Resolving harmonic problems is easier than some people would have you think. If you understand some basics, you'll be able to eliminate most of the mystery.

In Part 1 (March 1998 issue), we showed you the problems with high energy in the higher frequency components of any waveform. In Part 2, we'll look at these problems more closely. The bar graph (original article) is from the input current waveform of a three-phase, six-pulse power conversion scheme. So what are we looking at, here? It's a typical frequency spectrum plot of amplitude of harmonic multiples for a waveform.

Let's cover some basics first, so we can make the bar graph useful to you. For example, how do you find the specific frequency of a harmonic? To do that, you multiply the fundamental frequency by the harmonic multiple. We know the fundamental frequency is 60 Hz. If you're looking at the fifth harmonic, your multiple is five. If your multiple is five, then your specific frequency is 300 Hz (5260 Hz).

Now, back to the bar graph. Here, the data show a current of almost 24A exists at a 300 Hz frequency. To express this as a percentage, you simply divide the current by the specific frequency. In the example here, this calculation gives you 0.75 (24 divided by 32), or 75%. So, the current at 300 Hz is 75% of the fundamental current.

How else can you use this bar graph? You can use it to estimate the total harmonic distortion (THD) for a waveform. To do this, use the equation for THD, which is Eq. 2 of "Total Harmonic Distortion Equations," on page 57 (of the original article). Here, you represent the total amount of energy contained in harmonics as a percentage of energy contained in the fundamental frequency.

Effect on power transformers. If you ask 100 people: "What's the biggest effect of harmonics?" you'll probably get 100 different answers. So, what's correct? The biggest effect is the increased heating of a power transformer's core. The degree of increased heating depends on a few variables: the transformer's construction, its load, and the magnitude of harmonic distortion. What about harmonic current and voltage distortion? The magnitude of these variables depends on the impedance of the power source and that of the distribution line downstream of it.

The effect of harmonics on transformers is twofold. First, current harmonics cause an increase in copper losses and stray flux losses. Second, voltage harmonics cause an increase in iron losses. The overall effect is an increase in transformer heating.

A transformer's K-factor rating describes how well it can handle the additional heat generated by high harmonic content. You can find a definition of transformer K-factor in the ANSI/IEEE Standard C57.110-1986, Recommended Practice for Establishing Transformer Capability When Supplying Non-Sinusoidal Load Currents.

Developers of this rating intended for people to use it as a tool to derate existing small and medium transformers when powering high-harmonic three-phase loads. The current they had in mind included that from such devices as adjustable frequency drives (AFDs). This rating may be inadequate for applications where you have single-phase switch mode power supplies, (found in copiers, faxes, computers, and other office equipment).

When dealing with K-factor, don't assume that more is better. Too much K-factor can reduce the transformer's ability to withstand power glitches. Why? A higher K-rating means less impedance. You need a certain amount of impedance to handle surges and sags. It's not rare for a high-K-rated transformer's impedance to be under 3%.

We know harmonics generate heat. You may have measured high harmonics and are wondering if you are burning up your transformer. Typically, this excess heat is not a problem. To determine if it is, you need to compare the temperature with the rating of the transformer. Here's a comforting thought. Most transformers have some "over engineering" built into them, so their ratings are on the conservative side. This means you don't have to rush out and replace an existing transformer just because you added AFDs and now have harmonics. In fact, when you add AFDs, your transformer load will drop, most likely canceling out the harmonics-induced heating. Sound too good to be true? Consider one case study in which kilowatt consumption dropped by 12% when AFDs replaced across-the-line motor configurations. If you were fine before, you are probably fine now-unless you added more loads to the transformer.

Harmonics can cause your neutral to overheat. Why is this? And, why are neutral conductors subject to more heating than their companion phase conductors? In balanced 3-phase systems, line currents cancel each other. However, triplen harmonics (3rd, 9th, 15th, and so on) add to each other in the neutral (which carries your unbalanced current). How do you fix this? Simply go to a larger wire or run a parallel wire of the same gauge.

In other situations, you may notice an increased temperature in the power wires. How can this be, if the neutral is carrying the unbalanced current? Well, this problem is a different animal. You've probably heard of "skin effect." Basically, it's a phenomenon that happens when high frequencies travel through a wire. They travel on the outside of the wire-along its skin. This is one reason metal conduit makes such a good ground for noise-the high frequencies travel along the skin of a hollow tube. The skin effect increases with frequency.

