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Abstract
Interharmonics are one of the most complex power quality quantities to measure and analyze. The concepts are advanced, the terminology is confusing, the raw data is voluminous, and the interpretation difficult. The Revolution is capable of recording any interharmonic data, and ProVision can present the data, but the straightforward choice – enabling and analyzing over 600 interharmonics for four voltage and current channels – is usually not the best choice. This whitepaper gives an overview of interharmonic recording methods with the Revolution, presents some recommendations for getting started, and best practices for analyzing the data in ProVision.
Interharmonic Overview
Interharmonics are periodic distortions of the 60 Hz sine wave whose periods are not multiples of the fundamental. Simple nonlinear loads, whose waveforms are distorted but the same distortion in each cycle, produce harmonic currents (and thus introduce harmonic voltage distortion). Complex nonlinear loads, whose waveforms are distorted by differing distortion in each cycle, produce interharmonics – frequency components in between the 60Hz-spaced harmonic components. For example, a traditional Variable Frequency Drive (VFD) with a constant load will produce harmonics due to the nonlinear current draw. A VFD with a varying load, significant mechanical vibration, or unbalanced rectifiers will also produce interharmonic currents.
In theory the frequency space between the harmonics could be finely divided into an infinite set of interharmonic components. The IEC 61000-4-7 standard creates a precise definition for harmonics, interharmonics, and various groupings based on a 5 Hz component width. The power line frequency domain is divided into 5 Hz “bins”, from DC to just past the 51st harmonic (3115 Hz). Any frequency domain component of the signal that falls in a 5 Hz bin is lumped into that particular interharmonic’s magnitude reading. Every 12th frequency bin is a multiple of 60 Hz – these are regular harmonics, technically not interharmonics.
IEC 61000-4-7 also defines harmonic and interharmonic groups and subgroups. These are combinations of harmonics and interharmonics. Groups and subgroups are used to aggregate harmonics and interharmonics to avoid recording hundreds of separate frequencies when more specific detail isn’t needed, but the distinction between harmonics and interharmonics is needed.
Figure 1 shows the relationship between interharmonics and harmonics, and groups and subgroups. Groups are broad aggregations of 5 Hz bins. Harmonics are spaced twelve 5 Hz bins apart (60/5 =12). A harmonic group aggregates the surrounding 6 interharmonics on either side of a harmonic (this is shown for 4th harmonic in Figure 1). An interharmonic group is a similar aggregation of all 11 interharmonics between two harmonics. In Figure 4 (top right), the interharmonic group between the 4th and 5th harmonic is shown. This is the 4th interharmonic group (due to its location adjacent to the 4th harmonic).
Figure 1. Interharmonic and group / subgroup definitions
Harmonic subgroups are a more narrow collection of 5 Hz bins – just the harmonic and the adjacent two interharmonics are combined, resulting in a 15 Hz total width. The 4th harmonic subgroup is shown in Figure 1 – the 235, 240, and 245 Hz bins are combined.
The interharmonic subgroup is a combination of the 9 interharmonics between harmonic subgroups. Figure 4 shows the interharmonic subgroup for the 4th harmonic, combining the 9 interharmonics starting at 250 Hz and ending at 290 Hz.
Figure 2 shows a summary of the different measurement types, with some notes as to their use. The table is ordered from most specific (narrowest frequency width) to most coarse (widest frequency width). The raw harmonic and interharmonic quantities are only 5 Hz wide, resulting in 50 x 12 = 600 different measurements for just one channel of voltage. At the other extreme, the harmonic group measurements give just one reading every 60 Hz, for 50 values per channel. There is some overlap in these measurements, with some encompassing a wider bandwidth than others. The raw 5 Hz interharmonic and harmonic values are used as building blocks for the subgroups which incorporate several 5 Hz readings. The group measurements include even more 5 Hz values, and overlap with the subgroup definitions. It’s rarely necessary to record groups and subgroups at the same time and often not necessary to record each individual interharmonic.
Figure 2. Interharmonic measurement breakdown
Also noted in Figure 2 are the complementary measurements. For example, the Harmonic and interharmonic subgroups do not have any overlapping frequency bins, and together they exactly cover the entire spectrum.
There are THD measurements defined for each harmonic and interharmonic grouping. These allow for quantifying the level of each aggregation without recording all the specific measurements themselves. On the other hand, there is overlap between the harmonic subgroups and interharmonic groups. To avoid redundant information it’s best to avoid overlapping data types unless needed for a specific application.
