Cable and Earthing Design for a Workshop Extension
A textile workshop adds 45 kW of new machine load at 415 V, 0.82 pf, on a 60 m route from the main LT panel. The cable will run on a perforated tray carrying six other loaded circuits, in a shed where the ambient reaches 45 °C. The selected cable is 3-core copper XLPE, armoured, installed in free air, protected by a 100 A MCCB. The permissible voltage drop from the main panel to the machine is 3 %. Separately, the existing earth pit for the LT panel measures 12 Ω by the fall-of-potential method; the utility requires ≤ 5 Ω. The local soil resistivity is about 120 Ω·m. The contractor says 'just drive two more 3 m GI pipes and it will come down', using 16 mm rods.
1. Compute the design current and select a cable size that satisfies both the derated current-carrying capacity and the 3 % voltage drop.
Read the worked answer
Design current: I_b = 45 000 / (√3 × 415 × 0.82) = 45 000 / 589.4 = 76.3 A
Derating: ambient correction at 45 °C for XLPE, Ca ≈ 0.87; grouping of 7 loaded circuits on a tray, Cg ≈ 0.70. Combined = 0.609. Required tabulated rating = 76.3 / 0.609 = 125 A.
Protection rule (I_b ≤ I_n ≤ I_z) with I_n = 100 A means the installed, derated capacity must be at least 100 A, not merely 76.3 A:
- 35 mm² (≈ 129 A tabulated) → 129 × 0.609 = 78.6 A - below 100 A, non-compliant
- 50 mm² (≈ 153 A) → 93 A - still below 100 A
- 70 mm² (≈ 196 A) → 119 A - compliant with a 100 A MCCB
Voltage drop check (70 mm², ≈ 0.63 mV/A/m): 0.63 × 76.3 × 60 / 1000 = 2.9 V = 0.70 % - well within 3 %.
Judgement: voltage drop is not the limiting criterion; grouping and ambient are. Two compliant options: 70 mm² with the 100 A MCCB, or 50 mm² with an 80 A MCCB (93 A ≥ 80 A), provided the motor starting current and the MCCB's setting are verified. The 50 mm² option is materially cheaper on a 60 m run.
2. Quantify the earthing problem - will two additional 3 m rods achieve 5 Ω?
Read the worked answer
Single rod resistance (ρ = 120 Ω·m, L = 3 m, d = 0.016 m):
R = ρ/(2πL) × [ln(4L/d) − 1] = 120/(2π × 3) × [ln(750) − 1] = 6.37 × (6.62 − 1) = 6.37 × 5.62 ≈ 35.8 Ω
Parallel rods are not simply additive because their resistance areas overlap. With a mutual-resistance efficiency of about 0.7 for closely spaced rods, three rods give ≈ 35.8/(3 × 0.7) ≈ 17 Ω - and even with the existing pit's 12 Ω in parallel the result is only ~7 Ω, still above 5 Ω. To reach 5 Ω with rods alone you would need roughly 10–12 rods at proper spacing, which is not what 'drive two more pipes' means.
The physics point: a 3 m rod only influences soil within a couple of rod lengths. Adding rods in the same small pit simply moves the same current through the same soil volume.
Practical remedies:
- Use a maintenance-free chemical/backfill electrode or a plate, which presents a much larger effective surface to the soil.
- Or lay a buried ring/tape conductor around the shed, or bond to the building's structural steel foundation earth, where available.
- Treat the soil with bentonite or a proprietary compound only where the resistivity genuinely justifies it; verify by fall-of-potential test afterwards, never by a clamp-on tester on a live system with parallel paths.
3. What safety and verification checks must accompany this extension before energisation?
Read the worked answer
Before energisation:
- Insulation resistance - 500 V DC IR test on the new 70 mm² (or 50 mm²) run; expect ≥ 1 MΩ, in practice hundreds of MΩ for a new XLPE cable. Record phase–phase, phase–neutral and phase–earth.
- Continuity and polarity of the earth conductor and the armour bonding; confirm the armour is earthed at the panel end and the gland is correctly made off.
- Earth resistance re-measured by fall-of-potential to prove ≤ 5 Ω - the design value is not a measurement.
- Protection settings - verify the MCCB's thermal setting matches the cable's derated capacity (80 A or 100 A as selected) and the magnetic setting is above the motor starting inrush.
- Labelling and documentation - updated single-line diagram, cable schedule and the derating assumptions (Ca, Cg) recorded so the next addition does not silently overfill the tray.
Judgement call: the single most common mistake here is to energise on the basis of the contractor's verbal assurance and the original 12 Ω reading. Insist on a witnessed, recorded test; the 3 % voltage-drop and derating calculations are worthless if the installation is later modified without re-checking the grouping factor.