The same concepts can take a simple PQ audit or troubleshooting session and lead to a waste of time and money, the wrong conclusions or both. Past articles have covered the Golden Rules of Ohm and Kirchoff, but here is an even more fundamental issue.
RMS or rms, more formally know as Root Mean Squared, is a mathematical method developed to find a way to equate DC voltage and AC voltage. Since the impedance of a pure resistance is not affected by frequency (though the impedance of a capacitor or inductor does change with frequency), Vrms of an AC signal will produce the same power loss as the equivalent DC voltage if applied to a pure resistance.
In most of today’s PQ instruments, the input section will sample and convert the analog signals to digital data points, and then take the square root of the sum of the squared value of each data point over a window of time.
This window is one of the keys in this method. Either the window must be synchronized to include exactly all of the data points in an integral number of waveform cycles, or it must be of sufficient long duration that any errors introduced by not having the window synchronized to the waveform would be insignificant.
Why should you care about this? The other day, someone presented me with data showing the rms values of the voltage signal moving up and down 2 to 3 percent or so with each updated meter reading.
The first impression is that the voltage stability of the system is poor, and that there must be some horrendous light flicker going on with that much modulation. But when I examined the waveforms, each sine-wave cycle looked pretty much like the previous one. So why was the rms value changing?
It turned out that the instrument had the ability to set a fixed window size, which is useful for calculating the rms of a “mostly” DC signal with modulating noise. The window size selected was 100m/sec. The voltage being monitored was a 47Hz AC signal out of a drive, which has a 21.3m/sec cycle duration.
This does not fit evenly into a 100m/sec window, so the rms value from one window would have different data points than the next (see the figure). When they were squared, summed and square rooted, a different value would be obtained with each update, even though the waveforms looked identical from cycle to cycle.
In the example, one window has an rms value of 0.69, while another is 0.72 (normalized where the peak value of the waveform is 1). With a pure sine wave as used in the example, the rms value is expected to be 0.707.
The instrument was not wrong—it was just given the wrong task to do with a fixed window size that wasn’t an integral multiple of the waveform. The IEC and IEEE standards relating to power quality require that the rms voltage be calculated over an exact one-cycle window and recalculated every half cycle (or 180 degrees).
To do this, the instrument must be able to determine the fundamental frequency and track it when it changes, so that the rms window is always exactly one cycle. Using a multiple cycle window would mean that rms variations may not be detected if they do not last long enough and/or vary enough to make the rms value go below/above the threshold limit.
For example, if the limit for a sag is set to 90 percent of nominal, and you had a 10-cycle window, one cycle to 80 percent of nominal followed by nine cycles at 92 percent would yield an rms value of 90.8 percent, hence, no sag according to the instrument. The equipment tripped off line, the process shut down but the instrument said nothing happened—another missed tackle.
Such windowing functions are not unique to rms calculations. The IEC and proposed IEEE standards require a 200m/sec for calculation of harmonic values. The 200m/sec window came about as it is an integral value for both 50 and 60 HZ fundamental power frequency systems, being 10 and 12 cycles respectively.
Again, the requirement exists to have the window synchronized to exactly that number of cycles before running the discrete or fast Fourier transform (DFT or FFT) to calculate the harmonic magnitudes and phase angles.
So why is the longer window okay here, but not for voltage rms variations? It is back to those fundamentals again. Harmonics are steady-state conditions, not something that change every cycle, as with the rms variations. Since the values are supposed to be stable for the longer duration, the window will yield the correct rms value of the harmonics.
Without being able to execute the basics properly, you just might find yourself “benched.” EC
BINGHAM, a contributing editor for power quality, can be reached at 732.287.3680.