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Abstract
Although interval (stripchart) data can show cycle max and min readings, it’s not normally used to get the duration of an event like a sag– waveform capture, event capture, etc. are designed for that. But, if those aren’t available, it’s often possible to estimate sub-second event durations even with 1 minute interval data. For older recorders without waveform or event capture, or if the waveform memory filled up (or wrapped around), or the settings weren’t correct, etc. the interval data may be the only option for estimating event duration. A method for calculating event durations is described here.
Interval Data
Interval data in a PMI recorder is a time series of min, max and average data points collected at a periodic interval. The min and max values are one cycle measurements, and the average is the mean value over the interval. The default interval of one minute is the most common, but the interval can range from one second to over four hours (one cycle intervals are also supported in the Revolution, Vision, and Eagle series). With a one minute interval, every minute three measurements are recorded for each channel – the one cycle min and max during that interval, and the average of all cycles during the interval. Although the worst-case cycle values are recorded, there’s no information on where in the interval they occurred, or how long the worst-case reading lasted during the interval. It would seem impossible to determine the length of a short voltage sag with just one minute interval data. But, it’s possible to glean more from the data with a careful analysis.
It’s helpful to start with a simple artificial example from a test recording. A Revolution was connected to a programmable voltage source. The source supplies a steady 120V RMS voltage, and was programmed to generate a 15 cycle sag down to 93V. A short recording was made with a one second stripchart interval. In Figure 1, I’ve zoomed in on the sag in the interval graph, and enabled the Toggle Point Table, with the time of the sag selected.
Figure 1. Interval graph zoomed to show a sag and Toggle Point Table enabled
The average RMS value before the sag was 119.8V, the minimum during the sag was 93.0V, and the average during the sag was 113.0V. The timestamp on that interval point is 19:35:22. So, during the one second between 19:35:21 and 19:35:22, there were 60 AC cycles, and the lowest of them was 93.0V, and the average of all 60 was 113.0V. What isn’t apparent is the sag duration. But there’s more that can be determined from this data.
Mathematically, the average during that second was the sum of all 60 one-cycle RMS readings, divided by 60. The minimum and maximum one-cycle readings are included, so two of those 60 values are known. If it’s assumed that the sag was roughly the same RMS voltage during the sag time, then the average RMS voltage during the interval gives some indication of the sag duration. The longer the duration, the more the sag “pulls down” the average. For example, if the sag were one cycle long, it would only have 1/60th relative influence compared to the non-sag readings. If it were 59 cycles long, then it would dominate the average, and the average voltage would be almost the same as the sag voltage.
In this case, we know the sag duration and magnitude– 15 cycles, 93V. Mathematically, 15 cycles at 93V and 45 cycles (60 cycles in 1 second minus the 15 for the sag time) at 119.8V averages to (15 x 93 + 45 x 119.8)/60 = 113.1V. This is very close the 113.0V actually recorded as the average (Figure 1). The sag value is measured– it’s the one-cycle minimum RMS value, and the average is measured. Rewriting the above expression for the average with variables, and solving for the duration, given the minimum (Vmin) and average (Vave) readings during the interval containing the sag, and the nominal (e.g. average) voltage before and after the sag (Vnom) gives this expression for N, the sag duration:
Here N is a dimensionless quantity, basically a fraction of the interval. Plugging in the values of 93.0, 113.0, and 119.8 for Vmin, Vave, and Vnom gives n = 0.2537. This is normalized to the interval size of 1 second, or 60 cycles. Multiplying n by 60 gives the event duration in cycles: 0.2537 x 60 = 15.2 cycles, which is very close to the actual 15 cycles.
Figure 2. Revolution Waveform Capture and RMS Capture graphs.
With a Revolution, this result can be cross-checked with waveform capture and RMS capture graphs (Figure 2 above), and Event Capture (Figure 3 below), all of which match the 15 cycle duration computed from the interval data.
Figure 3. Event Capture.
The faster the stripchart interval, the more resolution that can be obtained for event duration. With a one second interval, each cycle of a sag contributes to the average by a factor of 1/60th. As the first example showed, that’s enough resolution to make a very good estimate for a 15 cycle sag, since it pulled the average down to 113.0V (a 6.8V change from the nominal 119.8V level). A more common interval size is 1 minute – 60 times worse resolution than the 1 second value. With a 1 minute interval, each cycle in only contributes by a factor of 1/3600th to the interval average. In Figure 4, the interval graph for a 1 minute interval is show, with the same sag applied.
Figure 4. Interval graph for a 1-minute interval.
In this case, the average during the event is only 0.1V less than the average before and after the event. Instead of pulling down the average by 6.8V (as in the 1 second period), the 1 minute average is only pulled down by 0.1V, since the 15 cycles is such a small fraction of the 3600 cycles in a 1 minute period. Plugging 93.0, 119.7, and 119.8 in the above formula gives 13.4 cycles (0.003731343 x 3600) for the estimated duration, which is pretty close for such a small change in voltage. This is on the edge of resolvability – a single 0.1V change in the average reading (e.g. 119.6 instead of 119.7) gives 26 cycles for the event duration. The one minute average should have the resolution though, given that it’s composed of 3600 readings internally in the recorder before rounding to 0.1V. Fortunately (since no averaging is involved), the result is much less sensitive to the min reading – a 0.1V change in the min voltage results in a 0.1 cycle change in duration. If the event is a 3-phase sag, averaging the results from all three phases should improve the resolution. Another factor working in our favor is that we don’t need exact absolute accuracy, just relative accuracy. Even if the recorder is out of calibration and reading off by a couple of volts, the relative accuracy, that is, the ability to measure a change in voltage, should still be good.
