35 mm² Submain Through an Insulated Wall
A 415 V, 3-phase submain is to be run from the main switchboard to a new workshop distribution board. The design current is 70 A, the route is 60 m, and the cable is 4-core 35 mm² copper PVC-insulated, armoured, clipped to a wall. For 8 m it shares a conduit with three other circuits that are fully loaded; for 1.2 m it passes through a 100 mm insulated wall without a sleeve; the summer ambient is 45 °C. The cable schedule gives a tabulated current-carrying capacity of 96 A for this cable in free air at 30 °C, and the voltage-drop figure is 1.1 mV/A/m. The upstream device is a 100 A MCCB with a 10 kA breaking capacity; the calculated prospective fault current at the board is 6.5 kA. The installer argues that 96 A is greater than 70 A, so 35 mm² is adequate.
1. Apply derating factors, show the effective current-carrying capacity, and decide whether the 35 mm² cable is acceptable. Identify the dominant constraint.
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Thermal capacity after derating
Use the site cable table and correction factors. Taking typical PVC values for a 30 °C base:
- Ambient 45 °C: factor ≈ 0.79.
- Four loaded circuits grouped in one conduit: factor ≈ 0.65.
- Cable passing through thermal insulation for more than 0.5 m without a sleeve: factor ≈ 0.50.
[I_{eff}=96\times0.79\times0.65\times0.50\approx24.7\text{ A}]
That is far below the 70 A design current. Even if the wall section is sleeved so that the 0.50 factor is not applied, the capacity is only:
[96\times0.79\times0.65\approx49.3\text{ A}]
Still below 70 A. Therefore the 35 mm² cable is not acceptable on thermal grounds. The installer compared the free-air 30 °C tabulated value directly with the design current and ignored the installation conditions.
Voltage drop
[\Delta V=\frac{1.1\times70\times60}{1000}=4.62\text{ V}]
This is about 1.1% of 415 V, well within the usual 5% overall limit. Voltage drop is not the limiting factor.
Fault withstand
Using the adiabatic approximation with k = 115 for PVC copper and a clearing time of 0.1 s:
[S=\frac{I\sqrt{t}}{k}=\frac{6500\sqrt{0.1}}{115}\approx17.9\text{ mm}^2]
35 mm² is thermally adequate for the fault, and the 10 kA MCCB exceeds the 6.5 kA prospective fault current. The dominant constraint is the combined ambient, grouping and thermal-insulation derating.
2. Recommend a practical remedy that satisfies the thermal and voltage-drop requirements, and specify the protective device rating.
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The cheapest acceptable solution is to change the route, not simply to enlarge the cable. The 0.50 thermal-insulation factor is the most damaging and can often be removed by passing the cable through a rigid sleeve in the insulated wall, or by routing around the wall. However, the grouping factor and the 45 °C ambient remain.
With a sleeve and the four-circuit grouping retained, the required tabulated rating is:
[I_{required}=\frac{70}{0.79\times0.65}\approx136\text{ A}]
A 70 mm² PVC copper cable with a tabulated rating of about 150 A gives:
[150\times0.79\times0.65\approx77\text{ A}]
This is acceptable for a 70 A design current. A 50 mm² XLPE cable may also work, but the higher conductor temperature and the termination rating must be checked; do not mix PVC and XLPE factors.
Protective device: the cable capacity after derating is about 77 A, so a 100 A MCCB is too large for overload protection. Use an 80 A MCCB (or a 100 A frame set to 80 A) with a breaking capacity of at least 10 kA. The device must satisfy:
[I_B\le I_n\le I_z]
that is, 70 A ≤ 80 A ≤ 77 A is not quite satisfied if the derated capacity is exactly 77 A; select a cable with a slightly higher rating, or set the device to 75–80 A only after checking the actual cable table. The safe answer is to choose the next cable size so that the derated capacity is at least 80 A.
Also separate the grouped circuits if practicable, and keep the cable away from the hot wall surface. Do not use the 96 A free-air value in the calculation.
3. What checks and tests would you require after installation before energizing the submain?
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Before energizing:
- Insulation resistance – test each phase to earth and between phases with a 500 V or 1000 V insulation tester, with the cable disconnected at both ends. Record the values; a very low reading may indicate moisture or mechanical damage from pulling.
- Continuity and polarity – confirm phase identification, neutral and protective conductor continuity, and correct termination at both boards.
- Earth loop/impedance and protective-device operation – verify the MCCB rating and setting, check that the breaking capacity is adequate, and confirm the earth-fault path will operate the protection.
- Thermal verification – after energizing at normal load, measure all three line currents and use a thermal imager on terminals, glands and the wall penetration. The wall section is the critical point; a hot spot there means the derating assumptions were wrong.
- Documentation – record the route, the correction factors used, the cable size, the device setting and the test results on the cable schedule.
The important point is that the original 96 A argument is a free-air laboratory value. The installation test must confirm the real installed condition, especially the grouped conduit and insulated-wall section.