Motor Feeder Sizing: Derated Cable, Voltage Drop and Starting Method
A 15 kW, 415 V, three-phase squirrel-cage motor drives a crusher through a belt. The nameplate gives 28 A full-load current, 89 per cent efficiency, 0.85 power factor, direct-on-line starting with a starting current of six times full load and a starting torque of 180 per cent. The feeder is 30 m of four-core copper PVC cable laid in a covered tray with four other loaded cables, in a shed that reaches 45 °C. The contractor's chart, valid for a single cable in free air at 40 °C, lists 4 mm² = 32 A, 6 mm² = 41 A, 10 mm² = 57 A. Derating factors are 0.87 for 45 °C ambient and 0.80 for five grouped cables. The overload relay is set at 28 A. The supply authority allows 3 per cent drop when running and 10 per cent at the motor terminals during starting, including a transformer and MCC drop of about 2.5 per cent. The contractor has quoted 6 mm² and calls it adequate.
1. Check the nameplate current against the rating and select the cable from the derated table, justifying the choice against the overload setting.
Read the worked answer
Full-load current from the rating: I = P/(√3 V cos φ η) = 15 000/(1.732 × 415 × 0.85 × 0.89) = 15 000/543.8 = 27.6 A, consistent with the 28 A nameplate. Work with 28 A.
Combined derating = 0.87 × 0.80 = 0.696.
- 4 mm²: 32 × 0.696 = 22.3 A, below 28 A - reject.
- 6 mm²: 41 × 0.696 = 28.5 A, only 1.02 times full load.
- 10 mm²: 57 × 0.696 = 39.7 A, 1.42 times full load - acceptable.
Judgement: 6 mm² passes only because 28.5 exceeds 28.0 by 2 per cent, a margin that vanishes with one more loaded cable in the tray, a hotter afternoon, or a relay raised to 30 A to stop nuisance trips. The cable must carry at least the relay setting continuously; with a 28 A relay on a 28.5 A cable, protection and cable capability are effectively the same number, which is poor practice. Specify 10 mm², or accept 6 mm² only with a documented derating review and a 26 A relay setting.
2. Estimate voltage drop when running and during direct-on-line starting for 6 mm² and 10 mm², and judge whether DOL starting is acceptable.
Read the worked answer
Copper resistivity at about 70 °C is close to 0.0222 ohm·mm²/m, so R = 0.0222/A ohm per metre. Three-phase drop = √3 × I × R × L, with L = 30 m.
6 mm²: R = 0.0037 ohm/m. Running: 1.732 × 28 × 0.0037 × 30 = 5.4 V = 1.3 per cent, fine. Starting: 6 × 28 = 168 A gives 32.3 V = 7.8 per cent on the feeder, plus 2.5 per cent upstream = 10.3 per cent, at or over the 10 per cent limit.
10 mm²: R = 0.00222 ohm/m. Running: 3.2 V = 0.8 per cent. Starting: 19.4 V = 4.7 per cent, plus 2.5 = 7.2 per cent, inside the limit.
Starting torque falls with the square of terminal voltage. At 10 per cent drop, available torque = 180% × 0.90² = 146 per cent of full-load torque; at 7.2 per cent, 180% × 0.928² = 155 per cent. Either can start an empty crusher; a crusher started with material in the chamber needs roughly 150 to 180 per cent and is marginal on 6 mm².
Judgement: DOL starting is acceptable on 10 mm², not on 6 mm².
3. The contractor offers star-delta starting to keep the 6 mm² cable. Evaluate that offer and give your final recommendation.
Read the worked answer
Star-delta applies 1/√3 of line voltage to each winding at start, so line current falls to one third and torque to one third, both by V².
On 6 mm²: starting current = 168/3 = 56 A, drop = 1.732 × 56 × 0.0037 × 30 = 10.8 V = 2.6 per cent, plus 2.5 upstream, comfortably inside limits. But starting torque = (180%/3) × (0.949)² ≈ 54 per cent of full-load torque.
A jaw crusher is a high-inertia, high-torque load. Fifty-four per cent will not break it away if the chamber is loaded; the motor stalls in star, or the changeover happens at a speed where the delta current is worse than a straight DOL start. Star-delta is right only if the crusher is guaranteed to start empty and the changeover is timed above about 80 per cent speed.
Recommendation: 10 mm² cable with DOL starting. It fixes both the thermal margin (39.7 A derated) and the starting drop (7.2 per cent total) with no new starter. If the supply authority insists on lower starting current, fit a soft starter on the 10 mm² cable rather than star-delta on 6 mm².