Contactor Sizing Formulas

Motor contactor formulas: the full-load current of the motor, the AC-3 contactor rating with a margin and the starting current the contacts must make.

The formulas

P is the shaft power in kW, V the line voltage, η the efficiency and pf the power factor of the motor at full load, k a derating factor for the ambient temperature, the altitude and the starts per hour (1 if the maker gives none), and m the ratio of the starting current to the full-load current, often 6 to 8 for a direct-on-line start. The AC-3 rating is the rated operational current of a contactor that starts squirrel-cage motors and breaks them while they run. Plugging and inching (AC-4) need a much larger contactor or a lower rating from the maker's table. Take the motor current from the nameplate when it is known. The list of sizes, 0.9, 7, the efficiency and the power factor here are examples, and each maker has its own series.

Worked example: a 30 kW motor on 415 V

Efficiency 0.92, power factor 0.86, derating 0.9.

1. I = 30,000 / (√3 × 415 × 0.92 × 0.86) = 52.75 A
2. Ie ≥ 52.75 / 0.9 = 58.61 A, so the next size in the example list is 65 A
3. Ist = 7 × 52.75 = 369.3 A

Full-load current on 415 V (efficiency 0.92, power factor 0.86)

Frequently asked questions

What does AC-3 mean?

It is the utilisation category of the standard for starting squirrel-cage motors and switching them off while they run. The rating of a contactor depends on the category.

Why add a margin?

High ambient temperature, many starts and the contact wear lower the usable rating, so the contactor is chosen above the motor current.

Does the contactor protect the motor?

No. A contactor switches the load. The short-circuit protection and the overload relay are separate devices, and the contactor must be co-ordinated with them.

What about star-delta and soft starters?

The contactors in a star-delta starter carry a part of the line current. Use the maker's table, or see the motor starting and soft starter articles for the currents.

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