Harmonic Distortion: Definitions And Countermeasures

March 1, 1998
While harmonics are important, they need to fit into the larger context of power quality. While you must consider harmonics, they are not the demon some would have you believe they are.Why the hubbub about harmonics? Modern technology's sensitive components present new challenges for plant engineers and others who design, specify, install, or maintain plants and equipment. For example, SCR and diode

While harmonics are important, they need to fit into the larger context of power quality. While you must consider harmonics, they are not the demon some would have you believe they are.

Why the hubbub about harmonics? Modern technology's sensitive components present new challenges for plant engineers and others who design, specify, install, or maintain plants and equipment. For example, SCR and diode rectifiers in computers, copiers, solid-state lighting ballasts, and power conversion sections of adjustable frequency drives increase the need to thoroughly address harmonic distortion and its role in overall power quality.

Does this mean your equipment will self-destruct unless you employ expensive strategies to combat harmonics? Perhaps, but not necessarily. It may be able to tolerate a good deal more harmonics than some would have you believe, and you can mitigate the harmonics you do have with some fundamental steps. This is not to say you can disregard the issue of harmonics. But the plain truth is, you can deal with harmonics effectively when (and only when) you understand more about the issue than "harmonics are bad."

Of course, you can't discuss power quality for long without looking at waveforms. Electrical waveforms are either linear (sinusoidal) or non-linear (non-sinusoidal). In Fig. 1 (original printed medium), you see a linear waveform. This waveform, a sinewave, is simple to describe mathematically. The other waveform (on the right) is a non-linear waveform. You can't easily describe non-linear waveforms mathematically.

Voltage and current waveforms appear neat in illustrations. In reality, you'll be hard-pressed to see a pure sinewave on any distribution system. For practical purposes, it is true every waveshape has a harmonic distortion value.

A harmonic estimation performed on the waveforms in Fig. 1 (original printed medium) might show the linear waveform has a total harmonic distortion of 3%. (Remember, no waveform is purely sinusoidal.) An analysis performed on the non-linear waveform might show a total harmonic distortion exceeding 100%.

How do you calculate the total harmonic distortion (THD)? One way is simply to add all existing individual harmonic multiples. Individual harmonics usually show as a percent of the fundamental component. In a 60-Hz system, the fundamental component is 60. Likewise, on a 50-Hz system, the fundamental component is 50. If an individual harmonic has 50A of energy and the fundamental has 100A, the percent of the fundamental is 50/100 or 50%. You can measure harmonic multiples in the same fashion and summarize them as THD.

Suppose your power distribution grid contains 200A (fundamental) of current. Significant harmonic multiples present in the system have 75A, 30A, 10A, and 2A. You can estimate the THD in that system, as shown in the example (original printed medium). Change the fundamental current to 400A, and make the others 150A, 30A, and 20A. Now what value do you come up with?

Equation 3 (original printed medium) expresses THD as a percentage. This formula uses the Fourier Theorem to describe the characteristics of a non-linear waveform. The Fourier Theorem says you can describe any periodic function by a constant term plus an infinite series of sine and cosine terms of frequency, where n is an integer. You can express any periodic function by positioning sine waves of different amplitude and frequencies over one another. Likewise, you can break down any waveform into some number of pure sinewaves.

These sinewaves of different frequencies and amplitudes show the electrical conditions we typically refer to as harmonics. When either current waveform or voltage waveforms are no longer sinusoidal, the waveform can be expressed by the Fourier Theorem and is said to have harmonic distortion. Let's look at some waveforms to illustrate how the Fourier Theorem may describe non-linear waveforms.

If you algebraically combine the waveform in Fig. 2 (original printed medium) with the one in Fig.3 (original printed medium), you get the one in Fig. 4 (original printed medium). This is the fundamental concept behind the Fourier Theorem.

Unfortunately, determining THD for a system depends on many factors. Those factors include system impedance, transformer impedance, ratio of non-linear to linear power-consuming devices, and pre-existing harmonic distortion levels. These factors also limit how accurately you can predict harmonic distortion prior to actually installing electronic devices.

