Improving Your Phase Relations
by
“The illiterate of the
21st century will not be those who cannot read and write, but those
who cannot learn, unlearn, and relearn.” – Alvin Tofler
Q: When does one plus one not equal two?
A: When they are out of phase.
Okay, that may seem to make about as much sense as Paris Hilton quoting bible verses. But there is a certain logic to it.
If you’re talking about three-phase power, you might wonder why you can measure 120V from phase to neutral but only 208V from phase to phase. Why doesn’t 120V plus 120V equal 240V?
To unravel this mystery, it helps to understand how you get 120V in the first place.
Alternating current, or AC, is constantly changing direction and intensity. If you could periodically sample the voltage at sequential intervals in one cycle, you would find that in a 120V system the instantaneous voltage varies between -169.7V and +169.7V. Because the positive half of a pure sine wave is perfectly symmetrical to the negative half, the average voltage over one complete cycle is actually zero. But common sense dictates that the energy produced by a cycle of alternating current is anything but zero – just try licking a hot leg of three-phase power (NO, NOT LITERALLY!) and you’ll agree that the average voltage is not zero. So we need a way to represent the amount of potential power that might be produced by this AC voltage.
Sometimes you have to take the long way around to get to where you want to go. This is one of those times. Mathematicians know that when you square a negative number you get a positive number. Then you can take the square root of the squared number and you end up with the absolute value of the original number.
In order to represent the average voltage of a sine wave, you can first square the instantaneous voltage in order to make it positive. Then you average the numbers over one cycle, and finally you take the square root, thus undoing the squaring action you performed in the first place. The process is known as the (square) root (of the) mean (or average) squared, or RMS.
Without doing any actual math, it turns out that the RMS value of a sine wave is 0.707 times the peak value. The peak voltage for a 120VAC sine wave is actually 169.7V. The average voltage is 120—that is; of course, the average voltage from one phase of a three-phase system to neutral on a 120V/208V system.
With that in mind, we can look behind the curtain at the voltage from one phase to another.
When you measure the voltage between any two points, you are actually measuring the difference in voltage between them, not the sum. One of the points of measurement is the reference against which the other is measured. If they are at the same potential, then the voltage is zero. When you measure the voltage from a hot leg to neutral, you are using the neutral as a reference. Since it is bonded to ground it is at zero volts.
At first glance, you might think that measuring the voltage
between two phases would be a simple addition. In fact, if they were in phase with
each other the resultant voltage would be zero because there would be no
difference between them. But the reason there is a voltage difference is because they are 120 degrees out of
phase with each other.
Figure 1 - Two sine waves 120 degrees out of phase with each other (blue line and magenta line). The yellow line is the voltage difference between the two.
If you look at the pretty picture on this page you will see three squiggly lines representing three separate voltage waveforms. The blue waveform represents the first phase, phase A, of a three-phase wye system. It starts from zero volts at zero degrees. The magenta waveform represents phase B; it’s 120 degrees behind phase A. We know this because it starts from zero volts at 120 degrees. It follows the exact waveform as phase A, only 120 degrees later.
If you subtract the two waveforms, the result is the yellow waveform. You can confirm this by looking at some critical sample points. At zero degrees, phase A is zero and phase B is -147 volts; the yellow waveform starts at +147V because zero minus -147V is +147V. At 150 degrees, phase A and phase B intersect at about 85 volts. Their difference is zero, which is what the yellow waveform shows at 150 degrees. At 330 degrees, phase A and B are both -85 volts, again resulting in a difference of zero. The yellow waveform again confirms the result.
The yellow waveform peaks at 294 volts at 60 degrees. You can find the RMS value by multiplying by 0.707 and you will find that the result is 208 volts.
When it comes to three-phase systems, electricity is not always intuitive. Sometimes you have to understand more than simple addition or multiplication. Fortunately for some, there are lots of jobs that require less complex thinking. That’s why we have managers and bosses.
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