Capacitor for a three-phase motor on single-phase

A small three-phase motor can run on a single-phase supply if you add a capacitor that acts as the "third phase". This is the Steinmetz connection, used in workshops and homes for pillar drills, saws or small pumps. This calculator gives the capacitor size with the rule of thumb of about 70 µF per kW at 230 V and 50 Hz, and how much power the motor will lose.

How to wire it

• The windings must be able to run at the supply voltage: on a 230 V supply, a 230/400 V motor connected in delta.
• Line and neutral go to two motor terminals, for example U1 and V1.
• The capacitor goes between the third terminal (W1) and one of the other two. Which one you choose sets the direction of rotation.
• The start capacitor, if needed, goes in parallel with the run capacitor and is switched out as soon as the motor is up to speed: with a push button, a start relay or a centrifugal switch.

How it is calculated

The most common rule of thumb is C ≈ 70 µF per kW at 230 V and 50 Hz. If the voltage or the frequency change, the capacitance changes like this:

C (µF) = 70 × P (kW) × (230 / V)² × (50 / f)

It is an approximation: the right value depends on the motor and the load. Ideally, tune it with the motor working, measuring with a clamp meter the current in the three motor leads (the two from the supply and the capacitor’s) and keeping the capacitor that makes the three most alike.

Rated in horsepower? Multiply by 0.746 to get kW: a 1 HP motor is 0.75 kW.

Example

A 0.75 kW motor on a 230 V, 50 Hz supply: 70 × 0.75 = 52.5 µF, so a 50 µF run capacitor rated at least 400 V. If it has to start under load, add a start capacitor of about 105 to 160 µF. The motor will deliver around 0.45–0.6 kW. On 60 Hz the same motor would need about 44 µF.

What to keep in mind

• It loses power: in practice it delivers around 60–80 % of its nameplate rating.
• Low starting torque: without a start capacitor it only starts unloaded or lightly loaded.
• Two kinds of capacitor: the run capacitor is polypropylene, made to stay connected (400 to 450 V AC). The start capacitor is electrolytic and only withstands being connected for a few seconds.
• Above about 2 kW a VFD with single-phase input and three-phase output is the better option: the motor gives its full power, starts smoothly and its speed can be adjusted. In North America, rotary phase converters are also common.

To understand the topic in depth: Motors and variable frequency drives, with theory and a practice test.

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