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design and operation that consider only the fundamental frequency Therefore, the engineer is faced with unfamiliar phenomena that require unfamiliar tools to analyze and unfamiliar equipment to solve Although harmonic problems can be difficult, they are not actually very numerous on utility systems Only a few percent of utility distribution feeders in the United States have a sufficiently severe harmonics problem to require attention In contrast, voltage sags and interruptions are nearly universal to every feeder and represent the most numerous and significant power quality deviations The end-user sector suffers more from harmonic problems than does the utility sector Industrial users with adjustablespeed drives, arc furnaces, induction furnaces, and the like are much more susceptible to problems stemming from harmonic distortion Harmonic distortion is not a new phenomenon on power systems Concern over distortion has ebbed and flowed a number of times during the history of ac electric power systems Scanning the technical literature of the 1930s and 1940s, one will notice many articles on the subject At that time the primary sources were the transformers and the primary problem was inductive interference with open-wire telephone systems The forerunners of modern arc lighting were being introduced and were causing quite a stir because of their harmonic content not unlike the stir caused by electronic power converters in more recent times Fortunately, if the system is properly sized to handle the power demands of the load, there is a low probability that harmonics will cause a problem with the power system, although they may cause problems with telecommunications The power system problems arise most frequently when the capacitance in the system results in resonance at a critical harmonic frequency that dramatically increases the distortion above normal amounts While these problems occur on utility systems, the most severe cases are usually found in industrial power systems because of the higher degree of resonance achieved 51 Harmonic Distortion Harmonic distortion is caused by nonlinear devices in the power system A nonlinear device is one in which the current is not proportional to the applied voltage Figure 51 illustrates this concept by the case of a sinusoidal voltage applied to a simple nonlinear resistor in which the voltage and current vary according to the curve shown While the applied voltage is perfectly sinusoidal, the resulting current is distorted Increasing the voltage by a few percent may cause the current to double and take on a different waveshape This is the source of most harmonic distortion in a power system
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Downloaded from Digital Engineering Library @ McGraw-Hill (wwwdigitalengineeringlibrarycom) Copyright 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website
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Fundamentals of Harmonics Fundamentals of Harmonics 169
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Figure 51 Current distortion caused by nonlinear resistance
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Figure 52 illustrates that any periodic, distorted waveform can be expressed as a sum of sinusoids When a waveform is identical from one cycle to the next, it can be represented as a sum of pure sine waves in which the frequency of each sinusoid is an integer multiple of the fundamental frequency of the distorted wave This multiple is called a harmonic of the fundamental, hence the name of this subject matter The sum of sinusoids is referred to as a Fourier series, named after the great mathematician who discovered the concept Because of the above property, the Fourier series concept is universally applied in analyzing harmonic problems The system can now be analyzed separately at each harmonic In addition, finding the system response of a sinusoid of each harmonic individually is much more straightforward compared to that with the entire distorted waveforms The outputs at each frequency are then combined to form a new Fourier series, from which the output waveform may be computed, if desired Often, only the magnitudes of the harmonics are of interest When both the positive and negative half cycles of a waveform have identical shapes, the Fourier series contains only odd harmonics This offers a further simplification for most power system studies because most common harmonic-producing devices look the same to both polarities In fact, the presence of even harmonics is often a clue that there is something wrong either with the load equipment or with the transducer used to make the measurement There are notable exceptions to this such as half-wave rectifiers and arc furnaces when the arc is random
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Downloaded from Digital Engineering Library @ McGraw-Hill (wwwdigitalengineeringlibrarycom) Copyright 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website
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