, the resistivity of the bottom layer soil is 500 m, and the thickness of the upper-layer soil is 40 m. 1) First, according to the soil model in normal season, when the length of the vertical grounding electrodes is 30 m, the analyzed OCR is 0.63, the respective maximum touch voltage at the optimum design is 384 V. In the frozen season, when the thickness of the frozen soil is 0.5 or 1.5 m, then the calculated maximum touch voltage is 422 or 3586 V, respectively, which increases 9.9%, or 8.34 times. When the length of the vertical grounding electrodes is 60 m, the analyzed OCR is 0.64, the respective maximum touch voltage is 335 V. In the frozen season, when the thickness of the frozen soil is 0.5 or 1.5 m, then the calculated maximum touch voltage is 380 or 2848 V, respectively, which increases 13.4%, or 7.5 times. 2) Second, the grounding grid is designed according to the soil model in the frozen season. When the length of the vertical grounding electrodes are 30 m, if the thickness

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of the frozen soil is 0.5 m, the analyzed OCR is 0.73, and the respective maximum touch voltage is 351 V, but in normal season, the maximum touch voltage is 396 V, which increases 13.1%. If the thickness of the frozen soil is 1.5 m, the analyzed OCR is 0.78, and the respective maximum touch voltage is 3400 V, but in normal season, the maximum touch voltage is 400 V, which decreases 88.2%. When the length of the vertical grounding electrodes is 60 m, if the thickness of the frozen soil is 0.5 m, the analyzed OCR is 0.72, and the respective maximum touch voltage is 325 V, but in normal season, the maximum touch voltage is 343 V, which increases 10.5%. If the thickness of the frozen soil is 1.5 m, the analyzed OCR is 0.78, and the respective maximum touch voltage is 2725 V, but in the normal season, the maximum touch voltage is 347 V, which decreases 87.3%. So for the case that the resistivity of upper-layer soil is smaller than that of the bottom-layer soil, synthesizing the analysis results in (1) and (2), for the design of grounding system with vertical grounding electrodes in double-layer soil if the thickness of the frozen soil is smaller than the burial depth of the grounding system, no matter the grounding system is designed according to the normal season soil model or the frozen soil model, its safety decreases in the respective frozen season or normal season, but if about 15% of safe margin is considered in design, then the grounding system would be safe in all seasons. But when the thickness of the frozen soil exceeds the burial depth of the grounding system, then the grounding system should be designed according to the frozen soil model. When a grounding grid is arranged in the optimum design, the conductor span in the middle of the grounding grid is larger than that near the periphery. This perhaps leads to difficultly providing the power apparatus a short grounding connection with the grounding grid. In order to overcome this shortcoming of the optimum design of the grounding grid, we can adopt a middle scheme–the grounding conductors in the middle region of the grounding grid with a big conductor span can be changed as an equal span arrangement, and other conductors still keep the optimum design. This would keep the merit of the optimum design and not increase the touch voltage. This will be introduced in a follow-up paper about the actual field application of grounding grid optimal design. VII. CONCLUSION The influential regularity of the frozen soil on the optimum design of grounding system is different for different soil models. The design of the grounding system in the area with the seasonal frozen soil layer should be based on the full investigation of the actual maximum depth of the frozen soil and the actual soil models. The final design scheme of the grounding system should be determined synthetically from two phases–first, the grounding system is arranged according to the optimum design in the normal soil model and its safety is checked in the seasonal frozen soil model, second, it is arranged according to the optimum design in the frozen soil model and its safety is checked in the normal soil model.

For the design of the grounding grid in homogeneous soil–if the thickness of the seasonal frozen soil in winter is smaller than the burial depth of the grounding grid, regardless of whether the grounding grid is designed according to the soil model in normal season or the soil model in frozen season, its safety decreases in the respective frozen season or normal season, but if about 10% of the safe margin is considered in the design, then the grounding system would be safe in all seasons. But when the thickness of the frozen soil exceeds the burial depth of the grounding system, then the grounding system should be designed according to the frozen soil model. For the case of double-layer soil model with the resistivity of upper-layer soil being smaller than that of the bottom-layer soil, if the grounding system is buried in the top-layer soil, when the thickness of the frozen soil is smaller than the burial depth of the grounding grid, the grounding grid should be designed according to the normal soil model; but when the thickness of the frozen soil exceeds the burial depth of the grounding, then the grounding grid should be designed according to the frozen soil model with the largest thickness of the frozen soil. If the grounding system is buried in the bottom-layer soil, the grounding grid should be designed according to the frozen soil model with the largest thickness of the seasonal frozen soil layer. The vertical grounding electrodes added to the grounding system can effectively improve the safety of the grounding system, and affect the optimal design of the grounding system. The grounding grid is arranged more uniformly when the vertical grounding electrodes are added because these vertical grounding electrodes disperse a portion of fault current into the soil. REFERENCES [1] ANSI/IEEE Std. 80-2000. IEEE Guide for Safety in AC Substation Grounding, 2000. New York, IEEE. [2] L. Huang, X. Chen, and H. Yan, “Study of unequally spaced grounding grids,” IEEE Trans. Power Del., vol. 10, no. 2, pp. 716–722, Apr. 1995. [3] F. Dawalibi and D. Mukhedkar, “Optimum design of substation grounding in a two layer earth structure, part I: Analytical study,” IEEE Trans. Power App. Syst., vol. PAS-94, no. 2, pp. 252–261, Mar. 1975. , “Optimum design of substation grounding in a two layer earth [4] structure, part II: Comparison between theoretical and experimental results,” IEEE Trans. Power App. Syst., vol. PAS-94, no. 2, pp. 262–266, Mar. 1975. , “Optimum design of substation grounding in a two layer earth [5] structure, Part III: Study of grounding grids performance and new electrode configuration,” IEEE Trans. Power App. Syst., vol. PAS-94, no. 2, pp. 267–272, Mar. 1975. [6] J. G. Sverak, “Optimized grounding grid design using variable spacing techniques,” IEEE Trans. Power App. Syst., vol. 95, no. 1, pp. 362–374, Jan. 1976. [7] W. Sun, J. He, Y. Gao, R. Zeng, W. Wu, and Q. Su, “Optimal design analysis of grounding grids for substations built in nonuniform soil,” in Proc. Int. Conf. Power System Technology, Perth, Australia, 2002, pp. 1455–1460. [8] J. He, R. Zeng, Y. Gao, Y. Tu, W. Sun, J. Zou, and Z. Guan, “Seasonal influences on safety of substation grounding system,” IEEE Trans. Power Del., vol. 18, no. 3, pp. 788–795, Jul. 2003. [9] F. P. Dawalibi and F. Donoso, “Integrated analysis software for grounding, EMF, and EMI,” IEEE Comput. Appl. Power, vol. 6, no. 2, pp. 1–24, Apr. 1993.


