EARTHING CALCULATION METHODOLOGY
A. DESIGN BASIS FOR EARTHING
Site Conditions:
Maximum ambient temperature
50 Deg. C
Relative humidity (max)
95%
Height
<1000 Meters
Atmosphere
Dusty and Corrosive
Power supply conditions:
Voltage Level
Voltage Variation
Short Circuit Level
415 V
+/- 10%
50 kA for 1 second
Applicable standards:
IS 3043, 2018 and Reaffirmed 2019 (Code Practice for Earthing) and Indian Electricity Rules/Acts
B. EARTHING DESIGN CALCULATION
Input Design data & Considerations
RMS value of the AC Ground fault current, which
50 kA
can flow through the conductor in Amps (I)
Withstand time for disconnecting protective
1.0 Sec
devices
Considering breaker opening time, Fault duration
0.2 Sec
for selection of conductor dimension (T)
Average Soil Resistivity (ρ) as per actual site
condition
40 Ω m
Adequacy of Size of GI Earth Strip
As per IS 3043-1987 clause no. 12.2.2.1,
The cross sectional area of earth strip A = (I x√T) / k
where,
Value of the fault current in Amp
I = 50000
Factor dependant on material of the conductor
K = 80.69
Operating time of fault clearing device in sec
T = 0.2
and
√[{Qc(B+20)}
K=
ln {1+ (θf−θi)
───────
─────
δ20
(B+θi)
}]
For Steel Earth Strip (as per Cl. No.-12.2.2.1, sh no, 29-31 of IS 3043):
Volumetric heat capacity of conductor material ( j/° C mm³) Qc
0.0038
Reciprocal of temperature coefficient of resistivity at 0° C for the conductor (° C) B
202
Electrical resistivity of conductor material at 20° C(Q-mm)δ20
0.000138
Initial temperature of conductor (° C) θi
40
Final temperature of conductor (° C ) (Non Hazardous Area) θf
500
√[ 𝟑. 𝟖 × 𝟏𝟎⁻³ × (𝟐𝟎𝟐 + 𝟐𝟎) 𝐥𝐧(𝟏 + (𝟓𝟎𝟎 − 𝟒𝟎)) ]
𝐤 =
───────────────── ────────────────
𝟏𝟑𝟖 × 𝟏𝟎⁻⁶
= 80.69
(𝟐𝟎𝟐 + 𝟒𝟎)
Putting value of K=80.69, I=50kA and T=0.2 sec
The cross sectional area of earth strip A = (I x V √T)/k
A =277.2 sqmm
The selected Earth strip size of 50x6 mm Gl Strip for Main earthing ring with cross section
area 300 sq.mm is more than the required cross-section.
Calculation of Resistance of Earth Electrode:
Length of Electrode
LE
300 cm
Dia of Electrode
d
8 cm
Resistivity of soil
ρ
40 ohm-m
Resistance of the pipe electrode (RE) =
No.of earthing rod considered N =
100 𝐗 𝛒 X
𝐥𝐧 (𝟐 𝐗 𝐋𝐄)
────────
──────
2Π x LE
d
INPUT PARAMETERS:
• Soil resistivity (ρ)
40 Ω-m (natural)
• Number of electrodes
2
• Electrode material
GI pipe
• Electrode diameter (d)
80 mm
• Electrode length (L)
6 m (2×3m coupled)
• Backfill type
Crystalline conductive compound
• Backfill resistivity (ρᵦ)
0.5 Ω-m
• Effective diameter (D)
150 mm (with backfill)
• Electrode spacing (S)
10 m
• Fault current (I)
50 kA
• Fault duration (T)
0.2 sec
STEP 1: SINGLE ELECTRODE RESISTANCE CALCULATION
Using Dwight's formula:
ρᵦ
R₁ =
4L ⎞
⎛
× ln
2πL
⎝
0.5
⎛ 4×6 ⎞
D⎠
= ------- × ln ⎜ ---- ⎟
2π×6
⎝ 0.15⎠
= (0.01326) × ln(160)
= 0.01326 × 5.075
= 0.0673 Ω (theoretical minimum)
Applying practical adjustment factor (k = 4.2):
R₁ₐ = 0.0673 × 4.2 = 0.28 Ω
===============================================================================
STEP 2: PARALLEL SYSTEM RESISTANCE
-------------------------------------------------------------------------------
Using parallel resistance formula with mutual coupling:
R₁ₐ
⎛ λ⎞
Rₜ = ------- × ⎜ 1 + --- ⎟
n
n⎠
⎝
Where:
n = 2 (number of electrodes)
λ = 1.15 (for S/L = 10/6 = 1.67)
0.28
⎛ 1.15 ⎞
= ------- × ⎜ 1 + ---- ⎟
2
⎝ 2 ⎠
= 0.14 × 1.575
= 0.2205 Ω
===============================================================================
STEP 3: SAFETY FACTOR APPLICATION
------------------------------------------------------------------------------Environmental degradation factor = 1.3
Worst-case expected resistance:
R_wc = 0.2205 × 1.3 = 0.2866 Ω (<1.0 Ω target)
===============================================================================
STEP 4: CONDUCTOR SIZING VERIFICATION
------------------------------------------------------------------------------Per IS 3043 Clause 12.2.2.1:
I × √T
A = --------K
Where:
K = 80.69 (for GI material)
50,000 × √0.2
= ---------------80.69
= 277.2 mm²
Selected conductor: 50×6 mm GI strip (300 mm²) → SAFE
===============================================================================
SUMMARY OF RESULTS:
------------------------------------------------------------------------------1. Single electrode resistance = 0.28 Ω
2. Parallel system resistance
= 0.22 Ω
3. Worst-case resistance
= 0.29 Ω
4. Conductor size verification = 300 mm² (Safe)
5. Design meets all requirements
===============================================================================
END OF CALCULATION