A harmonic multiple is a multiple of the fundamental frequency. For example, a harmonic frequency of 300 Hz developed on a 60-Hz system is the fifth harmonic (5 3 60 5 300). In the case of adjustable frequency drives (AFDs), determining significant harmonic multiples is relatively easy.

The odd harmonics are significant, because the even harmonics tend to cancel each other out. Note, the 12-pulse rectifier produces fewer harmonics than does the 6-pulse.

Harmonic currents are the result of nonlinear loads, in which the resultant current waveform does not conform to the shape of the applied voltage waveform. The THD is the contribution of all harmonic-frequency currents to the fundamental current.

Any harmonic current flowing in the system will create voltage drops across the various impedances, thus giving you resultant voltage waveform distortions. However, high current distortion levels do not necessarily translate into high-voltage distortion levels.

The contribution of all harmonic-frequency voltages to the fundamental voltage is known as total voltage distortion (TVD).

SCR and diode power conversion sections affect voltage and current harmonics differently. System impedance has a large impact on voltage and current harmonics present in the system.

Most DC drives use phase-controlled converters, also known as silicon-controlled rectifiers (SCRs), in the input rectifier stage. See Fig. 5 (original printed medium). Substitute SCRs for the diodes, and this application would produce a line current relatively square in shape. This is generally the case for DC drives having a DC link choke, which we see as an option in Fig. 5. Reactance located on the AC side of the SCR bridge will have a relatively small effect on total current distortion, but may drop the TVD considerably. In this situation, TVD levels will be relatively high and may affect low-voltage equipment.

In most AC drives, the input rectifier uses a diode bridge. An example appears when you have the diodes shown in Fig. 5. When you add the choke (shown as optional), this power conversion scheme eliminates line voltage notches, as shown in Fig. 6 (original printed medium), but does pull pulses of current from the utility line when the diode conducts. The DC circuit uses capacitors to provide additional filtering for the DC bus voltage. If possible, these capacitors would charge (draw current) instantaneously. Circuit inductance is the only limiting element opposing instantaneous current flow.

With little or no inductance in the circuit, the current drawn from the AC line will appear as two separate rounded pulses every half cycle. This type of waveform, shown in Fig. 7 (original printed medium), is commonly known as the rabbit ear waveform. Some AFDs incorporate a DC link choke into the power conversion scheme or allow the end user to supply the DC link choke as an option to reduce the peak currents the capacitors draw to charge.

System impedance is the amount of AC reactance in a power distribution system. Reactance opposes instantaneous current change, thus affecting how devices such as capacitors in an AFD draw current (or charge). If a power distribution system has a relatively high impedance (between 5% and 10%), the total current distortion will be relatively low because the current waveform is more sinusoidal. Likewise, if a power distribution system has a relatively low impedance (between 2% and 5%), the total current distortion may be relatively high.

It's relatively easy to add more impedance to a power distribution system. If the system is a new installation, you can specify a power transformer with a high impedance. If it's an existing installation, you can add 3-phase line reactors to the system to raise overall system impedance. The overall effect will be to lower total current harmonic distortion in the power distribution system.

Remember two things: In an AFD, the circuit elements most significantly influencing the amount of harmonic current present are the amount of system impedance and where it's located.

To handle harmonic distortion effectively, you must have a solid understanding of the basics. Just because you can measure harmonics in a system does not mean there will be a problem with harmonic distortion.

In the Part II of this series, we'll look at ways to find out if you must correct for power system harmonics. In Part III, we'll look at ways to correct for power system harmonics. We'll evaluate the various countermeasures and see which ones are appropriate for the challenges presented by your power system's harmonics.

Rule of Thumb No.1: The higher the total harmonic distortion, the less sinusoidal the waveform appears.

Rule of Thumb No. 2: Every waveform has associated harmonic distortion.

Rule of Thumb No. 3: Actual values of harmonics for a system are unique to that system, and such information is typically not available for use at the design stage.

About the Author

Cory J. Lemerande

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