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Annex X
Benchmarks
(Informative)
1. Overview
This annex provides the users with benchmark case results to use in comparing and evaluating software tools and methodologies that provide analysis of substation grounding.. The specific objectives are as follows:
a) Compare equations and methods found in this guide with some of the available commercial software.
b) Illustrate the variations in complexity of simple grids versus more complex and interconnected grounding systems, and demonstrate some of the limitations of some of the methods or software.
c) Provide a basis for checking the accuracy of other or future software or methodologies.
All methods, whether simple formulas or complex computer modeling, involve some approximations or assumptions for grounding analysis; thus, no representation is made that these benchmark results are exact. For each category of analysis, several methods were compared and the results tabulated. These results were also reviewed by the developers of the computer programs.
The computer software used in these benchmark cases include: CDEGS, ETAP, SGW, SDWorkstation and WinIGS. This is not a complete list of all available software, but is representative of the most widely used commercially-available software. Not all software has the same modeling capabilities – each type of analysis lists the software used for that specific analysis. The following provides contact information for obtaining these softwares.
- CDEGS: Safe Engineering Services (SES), 1544 Viel, Montreal, Quebec, Canada, H3M-1G4, www.sestech.com
- ETAP: Operations Technology, Inc. (OTI), 17 Goodyear, Suite 100, Irvine, CA, 92618-1812, www.etap.com
- SGW: Electric Power Research Institute (EPRI), 3412 Hillview Avenue, Palo Alto, CA, 94304, www.epri.com
- SDWorkstation: Electric Power Research Institute (EPRI), 3412 Hillview Avenue, Palo Alto, CA, 94304, www.epri.com
- WinIGS: Advanced Grounding Concepts (AGC), P. O. Box 29547, Atlanta, GA 30359, www.ap-concepts.com
The benchmarks are divided into three categories – soil analysis, grid analysis (resistance, touch and step voltages, transfer voltages), and ground fault current division.
2. Soil analysis
Though there are several methods and software available that can evaluate soil resistivity field measurements into multi-layer soil models, the equations of this guide are limited to uniform soil models and most grounding analysis software (all but one of those listed aboveCDEGS) is limited to a two-layer soil model. There are also many methods, as described in IEEE Std. 81-1983, for measuring soil resistivity. By far, the most common method of measurement is the four-pin (Wenner) method. A less seldom used method is the three-pin (driven-rod) method. The benchmark cases of soil resistivity interpretation are restricted to analysis of measurements made using the four-pin and three-pin methods.
In order to make it possible to compare at least two computation methods for all examples, the soil structure has been limited to uniform and two-layer soils, although there are frequently situations in which it is desirable to model more complex soil structures. Because of the difficulties and errors introduced into the actual field measurements, it is difficult, if not impossible, to determine the “correct” two-layer soil model for a set of field measurements. In fact, the soil resistivity usually varies both laterally and with depth over the substation area, so there is no exact two-layer or multi-layer soil model. Because of this, “exact” sets of field measurements were mathematically derived that correctly represent a perfect two-layer soil. In order to make it possible to compare at least two computation methods for all examples, the soil structure has been limited to uniform and two-layer soils, although there are situations in which it is desirable to model more complex soil structures.
The mathematically-derived field measurements are shown in Tables X.1 and X.3 for soil models with ρ1=300 W-m, ρ2=100 W-m, and h= 6.096 m (20 ft), and for ρ1=300 W-m, ρ2=100 W-m, and h= 6.096 m (20 ft). The plots of apparent resistivity vs. pin spacing for these two soil models are shown in Figures X.1 and X2.
Table X.1 – Four-pin field measurements for two-layer soil models
RESISTANCE (W) / APPARENT RESISTIVITY (W-m) / RESISTANCE (W) / APPARENT RESISTIVITY (W-m)
0.3048(1.0) / 109.38 / 209.5 / 36.46 / 69.8
0.9144(3.0) / 48.84 / 280.6 / 16.32 / 93.8
1.524(5.0) / 30.40 / 291.1 / 10.25 / 98.2
3.048(10.0) / 15.01 / 287.5 / 5.40 / 103.4
4.572(15.0) / 9.42 / 270.6 / 3.86 / 110.9
6.096(20.0) / 6.48 / 248.2 / 3.16 / 121.0
9.144(30.0) / 3.52 / 202.2 / 2.49 / 143.1
15.24(50.0) / 1.50 / 143.6 / 1.90 / 181.9
21.336(70.0) / 0.90 / 120.7 / 1.56 / 209.1
27.432(90.0) / 0.64 / 110.3 / 1.32 / 227.5
33.528(110.0) / 0.51 / 107.4 / 1.15 / 242.3
39.624(130.0) / 0.42 / 104.6 / 1.01 / 251.5
45.72(150.0) / 0.36 / 103.4 / 0.90 / 258.5
These data were analyzed using the guidance in 13.4.2.2 and the computer programs RESAP (component of CDEGS), SOMIP (component of SGW), SDWorkstation and WinIGS. The comparisons for each soil model are presented in Table X.2.
