谐波、中性线电流及 k 系数

How this is calculated#

Electronic loads draw current in pulses, not as a smooth wave. A power quality analyser splits that current into the fundamental and its harmonics, each shown as a percent of the fundamental. The tool takes the true rms phase current and that spectrum, from the third to the fifteenth order.

The total harmonic distortion is the rms of all the harmonic percents. The fundamental current is the rms current divided by the square root of one plus the distortion squared.

The third, ninth and fifteenth harmonics are the triplens. In the three phases they are in step, so they add in the neutral instead of cancelling. With equal phases the neutral carries three times one phase's triplen current. That is the tool's main answer.

AS/NZS 3008.1 Table 2 bands the third harmonic as a percent of the phase current. So the tool converts the analyser's percent of the fundamental to a percent of the rms current. It reads the band through the cable size tool's own path, and gives the reduction factor, whether the cable is picked on the phase or the neutral current, and the current to carry to cable size.

AS/NZS 3000 Cl 3.5.2(b)(i) gives a minimum for the neutral of a substantial harmonic load: the out-of-balance current plus one phase's harmonic current. Size the neutral for the larger of it and the triplen figure. AmpSize reads the harmonic current as the rms of the third and higher orders. Note 1 sets what substantial means.

The K-factor weights each harmonic by its order squared, because eddy current loss in a transformer rises with frequency squared. A clean load gives 1.

Worked examples#

• An office floor of 80 A with 40 % third harmonic puts 87.16 A in the neutral, more than a phase. The current has 49.34 % THD and a K-factor of 4.37.
• Six-pulse drives drawing 150 A put only 13.43 A in the neutral, as their harmonics are mostly fifth and seventh. The current has 35.14 % THD and a K-factor of 5.12.
• An LED lighting circuit of 40 A puts 64.28 A in the neutral. The current has 89.16 % THD and a K-factor of 10.01.
• A 60 A board where electronics are 30 % of the load puts 58.73 A of triplens in the neutral if every load had this spectrum. The current has 42.18 % THD and a K-factor of 3.59. Below 40 % the clause figure does not apply.

Limits#

The tool assumes three equal phases with the same spectrum. A real board has a mix. Enter the worst phase's readings for a safe answer.

It does not work voltage distortion, resonance with power factor capacitors or filter design. Those need the supply's impedance and a harmonic study.

See also: Neutral current, Cable size and Transformer.