Since harmonics are always greater then 60 Hz, current flow migrates toward the outer part of the conductor as you reach the higher orders. As a result, you have less of your current traveling through the cross-section. Instead, you have current density at the outer limits of the conductor. This gives you a rise in temperature, because the temperature is a function of current per unit volume of the conductor. If the temperature rise is out of specifications, you'll have to apply a larger wire. The current density will decrease, and so will your temperature.

High harmonic distortion may affect electromagnetic equipment. Such equipment includes motors, ballasts, transformers, and solenoids. This equipment is sensitive to additional heat generated by eddy-current losses. It's also sensitive to the higher rms currents. Eddy-current losses increase as a function of the square of the applied frequency. The possible effects could be decreased machine efficiency and torque, and increased audible noise in the equipment.

Since most electronic equipment operates at a low voltage level, it is sensitive to voltage notching. Typical victims include programmable logic controllers (PLCs) and telephones. If you locate your equipment close to conductors carrying a high degree of harmonic content, you could have problems. The typical approach is to add line filtering, and then blame the filter manufacturer when you still have the problem. That's sort of like blaming your furnace filter when you have odors from your garbage disposal. That furnace filter does its job just the way it's supposed to, but it cannot correct for a dirty disposal unit. Don't try to make a line filter correct for poor design in your distribution system. A better approach is to observe proper routing of your conductors. Many times, just routing conductors away from affected equipment will do the trick.

Capacitors in a power system give rise to concerns over system resonance. "System resonance" sounds like it's right up there with psychic levitation and planetary alignments-what is this all about? System resonance is real. It's the inadvertent tuning of a power system to one of the harmonics present. System resonance will impose voltages and currents that are considerably higher than would otherwise exist. The result is increased electrical stress on all electrical equipment. Resonant tuning can result in random circuit breaker tripping, failure of transformers and switchgear, and various capacitor problems including blown fuses and ruptured cells. You also have a strong likelihood of straining permanent split capacitor and capacitor start motors or RC snubber networks beyond specifications.

How can this resonance occur? This is a direct result of the electric properties of capacitors. Capacitive reactance varies inversely with the applied frequency. This means that as the frequency increases, the effective impedance of the capacitor network goes down. High frequency components that may exist on the line could see the capacitor as a short to ground. In addition, this results in excessive inrush currents from different parts of the plant.

Correct for these capacitor problems by adding inductive reactors. Inductive reactance varies directly with frequency. As the applied frequency goes up, the effective impedance of the reactor also increases. Installing line reactors between the power factor correction devices and non-linear loads mitigates inrush current. It also dampens surge voltages caused by the turning on/off of the capacitor racks.

The classical representation of power factor (PF) in terms of the phase displacement between AC current and voltage is inadequate for non-linear loads. This is because it leaves out the harmonic power that is present. The total or "true" PF accounts for the phase displacement as well as harmonic power. Use equations 2 and 3, on page 57 (of the original article), to determine displacement PF.

Most utilities measure total kVA and show either the kW demand or the calculated PF. The calculated PF can be either displacement PF or true PF. An AFD has a displacement PF of approximately 0.98. True PF depends on the harmonic distortion present in the system. You can use utility data to see if you need corrective procedures to mitigate PF penalty charges. Measuring PF for an individual drive provides useful information, but if PF is a problem, it shows up on the utility bill.

K-1: Conventional transformer designed to handle eddy current losses from 60 Hz sinewave current. K-4: Designed to meet four times the eddy current losses of a K-1 transformer. K-9: Designed to meet higher eddy current losses than a K-4 transformer. K-13: Designed to handle twice the eddy current losses as a K-4 transformer.

Fortunately, transformer designers already build in some harmonics handling ability. For example, a transformer designed to meet UL1502 type "NS" can handle the following: 16% of the fundamental as 3rd 10% of the fundamental as 5th 7% of the fundamental as 7th 5.5% of the fundamental as 9th A transformer designed as type "R" can handle even higher levels of harmonic distortion. At this level, we have a "K factor" of 4. Here are the particulars of what this type "R" transformer can handle: 33% of the fundamental as 3rd 20% of the fundamental as 5th 14% of the fundamental as 7th 11% of the fundamental as 9th