Example 1 of Annex B of IEEE Std 80-2013 designs a 70 m × 70 m square grid, with no rods, in 400 Ω·m soil. The proposed grid gives a resistance of 2.78 Ω, a ground potential rise of 5,304 V and a mesh voltage of 1,002.1 V, higher than the tolerable touch voltage of 838.2 V: the design fails and must be modified. Example 2 corrects it with 20 rods.
Short answer
Example 1 of Annex B of IEEE Std 80-2013 walks through the design procedure with a 70 m × 70 m square grid, with no rods, in 400 Ω·m soil. The result teaches something useful: the first proposal does not comply, because its mesh voltage (1,002.1 V) exceeds the tolerable touch voltage (838.2 V). The general procedure is in the substation grounding grid guide; here the numbers are shown. The tolerable limits come from the tolerable body current.
Starting data of the example
| Data | Value |
|---|---|
| Grid | Square, 70 m × 70 m (4,900 m²), no rods |
| Soil resistivity | 400 Ω·m |
| Fault and shock duration | 0.5 s |
| Surface layer | 0.102 m (4 in), 2,500 Ω·m wet |
| Person’s weight | 70 kg (area not accessible to the public) |
| Fault at the 115 kV bus | 3,180 A (X/R ratio of 3.33) |
| Fault at the 13 kV bus | 6,814 A (X/R ratio of 16.2) |
| Current split factor | 0.6 |
The substation’s real grid sits in a 63 m × 84 m rectangle (5,292 m²); for the initial evaluation an equivalent 70 m × 70 m square grid is assumed.
The calculation step by step
Step 2: conductor size
The 13 kV fault is the larger, 6,814 A, and is used to size the conductor. With a time of 0.5 s, the standard takes the decrement factor as approximately 1.0 (fault asymmetry is explained in short-circuit peak factor and X/R ratio), so the asymmetrical current is also 6,814 A.
With hard-drawn copper, a 40 °C ambient and a melting temperature of 1,084 °C, the cross-section is 6.814 × 7.06 × √0.5 = 34.02 kcmil (17.2 mm²). That is equivalent to a solid conductor of about 4.7 mm. A No. 4 AWG cable could do, but for mechanical strength a stranded 2/0 AWG, 0.0105 m in diameter, is preferred as a minimum. The resistance formula is explained in grounding resistance of a grid.
As an alternative, a copper-clad steel of 30 % conductivity with a conservative limit of 700 °C gives a cross-section equivalent to 6.2 mm in diameter, less than the 10 mm desired. A 2/0 AWG of that material also works.
Step 3: tolerable voltages
- Reduction factor of the surface layer (Cs): 0.74. It is calculated with the standard’s empirical form: 1 − 0.09 (1 − ρ/ρs) / (2 hs + 0.09), with ρ = 400 Ω·m, ρs = 2,500 Ω·m and hs = 0.102 m.
- Tolerable step voltage (70 kg person): (1000 + 6 Cs ρs) × 0.157 / √ts = 2,686.6 V.
- Tolerable touch voltage (70 kg person): (1000 + 1.5 Cs ρs) × 0.157 / √ts = 838.2 V.
Step 4: initial design
A 70 m × 70 m grid with conductors equally spaced every 7 m (D = 7 m), a depth of 0.5 m and no rods. That gives 11 conductors in each direction and a total buried length of 2 × 11 × 70 m = 1,540 m.
Step 5: grid resistance
Resistance = ρ [1/LT + 1/√(20 A) × (1 + 1/(1 + h √(20/A)))], with LT = 1,540 m and A = 4,900 m². Result: 2.78 Ω.
The EPRI calculation program gave 2.67 Ω for this case.
Step 6: maximum grid current
IG = Df × Sf × 3I0 = 1.0 × 0.6 × 3,180 = 1,908 A.
