Line and Phase Current in Three-Phase Systems

3 min
Beginner

The line current and the phase current are two different currents that may or may not coincide depending on the three-phase connection.

In the previous article, we saw that the voltage changes depending on whether we measure between phases (400V) or phase-to-neutral (230V). Now we will see what happens with the electron flow: the Current (I).

Here, the rule is not as fixed as with voltage. Here it depends on the way we connect the load (the motor or the resistors).

Let’s first define the players:

Line current (): It is the current flowing through each phase conductor supplying the load. It is the value you get by placing an ammeter clamp around a single line conductor.
Phase current (): It is the current flowing through each branch of the load, for example, through one coil of the motor.

Depending on whether we connect in Star or Delta, the relationship changes.

In star connection (Y)

Recall the star shape: the three line conductors are connected to the start of each coil. The other ends are joined at the star point, which can be connected to neutral or left isolated.

Since each line is in series with a single coil, the same current flows through both.

Therefore, in Star:

What you measure outside is what the coil experiences inside.

Here, the phase voltage is .

In delta connection (Δ)

In a Delta, the Line cable arrives at a vertex where two coils meet. At this vertex, the currents from the two coils converge.

Since they are out of phase, the line current is the phasor difference between them, not a simple arithmetic division.

How much smaller? Our friend appears again:

Or, solving for what the coil experiences:

Example: If you measure 17.3 Amperes on the incoming cable, only 10 Amperes are flowing inside each coil.

Here, the phase voltage coincides with the line voltage ( in this example)

The complete relationship

The factor always appears once:

Connection Type	Voltage ()	Current ()
STAR (Y)	It Divides () Voltage drops to 230V	It is Equal () Current goes straight in
DELTA (Δ)	It is Equal () Coil receives 400V	It Divides () Current gets divided

Application in motor protection

Think about the thermal relay, which protects the motor against overloads. Where is this relay installed?

If it is placed on the Line (outside the motor): You must set it to the nameplate rated current value ().
If it is placed in a Star-Delta starter (below the contactors): Sometimes the relay is measuring the Phase current ().

If you set the relay to the line current value (e.g., 17A) but only 10A (Phase) flow through it, the motor can burn out and the relay will never trip. You have to do the calculation.

The vast majority of the time, we measure and protect on the Line. Whenever you look at a motor nameplate, the current indicated (e.g., 10A at 400V) is the Line Current.

That is what it will draw from the grid. What happens inside the coils is the manufacturer’s concern.