Interharmonics and the Revolution
There are two methods for recording interharmonics with the Revolution – directly as individual stripcharts, or indirectly with periodic waveform capture. For stripchart recording, the Revolution computes each 5 Hz bin using 12 cycles per IEC 61000-4-7 for each channel of voltage and current. These raw measurements are used to compute the harmonic and interharmonic groups and subgroups. Average readings are generated once per second and also combined to form the various THD measurements. These averages feed into the stripchart processing system. If enabled, any harmonic, interharmonic, group, or subgroup average is then recorded at regular stripchart intervals along with other more traditional stripchart readings such as RMS voltage, real power, etc.
Interharmonic stripcharts can consume a great deal of recorder memory. Just enabling all 51 harmonics can significantly impact recording time, and with 11 interharmonics between each harmonic, including them is another factor of 11 increase. Recording all interharmonics simultaneously along with groups and subgroups will drastically reduce the recording time even with a 1 GB Revolution.
A second method of capturing and analyzing interharmonics is through periodic waveform capture. With this feature, baseline “normal” waveform snapshots are taken by the Revolution on a regular basis (e.g. every 30 minutes) throughout the recording session. The raw waveforms may be analyzed in ProVision directly for harmonics, and exported to Excel for a full interharmonic breakdown. These techniques are described in detail in whitepapers Harmonics from Periodic Waveform Capture and Calculating Interharmonics with Raw Waveform Data. In both cases, waveform capture data enables every individual harmonic and interharmonic to be measured, along with every group and subgroup value. This method is a great way to record the entire frequency spectrum on a periodic basis without the memory requirements of a continuous stripchart spectral recording.
Initializing the Revolution for Interharmonic Recording
The stripchart settings for harmonics and interharmonics are shown in Figure 3. The traditional harmonic settings are in the Harmonic Graphs section (circled in orange), and Interharmonics are in the Interharmonics region (circled in green). To configure interharmonics, begin at the top in the harmonics section, then work downwards towards the interharmonic region.
Figure 3. ProVision setup screen for harmonics (orange) and interharmonics (green)
To avoid having to configure each of the 600+ interharmonics, groups, subgroups, etc., they are enabled in conjunction with their closest harmonic. To enable interharmonics, first enable harmonics by checking “V Harmonics Magnitude”, and or “I Harmonics Magnitude”, and then entering a range or list of harmonics in the “Selected Harmonics” field. In Figure 3, the range “1-11” is entered. This will enable recording for harmonics 1 through 11, including the even harmonics.
Now that this range is entered, move to the Interharmonics region circled in green. To enable voltage or current interharmonics, check the applicable Voltage or Current checkbox. This will enable the global recording of interharmonic data. To specify the type of interharmonic data, use the check boxes below those two. For example, select “Interharmonic Subgroups” as shown in Figure 3 to record a stripchart for each Interharmonic Subgroup associated with harmonics 1 through 11. Checking “Individual” will record all interharmonics between the 1st and 11th (e.g. 65 Hz, 70 Hz, etc. through 715 Hz). The other Group and Subgroup choices may be checked or unchecked as needed.
The various interharmonic THDs are shown on the right side of the region. These THD values are defined in IEC 61000-4-7, and are computed from different combinations of individual interharmonics, groups, or subgroups. These may be recorded without enabling the specific interharmonics, and are a good way to quantify the amount of interharmonics present without recording each of them. The settings in Figure 3 are a good starting point for interharmonic studies.
The periodic waveform setup is show in Figure 4. The key here is to insure that 12 cycles are recorded for each capture (settings circled in red), and that periodic capture is enabled (circled in green). A 12 cycle capture is needed to generate 5 Hz interharmonic data. If only three channels are used, the voltage and current channels captured can be reduced to increase recording time. Adjust the Capture Period so the overall recording time is long enough to cover the time planned. With the settings shown waveform capture memory will start overwriting in 10 days.
Figure 4. Periodic Waveform Capture setup screen, with number of cycles in red & capture period in green
Recommendations
There’s usually no need to record interharmonic and harmonic groups and subgroups at the same time. In order of increasing detail (and higher memory usage), here’s a suggested progression for recording setup:
THD values only – provides no breakdown on harmonic content, but can reveal if distortion may be a problem. Since the THD values are aggregates over the entire spectrum (regardless of the harmonics selected), they don’t take up much memory, so there is little penalty in recording each THD type
Harmonic groups – 60Hz-spaced bands, useful for determining spectrum of distortion, no distinction between harmonics and interharmonics. Not much different than recording traditional harmonics
Harmonic subgroups + interharmonic subgroups (or harmonics plus interharmonic groups) – provides detail on harmonic vs. interharmonic sources
Raw harmonics + interharmonics – full 5Hz resolution throughout band of interest – provides maximum detail, but uses the most memory. If the region of interest has been narrowed down (e.g. between 3rd and 7th harmonics), memory requirements are lessened.
