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Fundamentals of Harmonics Fundamentals of Harmonics 181
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Figure 57 Flow
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of third-harmonic current in three-phase transformers
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large magnitudes in the line current However, during scrap meltdown, the furnace will frequently operate in an unbalanced mode with only two electrodes carrying current Large third-harmonic currents can then freely circulate in these two phases just as in a single-phase circuit However, they are not zero-sequence currents The third-harmonic currents have equal amounts of positive- and negative-sequence currents But to the extent that the system is mostly balanced, triplens mostly behave in the manner described 55 Harmonic Indices The two most commonly used indices for measuring the harmonic content of a waveform are the total harmonic distortion and the total demand distortion Both are measures of the effective value of a waveform and may be applied to either voltage or current
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551 Total harmonic distortion
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The THD is a measure of the effective value of the harmonic components of a distorted waveform That is, it is the potential heating value of the harmonics relative to the fundamental This index can be calculated for either voltage or current:
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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 182 Five
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Figure 58 Arc furnace operation in an unbalanced mode allows
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triplen harmonics to reach the power system despite a deltaconnected transformer
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hmax
THD =
(512)
where Mh is the rms value of harmonic component h of the quantity M The rms value of a distorted waveform is the square root of the sum of the squares as shown in Eqs (53) and (54) The THD is related to the rms value of the waveform as follows:
hmax
THD2
(513)
The THD is a very useful quantity for many applications, but its limitations must be realized It can provide a good idea of how much extra heat will be realized when a distorted voltage is applied across a resistive load Likewise, it can give an indication of the additional losses caused by the current flowing through a conductor However, it is not a good indicator of the voltage stress within a capacitor because that is related to the peak value of the voltage waveform, not its heating value
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Fundamentals of Harmonics Fundamentals of Harmonics 183
The THD index is most often used to describe voltage harmonic distortion Harmonic voltages are almost always referenced to the fundamental value of the waveform at the time of the sample Because fundamental voltage varies by only a few percent, the voltage THD is nearly always a meaningful number Variations in the THD over a period of time often follow a distinct pattern representing nonlinear load activities in the system Figure 59 shows the voltage THD variation over a 1-week period where a daily cyclical pattern is obvious The voltage THD shown in Fig 59 was taken at a 132-kV distribution substation supplying a residential load High-voltage THD occurs at night and during the early morning hours since the nonlinear loads are relatively high compared to the amount of linear load during these hours A 1-week observation period is often required to come up with a meaningful THD pattern since it is usually the shortest period to obtain representative and reproducible measurement results
552 Total demand distortion
Current distortion levels can be characterized by a THD value, as has been described, but this can often be misleading A small current may
VTHD
0% Mon Tue Wed Thurs Fri Sat Sun
Figure 59 Variation of the voltage THD over a 1-week period
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Fundamentals of Harmonics 184 Five
have a high THD but not be a significant threat to the system For example, many adjustable-speed drives will exhibit high THD values for the input current when they are operating at very light loads This is not necessarily a significant concern because the magnitude of harmonic current is low, even though its relative current distortion is high Some analysts have attempted to avoid this difficulty by referring THD to the fundamental of the peak demand load current rather than the fundamental of the present sample This is called total demand distortion and serves as the basis for the guidelines in IEEE Standard 519-1992, Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems It is defined as follows:
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