PW-A5 · Three-phase AC

Unbalance, first look: where the nonzero sum goes

In balance (A1) the three currents add to 0, so the neutral carries nothing. When one phase is off, the sum moves away from 0 and the leftover residual flows along the neutral of the Y; drag it yourself to see where current leaks when the balance breaks.

Drag I_a to break the balance

Among the three current phasors, dragging the tip of I_a changes its size and direction, and the gold residual sum grows from 0. This gold vector is exactly the current that flows along the Y neutral.

Drag the tip of I_a to create unbalance. The faint gold dashed ring is the balanced position, and I_b and I_c stay fixed where they sit in balance.

Neutral current |I_N| = |I_a + I_b + I_c|

|I_N| ≈ 0.56   (|I_a| ≈ 1.35)

At the balanced position |I_N| = 0, and the farther away, the larger the neutral current.

Balanced means an empty neutral

As seen in A1, three currents of equal size 120° apart add to 0. So the three currents gathered at the neutral point of a Y cancel one another and no current flows in the neutral, which is the basis for making the neutral thin, or leaving it out, in balanced systems. The 3rd-harmonic currents drawn by nonlinear loads such as rectifiers and lamp ballasts, however, are in phase in all three phases, so even with balanced loads they do not cancel in the neutral but add up.

Off balance, the leftover leaks out

When the size or phase of one phase changes, the three currents no longer cancel neatly, and the residual that strays from 0 has only the neutral to go to. I_N = I_a + I_b + I_c. The gold vector you dragged is exactly this sum, and the more the load leans to one phase, the larger the neutral current.

This leftover has a name · zero sequence

Calling 1/3 of the residual the zero-sequence component, I_0 = (I_a + I_b + I_c)/3, the neutral current is I_N = 3 I_0. Balance is only the special case I_0 = 0. A delta has no neutral, so its line currents always add to 0, and any zero-sequence part of the phase currents becomes a circulating current around the Δ loop. The zero-sequence component is the tool for handling unbalance systematically, completed later in symmetrical components (D2) as positive, negative and zero sequence.

ObserveI_N = I_a + I_b + I_c

The neutral current is the sum of the three currents.

ChooseBalanced → I_N = ?

In balance the sum is 0 (A1).

Fill inI₀ = (I_a + I_b + I_c) / ?

The zero-sequence component is 1/3 of the residual.

On your ownI_N = ?

In a delta, the zero-sequence part of the phase currents circulates inside the loop.

Back to the first screen

With I_a at the balanced position the gold residual vanished, and the farther it was dragged, the more the residual grew. That gold vector is the neutral current I_N = I_a + I_b + I_c = 3 I_0. The sum of 0 in A1, where section A began, turns out to be one special point within the general situation of unbalance. Balance is not a rule that comes by itself but a balance we have set up.

In unbalanced three-phase, the three currents (or voltages) do not add to 0. That residual flows as the neutral current of a Y, I_N = I_a + I_b + I_c = 3 I₀ (the zero-sequence component), and balance (A1) is the special case I₀ = 0. A delta has no neutral, so the zero-sequence part of the phase currents becomes a circulating current inside the loop.

The next step

Here section A (three-phase AC) ends. From the next unit (PW-B1) on, we look at the shape of power itself: the power triangle, which ties active, reactive and apparent power into a right triangle. When a load draws current out of step with the voltage, that offset becomes reactive power, and what ratio the power factor cosφ is within the triangle becomes clear at a glance. The zero-sequence component seen here returns later in symmetrical components (D2).