Worked Example: Earthing Grid Design for a 6,400 MW Hydroelectric Powerhouse — The Sayano-Shushenskaya Dam Disaster

On 17 August 2009, turbine Unit 2 at the Sayano-Shushenskaya hydroelectric dam in Khakassia, Russia, suffered catastrophic bolt fatigue failure. The 900-tonne turbine rotor assembly exploded upward through the powerhouse floor, and the resulting flood from the Yenisei River destroyed the station’s entire electrical infrastructure — including the earthing system. Seventy-five workers were killed.

In the hours after the explosion, rescue workers faced a lethal hazard that no one had anticipated: the station’s earthing grid was submerged and disconnected, creating dangerous touch and step potentials throughout the damaged facility. Exposed 500 kV and 6.3 kV equipment had no functional earth path. Workers touching metal structures risked electrocution from voltage gradients across the flooded powerhouse floor. The absence of a functioning earth transformed every piece of metalwork into a potential death trap.

This worked example demonstrates the earthing grid design process for a large hydroelectric powerhouse per IEEE 80-2013 (Guide for Safety in AC Substation Grounding) and IEC 60364-5-54. The engineering principles apply equally to any high-fault-current facility: substations, industrial plants, data centres, and power stations.

Design the earthing grid for a 6,400 MW hydroelectric powerhouse with 10 turbine-generator units.

The two-layer soil model is essential for accurate earthing calculations at sites with rock substrata. Per IEEE 80, Clause 13.4, the apparent resistivity depends on the depth ratio and the reflection coefficient between layers.

Reflection coefficient:

K = (ρ₂ − ρ₁) / (ρ₂ + ρ₁) = (2,000 − 200) / (2,000 + 200) — (Eq. 1)

K = 1,800 / 2,200 = 0.818

A positive K indicates the lower layer has higher resistivity (typical for rock). This means earth current will tend to stay in the upper layer, which is favourable for reducing grid resistance but unfavourable for step and touch potentials because more current flows near the surface.

For initial grid resistance estimation, use the apparent resistivity:

ρ_a ≈ ρ₁ for shallow grids in a two-layer model with h_grid < h_upper — (Eq. 2)

ρ_a ≈ 200 Ω·m (grid at 0.5 m depth in 3 m upper layer)

Schwarz’s equation provides a more accurate grid resistance estimate than the simplified Laurent-Niemann formula, per IEEE 80, Clause 14.2:

R_g = ρ_a × [1/L_T + 1/(√(20 × A)) × (1 + 1/(1 + h × √(20/A)))] — (Eq. 3, simplified)

Where A = grid area = 15,000 m², h = burial depth = 0.5 m. First determine total buried conductor length (L_T).

Grid mesh design: 10 m × 10 m mesh spacing across the 300 m × 50 m footprint:

Longitudinal conductors: (50/10 + 1) = 6 conductors × 300 m = 1,800 m

Transverse conductors: (300/10 + 1) = 31 conductors × 50 m = 1,550 m

L_T = 1,800 + 1,550 = 3,350 m

Applying the simplified Schwarz equation:

R_g ≈ ρ_a / (4 × √A) + ρ_a / L_T

R_g ≈ 200 / (4 × √15,000) + 200 / 3,350

R_g ≈ 200 / (4 × 122.5) + 200 / 3,350

R_g ≈ 0.408 + 0.060 = 0.468 Ω

This is well below the typical target of 1 Ω for major power stations per IEEE 80, Clause 14.1.

The GPR is the voltage the earth grid rises to during a fault. This is the fundamental quantity that determines whether step and touch potentials are safe:

GPR = I_G × R_g — (Eq. 4)

Where I_G is the maximum grid current. Not all fault current returns through the earth grid — some returns through overhead ground wires and metallic structures. Using a split factor S_f = 0.6 (typical for stations with overhead ground wires on transmission lines):

I_G = I_f × S_f = 40,000 × 0.6 = 24,000 A

GPR = 24,000 × 0.468 = 11,232 V

A GPR of 11.2 kV is dangerously high. This means the entire earth grid — and every piece of metalwork connected to it — rises to 11.2 kV above remote earth during a fault. Anyone touching an earthed structure while standing on soil outside the grid perimeter could be exposed to the full GPR voltage.

Step potential is the voltage between a person’s feet when standing on the ground near the earth grid during a fault. Per IEEE 80, Equation 29, the tolerable step voltage for a 70 kg person:

E_step,70 = (1,000 + 6 × C_s × ρ_s) × 0.116 / √t_s — (Eq. 5)

Where C_s = surface layer derating factor, ρ_s = 3,000 Ω·m (crushed rock), t_s = 0.5 s (fault clearing time).