Figure X.1 – Soil resistivity vs. pin spacing for 4-pin test
Table X.2 – Two-layer soil models derived from four-pin field measurements of Table X.1
ρ1 (W) / ρ2 (W) / h / ρ1 (W) / ρ2 (W) / h
STD 80-2000 (SUNDE CURVE) / 290.0 / 100.0 / 5.6 m (18.37 ft) / 100.0 / 270.0 / 7.0 m (22.97 ft)
RESAP / 297.6 / 100.2 / 6.13 m (20.1 ft) / 99.0 / 297.9 / 5.94 m (19.5 ft)
SOMIP / 300.1 / 100.4 / 6.07 m (19.9 ft) / 99.8 / 298.8 / 6.04 m (19.8 ft)
SDWorkstation* / 294.5 / 100.1 / 6.22 m (20.4 ft) / 84.4 / 237.8 / 2.54 m (8.33 ft)
WinIGS / 300.7 / 100.4 / 6.035 m (19.8 ft) / 100.1 / 299.5 / 6.096 m (20.0 ft)
*Does not allow measurements below 1.77ft spacing.
Table X.3 – Three-pin field measurements for two-layer soil models
RESISTANCE (W) / APPARENT RESISTIVITY (W-m) / RESISTANCE (W) / APPARENT RESISTIVITY (W-m)
0.3048(1.0) / 647.6 / 299.27 / 218.3 / 100.88
0.9144(3.0) / 270.6 / 296.54 / 92.68 / 101.56
1.524(5.0) / 177.1 / 294.74 / 61.52 / 102.39
3.048(10.0) / 97.63 / 290.03 / 35.13 / 104.36
4.572(15.0) / 67.85 / 284.45 / 25.43 / 106.61
6.096(20.0) / 50.82 / 272.63 / 20.63 / 110.67
9.144(30.0) / 21.77 / 165.77 / 18.22 / 138.73
15.24(50.0) / 10.91 / 129.68 / 14.58 / 173.30
21.336(70.0) / 7.41 / 118.36 / 12.16 / 194.23
27.432(90.0) / 5.64 / 112.46 / 10.42 / 207.77
33.528(110.0) / 4.57 / 108.85 / 9.13 / 217.46
39.624(130.0) / 3.84 / 106.09 / 8.12 / 224.33
45.72(150.0) / 3.32 / 104.18 / 7.31 / 229.38
These data were analyzed using the guidance in 13.4.2.2 and the computer programs SDWorkstation and WinIGS. The comparisons for each soil model are presented in Table X.4.
Figure X.1 – Soil resistivity vs. pin spacing for 3-pin test
Table X.4 – Two-layer soil models derived from three-pin field measurements of Table X.3
ρ1 (W) / ρ2 (W) / h / ρ1 (W) / ρ2 (W) / h
STD 80-2000 (SUNDE CURVE) / NA / NA / NA / NA / NA / NA
CDEGS / NA / NA / NA / NA / NA / NA
SDWorkstation / 289.6 / 97.0 / 6.096 m (20 ft) / 96.7 / 291.5 / 6.04 m (19.8 ft)
WinIGS / 301.5 / 100.6 / 6.096 m (20 ft) / 104.1 / 268.8 / 6.096 m (20 ft)
3. Grounding system analysis
In the 1961 edition of IEEE Std 80, the equations for touch and step voltages were limited to analysis at very specific points and were limited to analysis of uniformly-spaced conductors in symmetrical grids. IEEE Std 80-2000 included improvements on those equations to account for odd-shaped grids and ground rods, but still analyzed only specific points for touch and step voltages. Other methods, and especially computer programs based on a fine-element analysis of the grounding system, might allow more flexibility in modeling the conductors and ground rods making up the grounding system, and might analyze touch and step voltages and transferred voltages at any point desired. This clause analyzes the grid resistance, touch and step voltages, and transferred voltages (if applicable) for grids ranging from simple evenly-spaced symmetrical grids with no ground rods to non-symmetrically shaped and spaced grids with random ground rod locations and with separately-grounded fences. The grid current for all cases is 744.8A. The grid analysis is performed using the equations in IEEE Std 80, and computer programs CDEGS, ETAP and WinIGS. Again, in order to make it possible to compare at least two computation methods for all examples, the soil structure has been limited to uniform and two-layer soils, although there are situations in which it is desirable to model more complex soil structures.
