Engineering earthing calculator implementing IEEE Std 80-2013 Sverak's formula for grounding grid resistance, Ground Potential Rise (GPR in kV), and tolerable touch and step potential limits for 50 kg and 70 kg human body weights with surface crushed rock layer reflection factor.
Governing Formulas & Standards
Standards Basis: IEEE Std 80-2013 / IEEE Std 81 / IS 3043
R_g = \rho \cdot \left[\frac{1}{L_t} + \frac{1}{\sqrt{20 A}} \left(1 + \frac{1}{1 + h\sqrt{20/A}}\right)\right] \quad ; \quad E_{touch} = \frac{1000 + 1.5 C_s \rho_s}{\sqrt{t_s}} \cdot 0.116
Calculates substation grounding resistance R_g (Ω) where ρ is soil resistivity (Ω·m), L_t is total buried conductor length, A is grid area (m²), and h is burial depth. E_touch is tolerable touch voltage limit for a 50 kg person over shock duration t_s.
Worked Engineering Example: 132 kV Substation Grounding Grid Safety Design (60m × 40m)
- Grid Resistance by Sverak Formula: R_g = 50 × [1/950 + 1/√(20×2400) × (1 + 1/(1 + 0.6×√(20/2400)))] → R_g = 0.542 Ω
- Ground Potential Rise (GPR): GPR = I_g × R_g = 8,500 × 0.542 → 4,607 V (4.61 kV)
- Surface Derating Factor (Cs): K = (50 - 2500) / (50 + 2500) = -0.96 | C_s ≈ 0.74 → C_s = 0.74
- Tolerable Touch Voltage (50 kg body): E_touch = (1000 + 1.5 × 0.74 × 2500) / √0.5 × 0.116 → 619.4 V
- Tolerable Step Voltage (50 kg body): E_step = (1000 + 6.0 × 0.74 × 2500) / √0.5 × 0.116 → 1,985.3 V
Final Solution: Grid Resistance: 0.542 Ω | GPR: 4.61 kV | Tolerable Touch: 619.4 V | Tolerable Step: 1,985 V
Frequently Asked Questions
- Why is a layer of crushed rock / gravel spread across substations?
- High-resistivity crushed rock (typically 2,000–3,000 Ω·m wet) introduces high series contact resistance beneath human feet, raising the tolerable touch and step voltage limits from ~200 V on bare soil to over 600–800 V, preventing fatal electrocution.
- What is the acceptable earth resistance for an electrical substation?
- IEEE 80 and utility standards typically mandate grid resistance < 1.0 Ω for large distribution and transmission substations (< 0.5 Ω for ultra-high voltage / mega power stations) to limit GPR and equipment enclosure potentials.
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