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Abstract
K Factor is a measurement of current harmonic distortion that is used to de–rate transformers for harmonics.
This white paper will discuss how K Factor is calculated, what its uses are and how PMI’s power quality recorders can provide the user with these measurements.
Calculation
As mentioned above, K Factor (Figure 1) is a measurement of current harmonic distortion, used in rating transformers, and it’s used in calculating the value necessary to de-rate a transformer for harmonics.
Figure 1. Clicking THD graph annotations in ProVision shows K-Factor
Harmonic current flow in a transformer causes increased heating (due to various losses in the core). Some of these losses increase linearly or even more than linearly with the harmonic number.
As an example, if 10 amps of current at 60Hz produces a 5 degree rise in temperature, then 10 amps at the 3rd harmonic (e.g. 180 Hz) might cause a 10 or 15 degree rise. For transformers, more heat equals less lifetime, and too much heat can cause a transformer to fail. This means that K Factor is an important measure of how much extra heating the transformer will experience for a given harmonic current pattern vs. if all that current were at 60Hz.
K Factor is calculated with a formula that weights higher harmonics much more heavily than lower harmonics (actually by the square of the harmonic number), since the heating losses increase with frequency. So, 1A of current at the 3rd harmonic counts 9 times more than 1 at 60Hz (3^2 =9). A K Factor of 1.0 means no harmonics (all 60Hz).
Formula:
where h is the harmonic # and ih is the RMS current at the hth harmonic
Transformer K Ratings
Transformers have a K rating, which indicates what level K Factor they’re designed to withstand, at the full rated current. If the K factor of the actual load is above the transformer rating, then it will be necessary to de-rate the transformer, that is figure out a new maximum allowed load. For example, a 100kVA transformer with a K rating of 5 may only be good for up to 70 kVA if the actual load has a K Factor of 15.
K Factor is computed from the harmonics of the current waveform. In ProVision, after loading a waveform capture, it’s possible to click on the harmonic toolbar icon to switch to a harmonic analysis of that waveform. It is also possible to go directly to that with Graph, Harmonic Analysis, Magnitudes on the toolbar. Once there (after selecting a waveform capture record), THD will be visible, drawn on the graph. A little known fact is that those graph annotations are clickable. After clicking a few times, it will switch to showing K Factor for the displayed waveforms. To select the cycle that is being computed, move the grey cycle in the top trace to select the appropriate cycle. (PMI’s recorders do not actually compute K Factor– it is a calculation performed on the individual waveform captures by ProVision.
Analyzing K Factor
Since the point of K Factor is transformer heating, it is better to use steady state readings (heating is a slow process). When computing from waveform capture data, slide the grey cycle selector to a “normal” looking cycle, not a disturbance. Most of the time, waveform capture is triggered by some kind of disturbance, K factor shouldn’t be computed from an abnormal waveform. Since several cycles before and after the trigger are usually recorded, it’s usually possible to find a normal looking cycle in that span.
Alternatively, if K Factor is a desired measurement, the user can turn on periodic waveform capture. This forces a waveform trigger periodically (for example, every 4 hours), and those will be more representative of steady state “normal” waveforms than those triggered by a disturbance.
A high K Factor isn’t necessarily bad, if the absolute current level is low. A high K Factor just lowers the max current rating of a transformer. If the load is nowhere near the max rating anyway, a high K Factor may not be an issue.
Conclusion
Using K Factor as a measurement for de-rating transformers is a simple process, especially when using ProVision and one of PMI’s many harmonics-enabled recorders.
Caleb Payne
PMI Lead Software Engineer
cpayne@powermonitors.com
http://www.powermonitors.com