Each program has several features for displaying the touch and step voltages, as well as determining the absolute worst case voltages. For consistency in comparing results between the programs, the touch and step voltages were evaluated at very specific points and with specific guidelines on the points evaluated to determine the worst case voltages. For example, to determine the step voltage at the corner of the grid, the earth surface potentials were determined at points over the corner of the grid and 1m outside the grid along the diagonal. The step voltage was computed as the difference between the potentials at these two points. For cases where several points (i.e. a grid of points) were used to determine the worst case touch voltage, the evaluated points were spaced 0.5m apart.
In order to make it possible to compare at least two computation methods for all examples, the soil structure has been limited to uniform and two-layer soils
3.1 Grid 1 – symmetrically spaced and shaped grid, uniform soil, no ground rods
The ground grid for this comparison is shown in Figure X.3. The equations in IEEE Std 80 compute the touch voltage at the center of the corner mesh (T1), so this point was chosen for comparison. The actual maximum touch voltage for this grid shape might be on the diagonal near the center of the corner mesh, but located slightly nearer the perimeter of the grid (T3). For some cases, it might also be directly over the extreme corner (perimeter) of the grid (T2). Thus, these two points were also analyzed for comparison. The equations in IEEE Std 80 compute the step voltage as the difference between the earth surface potential 1m apart, with one point directly over the corner of the grid and the other on a diagonal and 1m beyond the first point. Though the actual worst case step voltage might be at a different location, comparisons were limited to this one location (S1) for this case. The comparisons are shown in Table X.5.
Figure X.3 – Grounding system parameters for Grid 1
3.2 Grid 2 – symmetrically spaced and shaped grid, uniform soil, with ground rods
The ground grid for this comparison is shown in Figure X.4. This case is the same as Grid 1, with the addition of twenty 7.5m (24.6 ft.) rods located at each intersection around the perimeter of the grid. The touch and step voltages were computed at the same locations as for Grid 1. The comparisons are shown in Table X.5.
Figure X.4 – Grounding system parameters for Grid 2
3.3 Grid 3 – symmetrically spaced and shaped grid, two-layer soil, with ground rods
The ground grid for this comparison is the same as for Grid 2, except the soil model is changed to a two-layer soil with ρ1=300 W-m, ρ2=100 W-m, and h=6.096m (20ft). See Figure X.5. The touch and step voltages were computed at the same locations as for Grid 1. The comparisons are shown in Table X.5.
Figure X.5 – Grounding system parameters for Grid 3
3.4 Grid 4 – symmetrically spaced and shaped grid, separately-grounded fence, two-layer soil, with ground rods
The ground grid for this comparison is the same as for Grid 3, except a separately-grounded fence is added, located 3m outside the grid perimeter conductor, and with a fence perimeter ground conductor located 1m outside the fence. The touch and step voltages were computed at similar locations as for Grid 1. In this case, however, additional touch and step points were computed. For this case, touch voltages T1, T2 and T3 were computed as differences between the surface potentials at these points and the GPR of the main ground grid. T4 was computed as the difference between surface potential at the corner of the fence perimeter conductor and the GPR of the fence perimeter conductor (connected only to the separately-grounded fence). Step voltages S1 and S2 were computed as differences between earth surface potentials 1m apart along the diagonal. S1 had the first point located over the corner of the perimeter conductor of the main grid, while S2 had the first point located over the outer (fence) perimeter conductor. The comparisons are shown in Table X.5.
Figure X.6 – Grounding system parameters for Grid 4
3.5 Grid 5 – symmetrically spaced non-symmetrically shaped grid, fence grounded to main grid, two-layer soil, with ground rods
The ground grid for this comparison is shown in Figure X7. This grid is non-symmetrical in shape (L-shaped), though it still has symmetrically spaced grid conductors. It also has ground rods of uniform length at every other intersection around the perimeter, and has a grounded fence within the confines of the main grid and bonded to the grid. The touch and step voltage equations in Clause 16 can be used for this type of grid, but it is not known exactly where the touch and step voltages are being computed. For the computer programs, the touch and step voltages were computed at numerous points to determine the worst case for each. The worst case touch voltage was computed at all points 0.5m apart within the fence, plus all points within reach (1m) outside the fence. The worst case step voltage (S1) was computed at all points 0.5m apart within an area defined inward from 1m outside the perimeter of the grid. For direct comparison, the step voltage (S2) was also compared by determining the difference between earth surface potentials 1m apart along the diagonal at the upper left corner of the grid. The comparisons are shown in Table X.5.