“Know the light, but keep the shadow.”—Tao saying
Three-phase power distribution systems are very common around the world for a couple of reasons; they save money, and…I forget the other reasons.
Three-phase distribution saves money because it takes less copper to transmit the same amount of power with a three-phase system than with a single-phase system. In fact, it takes about 25 percent less copper to transmit the same amount of power with a three-phase three-wire delta system as with a single-phase three-wire system because the conductors need only be half the cross sectional area. And with a three-phase four-wire system it takes even less copper — about 66 percent less than with a single-phase three-wire system.
It All Adds Up
{mosimage}If, for example, you are using a three-phase delta system with 1/0 cable, then you would have to use 4/0 cable if you had to swap it for a single-phase three-wire system. For every 100 feet of feeder cable, you would be carrying about 130 pounds extra. That may not seem like a lot compared to the thousands of pounds you load in and out of venues every day, but for a utility company that generates millions of megawatt-hours of energy and transports it thousands of miles, it’s huge.
For that reason, utilities most often supply three-phase power and we have little choice but to use three-phase power most of the time. One of the first things to know about three-phase systems is that they like for the loads to be balanced equally among the three phases. If, for example, we have 48 208V 1500-watt automated lights that we want to power, then it just makes sense to split them up three ways and connect 16 across each of the three phase combinations (A-B, B-C, and C-A). Otherwise, you’ll need bigger and heavier feeder cable. If the fixtures are equally balanced among the phases, we can use 2/0 feeder cable; but if we put all of the fixtures across two phases (A-B), then they would overload 4/0 cable. Distributing the loads equally will minimize the current in each of the phase conductors.
The next thing to know about three-phase power is that it’s virtually impossible to perfectly balance a three-phase system and keep it in balance. Even if we manage to even out the loads, there’s no guarantee they will all be turned on at the same time or in any semblance of balance. Fortunately, a three-phase system in the worst case of unbalance is safe as long as the neutral is sized correctly, and the term “correct” is relative to the case.
In the case where we have nothing but linear loads, the neutral need only be the same size as the feeder phase conductors. A balanced three-phase system generates no current in the neutral but in the worst case scenario — when the load is totally unbalanced — then the neutral current is the same as the maximum phase current.
In Article 220.61 – Feeder or Service Neutral Load, the NEC says that the “feeder or service neutral load shall be…the maximum net calculated load between the neutral conductor and any one unbalanced conductor.” In such a system, the vectorial sum of the phase currents in any unbalanced situation can never exceed any one of the phase currents. It’s mathematically impossible. To get a better idea of why that is, look at the spreadsheet currently posted at www.plsn.com/balance.xls . It shows how three current waveforms, each of which are the same frequency and amplitude but 120° out of phase with each other, combine in the neutral to cancel each other out, producing zero current. You can play with the magnitude of the three phases and see how they change the neutral current.
Linear loads are ones that don’t distort the voltage waveform; for example, fog machines, motors, and automated lights with magnetic ballast power supplies are linear loads. If you have no phase-control dimmers (the vast majority of dimmers out there are phase-controlled), electronic switching power supplies, or any other non-linear loads and your neutral is the same size as the other feeder cables, then you have nothing to worry about.
But if you do have phase-control dimmers in your system, then that is yet another case. According to the National Electrical Code, you should then size your neutral feeder cable with at least 130 percent ampacity of the phase conductors. Article 520.60 (O)(2) says, “Where single-conductor feeder cables, not installed in raceways, are used on multiphase circuits feeding portable switchboards containing solid-state phase-control dimmers, the neutral conductor shall have an ampacity of at least 130 percent of the ungrounded circuit conductors feeding the portable switchboard.” That’s because phase-control dimming distorts the waveform in such a way that can cause current to flow in the neutral in excess of the phase control currents.
The USITT did a study and found that the worst case scenario in an unbalanced three-phase phase-control dimming system is when one phase is 100 percent, another is 55 percent, and the third is 0 percent. This worst case scenario produces a neutral current of 125 percent of the phase current. Therefore, the NEC requires 130 percent ampacity in the neutral.
But many of us use double neutrals with dimming systems. Why is that?
Bozo the Electrician
Suppose you worked for a production company and you were touring with the circus (but I repeat myself). After some staff cuts, Bozo the Clown is assigned to work with you on the lighting crew. On your first gig, Bozo sets up the power distro and because you designed the system and Bozo carefully followed your instructions, everything goes smoothly.
But the night before the next gig, Bozo had been up late partying and clowning around with the bearded lady. So he comes in hung over the morning of a load-in in which the service in the venue is a single-phase three-wire plus ground system. His dimmer rack is a three-phase four-wire plus ground system. In his stupor, he doesn’t realize that he’s hooking up a three-wire system to a four-wire system and he connects phase A and B of the dimmer rack to L1 of the system power, phase C of the dimmer rack to L2 of the system power, and the neutral from the dimmer rack to the neutral of the system power. Will Bozo get away with it?
Because you designed the system, you were smart enough to design for the worst case scenario. That means you doubled the neutral feeder cable and you made sure that the dimmer rack complied with NEC Article 520.53 (O)(1), which says, “In portable switchboard equipment designed for use with 3-phase, 4-wire with ground supply, the supply neutral terminal, its associated busbar, or equivalent wiring, or both, shall have an ampacity equal to at least twice the ampacity of the largest ungrounded supply terminal.” You did that because when phase A and B in the dimmer rack are on full and phase C is at zero, then a neutral current would be twice the dimmer phase current.
Luckily, Bozo will not have to call the clowns with the fire truck and the squirting daisy.
