# Variation on an Amplitude: Calculating and understanding RMS voltage values for sags

Richard P. Bingham
Published On
Nov 15, 2022

Many power quality benchmark surveys indicate that sags are the most common PQ phenomenon experienced on sites. A sag (also called a dip in other parts of the world, or a blink in lineworker lingo) is defined in the standards as a reduction in the root mean square (RMS) voltage below a specified threshold for a certain duration.

A thorough discussion can be found in IEEE 1159-2019, IEEE Recommended Practice for Monitoring Electric Power Quality. Sags are listed in Table 2, Line 2 as one of the short-duration RMS variations. Sags can be either voltage or current, though people mean a voltage sag when they use the term.

### What’s RMS again?

A brief review of what RMS means might be helpful. In the early days of electrical networks, there was a need to compare the power from DC versus AC. DC voltage is nominally at one level, such as a 12V DC battery, while AC voltage constantly changes. In a typical harmonic-free circuit, the AC voltage follows a sine wave pattern, with the positive half of the signal being a mirror image of the negative half. If the AC signal was full wave rectified and the energy stored in a capacitor, it would be a DC voltage equivalent.

With newer instrumentation that samples the signal many times over one cycle (typically 32 to 1,024), these values are put through a mathematical formula called root mean square. In the reverse order of the terms, each sample value is squared, summed up and divided by the number of samples (mean) and then the square root of that value becomes the RMS value of that cycle. While the RMS can be computed over multiple cycles, present PQ standards state that it should be computed over one complete cycle (16.66 milliseconds at 60 Hertz) and then recomputed every half-cycle.

These RMS voltage values are then compared against the limits, which are a percentage of the nominal value. In the standards, they may use “pu” (per unit), which is similar to percent of nominal: 0.1 pu is 10%, 0.9 pu is 90%, 1.2 pu is 120%, etc. The RMS value is checked every half-cycle against the limits, which are typically between 10%–90% of nominal for a sag. Lower than the lower limit is an interruption. The RMS variation event will end when the RMS value is back within the limits plus the hysteresis value, so that a signal riding right on the limit doesn’t generate millions of events with minuscule variations.

### RMS variation

The duration of the RMS variation event also gets a characteristic label. The chart below shows how IEEE 1159 applies the instantaneous, momentary and temporary labels to sags and swells. Interruptions only have momentary and temporary categories. If the RMS variation lasts longer than 1 minute, the names change to overvoltage, undervoltage and sustained interruption (often called outage). These long-duration events are generally not considered power quality disturbances, but fall under the realm of distribution voltage issues.

Note also that the limits get much narrower as the duration continues, especially for voltages greater than nominal. Such voltage levels are often very destructive for equipment. While surge protective equipment may protect against such levels for a very short duration, it’s likely they will be damaged with the equipment being protected when those voltage levels are elevated that long.

### Duration ranges

The duration ranges are often related to the source of the RMS variation. When there is a fault on a distribution system, most system protection breakers will operate in the 6–10 cycle range, an instantaneous sag.

A large HP motor start can cause momentary sags. The end-of-day reduction in current of a large industrial facility may result in a temporary swell until the automatic tap changer senses the change and switches the transformer to a new tap to lower the voltage back into the nominal range. Temporary sags and interruptions are generally more serious system faults requiring operator intervention at a substation to isolate the faulted area and restore nominal voltage to the other circuits.

If the duration lasts longer than a minute, it may take hours or even days to restore the voltage from a sustained interruption, such as a severe weather event. Undervoltage events used to be referred to as brownouts. The electric utility would reduce the voltage to lessen the current levels on overloaded circuits. This concept isn’t as effective anymore, as loads today are more likely the constant power type. As the voltage goes down, the current demand goes up to maintain constant power to the equipment. Hence, if the utility reduces the voltage, this will actually increase the current demand, compared to linear loads where lower voltage means lower current.