How current harmonics affect the sizing of the components?

[aledam]

I believe that most of us know that in an ideal sinusoidal wave, the RMS value can be obtained from the peak divided by the sqrt of 2.
However, when harmonics are involved, the peak can be much higher than RMS*sqrt(2). For example, the current consumed by a rectifier contains low order harmonics (5th and 7th especially) with high amplitude.

Here is my question: how should we take these current harmonics into account when sizing the cables and the transformers? Here are my thoughts.

For cables. Assuming that the skin effect is negligible due to the low frequency of the harmonics, the main problem comes from the Joule losses. These losses are always calculated from the true RMS value of the current, regardless of the peak value. For this reason, I would NOT consider how high the peak of the current is when dimensioning the cables. For instance, if the true RMS current is 100A and the peak is 180A, I would consider the 100Arms when sizing the cable.

Different story is for the transformer. If the peak of the current is too high, we can saturate the core. If a transformer has a rated current of 100A, it means that it can handle a peak up to 100*sqrt(2)=141A. Considering the same example as above, a 100Arms transformer would not be good enough, because our peak is 180A. The equivalent RMS value of a pure sinusoid with such peak is 180/sqrt(2)=127A. Therefore, I should find a transformer that is rated for 127Arms at least.

Does it make sense, or do you have something to say against this?

 

[electrofelon]

I believe that most of us know that in an ideal sinusoidal wave, the RMS value can be obtained from the peak divided by the sqrt of 2.
However, when harmonics are involved, the peak can be much higher than RMS*sqrt(2). For example, the current consumed by a rectifier contains low order harmonics (5th and 7th especially) with high amplitude.

Here is my question: how should we take these current harmonics into account when sizing the cables and the transformers? Here are my thoughts.

For cables. Assuming that the skin effect is negligible due to the low frequency of the harmonics, the main problem comes from the Joule losses. These losses are always calculated from the true RMS value of the current, regardless of the peak value. For this reason, I would NOT consider how high the peak of the current is when dimensioning the cables. For instance, if the true RMS current is 100A and the peak is 180A, I would consider the 100Arms when sizing the cable.

Different story is for the transformer. If the peak of the current is too high, we can saturate the core. If a transformer has a rated current of 100A, it means that it can handle a peak up to 100*sqrt(2)=141A. Considering the same example as above, a 100Arms transformer would not be good enough, because our peak is 180A. The equivalent RMS value of a pure sinusoid with such peak is 180/sqrt(2)=127A. Therefore, I should find a transformer that is rated for 127Arms at least.

Does it make sense, or do you have something to say against this?

Harmonics are almost never an issue anymore. Do you have some specific equipment in mind that is not PF corrected and that you are concerned about?

 

[jim dungar]

Harmonics were almost a big deal some 30 years ago, with the major concern being heating internal to transformers. Specific items were built to attenuation or tolerate the harmonics, such as K-Rated transformers. Over the decades harmonics have proven not to be a universal problem and instead could be treated on a case by case basis.

The branch circuit conductor sizes chosen by the NEC are very conservative so they have never been a concern. Feeder conductors usually see a large amount of natural harmonic cancellation and are rarely, to almost never, a concern in actual installation.

However there are a few situations where harmonics are a concern but they are hard to predict in advance of problems. Every time I have calculated the harmonic loading of large transformers, the load profile was such that a K rating of 1 was still sufficient.

 

[winnie]

Here is my question: how should we take these current harmonics into account when sizing the cables and the transformers? Here are my thoughts.

For cables. Assuming that the skin effect is negligible due to the low frequency of the harmonics, the main problem comes from the Joule losses. These losses are always calculated from the true RMS value of the current, regardless of the peak value. For this reason, I would NOT consider how high the peak of the current is when dimensioning the cables. For instance, if the true RMS current is 100A and the peak is 180A, I would consider the 100Arms when sizing the cable.

Different story is for the transformer. If the peak of the current is too high, we can saturate the core. If a transformer has a rated current of 100A, it means that it can handle a peak up to 100*sqrt(2)=141A. Considering the same example as above, a 100Arms transformer would not be good enough, because our peak is 180A. The equivalent RMS value of a pure sinusoid with such peak is 180/sqrt(2)=127A. Therefore, I should find a transformer that is rated for 127Arms at least.

Does it make sense, or do you have something to say against this?

The above comments address the lack of practical implications of harmonics in building power systems. But if you are specifically designing components that have to deal with harmonics (say you are actually designing the transformer that feeds a simple diode bridge for a system), then you are on the right track.

The impact is that ordinary wires will heat per the RMS current (unless the wires are so large that the harmonics see 'skin effects' that increase wire resistance). (Note that for 5th and 7th harmonics and normal feeder size wires, skin effect is noticeable if not significant.) Thinks like transformers will have a non-linear response to the harmonics and need to be looked at more closely.

I think you might have the effect on the transformer a bit off. Core saturation is caused by excess magnetizing current flow, which is caused by the applied voltage. I'd expect harmonic load currents to reduce the primary supply voltage (because of the impedance of the primary supply circuit), and to thus _reduce_ core flux levels. If the harmonic currents somehow cause _increased_ supply voltage, then remember that core saturation is not from the RMS voltage, but from the volt-second integral of the applied voltage; short high voltage spikes won't instantly saturate the core. (To understand this latter point simply, think about the RMS voltage that will saturate the core as supply frequency changes. A transformer rated for 480V 60Hz primary would be limited to 240V on a 30Hz supply.)

 

[jim dungar]

You might want to do some research on K-Rated transformers I know IEEE has some white papers on them. Here is an example discussion

K Factor of Transformer: Significance, Rating & Formula

The k-factor of the transformer is a weighting of the harmonic load currents based on their effects on transformer heating, derived from

electricalampere.com

Now most people think of 200% rated neutral conductors, but K Ratings are much more than that.