The challenges presented by some newer technologies incorporated in electrical loads and power sources haven’t changed the basic rules of electrical theory. Ohm’s and Kirchhoff’s laws are invaluable tools for analyzing and preventing power quality problems, whether it’s with LED versus incandescent bulbs, electric motors versus adjustable-speed drivers or rotating generators versus photovoltaic panels.

Measuring and monitoring the power quality phenomena associated with all these devices is also bound by the same rules. One, the Nyquist Theorem, has to do with the sampling mechanism used to convert analog to digital signals in most power quality monitors.

## The saga continues

This multipart saga of the flickering LED bulbs and AFCI breaker tripping is a good example of using the basic rules of electrical theory to identify power quality problems. Though parts 1 and 2 generated a number of reader comments and questions, no one has yet raised the question of how the 12W LED bulb was able to generate enough energy to corrupt the voltage and current waveforms and confuse the AFCI breaker.

The rms of the voltage deviation was 4.5–8.5 Vrms, or 7% max. That is clearly enough to cause an incandescent bulb to flicker. The flicker parameter P_{st}, which was 1.2, is well over the perceptibility limit of 1.0. (We will ignore here
the issue with using the standard 60W incandescent bulb P_{st} calculations for LED bulbs.) The rms current deviation was recorded as between 120–140 mArms. Since the normal steady-state current level of such bulbs should be 100 mA,
this deviation was more than twice the steady-state value, but still less than 0.25A. It doesn’t seem like 0.25A on a 20A circuit could corrupt a 120V signal as much as it did.

Ohm’s and Kirchhoff’s laws are used to explain rms variations (such as voltage sags from large load current changes), voltage harmonic distortion (from the current harmonics of nonlinear loads), transients and noise distortion. If we use our simplified circuit diagram of a 100V source feeding current through a 1-ohm source impedance, a 100-ohm load would result in 99V across the load due to the 1V drop across the source impedance at 1A. A 7% deviation would require approximately 8.5A, a far cry from 0.25A. Since the two laws can’t be broken without rewriting Maxwell’s Equations and winning a Nobel Prize, what went wrong?

## Instrument specifications

The voltage and current harmonic spectrum showed values for the 3rd, 5th, 7th and 9th harmonics in decreasing magnitudes, which we would expect for rectified input power supplies as used in LED bulbs and other single-phase electronic loads. A detailed look into the harmonic current spectrum found levels higher than the 5th harmonic current all the way up to the maximum frequency on the chart of 7.5 kHz. It showed no signs of tapering off all the way out to the 5th harmonic. Is the instrument misperforming, or are we misusing it?

A look into the specifications for the instrument and current probe used shows that there is a limitation with both that cannot be ignored. The current probe has a specified bandwidth up to 5 kHz. It will read beyond there with reduced accuracy, but at a high enough frequency, its output will be so severely attenuated as to render the readings meaningless.

The second limitation is the sampling rate of the analog-to-digital converters (ADC) in the instrument. This particular model of PQ monitor has approximately a 15-kHz ADC sampling rate. It takes a sample of waveforms 256 times in every 16.66 millisecond cycle (at 60 Hz). According to the Nyquist Theorem, the highest frequency signal that can be accurately determined is half the sampling rate, or 7.5 kHz in this case. That is why the harmonic of the instrument’s spectrum graph stopped at 7.5 kHz, even though there are likely signals of greater frequency. In order not to corrupt the accuracy of signals less than that Nyquist frequency when aliasing occurs, instruments use filtering techniques to severely attenuate frequencies higher than the limit.

In simpler terms, if you close your eyes and open them up every few seconds, you won’t see what occurs while you are not looking, such as a bird flying by, even though it happened. Even if the current level caused by the defective bulb was 10A but lasted only a very short duration, the instrument would be basically blind to it. It is conceivable that could happen if the circuitry caused a low impedance path between the line and neutral. If short enough, the bulb could survive for days while causing the LEDs to flicker and the AFCI breaker to think it detects an arcing fault and trip.

The next step in identifying what really happened would be to have a higher-bandwidth current probe connected to an instrument with a 1-MHz or faster sampling rate so the hypothesis can be proven (or disproven). We’ll see if we can borrow one.

stock.adobe.com / Alan

### About The Author

**BINGHAM**, a contributing editor for power quality, can be reached at 908.499.5321.