The 115 kV fault (3,180 A) is used and not the 13 kV one (6,814 A), even though the latter is larger, because the grounded 13 kV winding is a local source of current and does not contribute to the ground potential rise.
Step 7: ground potential rise
GPR = IG × Rg = 1,908 × 2.78 = 5,304 V. It far exceeds the 838 V of tolerable touch voltage, so the mesh voltage check continues. The origin of that current is in maximum grid current and split factor.
Step 8: mesh voltage
- Km (geometric factor), with Kii = 0.57 and Kh = 1.225: 0.89.
- n (effective parallel conductors): 11 (square grid).
- Ki (irregularity factor) = 0.644 + 0.148 n: 2.272.
- Mesh voltage = ρ × IG × Km × Ki / LM = 400 × 1,908 × 0.89 × 2.272 / 1,540 = 1,002.1 V.
Step 9: comparison
The mesh voltage, 1,002.1 V, is higher than the tolerable touch voltage, 838.2 V. The design must be modified. The EPRI program gave 984.3 V, a very close result.
- Data and conductor size. Soil, fault current and clearing time
- Tolerable voltages. Step: 2,686.6 V; touch: 838.2 V
- Resistance, grid current and ground potential rise. 2.78 Ω, 1,908 A and 5,304 V
- Is the mesh voltage lower than the tolerable one? Yes: continue; No: The design is modified; example 2 adds rods.
- Complete design. With the refinements for equipment and arresters
What changes in the following examples
- Example 2 (square with rods). With the same grid, 20 rods of 7.5 m are added on the perimeter. The mesh voltage drops to 747.4 V, below the 838.2 V tolerable, and the design complies. Only the detail remains to be completed: equipment pigtails and additional rods at arresters.
- Example 3 (rectangular with rods). The grid takes the real dimensions of 63 m × 84 m, with 1,659 m of conductor and 38 rods of 10 m.
- Example 4 (L-shaped with rods). It shows the calculation for an irregularly shaped grid.
The lesson: in this example, the rods on the perimeter lowered the mesh voltage from 1,002.1 V to 747.4 V, and covering the whole area with grid was not enough to comply.
How to use the example
The example is useful to understand the order of the calculation and to compare your own values. With real data, the fault current comes from the short-circuit study, the soil model from the resistivity measurement and the clearing time from the protection. You can try your own data with the free Grounding resistance tool.
How we do it at Tiza Group
At Tiza Group we do the design and verification of the grid for medium, high and extra-high voltage substations and industrial plants with real data and, when the case requires it, with calculation programs. Learn about our engineering design and studies service or write to us. We deliver it remotely, worldwide.
Related guides
- IEEE 80: Safety in Substation Grounding
- Substation Grounding Design: IEEE 80 Method
- Gravel Layer in Substations: Cs Factor and Safety
- Substation Grounding Grid: Design and Testing
- Step and Touch Voltage: Difference and IEEE 80
References
- IEEE Std 80-2013, IEEE Guide for Safety in AC Substation Grounding, Annex B, examples 1 to 4; clauses 16.4 and 16.5.
Frequently asked questions
Why does the example fail if the grid looks large?
Because the calculated mesh voltage, 1,002.1 V, exceeds the tolerable touch voltage of 838.2 V. The grid's ground potential rise, 5,304 V, also far exceeds the tolerable value, so it is not enough for the grid to cover the whole area: the mesh voltage must be lowered, for example with rods or with closer conductors.
What fault current was used for the example design?
The fault was calculated at the 115 kV bus (3,180 A) and at the 13 kV bus (6,814 A). The conductor is sized with the larger one, 6,814 A. But the ground potential rise is calculated with the 115 kV fault, because the grounded-wye 13 kV winding is a local source of fault current and does not contribute to the ground potential rise.
Can I use these numbers in my substation?
No. They are data from the standard's example: the soil, currents, area and clearing time change in every substation. The example is useful to understand the order of the calculation and to compare with your own values.