Cable Derating and Voltage Drop on a Long Ceiling-Void Submain
A workshop submain runs 95 m from the main LV switchboard to a distribution board in a ceiling void. The load is 250 A three-phase, 400 V, power factor 0.85, and the designer has selected a single 4-core 95 mm² copper XLPE/SWA cable. Manufacturer data give a tabulated current-carrying capacity of 289 A for this cable on a perforated tray, conductor resistance at operating temperature of 0.247 Ω/km and reactance of 0.080 Ω/km. The tray already carries three other loaded circuits of similar size, and the summer temperature in the void has been logged at 45 °C. Correction factors from the project tables are 0.91 for the 45 °C ambient and 0.78 for the grouping. The board's incoming terminals are rated 70 °C. The client has asked whether the cable can be installed as designed, and the voltage drop limit for the submain is 2.5% of 400 V.
1. Check the 95 mm² selection against the load and installation conditions, showing your calculation.
Read the worked answer
Current-carrying capacity
- Tabulated capacity: 289 A.
- Ambient factor: 0.91. Grouping factor: 0.78.
- Effective capacity: 289 × 0.91 = 263.0 A; 263.0 × 0.78 = 205 A.
- The load is 250 A, so the cable is overloaded by about 22%. The required tabulated capacity is 250 / (0.91 × 0.78) = 352 A, well above 289 A.
Voltage drop
- sin φ from cos φ 0.85 is 0.527.
- Per-phase drop per kilometre: 250 × (0.247 × 0.85 + 0.080 × 0.527) = 250 × (0.210 + 0.042) = 63.0 V/km.
- Line-to-line drop over 95 m: √3 × 63.0 × 0.095 = 10.4 V, which is 2.6% of 400 V.
- This exceeds the 2.5% limit (10 V) even before the terminal rating is considered.
Terminal constraint
- The board terminals are rated 70 °C while the cable is a 90 °C XLPE product. The 289 A figure cannot be used at full value into 70 °C equipment; a conductor selected from the 70 °C basis, or a larger size, is required. This makes the selection even more marginal.
Conclusion: the 95 mm² cable fails on current capacity, fails marginally on voltage drop, and is not supportable on the terminal temperature rating. It cannot be installed as designed.
2. Select a replacement size from the following data - 120 mm²: 331 A; 150 mm²: 377 A; 185 mm²: 429 A - and check the voltage drop for the chosen size using R = 0.160 Ω/km and X = 0.075 Ω/km at 150 mm².
Read the worked answer
Capacity check with derating factors 0.91 and 0.78
- 120 mm²: 331 × 0.91 × 0.78 = 235 A < 250 A. Rejected.
- 150 mm²: 377 × 0.91 × 0.78 = 268 A ≥ 250 A. Acceptable on capacity, with about 7% headroom.
- 185 mm²: 429 × 0.91 × 0.78 = 304 A. Acceptable with generous headroom, and the size to prefer if the 70 °C terminal limitation is applied strictly.
Voltage drop for 150 mm²
- Per-phase drop per kilometre: 250 × (0.160 × 0.85 + 0.075 × 0.527) = 250 × (0.136 + 0.0395) = 43.9 V/km.
- Line-to-line over 95 m: √3 × 43.9 × 0.095 = 7.2 V, i.e. 1.8% of 400 V, comfortably within the 2.5% limit.
Judgement The 150 mm² satisfies both capacity and volt drop on paper. However, its 268 A effective capacity against a 250 A load leaves little margin for the 70 °C terminal rating, future load growth, or a higher measured summer temperature than the 45 °C logged. Recommending 185 mm² is defensible and often the better engineering answer, but 150 mm² with the terminal limitation formally resolved is the minimum compliant choice. Either way, the protective device rating must satisfy Ib ≤ In ≤ Iz with the derated value - a 250 A device leaves virtually no margin at 150 mm², which is a further argument for the larger size.
3. Beyond current capacity and voltage drop, what else must be verified before this submain can be signed off?
Read the worked answer
- Protective device coordination: the device rating must satisfy Ib ≤ In ≤ Iz with the derated Iz, its breaking capacity must exceed the prospective fault current at the board, and discrimination with the upstream device must be confirmed so a downstream fault does not take out the main incomer.
- Earth fault loop impedance at the far end of the 95 m run, compared with the maximum permitted for the device type and rating; a long run is where this usually fails, and a Type D or C device may need replacing or an RCD adding.
- Earthing conductor sizing, both by the table method and by the adiabatic check k²S² ≥ I²t against the actual fault level and disconnection time; the SWA armour alone is rarely an adequate CPC at this fault level.
- Tray loading and spacing actually achieved on site, since the 0.78 grouping factor assumed a defined arrangement; cables added during installation invalidate the calculation.
- Fire sealing and support at the wall penetration and in the ceiling void, and confirmation that thermal insulation has not been laid over the cable - a common cause of overheating after handover.
- Neutral sizing if any harmonic-rich load (IT, drives, LED) is expected on the submain.
- Testing and records: insulation resistance, continuity of protective and bonding conductors, polarity, and a schedule of test results with the as-installed route length, plus labelling at both ends.