Earthing (grounding) provides a reference point of zero volts for the electrical system and a safe path for fault currents. This ensures that overcurrent devices operate correctly and reduces touch voltages for safety. Earthing design calculations focus on:
For a given circuit, the loop impedance (Zs)—which includes the source (e.g., transformer winding), line conductor, and the return path (CPC and possibly the earth/ground path in a TT system)—is calculated by summing the resistances of each component. Once Zs is known, the prospective earth fault current is:
If = U₀ / Zs
(Here, U₀ is the phase-to-neutral voltage for a single-phase fault.) The protective device must interrupt this fault current within a specified time (e.g., 0.4 s for final circuits in TN systems per BS 7671). BS 7671 provides maximum Zs values for each protective device, essentially as:
Zs ≤ U₀ / I₂
where I₂ is the current needed to ensure trip within time. Designers calculate Zs from cable lengths, sizes, and transformer source impedance, ensuring it is below the maximum. If not, either larger conductors or additional bonding is required.
For TT (Terra-Terra) systems, the sum of the electrode resistance and the earth conductor resistance (RA) is used along with the RCD trip current (IΔn) to ensure:
RA × IΔn ≤ 50 V
This calculation ensures that touch voltages remain safe.
A basic formula for a single rod electrode (of length L and diameter d) in homogeneous soil (with resistivity ρ) is derived from integrating the spreading resistance along the rod. For example, consider a 12 mm diameter rod, 3 m long, in soil with ρ = 100 Ω·m:
R ≈ [100 / (2π×3)] × (ln(43/0.012) − 1)
In practice, if the calculated resistance is high (e.g., ~31 Ω in this example), multiple rods or a grid is used to achieve a target resistance below, say, 10 Ω.
In substations, an earth grid is installed under a gravel bed. Under fault conditions, not all parts of the grid remain at 0 V; portions may rise in potential relative to remote earth.
IEEE 80 and equivalent IEC standards provide formulas to estimate these voltages based on grid geometry, fault current, and soil resistivity. Designers compute the grid resistance (Rg) and current splits, comparing the results to safe limits. If the computed step/touch voltage exceeds acceptable levels, adjustments (such as adding more electrodes or increasing mesh density) are made.
Earth and bonding conductors must safely carry fault current for the brief time until disconnection occurs without melting. The adiabatic formula used is:
I²t = (kS)²
where S is the cross-sectional area (in mm²), If is the fault current (in A), t is the duration (in s), and k is a material constant (for copper, typically ≈115 when considering a temperature rise from 90°C to 250°C). For example, if a 10 kA fault lasts 0.1 s:
I²t = (10,000)² × 0.1 = 10⁸ A²s
Then, for copper with k = 115:
S = √(10⁸) / 115 ≈ 27.7 mm²
A 35 mm² earth conductor would thus be adequate. In practice, standards provide tables correlating I²t values with conductor sizes.
ρ values. If layered soil is found, a two-layer soil model may be used.
Proper earthing is fundamental for electrical safety. Calculations ensure that if a phase conductor contacts a machine frame, the resulting fault current is sufficient to trip protective devices quickly—reducing the risk of electric shock. In supply networks, effective earthing helps control touch voltages during faults. Additionally, earthing affects electromagnetic compatibility by providing a reference for shielding. Poor earthing can lead to erratic RCD trips or dangerously high step voltages.
Earthing calculations combine theoretical formulas with empirical design rules. By following established standards and using specialized tools, engineers design grounding systems that protect people from electric shock and ensure that equipment withstands fault conditions.