showstack

Why three

Three phases, and the conductor that usually does nothing

A three-phase supply is three alternating voltages of the same size, 120° apart in time. That spacing is not an arbitrary convention — it is what lets three conductors carry three times the power of one while the return current cancels itself out. Add three equal sinusoids that are evenly spread around a cycle and the sum is exactly zero, at every instant, forever.

That sum is what the neutral carries. On a perfectly balanced linear load the neutral carries nothing at all, which is why it can historically be the same size as a phase or smaller. It is also why an unbalanced rig is a real problem rather than an aesthetic one: whatever the three phases fail to cancel comes back down the neutral, and the neutral is the one conductor with no breaker in it.

The catch

The neutral is not the spare conductor it looks like

Everything above assumes the load is linear: current follows voltage, a sine in gives a sine back. Almost nothing on a modern rig does that. An LED fixture, a media server, a switch-mode amplifier and a phase-control dimmer all draw current in bursts rather than smoothly, and a burst is a fundamental plus a stack of harmonics.

Most harmonics still cancel in the neutral. The third does not, and neither does the ninth or the fifteenth — the triplen harmonics. At three times the fundamental frequency, the 120° separation between phases becomes 360°, which is no separation at all. All three phases deliver their third harmonic to the neutral in step, and instead of cancelling it adds arithmetically.

The result is the one genuinely counter-intuitive thing about show power: a balanced rig full of LED fixtures can put more current down the neutral than any single phase is carrying. Published figures for LED drivers and electronic ballasts put current THD in the 15–40% range, which is why installations expecting heavy non-linear load size the neutral at up to 200% of the phase conductor rather than treating it as the small one.

Putting a number on it

THD, and the two versions of it that disagree

Everything above describes what harmonics do. The number that measures how many there are is total harmonic distortion, and there are two of them, both called THD, which is why a meter and a datasheet can give different answers while both are correct.

THD-F compares the harmonic content against the fundamental alone. THD-R compares it against the total RMS current. THD-F is the one usually meant in power work and it has no upper bound — a badly behaved load can exceed 100%, because the harmonics really can add up to more than the fundamental. THD-R can never pass 100% by construction. At low distortion they are nearly identical; at the levels a rig full of switch-mode supplies actually produces they are visibly different.

The consequence people meet first is the power factor. Distortion alone drags true power factor down even when nothing is inductive and the current is perfectly in phase with the voltage — there is a distortion power factor of one over the square root of one plus THD-F squared, and it multiplies whatever the displacement factor is. That is how a rig of LED fixtures with no motors anywhere in it presents a poor power factor to a generator, draws more current than the wattage suggests, and makes the genset work harder than the load sheet says it should.

And the other side of the same coin is crest factor — peak divided by RMS. A pure sine is 1.414. A switch-mode supply drawing in spikes near the voltage peak runs 2 to 3, and a generator or UPS sized on RMS alone will clip those peaks while its average reading sits comfortably inside its rating. It is the same distortion seen from the time domain instead of the frequency domain, and it is the reason a genset that is obviously big enough still misbehaves.

Phase rotation

The one wiring fault that makes a hoist go the wrong way

The three phases arrive in an order. L1 peaks, then L2 a third of a cycle later, then L3 — and swapping any two of them reverses that order. Nothing about the supply looks different: the voltages are right, the phase-to-phase voltages are right, a meter is happy, single-phase loads down the line neither know nor care. Every heater, lamp and dimmer works perfectly on a supply with reversed rotation.

A three-phase motor is not so relaxed. It turns in the direction the field rotates, and the field rotates in whatever order the phases arrive, so a motor on a reversed supply runs backwards. That is the whole fault, and on a touring rig it is attached to chain hoists. Up is down. The controller is fine, the pendant is fine, the labelling is fine, and the load goes the wrong way when somebody presses the button. This is why a rotation check is the first thing done on arrival at an unfamiliar supply, before anything is plugged into it, and why a phase rotation meter is in the electrician’s bag rather than in a drawer at the shop.

Two things make it likelier than it sounds. Generators and temporary supplies get terminated by hand, and a hand is what swaps two cores. And adaptors are a genuine hazard, because a badly made one, or a legitimately made crossover, changes rotation invisibly — the connector fits, the pins are live, the order is different. Which is also why some hoist controllers include phase reversal detection or an automatic rotation corrector, and why the ones that do not put the responsibility exactly where it was already.

The connectors themselves try to help. On a Powerlock or a camlock set the sequence is fixed by the colours and by the order they are terminated; on a 16 A or 32 A three-phase CEE connector it is fixed by the pin positions, and some carry a rotatable insert specifically so a wrong rotation can be corrected at the plug with a screwdriver rather than by re-terminating a tail. None of that helps if the supply upstream is wrong, which is the case the meter exists for.

Two different jobs

A breaker protects the cable. An RCD protects the person.

These get conflated constantly and they are not the same device doing the same thing at different sensitivities. A circuit breaker watches the current in the circuit and opens when it exceeds what the cable can carry without cooking. That threshold is tens of amps, because that is what melts insulation. A person is in serious trouble at a small fraction of one amp, so a breaker sized to protect a cable offers a person essentially nothing.

A residual current device does something else entirely. It does not care how much current is flowing; it compares the current going out with the current coming back. On a healthy circuit those match exactly. If they do not, the difference left by another route, and the most common other route is through somebody standing on damp ground holding a piece of metal.

The numbers are the point. A 30 mA RCD provided for additional protection has to operate within 40 ms at five times its rating, and within 300 ms at its rated residual current. Those times are chosen against what a heart will tolerate, not against what a cable will.

Down the cable

Volt drop is a length problem, not a load problem

Every conductor has resistance, and every amp pushed through it loses some voltage on the way. Over a 3 m tail it is nothing. Over 120 m of trailing socket to a stage-left position it is the reason a moving light browns out on a colour change while the console reports everything as fine.

The arithmetic is Ohm’s law twice: the drop is current times the loop resistance of the run, and the loop is both directions, so a 60 m run is 120 m of copper. Doubling the length doubles the drop; doubling the cross-section roughly halves it.

What makes it a rigging problem rather than a maths problem is that the load is not constant. A fixture that dips its voltage when the motor moves and the lamp strikes at the same time is drawing peak current exactly when it can least afford the drop.

Where the numbers live

The calculators, and what they assume

Power load converts between kW, amps and phases. Voltage drop takes a length and a cross-section. Phase balance shows what the neutral is carrying when the legs are uneven. Ohm’s law is there for the moment you need it and cannot remember which way round it goes.

All four run the same arithmetic the test suite checks. None of them knows your local wiring regulations, your supply impedance, or what the venue actually installed behind the panel, and none of them is a substitute for a competent person with a meter.