Three-Phase Motor: Cable Derating and Overload Setting
A 15 kW, 400 V three-phase induction motor drives a pump. The motor has a power factor of 0.85 and an efficiency of 90%. It is wired with 4 mm² four-core PVC-insulated cable enclosed in conduit on a wall, using a starter with an adjustable thermal overload. The conduit runs through a plant room where the ambient temperature is 40 °C and is grouped with two other similarly loaded circuits. The tabulated current-carrying capacity of 4 mm² for this installation method is 32 A. The designer has selected a 32 A type C MCB for short-circuit protection and intends to set the overload to 32 A to 'match the MCB'. The motor nameplate current is 28 A. Correction factors are 0.87 for 40 °C and 0.70 for grouping with two other circuits. Tabulated capacities for the method used are 41 A for 6 mm² and 57 A for 10 mm².
1. Calculate the motor design current and compare it with the nameplate current.
Read the worked answer
For a three-phase motor, Ib = P / (√3 × V × pf × efficiency). Substituting: Ib = 15 000 W / (1.732 × 400 V × 0.85 × 0.90) = 15 000 / 529.9 = 28.3 A. The calculated design current is close to the nameplate value of 28 A, which is a useful cross-check. The small difference arises from rounding of the efficiency and power factor. The design current must be used to select the cable and overload setting; the MCB rating alone is not the design current. The 32 A MCB is not intended to protect the motor against overload; it provides short-circuit protection, and its rating must be at least the design current and no greater than the corrected cable capacity.
2. Apply the correction factors and select the minimum cable size that satisfies Ib ≤ In ≤ It.
Read the worked answer
Combined correction factor = 0.87 × 0.70 = 0.609. For the 32 A MCB, the required tabulated capacity is It ≥ In / 0.609 = 32 / 0.609 = 52.5 A. Check the available sizes: 4 mm² gives 32 × 0.609 = 19.5 A (fails); 6 mm² gives 41 × 0.609 = 25.0 A (fails, and below the 28.3 A design current); 10 mm² gives 57 × 0.609 = 34.7 A. The 10 mm² cable satisfies 28.3 A ≤ 32 A ≤ 34.7 A. It is the minimum size of those listed that meets the overload and grouping conditions. The voltage drop over the actual route length must still be checked separately, as must the protective conductor's adiabatic capacity. If the ambient or grouping is temporary, the designer may use a lower factor only if the conditions are formally verified.
3. What is the correct thermal overload setting, and why is setting it to 32 A wrong?
Read the worked answer
The overload should be set to the motor's full-load current, about 28.3 A, or the nearest setting that does not exceed the motor rating, typically 28–29 A. Setting it to 32 A to 'match the MCB' fails to protect the motor: the motor can draw 30–31 A continuously, run hotter than its insulation class allows and be damaged before the overload trips. The MCB's 32 A rating is chosen for co-ordination and short-circuit protection, not for motor overload protection. The overload must also be within the corrected cable capacity; the 10 mm² cable at 34.7 A provides that margin. Correct co-ordination is: motor FLC ≤ overload setting ≤ cable corrected capacity, with the MCB selected for fault current and starting conditions.