The interharmonic and harmonic subgroups are a good compromise between too much detail and too little. These are the groupings recommended in IEEE 519, and give good separation between harmonics (including modulated harmonics) and true interharmonics. A useful strategy is to record stripcharts of the interharmonic THDs, and at most a range of subgroups, along with periodic waveform capture. If interharmonic subgroup readings are high, the periodic waveform capture data may be exported to Excel for a full interharmonic breakdown to determine which specific frequency is excessive.
For the stripchart interval, two good choices are 3 seconds or 10 minutes. The new IEEE 519-2014 standard recommends 3 seconds for “Very Short Time” and 10 minutes for “Short Time” analysis. Selecting one of these intervals and also harmonic/interharmonic subgroups provides a good starting point for analysis while staying compliant with IEEE 519 measurement recommendations.
To summarize, for basic recording where interharmonics aren’t known to be a problem but are a possibility, record at least the interharmonic THDs and periodic waveform capture. If the THD shows high interharmonics, the waveform data may be analyzed for more detail and will provide information for a more specific follow-up recording. If interharmonics are known to be a likely problem, record the harmonic and interharmonic subgroups as well. This will narrow down the problem to a 15/45 Hz range, and again periodic waveform capture can be analyzed if 5 Hz resolution is needed. Finally, if a frequency range is known in advance as a problem (e.g. power line carrier frequencies, VFD switching range), enable individual interharmonics as stripcharts in that range. Stripcharts of these values will enable direct comparison with RMS voltage and current, flicker, etc. for a full PQ analysis in ProVision.
Analyzing Interharmonics
Stripchart harmonic and interharmonic data are available in ProVision using traditional interval graphs and 3D graphs. The 3D graph is the fastest way to visualize all recorded harmonic/interharmonic data at once. Choose Graph, 3D Harmonic Graph from the menu, then choose a channel of voltage or current. A sample is shown in Figure 5, where individual interharmonics are denoted by their center frequency on the x-axis, and subgroups are denoted by “HSG”. For example, the 9th harmonic subgroup is shown as “9: HSG”. Here a power line carrier AMI system is shown with carriers at 555 and 585 Hz. These levels are higher than the surround interharmonics, but lower than the 9th harmonic.
Figure 5. ProVision 3D interharmonic graph showing harmonics, interharmonics, and subgroups
For more detail, individual stripcharts of each harmonic and individual interharmonic may be created. A complete set of customized graph templates is described in the whitepaper New Graph Templates for Interharmonics. Downloading the template package loads graph definitions for all 600 interharmonics, and also all groups and subgroups (shown in Figure 6). These generate graphs such as that shown in Figure 7. From these graphs, mixed graphs can be generated with combinations of any interharmonic, along with RMS voltage, current, power, etc. These templates may also be used to generate text-based interharmonic reports.
Figure 6. Interharmonic graph templates in ProVision (above)
Figure 7. Interharmonic stripchart graph showing measurements from four current channels of ten interharmonics (above)
Finally, waveform capture data may be analyzed within ProVision for harmonics, and exported to Excel for a full interharmonic breakdown including all groups and subgroups. This process is fully described in the previously referenced white paper, and the result is a measurement for every interharmonic value defined in the IEC 61000-4-7 standard, as shown in Figure 8. Here tests signals at specific interharmonics were injected, and the results circled in red for the applicable interharmonic subgroup, and harmonic groups and subgroups.
Figure 8. Spreadsheet calculation of all interharmonic and group / subgroup measurements from periodic waveform capture data
To get started with a new file, first examine the various THD levels to see if harmonics or interharmonics are a likely problem. If either is high, the next step is to examine the 3D graphs to determine which frequency regions are contributing to the high THD. A basic harmonic analysis of captured waveforms in ProVision is also helpful here – the harmonics computed by ProVision in this analysis are equivalent to IEC harmonic groups, which include interharmonic signals. If specific harmonics are high, problematic interharmonics are likely to be close to them. This method, along with the 3D graphs, can be used to isolate specific interharmonic subgroups or individual 5 Hz frequencies for a detailed analysis with interharmonic stripcharts.
Conclusion
Interharmonics present a challenge for PQ investigations, due to the complexity of the measurements and data presentation. The interharmonic implementation and setup in the Revolution is presented here, along with strategies for recording based on the expected likelihood of interharmonics being present. ProVision provides multiple methods of data analysis, and a strategy for working from the least detailed to the most detailed readings is presented.
Chris Mullins
VP of Engineering and Operations
cmullins@powermonitors.com
http://www.powermonitors.com
(800) 296-4120
