Unbalance & neutral current
The key idea
On a four-wire wye system the neutral carries the vector sum of the three phase currents. Load the three phases equally, and that sum is zero. The neutral then carries no current. Load them unequally, and the difference flows in the neutral.
The idea
A balanced three-phase load needs no return conductor. Three equal currents at 120° from each other add to exactly zero at every instant. That cancellation gives the three-phase system its advantage. The system carries three times the power of a single-phase system on wires of the same size.
Real low-voltage feeders are not balanced. Most of the load on them is single-phase: socket circuits, lighting, a water heater, an EV charger. Each load connects between one phase and the neutral, and these loads do not switch on in groups of three. A four-wire wye system therefore keeps a neutral conductor. The current that the three phases do not cancel flows in that conductor.
Neutral current is the vector sum of the three phase currents. That statement is Kirchhoff's current law at the star point. The word vector is important. The three currents point 120° apart, so they do not subtract like ordinary numbers. Put 40, 60 and 80 A on the three phases, and the neutral does not carry 80 − 40 = 40 A. It carries 34.6 A, at an angle that matches no phase.
Symmetrical components give the same fact a different description. The zero-sequence current is exactly one third of the neutral current. Zero sequence is three currents in step, and that pattern cannot cancel. It must return through a conductor. The unequal load also produces negative-sequence current, which is a balanced set with the reverse rotation. Equipment responds to both: negative sequence heats rotating machines, and an earth-fault relay measures zero sequence.
The remedy is rarely electrical. Redistribute the single-phase loads across the three phases until the three loads are close to equal. The total demand does not change, and no new equipment is necessary. The neutral current then falls, the negative sequence disappears, and the losses in the neutral conductor go away.
Try it
Move the three loads apart and watch the dashed neutral arrow appear. Then press Balance the load. The total demand stays the same. Each phase now carries an equal load, and the neutral is empty.
neutral current |IN|
34.6 A
unbalance factor
19.2 %
status
unbalanced
The neutral carries the vector sum of the three phase currents and nothing else. Equal loads cancel, and the neutral is empty. Move load onto one phase, and the difference appears in the neutral and in the negative and zero sequence. The neutral current can reach the full current of one phase. Every phase here is at unity power factor, so the arrows stay at 0°, −120° and +120° and only their lengths change. Real unbalance changes the angles as well.
Why it matters
- The neutral is not a spare wire. A badly distributed single-phase load can put as much current in the neutral as in a phase. Engineers therefore size the neutral as a phase conductor, and they do not reduce it. Triplen harmonics then add their own contribution on top of that. A switch or a fuse in the neutral alone is worse. If the neutral opens under unbalance, the phase voltages redistribute across the loads and the lightly loaded phase rises toward line voltage.
- Negative sequence overheats motors. An induction motor has a very low impedance to a field that turns in the reverse direction. That field passes the rotor at nearly twice synchronous speed. A few percent of negative sequence therefore drives a large rotor current. The rotor current makes heat and no useful torque. Motor protection relays therefore measure negative sequence directly.
- Zero sequence looks like an earth fault. Residual earth-fault protection adds the three phase currents, which is the identical sum. A permanent unbalance stays inside that measurement. It reduces the margin between normal operation and the relay setting.
- Unbalance spreads to other customers. An unbalanced current through the source impedance produces an unbalanced voltage drop. The phase voltages at the busbar are then no longer equal. Every other customer on that feeder receives the unbalance as a supply problem.
The math, if you want itOptional — the page reads completely without it
Kirchhoff's current law at the star point of a four-wire wye:
neutral current
IN = IA + IB + IC
This equation is a sum of phasors, not a sum of magnitudes. The widget puts every phase at unity power factor. The three currents therefore stay at their nominal angles, and only the magnitudes change:
the model on this page
IN = IA∠0° + IB∠−120° + IC∠+120°
The next equations give the same three currents in symmetrical components. The rotation operator is a = 1∠120°:
positive sequence
I₁ = ⅓ ( IA + a·IB + a²·IC )
negative sequence
I₂ = ⅓ ( IA + a²·IB + a·IC )
zero sequence
I₀ = ⅓ ( IA + IB + IC )
The last equation is the neutral current divided by three. The two quantities are the same:
neutral and zero sequence
IN = 3 · I₀
The standard measure of the amount of unbalance is the unbalance factor:
current unbalance factor
100 · |I₂||I₁| %
The unity-power-factor simplification has two consequences in the widget. Every current stays on its nominal angle. I₁ is therefore the plain average of the three magnitudes, and |I₂| always equals |I₀|. The negative bar and the zero bar keep the same length. Neither result holds when the phases differ in power factor as well as in magnitude, and a real feeder differs in both. The shape of the result is still correct, but the exact numbers are not.
See it in Phasor
A power flow is a balanced, positive-sequence study. It assumes the cancellation that this page describes. That assumption is the reason one line on the single-line diagram can represent three conductors and a neutral. Check the assumption against the feeder that you model. If the real load is a long row of single-phase connections, the phase current that Phasor reports is an average of three unequal currents. The neutral current that Phasor never draws can still be tens of amps.