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Topic Title: Total Harmonics Distortion (THD) addition
Topic Summary: Need to add THD from two different sources
Created On: 03 December 2012 04:25 PM
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 03 December 2012 04:25 PM
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Please advise if I can use the general summation Law for two THD % values from two different sources.

Source 1 - Grid - 1.42% THD
Source 2 - Wind farm - 0.231% THD

I'm after a combined value for the point of connection of the two sources

I used the general summation law and got 1.43% (using square root of addition of squares).

Please is this correct?

 04 December 2012 09:49 AM
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Almost certainly not .... I assume you are talking about current THD values. In that case, when you "add" them together at a point of common coupling, the harmonic currents will tend to increase, perhaps in an RMS manner (although it will depend on the relative phases of each harmonic). However, your fundamental will also increase, and normally you would expect the fundamentals to be coincident in phase if power factor is sensible (and they are both sources).

If, for example you added a third source with a large fundamental and 0% THD currents, you would essentially dilute down the THD of the overall summed currents and it would reduce towards zero.

Another example is to take two identical sources with THD=2% and add them. The THD would still be 2%, but the current would be twice as big. If you could arrange it so that the fundamentals were coincident in phase (power angle etc), but the harmonics were not coincident in phase between the 2 sources, then you could even reduce the THD below 2% by adding the 2 sources.

So, its more like a weighted average of the THDs, with the weights determined by the relative fundamental current magnitudes, and if you get really lucky you might end up with an even lower THD if the harmonics are not coherent between the 2 sources.

Watch out if either ever becomes a load instead. In that case, the fundamantal magnitude gets smaller and the THD can rise. However, this might not be an issue. It depends if you are worring about absolute harmonics through a transformer (heating etc) or waveforms with excessive THD corrupting measurements or relay functionality.


Dr. Andrew Roscoe
 04 December 2012 10:24 AM
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Thank you for your response.

In the rush, i did not include that the THD% value are for 33KV.

In effect this query is for summation of voltage THD% from two different networks at the same voltage meeting at a point of connection

Also pardon me if I am mistaken, from your response above if the values were for current THD% would the summation be

1.42 + 0.231 or sqrt(1.42sq+0.231sq).

Thanks again from your assistance.

 04 December 2012 03:05 PM
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If it was for current, I would (for two sources) use something like:

THD_sum = (THD1*abs(PowerFlow1)+THD2*abs(PowerFlow2))/(PowerFlow1+PowerFlow2)

If one of them becomes a load then set its flow to a negative value, and watch because then THD_sum could get very big.

For voltages, it's going to be different. The final result is going to impacted not only by the power flows, and coincidence (or not) of harmonic phases, but also by network impedances and fault levels.

If you knew the current THD levels, and all the network impedances, you could begin to make a stab at it.

Dr. Andrew Roscoe
 28 February 2013 11:55 AM
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You would probably find the content of Engineering Recommendation G5/4-1 (2005) useful (published by the Energy Networks Association).

As you mention, you are connecting at 33kV, so you will be subject to a "stage 3" assessment as detailed in the recommendation. This involves a background survey of existing voltage harmonics to which you will have to add your harmomics at the PCC.

The recommendation suggests using the worst possible case (harmonics in phase) when adding the largest harmonic component and an average phase angle of 90° for the remainder.

Using this assumption, the magnitude of the THD is then equal to the square root of the sum of the squares of the magnitude of the remaining harmonic voltage components.

To assume an average 90° phase angle seems reasonable? Or you could just use the worst case for all harmonic voltages to be safe and see if you're still under the limits...


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