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Contributed by Chris Mullins, February 2016
Abstract
IEEE 519-2014 specifies two time periods for analyzing harmonic data: “very short time”, or 3 seconds, and “short time” or 10 minutes. For achieving the best resolution, the 3 second interval should be used in a PQ recording, but without the 10 minute data, the IEEE 519 thresholds cannot be fully applied. A method is shown here to compute the 10 minute short time values from the recorded 3 second values, so both sets of readings are available from a single recording.
Formulas
In IEEE 519-2014 section 4.3, a formula is given to compute “short time” harmonic data from existing 3 second readings:
Where F represents a voltage or current harmonic measurement, n is the harmonic order, and “sh” and “vs” are “short” and “very short” readings. Essentially the nth short time reading is an RMS sum over the previous 10 minute’s very short time readings. With the standard 3 second measurement, it takes (10 x 60) / 3 = 200 readings to cover a 10 minute period, hence the 200 point RMS computation.
The IEEE 519-2014 current distortion limits are given in section 5.2, Table 2 (Figure 1). These limits are used for both short and very short time readings (with different multipliers), so it’s useful to have both sets of readings, especially over the same recording session. To accomplish this, record voltage and current THD, and also at least the fundamental (1st harmonic), at a 3 second interval. This setup is shown in Figure 2. Other individual harmonics may also be recorded, but the fundamental is important for accurate Total Demand Distortion (TDD) calculations in ProVision. The 10 minute short time readings may be calculated by exporting the 3 second data from ProVision into Excel, then using the supplied spreadsheet template to automatically compute a rolling 200 point RMS value, as described below. TDD is often the most important parameter to check for IEEE 519 compliance. It’s used as an example here, but this technique may be used for any individual harmonic.
Figure 1. IEEE 519-2014 Current Distortion Limits
Figure 2. Minimum setup for capturing 3 second very short time harmonic data
Once the data is downloaded into ProVision, the 3 second very short time readings are available immediately. After entering the 500A maximum load current for this location, very short time TDD can be graphed directly in ProVision (Figure 3). To determine the 10 minute readings, choose the TDD report (Report, Total Demand Distortion). Right-click on the report and choose Export to Excel (Figure 4). Copy/paste the section containing the TDD data into to the template available for download here. This spreadsheet will automatically calculate the 10 minute short time readings.
Figure 3. Very short time TDD graph computed by ProVision
Figure 4. Exporting the TDD report into Excel
The spreadsheet, shown in Figure 5, contains four sections. The section circled in orange is the raw data exported from ProVision - copy/paste new columns here as needed. The section circled in green contains the computed short time values, as a rolling RMS average of the previous 200 samples. The section boxed in blue contains adjustable parameters for varying the number of samples in the RMS average, and also percentile calculations for each channel. Finally, two graphs are embedded in the spreadsheet. The upper graph displays the three channels of short time TDD (or individual harmonic). The lower graph shows channel 1, with the very short time data plotted with the short time data, to illustrate how the RMS smoothing affected the readings.
Figure 5. Short time computation spreadsheet
A close-up of the parameter section is shown in Figure 6. The two parameters to enter are highlighted in yellow. The “interval” should be set to the actual recording interval in seconds (3 in this example), and the “desired” should be set to the desired short time period, also in seconds. This is set to 600 here for the standard 10 minute IEEE value. The number below these parameters (200 in this example) is the ratio of the short time to very short time settings, and is used to determine the length of the RMS average.
Figure 6. Spreadsheet section for entering adjustable parameters, reading percentiles
The IEEE standard values are 3 and 600, resulting in a 200 point RMS average, but any combination of settings may be used. For example, if 1 second raw data was recorded, enter “1” for the interval. Or, if a smoother TDD value is needed, use a longer average, such as 3600 for a one hour window length. The spreadsheet automatically adjusts the calculations for the correct computed length.
The 95% percentile values are displayed just above the parameters, for channels 1, 2, and 3. These are simply computed with the Excel PERCENTILE function (e.g. =PERCENTILE(H63:H27787,0.95) for channel 1), and the desired percentile can be edited directly in the formula.
The heart of the short time calculation is the Excel formula
Here the Excel SUMPRODUCT function automatically computes the square of a range of cells and sums them. Using the same range in both arguments of SUMPRODUCT results in each cell in the range getting multiplied by itself, then added to the total sum. The “/200” in the formula completes the average, and the final SQRT in the formula completes the RMS computation. Here the range from C23 to C223 spans 200 data points, matching the “200” in the division. To accommodate a variable number of data points (specified in the parameters shown in Figure 6), the actual formula ends up significantly more complicated:
= IF ( ROW()-23 >= $H$19,
SQRT
(
SUMPRODUCT
(
INDIRECT(“C”&TEXT(ROW()$H$19,”#”)):C223,
INDIRECT(“C”&TEXT(ROW()-$H$19,”#”)):C223
)
/$H$19
)
,””)
$H$19 is an absolute reference to the ratio of the desired interval to the raw interval (200 in the default case). The IF statement tests to see if there are at least the minimum number of readings available (e.g. 200), if not, a blank is output (the “” at the end of the statement). If there are enough readings, the SQRT and SUMPRODUCT functions are used as before, but instead of a fixed range such as C23:C223, the INDIRECT, TEXT, and ROW functions are used to construct the range dynamically from the number computed in cell $H$19 and the current cell position.
A close-up of the raw vs. short time computed data is shown in Figure 7. The blue is the raw, fast data, while the red is the slower smoothed data. There is a wide difference in span between the two, and in general the smoothed short time readings are lower compared to the very short time. The TDD is over 12% much of the time, with 95th percentile values of 18%, 15%, and 16% for channels 1, 2 and 3. These are significantly over the 12% limit for this circuit from Table 2 of IEEE 519.
Figure 7. Channel 1 raw very short time TDD (blue) plotted with 10 minute short time data (red)
To apply the full limits in Table 2, compute the short time TDD with the spreadsheet, and read the percentiles in the parameters section. For the applicable row in Table 2, compare with the 95% limit values. There are also separate limits for the 99th percentile for both the short time and very short time readings - these may be checked by editing the percentile number in the spreadsheet for the 99th, over either the short time or very short time data set.
Conclusion
A method is presented in this paper for evaluating a location according to the IEEE 519-2014 harmonic limits with a single recording. The raw data, recorded at 3 second intervals, may be used directly for the very short time IEEE limits. Exporting this data from ProVision to Excel allows for the computation of the short time values to complete the 519 limit analysis. This technique makes it possible to evaluate the same time period to the full standard, rather than creating two separate recordings over different time periods, or using two recorders.
Chris Mullins
VP of Engineering and Operations
cmullins@powermonitors.com
https://www.powermonitors.com
(800) 296-4120
