In an attempt to simplify complex mathematical equations, the summary value for harmonics called total harmonic distortion (THD) is derived from the individual harmonic values. The individual harmonic values are a magnitude (and phase angle) at the frequencies that are integer multiples of the fundamental frequency. In North America, these are 120 Hz, 180 Hz, 240 Hz, 300 Hz, and so on. By taking each magnitude, squaring, summing, taking the square root, and dividing by the magnitude at the fundamental frequencies, we end up with THD.
Whereas the math works for both voltage and current, it is only the voltage THD that should be normally used as a measure of the quality of electrical supply. A voltage harmonic distortion level of less than 3 percent at the service entrance (point of common coupling) is generally considered acceptable, though individual systems may vary. Measured at an individual piece of equipment, such as an adjustable-speed drive, this value may be a couple of percentage points higher. On the neutral conductor of a wye circuit, it is possible to have the VTHD greater than 100 percent, as there may be larger third or other triplen harmonics magnitudes than the fundamental itself, since the fundamental waveforms of the three-phase conductors should cancel out if balanced. (See Figures 1 and 2.)
Concerning the current, the use of the THD can be very misleading. Current is like the water flowing through a pipe. If you have a 5-inch pipe that has the capacity to flow 1,000 gpm at 60 psi, what would be the effect if you had just 75 gpm leaking out of it? The people in the neighborhood would still have plenty of water available to them, despite the system capacity’s 3 percent loss. But a 75-gpm leak in a 1-inch pipe with a 100 gpm at 60 psi is quite significant. Water flow on the upper floors of houses could be reduced to trickles.
The same concept is true for harmonic current, which causes unwanted losses in transformers, motors and other electromagnetic equipment. These losses also go up as the square of the harmonic number increases. The effect of the 11th harmonic (11 x 11 = 121) would be 12 times worse than the third harmonic (3 x 3 = 9).
What matters is the amount of harmonic current relative to the circuit’s current capacity, usually measured as the short-circuit current (SCC), which is how much current could be drawn from the system if the load were a short circuit. If the circuit has SCC of 30A, the total current is 1.5A and the harmonic current is 0.5A, the resulting 50 percent THD is basically meaningless. We are hardly tickling the systems capacity. However, take that same circuit with 24A total current of which 8A is harmonic current, then this 50 percent THD level is quite significant. If it is made up of higher harmonics, such as 13th, 19th or even 25th, then the eddy current and other losses in transformers and motors may result in significant derating of their capacity to do useful work.
IEEE Std 519-1992, IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems has a more detailed set of recommended limits for VTHD as well as individual harmonic current magnitudes based on the short-circuit current capacity, as measured at the point of common coupling to the utility service. It is also important to monitor the trending of the harmonic levels, as well as which harmonics are contributing to the change. If the seventh harmonic suddenly gets much larger in steady state levels, and no six-pole converters (such as ASDs) have been added to the system, look for a system resonance condition that is magnifying such, perhaps from a change in power-factor capacitors on the system. Such resonance conditions can create overvoltages that may damage equipment.
So the next time someone starts getting all excited about a current THD of 53 percent, remember which percents are meaningful, and which are just a misperception. EC
BINGHAM, a contributing editor for power quality, can be reached at 732.287.3680.