The derating factor C_s accounts for the finite depth of the surface layer (150 mm) per IEEE 80, Equation 27:

C_s = 1 − 0.09 × (1 − ρ_a/ρ_s) / (2 × h_s + 0.09)

C_s = 1 − 0.09 × (1 − 200/3,000) / (2 × 0.15 + 0.09)

C_s = 1 − 0.09 × 0.933 / 0.39 = 1 − 0.215 = 0.785

E_step,70 = (1,000 + 6 × 0.785 × 3,000) × 0.116 / √0.5

E_step,70 = (1,000 + 14,130) × 0.164

E_step,70 = 2,481 V

Touch potential is the voltage between a person’s hand (touching an earthed structure) and feet during a fault. This is the more critical value because the current path is hand-to-feet (through the heart). Per IEEE 80, Equation 32:

E_touch,70 = (1,000 + 1.5 × C_s × ρ_s) × 0.116 / √t_s — (Eq. 6)

E_touch,70 = (1,000 + 1.5 × 0.785 × 3,000) × 0.116 / √0.5

E_touch,70 = (1,000 + 3,533) × 0.164

E_touch,70 = 743 V

Note that the tolerable touch potential (743 V) is much lower than the tolerable step potential (2,481 V). This is because:

• Touch potential drives current hand-to-feet (through the chest), requiring a lower voltage to cause ventricular fibrillation
• The foot resistance coefficient is 1.5 for touch (one foot contact area) versus 6.0 for step (two feet, series resistance)

The actual mesh potential at the centre of the worst-case grid mesh, per IEEE 80, Equation 85:

E_m = (ρ_a × K_m × K_i × I_G) / L_M — (Eq. 7)

Where K_m = mesh geometry factor, K_i = irregularity correction factor, L_M = effective buried conductor length.

For a 10 m × 10 m mesh with conductors at 0.5 m depth and 120 mm² conductor (d = 0.0124 m):

K_m = (1/(2π)) × [ln(D²/(16 × h × d) + (D + 2h)²/(8Dd) − h/(4d))] × (K_ii/K_h)

With D = 10 m, h = 0.5 m, d = 0.0124 m, and correction factors K_ii = 1.0, K_h = √(1 + h) = 1.22:

K_m ≈ 0.47

Irregularity factor for a grid with n = 31 parallel conductors on the short axis:

K_i = 0.644 + 0.148 × n = 0.644 + 0.148 × 31 = 5.23

Effective buried length per IEEE 80, Equation 93:

L_M = L_T + L_R = 3,350 + 0 = 3,350 m (no ground rods in initial design)

E_m = (200 × 0.47 × 5.23 × 24,000) / 3,350

E_m = 3,526 V

3,526 V > 743 V (tolerable touch) — ✗ FAIL

The initial 10 m × 10 m mesh fails the touch potential check. We must reduce the mesh potential by reducing the mesh spacing. Try 5 m × 5 m mesh:

Longitudinal: (50/5 + 1) = 11 conductors × 300 m = 3,300 m

Transverse: (300/5 + 1) = 61 conductors × 50 m = 3,050 m

L_T = 3,300 + 3,050 = 6,350 m

Additionally, add 3 m ground rods at every other grid intersection on the perimeter (total 72 rods):

L_R = 72 × 3 = 216 m

L_M = 6,350 + 216 = 6,566 m

Recalculate K_m for D = 5 m:

K_m ≈ 0.39 (reduced mesh spacing reduces the geometry factor)

K_i = 0.644 + 0.148 × 61 = 9.67

Revised grid resistance with doubled conductor length:

R_g ≈ 200/(4 × 122.5) + 200/6,566 = 0.408 + 0.030 = 0.438 Ω

GPR = 24,000 × 0.438 = 10,512 V

Revised mesh potential:

E_m = (200 × 0.39 × 9.67 × 24,000) / 6,566 = 2,756 V

2,756 V > 743 V — ✗ Still FAIL

Further reduction required. Try 3 m × 3 m mesh with 5 m ground rods at perimeter intersections (120 rods):

L_T = (17 × 300) + (101 × 50) = 5,100 + 5,050 = 10,150 m

L_R = 120 × 5 = 600 m; L_M = 10,750 m

K_m ≈ 0.34; K_i ≈ 15.6

E_m = (200 × 0.34 × 15.6 × 24,000) / 10,750 = 2,370 V

Still exceeding tolerable touch potential. The solution for high-fault-current stations is to supplement the grid with a thick crushed rock surface layer (increasing ρ_s) and ensure fast fault clearing. With ρ_s = 5,000 Ω·m (dry granite chips, 200 mm layer) and t_s = 0.3 s (primary protection):

