Sizing a Sub-Main for Six Split Units: Cable, MCB and RCCB Decisions
A computer training room in an office block is to be air-conditioned with six split units. Each unit's nameplate reads 230 V, single phase, input 1.60 kW, power factor 0.90. The units are fed from a new sub-distribution board 40 m away through two-core copper PVC cable run in conduit, and all six run together. For cable sizing the load is taken as 85% of the connected load. The panel builder supplies this rating table for PVC copper conductors in conduit at 30 degrees C ambient: 4 sq mm - 27 A, 6 sq mm - 34 A, 10 sq mm - 46 A, 16 sq mm - 62 A, 25 sq mm - 80 A. Correction factors are 0.87 for a 40 degrees C ambient and 0.80 for three circuits grouped in one conduit. Voltage drop for the 16 sq mm cable is 2.9 mV/A/m. The electrician proposes a 40 A MCB and a 30 mA RCCB at the board, with the room's socket outlets placed on the same RCCB.
1. Compute the design current and select the cable size using the given table and correction factors.
Read the worked answer
Step 1 - current per unit. I = P / (V x cos phi) = 1600 / (230 x 0.90) = 1600 / 207 = 7.73 A
Step 2 - connected and design current.
- Six units: 6 x 7.73 = 46.4 A
- Design current Ib = 0.85 x 46.4 = 39.4 A
Step 3 - derate the table. Combined factor = 0.87 (ambient) x 0.80 (grouping) = 0.696 Required tabulated rating = 39.4 / 0.696 = 56.6 A
Step 4 - select.
- 10 sq mm derated: 46 x 0.696 = 32.0 A - below 39.4 A, rejected.
- 16 sq mm derated: 62 x 0.696 = 43.2 A - above 39.4 A, accepted.
So the cable must be 16 sq mm, not the 10 sq mm the raw 46 A table figure might suggest. Checking the worst case, with no diversity at all (46.4 A), the derated 16 sq mm capacity of 43.2 A is still slightly short; the 85% diversity figure is what makes it valid, so any later addition of a seventh unit or a change of ambient must trigger a re-check.
2. Verify the proposed 40 A MCB and check the voltage drop on the 16 sq mm run.
Read the worked answer
MCB check - two inequalities must both hold:
- Ib (39.4 A) <= In (40 A) - satisfied, the breaker will not trip on normal load.
- In (40 A) <= Iz (43.2 A derated) - satisfied, the cable is protected against overload.
A 40 A MCB is therefore correct. A 32 A device would be too small (nuisance tripping at 39.4 A), and a 63 A device would leave the cable unprotected because 63 A exceeds the derated 43.2 A capacity.
Voltage drop: Vd = 2.9 mV/A/m x 39.4 A x 40 m / 1000 = 4.57 V As a percentage: 4.57 / 230 x 100 = 1.99%
That is comfortably inside the usual 5% limit for a power circuit and even inside a 3% limit, so no uprating for drop is needed. If the board had been 120 m away the drop would scale to about 13.7 V (6%), and the 16 sq mm would then have to be increased even though its current rating was adequate - a classic case of ampacity and drop pulling in different directions.
3. Assess the RCCB proposal: is 30 mA correct, and what is the problem with putting the room's socket outlets on the same device?
Read the worked answer
Is 30 mA right? Yes for the purpose of protecting people. A 30 mA residual current device is the sensitivity associated with supplementary protection against electric shock on socket circuits; a 100 mA device is a fire-protection device and will not reliably prevent ventricular fibrillation in a person receiving a shock. So the sensitivity chosen is correct.
Is sharing the device with the sockets wise? No, and the reasoning is operational rather than theoretical:
- Nuisance and safety-crippling trips. Six air-conditioners running together accumulate small leakage currents (filter capacitors, inverter drives in the indoor units, long wiring runs). Add socket loads and the standing leakage can approach the trip threshold, so the RCCB may trip for no fault - and it will take down the whole room, including the sockets, in one action.
- Loss of discrimination. A fault on one socket outlet disconnects the air-conditioning sub-main as well, so the fault cannot be located by isolation.
- An RCCB is not an MCB. It gives no overload or short-circuit protection; the 40 A MCB remains essential, and neither device replaces proper earthing of the panel and the unit bodies.
Recommendation: keep the 40 A MCB for the air-conditioner sub-main, give the socket outlets their own 30 mA RCCB (or RCBOs per circuit), and check the standing leakage of the six units with a leakage clamp before energising.