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- 1. The Harmonic Spectra of Interharmonics<br />Gary Malhoit<br />SRP<br />August 26, 2010<br />
- 2. Overview<br />Brief overview on harmonics and periodicity<br />Fourier’s Method and the DFT<br />Interharmonic Defined <br />Picket-Fence Effect & Spectral Leakage<br />Genuine & Non-Genuine Interharmonics<br />Interharmonic standards and allowed limits<br />Sources of Interharmonics<br />Interharmonic Problems<br />Measuring Interharmonics<br />IEC Grouping Standard and Understanding Spectra Measurements<br />2<br />
- 3. Sinusoids<br />Sinusoids are the basic building block of all periodic signals.<br />Periodic waveforms are comprised of component sinusoids having distinct frequencies. This includes distorted periodic waveforms.<br />3<br />
- 4. Fourier<br />1822, a French mathematician named Joseph Fourier, claimed that continuous periodic signals can be represented by the sum of properly chosen sinusoids. <br />4<br />
- 5. Limitations to Fourier Methods<br />5<br />Source: Wikipedia<br />5<br />
- 6. Fourier Tool Kit<br />6<br />The Scientist and Engineer's Guide to Digital Signal ProcessingBy Steven W. Smith, Ph.D.<br />
- 7. Assumptions in Applying DFTfor PQ Measurements<br />The signal is strictly periodic and stationary.<br />The sampling frequency is an integer multiple of the fundamental.<br />The sample frequency is at least twice the highest frequency being measured.<br />7<br />
- 8. Non-Stationary Signal<br />8<br />DFT Window<br />Source: A Notebook Compiled <br />While Reading Understanding <br />Digital Signal Processing by Lyons <br />2Pi<br />
- 9. Non-periodic Signal<br />DFT Window<br />Half a sinusoid<br />In time domain<br />Source: A Notebook Compiled While Reading<br />Understanding Digital Signal <br />Processing by Lyons <br />Spectral Leakage<br />in the frequency<br />domain<br />9<br />
- 10. What is Harmonic Spectra?<br />Harmonic spectra includes sub-harmonics, harmonics and interharmonics.<br />10<br />f = n f1 where n is an integer > 0.<br />Harmonic<br />f = nf1 where n is an integer > 0.<br />Interharmonic<br />0 < f < f1<br />Subharmonic<br />f1= fundamental frequency<br />Source: Power Quality Application Guide: European Copper Institute, AGH University of <br />Science and Technology and Copper Development Association.<br />
- 11. Harmonic Spectra<br />Characteristic Harmonics<br /> “Those harmonics produced by semiconductor converter equipment in the course of normal operation. In a six-pulse converter, the characteristic harmonics are the non-triple odd harmonics, for example, the 5th, 7th, llth, 13th, etc.”<br />11<br />Source: IEEE 519<br />
- 12. Harmonic Spectra (cont.)<br />Non-Characteristic Harmonics<br /> “Harmonics that are not produced by semiconductor converter equipment in the course of normal operation. These may be a result of beat frequencies; a demodulation of characteristic harmonics and the fundamental; or an imbalance in the ac power system, asymmetrical delay angle, or cycloconverter operation.”<br />12<br />Source: IEEE 519<br />
- 13. Interharmonics<br />Interharmonics- “Between the harmonics of the power frequency voltage and current, further frequencies can be observed which are not an integer of the fundamental. They can appear as discrete frequencies or as a wide-band spectrum.” <br /> Source: IEC 61000-2-1 <br />13<br />
- 14. Interharmonics Redefined<br />Interharmonics- “Any frequency which is not an integer multiple of the fundamental frequency”<br />Source: IEC-61000-2-2<br />14<br />
- 15. One-Cycle Window<br />15<br />DFT Window<br />16.67 ms<br />60 Hz<br />15<br />The 60 Hz component competes 1 cycle within the DFT window.<br />
- 16. Frequency Resolution<br />C<br />B<br />A<br />Time<br />16<br />
- 17. Picket Fence Effect<br />17<br />Source: <br />Azima DLI<br />
- 18. Expanded DFT Window<br />In order to see interharmonics the DFT window <br />must be larger than one cycle of the fundamental<br />frequency.<br />18<br />Source: Interharmonics: basic concepts & techniques for their detection<br /> & measurement, Chun Li, et al.<br />
- 19. The Fundamental with Harmonics<br />19<br />DFT Window<br />60 180 300<br />Time<br />60 Hz-Fundamental<br />Frequency<br />180 Hz-Third Harmonic<br />16.67 ms<br />300 Hz-Fifth Harmonic <br />19<br />
- 20. A Genuine Interharmonic<br />DFT Window<br />Genuine<br /> Interharmonic<br />Magnitude<br />60<br />90<br />Frequency (Hz)<br />Source: Interharmonics: Theory and Modeling, IEEE <br />Task Force on Harmonics Modeling and Simulation<br />33.34 ms<br />The 60 Hz component competes 2 cycles within the DFT window.<br />60 Hz<br />90Hz<br />The 90 Hz component completes 3 cycles within the DFT window.<br />20<br />
- 21. Non-Genuine Interharmonics<br />21<br />DFT Window<br />Non-Genuine<br /> Interharmonics<br /> (Black)<br />Magnitude<br />Source: Interharmonics: Theory and Modeling, IEEE Task Force on Harmonics Modeling and Simulation<br />33.34 ms<br /> 60 90 120 150 180<br />Frequency (Hz)<br />60 Hz<br />The 60 Hz component completes two cycles within the DFT window.<br />100 Hz<br />The 100 Hz component completes 3.33 cycles within DFT window.<br />
- 22. DFT Assumes Signal Repetitive<br />Discontinuities<br />Magnitude<br />Time<br />DFT Window<br />Source: Oppenheim, et al. “Discrete-Time<br /> Signal Processing”<br />Frequency Domain<br />22<br />Time Domain<br />
- 23. Determining if Interharmonics Are Real <br />The voltage and current spectral components should show correlation.<br />If the magnitude of the signal appears modulated, it is highly likely that the signal contains interharmonics.<br />Interharmonics usually coexist with harmonics.<br />If the signal is substantially non-varying or stationary, a longer DFT window can improve the frequency resolution.<br />23<br />Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.<br />
- 24. Interharmonics<br />The main reason for lack of interharmonic concerns is that interharmonics are produced by relatively few types of loads, unlike harmonics. <br />24<br />Survey of Interharmonics in Indian Power System Network, B.E. Kushare, et al.<br />
- 25. