Draft Guide for Harmonic Limits for Single-Phase Equipment



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5. Background


An approximate expression for determining the amount of each current harmonic present for single-phase converters is given by the following equation:


where: n = harmonic order (3, 5, 7, 9, 11, 13, etc.)

A similar approximate expression for determining the amount of each current harmonic present for three-phase (6-pulse) converters is given by the following equation:




where: n = harmonic order (5, 7, 11, 13, 17, etc.)

In both of these expressions, the harmonic is expressed in terms of the fundamental frequency term. The results of these two expressions are shown in the table below.



Table 4-1. Approximate Current Harmonic Content (%) for 1-Phase and 3-Phase Converters





Harmonic

3

5

7

9

11

13

15

1-phase converter

67

40

29

22

18

15

13

3-phase converter

x

20

14

x

9

8

x

As can be seen, most single-phase converters produce all the odd harmonics at about twice the amount of their three-phase converter counterparts. In addition, single-phase converters have significant amounts of third harmonic content, which the three-phase converters do not have.



It should be noted that the single-phase equation underestimates the % of each harmonic and the three-phase equation overestimates the harmonic content in most cases. The current total harmonic distortion (THD), which is the weighted or rms assessment of all harmonics, approaches 100% for many of these devices. The expression for THD is as follows:


where: THDI = current total harmonic distortion

In = harmonic rms current (in amps or %)

I1 = fundamental frequency rms current (in amps or 100%)

A similar equation for voltage THD results from V being substituted for I in the above. Using the values from Table 1-1, the THDI for a single-phase converter is around 95% versus 30% for a three-phase converter, based on odd harmonics up to the 50th. Up until now, because the typical system impedance up to a harmonic source is reasonably low and the typical harmonic source is a relatively small load, the resulting THDV (in %) will usually be in the single digits.

The harmonic content and THD can be obtained for different levels of load for some devices. For example, a battery charger has a variable load characteristic and the harmonic content and THD varies as a function of load. It us usually sufficient to note the THD and % of individual harmonics at rated load. At lower levels of load, the resulting percentages (of individual harmonics and THD) are usually offset by the lower base current at that load. For example, with two loads having the same base current, one that produces 20% THDI at 50% load is no worse than one which produces 10% THDI at 100% load. They both produce the same distortion in amperes.





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