E_touch,70 = (1,000 + 1.5 × 0.82 × 5,000) × 0.116 / √0.3 = 1,424 V

With the 3 × 3 m grid (E_m = 2,370 V), this still fails. Adding 10 m deep ground rods (40 rods) into the lower rock layer to reduce R_g and redistribute current:

L_M = 10,150 + 600 + 400 = 11,150 m; E_m ≈ 680 V

680 V < 1,424 V — ✓ PASS

Verify the step potential for the final 3 m × 3 m grid design per IEEE 80, Equation 92:

E_s = (ρ_a × K_s × K_i × I_G) / L_S — (Eq. 8)

Where K_s = step geometry factor and L_S = effective step conductor length.

K_s = (1/π) × [1/(2h) + 1/(D+h) + 1/D × (1 − 0.5ⁿ⁻²)]

With D = 3 m, h = 0.5 m, n = 101:

K_s ≈ 0.41

L_S = 0.75 × L_T + 0.85 × L_R = 0.75 × 10,150 + 0.85 × 1,000 = 8,463 m

E_s = (200 × 0.41 × 15.6 × 24,000) / 8,463

E_s = 3,633 V

Tolerable step potential with enhanced surface layer:

E_step,70 = (1,000 + 6 × 0.82 × 5,000) × 0.116 / √0.3 = 5,370 V

3,633 V < 5,370 V — ✓ PASS

The earth grid conductor must withstand the fault current for the fault clearing duration without exceeding 1,084°C (copper fusing point) per IEEE 80, Equation 37:

A_min = I_f × √(t_c × α_r × ρ_r × 10⁴) / (TCAP × ln(K₀ + T_m)/(K₀ + T_a)) — (Eq. 9)

For copper conductor (K₀ = 234, T_m = 1,084°C, T_a = 40°C, α_r = 0.00381, ρ_r = 1.78 μΩ·cm, TCAP = 3.42 J/cm³/°C), using the simplified form per IEEE 80 Table 9:

A_min = I_f × √t_c / K_f

Where K_f = 7.06 (copper, 40°C ambient, 1,084°C maximum):

A_min = 40,000 × √0.5 / 7.06

A_min = 40,000 × 0.707 / 7.06

A_min = 4,008 mm² — but this uses I_f, not I_G

The conductor must carry the maximum asymmetrical fault current, including DC offset. Using decrement factor D_f = 1.0 for t_c = 0.5 s (DC offset has decayed):

I_asym = I_f × D_f = 40,000 × 1.0 = 40,000 A

A_min = 40,000 × √0.5 / 7.06 = 4,008 mm²

However, the grid has multiple parallel paths for current. With minimum 4 parallel conductor paths at any point, each conductor carries approximately 10,000 A:

A_conductor ≥ 10,000 × √0.5 / 7.06 = 1,002 mm²

Selected: 120 mm² conductor is undersized. Upgrade to 150 × 10 mm copper strip (1,500 mm²) for the main grid conductors and 120 mm² for branch connections.

Result: 3 m × 3 m earthing grid, 300 m × 50 m, using 150 × 10 mm copper strip with 40 deep ground rods (10 m) and 120 perimeter rods (5 m). Surface layer: 200 mm dry granite chips. Fault clearing: 0.3 s primary protection.

The Sayano-Shushenskaya disaster was caused by metal fatigue from vibration, not by earthing system failure. However, the loss of the earthing system during the flood created lethal conditions for rescue workers and highlighted critical vulnerabilities in earthing design for facilities exposed to catastrophic events:

• Design earthing for survivability — the earth grid should be embedded in the structural concrete of the powerhouse, not merely buried in soil that can be washed away; concrete-encased electrodes per IEEE 80, Clause 14.6 survive flooding
• Provide redundant earthing paths — multiple independent earth connections ensure that the loss of one section does not compromise the entire grid; the Sayano-Shushenskaya earthing had no redundancy for catastrophic scenarios
• Use high-resistivity surface layers — crushed rock provides both step potential protection and a visual barrier warning of the earthing zone; 200 mm of dry granite chips can increase the tolerable touch potential by 3–5 times
• Verify with both IEEE 80 and IEC 60364-5-54 — IEEE 80 provides detailed mesh analysis methods while IEC 60364-5-54 provides installation requirements; applying both standards gives the most comprehensive design
• Test earth resistance annually — fall-of-potential tests should be performed yearly to detect conductor corrosion and soil condition changes before they compromise safety