Jinliang He (M’02–SM’02) was born in Changsha, China, in 1966. He received the B.Sc. degree in electrical engineering from Wuhan University of Hydraulic and Electrical Engineering, Wuhan, China, in 1988, the M.Sc. degree in electrical engineering from Chongqing University, Chongqing, China, in 1991, and the Ph.D. degree in electrical engineering from Tsinghua University, Beijing, China, in 1994. Currently, he is the Vice Chief of the High Voltage Research Institute at Tsinghua University. He became a Lecturer in 1994 and Associate Professor in 1996 in the Department of Electrical Engineering at Tsinghua University and from 1994 to 1997, was the Head of the High Voltage Laboratory there. From 1997 to 1998, he was a Visiting Scientist with the Korea Electrotechnology Research Institute, Changwon, Korea, involved in research on metal-oxide varistors and high-voltage polymeric metal-oxide surge arresters. In 2001, he was promoted to Professor at Tsinghua University. He is the Chief Editor of the Journal of Lightning Protection and Standardization. His research interests include overvoltages and electromagnetic compatibility (EMC) in power systems and electronic systems, grounding technology, power apparatus, dielectric material, and power distribution automation. He is the author of five books and many technical papers. Dr. He is a Senior Member of the China Electrotechnology Society, and Member of the International Compumag Society. He is the China representative of IEC TC 81, the Vice Chief of China Lightning Protection Standardization Technology Committee, and Member of Electromagnetic Interference Protection Committee and Transmission Line Committee of China Power Electric Society, Member of the China Surge Arrester Standardization Technology Committee, and Member of the Overvoltage and Insulation Coordination Standardization Technology Committee and Surge Arrester Standardization Technology Committee in the electric power industry.

Yanqing Gao (S’02) received the B.Sc. degree in 1999 from the Department of Electrical Engineering, Tsinghua University, Beijing, China, where he is currently pursuing the Ph.D. degree. His research interests include overvoltage analysis in power systems, grounding technology, and electromagnetic compatibility (EMC).

Rong Zeng (M’02) was born in Shanxi, China, in 1971. He received the B.Sc., M.Eng., and Ph.D. degrees from the Department of Electrical Engineering, Tsinghua University, Beijing, China, in 1995, 1997, and 1999, respectively. Currently, he is an Associate Professor in the Department of Electrical Engineering at Tsinghua University, where he has been since 1999. His research interests include high-voltage technology, grounding technology, power electronics, and distribution system automation.

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Weimin Sun received the B.Sc. degree from the Department of Electrical Engineering, Shandong Industry University, Jinan, China, in 1984, the M.Eng. degree from the Electric Power Research institute, Beijing, China, in 1989, and the Ph.D. degree from the Department of Electrical Engineering, Tsinghua University, Beijing, China, in 2002. Currently, he is a Senior Engineer with Shandong Electrical Power Co. Ltd., Jinan. His research fields include high-voltage technology and power distribution.

Jun Zou was born in Wuhan, China, in 1971. He received the B.S. and M.S. degrees in electrical engineering in 1994 and 1997, respectively, from Zhengzhou University, Zhengzhou, Henan Province, China, and the Ph.D. degree in electrical engineering from Tsinghua University, Beijing, China, in 2001. He became a Lecturer in the Department of Electrical Engineering, Tsinghua University, in 2001. His research interests include computational electromagnetics and electromagnetic compatibility (EMC).

Zhicheng Guan was born in Jilin, China, in 1944. He received the B.Sc., M.Eng., and Ph.D. degrees in 1970, 1981, 1984, respectively, from the Department of Electrical Engineering, Tsinghua University, Beijing, China. Currently, he is the Vice President of the Tsinghua University Council. From 1984 to 1987, he was a Lecturer and the Director of the High Voltage Laboratory in the Department of Electrical Engineering, Tsinghua University. From 1988 to 1989, he was a Visiting Scholar at the University of Manchester Institute of Science and Technology (UMIST) Manchester, U.K. From 1989 to 1991, he was an Associate Professor and the Director of the High Voltage Laboratory, Tsinghua University. In 1991, he was promoted to Professor at Tsinghua University. From 1992 to 1993, he was the Head of the Department of Electrical Engineering, Tsinghua University. From 1993 to 1994, he was the Assistant President of Tsinghua University, and from 1994 to 1999, he was the Vice President of Tsinghua University. His main research interests include high-voltage insulation and electrical discharge, composite insulators and flashover of contaminated insulators, electrical environment technology, high–voltage measurement, and application of plasma and high-voltage technology in biological and environment engineering. He holds many titles in academic societies and is the author of many academic papers.