Now that the theory has been demonstrated in the lab with a clean source, let’s look at a real-world file. In Figure 5, the stripchart for a 3 phase 240V delta, feeding a large water pump.
Figure 5. Stripchart for a 3 phase 240V delta, feeding a large water pump.
The interval size is the default 1 minute. I’ve zoomed into a time when the pump starts, showing the voltage and current during the motor start. Also, the interval voltage report is shown in Figure 6, with the applicable section displayed.
Figure 6. Interval voltage report.
Here, the pump starts, drawing almost 400 amps, and pulls the voltage down by 50V – an 80% sag . After the start, the pump continues to run for a couple of minutes at 44 amps, then shuts off. The question is, how long is the motor start? A 50V sag on a 240V nominal is significant, but does it last 1 cycle or several seconds? The ITIC/CBEMA limit for an 80% sag is 30 cycles – can we tell if that’s exceeded without any waveform or event capture data?
There is complication in this file, compared to the first example. After the motor start, the motor continues to run, and this running current also pulls down the voltage a bit. In the first example, it was assumed that the voltage before the event and after the event were the same, but in this real-world scenario, the motor’s running current must be accounted for. Although we can get the pre- and post- motor start voltage from the stripchart data, we can’t properly account for them without knowing the exact time of the motor start. Without accounting for the voltage drop due to the motor run current, the sag duration estimate will be off. Although the loaded voltage drop is much smaller than the sag, it likely lasts much longer than the sag, so its effect on the average for that interval is important.
Mathematically, the average during this event interval consists of three sections – 1) the no-load voltage before the motor starts, 2) the sag voltage, while the motor is starting, and 3), the loaded voltage while the motor is running. The sag duration depends on the motor start time, and should be relatively short. The other two portions depend on when the motor started inside the interval. For example, if the motor started 5 seconds into the 60 second interval, then the first 5 seconds would be the no-load voltage, and most of the time would be the loaded voltage, along with the sag voltage. To resolve this ambiguity, we need one more piece of information – the start time of the event. In this case, the event was in the one minute interval between 15:34 and 15:35 (red in Figure 6), but we don’t know where.
Fortunately, there is another report that can help. Although not usually thought of for sag/event investigations, the Significant Change report has the missing clue we need. In Figure 7, a portion of the report is shown.
Figure 7. A portion of the Significant Change Report
The sag is highlighted in red, and is time-stamped 15:34:39. This gives us the missing piece we need – the motor start begins 39 seconds into the interval between 15:34:00 and 15:35:00. So, there was 39 seconds of no-load voltage, N cycles of motor start time, and the remaining time was loaded voltage during that interval. From the interval data, the no-load voltage is 245.7V, and the loaded voltage is 238.4V. The average during the event is 238.4V, and the sag voltage is 194.8V (all taken on channel 1, see Figures 5 and 6). The resulting average, 238.4, is equal to (39 x 60 x 245.7 + N x 194.8 + (60-39) x 60 x 238.4)/(60 x 60). The extra 60s are there to convert the time-base to cycles, instead of seconds. This is an equation with one unknown, N. Normalizing the time and using t for the fraction of the interval before the event starts, VNL for the no-load voltage, VL for the loaded voltage, Vave for average interval voltage (for the interval that contains the event), and Vmin for the sag voltage during the event, and N for the event duration (normalized so 1 = the interval period), gives the following equation:
In this case, t = 39/60, VNL=245.7, VL= 238.4, Vave =243.0, and Vmin= 194.8 (see Figure 6 for where these values appear in the raw interval data). That gives N = 0.0033257, and multiplying by the interval size of 60, and again by 60 to convert to cycles gives 12 cycles for the estimated sag duration.
As it turns out, there was no waveform for this specific event, due to waveform capture memory filling up, overwriting the earlier captures. However, this pump started many dozens of times during the recording (hence the full waveform memory), and the very same event was caught with later waveform captures. The event duration was long enough to trigger two captures – one for the sag, and one for the voltage return from the sag. Figure 8 shows the RMS Waveform Capture graphs for a typical pump start in this file.
Figure 8. The RMS Waveform Capture graphs for a typical pump start.
The first waveform is triggered in cycle 33 of 6:28:13, and the second in cycle 48 of the same second. This gives a duration of 15 cycles, although there is at least one cycle of ambiguity due to triggering, and the soft return of the voltage when the pump reaches the running current.
So, with this real-world file we were able to estimate the duration of the 79% sag (194/245V) at 12 cycles solely from 1 minute interval data, and a Significant Change 1 second timestamp. The ITIC/CBEMA limit for an 80% sag is 30 cycles, so the crude stripchart estimate correctly indicates that the sag is within ITIC limits – a very useful result from data normally not considered suitable for sub-second analysis! Actual waveforms from later pump starts show a duration of around 15 cycles, corroborating the method. Even better resolution is possible with a finer stripchart interval, such as 10 seconds.
Conclusion
A careful analysis of stripchart data can tease out much more information than is commonly supposed. In situations where no waveforms or event captures are available (due to use of an older recorder, unfortunate trigger settings, or overflowing memory), all is not lost – the interval data can still reveal much about an event, especially when coupled with other “low resolution” data types, such as the Significant Change report.
Chris Mullins
PMI Vice President of Engineering & Operations
cmullins@powermonitors.com
http://www.powermonitors.com
1 (800) 296-4120
