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THE POWER FACTOR

by George Novacek

Start ý Nonlinear Loads ý Harmonic Distortion ý Power Factor Correction ý Sources and PDF

HARMONIC DISTORTION

Baron Jean Baptiste Fourier, a French mathematician, postulated that any waveform or function can be decomposed into sinusoids of different frequency and amplitude, which sum to the original waveform. Mathematically, Fourier transform of a function f(x) is:

For generations of budding engineers this was a dreaded, devious invention designed to torture them. Thanks to computers and the invention of the fast Fourier transform (FFT) algorithm by Tukey and Cooley in 1965, it has become a powerful and widely used analytical tool.

Figure 4 is the FFT of the current (red trace) waveform seen in Figure 3. Notice that the even harmonics have little effect and can be ignored. The odd harmonics are a completely different story. The first five odd harmonicsý amplitudes are nearly as high as the fundamental frequency of 60 Hz.

(Click to enlarge)

Figure 4ýThe fast Fourier transform of the current waveform in Figure 3 confirms a high level of distortion.

What does that mean? The total harmonic distortion (THD) is defined as:

where n is the harmonic number, and V_n is amplitude of that harmonic relative to the fundamental frequency V₁. In other words, the THD is a ratio of the sum of the harmonic frequencies over the fundamental. Distortion meters work on the same principle by using sharp filters to measure only the voltage of the harmonics with the fundamental filtered out relative to the fundamental alone. A clean sine wave with no harmonics will have a THD of 0%. This example, as you can guess by looking at Figure 4, has more energy in the harmonics than in the fundamental, and the calculation confirms that the THD is a whopping 242%.

Waveform distortion of the AC power causes the decreased power factor. In most industrialized countries, the utility companies maintain distortion at less than 4% but are allowed to occasionally go as high as 8%. In third-world countries, this distortion is often much higher.

The distortion is not as easily converted to the reduction in the power factor as the phase shift. We also know from looking at the tables that a THD of 10% results in a 99.5% power factor. At 20% THD, the power factor is down to 98% and drops to 90% at about 47% THD. Many of us who have been conditioned by Hi-Fi specifications where a THD reaching less than of 0.1% is the norm, may not be able to fathom 20% THD, which by the way, still looks good on the scope. Glance again at Figure 4 to see the distortion level caused by a simple rectifier and consider what 242% will do to the power factor. That wasted energy, which turns into heat and has to be dissipated somehow, may be expensive indeed.

And, there are other problems associated with the high level of distortion. The high harmonic content causes EMI interference, which may be difficult to bring under control, especially in high-power systems. Also, donýt forget that magnetic cores are usually optimized for the fundamental frequency. As a result of the high harmonic content, the efficiency of transformers and armatures will drop, more heat will be generated, and more energy wasted. So, what can be done?

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