THDðÞ¼%ffiffiffiffiffiffiffiffiffiffiffi
P^1
i¼ 2F^2 isF 1 *100 % (30:2)Because harmonic levels are never constant, it is difficult to establish utility-side or manufacturing-
side limits for these quantities. In general, a probabilistic representation is used to describe harmonic
quantities in terms of percentiles. Often, the 95th and 99th percentiles are used for design or operating
limits.Figure 30.5shows a histogram of the voltage THD inFig. 30.4, and also includes a cumulative
probability curve derived from the frequency distribution. Any percentile of interest can be readily
calculated from the cumulative probability curve.
Both the Institute of Electrical and Electronics Engineers (IEEE) and the International Electro-
technical Commission (IEC) recognize the need to consider the time-varying nature of harmonics
when determining harmonic levels that are permissible. Both organizations publish harmonic limits, but
the degree to which the various limits can be applied varies widely. Both IEEE and IEC publish ‘‘system-
level’’ harmonic limits that are intended to be applied from the utility point-of-view in order to limit
power system harmonics to acceptable levels. The IEC, however, goes further and also publishes
harmonic limits for individual pieces of equipment.
The IEEE limits are covered in two documents, IEEE 519-1992 and IEEE 519A (draft). These
documents suggest that harmonics in the power system be limited by two different methods. One set
of harmonic limits is for the harmonic current that a user can inject into the utility system at the point
where other customers are or could be (in the future) served. (Note that this point in the system is often
called the point of common coupling, or PCC.) The other set of harmonic limits is for the harmonic
voltage that the utility can supply to any customer at the PCC. With this two-part approach, customers
insure that they do not inject an ‘‘unreasonable’’ amount of harmonic current into the system, and the
0.00(^135791113151719212325272931)
Harmonic Number
2.00
4.00
Current (%A)
6.00
8.00
10.00
Magnitude Spectrum (% of Fundamental)
FIGURE 30.2 Harmonic magnitude spectrum.
0
0
Voltage 5th Harmonic (%)
0.05
0.1
0.15
0.2
0.3
0.4
0.35
0.25
12 24 36
Time (hours)
48 60
FIGURE 30.3 Example of time-varying nature of harmonics.