# So Much From So Little

While researching for new information about sags, I found the first reference on Google search to be familiar. It was a paper, “Sags and Swells,” that I wrote in 1994 for the NFPA 70B Technical Committee on Electrical Equipment Maintenance. Let’s focus here on how the algorithms in PQ monitors determine a sag occurred.

A sag is one of the types of root mean square (rms) variations listed in standards such as IEEE 1159 or IEC 61000-4-30 and usually the most common PQ phenomena. It is a reduction in the rms computed value of the voltage from the nominal value to below a specified limit. Most standards and users use the 90 percent limit, though it should actually be the susceptibility limit of the equipment being powered by the voltage. Since many users don’t know what that is and because it can change based on the sag duration, the default setting for nearly all PQ monitors is 90 percent, which equates to 108 volts (V) rms for 120V nominal.

In the past, different PQ monitors would produce different values for the sag magnitude and duration. Where does it start, where does it end, what value of magnitude to report (remaining voltage or depth from nominal), and other issues prompted the standard-making groups to set down the rules?

One key element is that the rms value is computed over one cycle, synchronized to the waveform’s zero crossing, and updated every half-cycle. The minimum resolution for the start and end of the sag is one half-cycle. The start is when that one cycle rms value is below the low limit and ends when the one cycle value is above the low limit plus the hysteresis value (typically 1–2 percent of nominal). The purpose of hysteresis is to avoid counting multiple events when the magnitude of the voltage oscillates about the limit level. The duration will be an integral number of half cycles, which at 60 hertz is 8.33 milliseconds. The magnitude reported is the lowest one cyclic value (computed in half-cycle steps) while below the low limit. Even if the voltage waveform goes to zero a quarter-cycle, the magnitude will be computed over the entire cycle and is likely not zero.

The figure above illustrates these elements. The top graph is the voltage waveform for channel A, and the bottom is the rms voltage. The annotation “cx” is the consecutive half-cycle steps of the one-cycle value used to compute rms. So c1 (orange bar) starts halfway through c0 (yellow), followed by c2 (red), which starts halfway through c1 and at the end of c0, and so on. The rms values are computed over the entire cycle and are time-stamped and recorded at the end of the cycle. The t1 value is when that one cycle of c3 (green) has gone below the low limit (108V) and is indicated by the blue down arrow. At the end of c5 (blue bar), the rms voltage has gone back above the low limit + hysteresis (109V rms) as indicated by the light blue up arrow at t2. The duration is three half-cycles long, or 1½ cycles = 25 milliseconds, as indicated by the purple bar. The magnitude of the remaining one-cycle rms voltage at its lowest point during the purple bar was 56V rms. The first fully “normal” cycle following the sag is c7 (brown). All of that math is calculated continually on all three phases of a wye or delta circuit.

An additional rule applies to polyphase circuits. The duration starts when any of the three phases or channels goes out of limits but doesn’t end until the last phase that goes below the limit during the sag returns above the limit. The magnitude is the lowest cyclic value among all of the phases. So a sag can have a duration that starts on Phase A, ends on Phase B, and a magnitude from Phase B.

For those interested, the original 20-page paper I wrote for 70B was worked over by the committee until it stated just what the intended audience of the document wanted. The result was a concise, two-page contribution to the subsequent revision of the 70B document and a great lesson for me on how to write for the reader, not for the writer. That text can be found in what eventually became an entire chapter on power quality: Chapter 10 in the 2016 edition of NFPA 70B, Recommended Practice for Electrical Equipment Maintenance.

#### Richard P. Bingham

Power Quality Columnist

Richard P. Bingham, a contributing editor for power quality, can be reached at 732.248.4393.