This actually is only an issue for IEC style bi-metal OL relays that have a feature called "differential biasing" that is used to change the trip point if there is a phase loss on a running 3 phase motor. The mechanism is basically a balancing spring on the trip bar that is looking for force being exerted against it from all three bi-metal strips equally. When one strip is not bending under load, it no longer exerts its force against the spring, so the spring moves the trip bar closer, resulting in the OL relay requiring LESS excess current in order to trip. The reasoning behind this is that if you have a 3 phase motor and lose a phase while it is running*, the motor will keep spinning, but the lost phase will create negative sequence current in the rotor, which can cause it to overheat disproportionately to the stator current. So in order to avoid damaging the motor, the trip point of the OL relay is biased, by this mechanism, to trip earlier.
If however you HAVE a single phase system, that differential biasing mechanism will not "know" that this is a normal situation and act to cause nuisance tripping. So you run the current through all three poles in order to have them all exert the same force resistance against that spring.
Eutectic melting alloy OL heaters and NEMA (North America) design bi-metal OL relays never had this feature, so single phase operation has no effect on them therefore you do not need to run current through all 3 poles on those types. Most Solid State OL relays will have a setting or switch that allows single phase operation however.
- If there is a single phase condition on a 3 phase motor BEFORE it tries to start, it will not start.
Graphic depiction of the differential biasing mechanism;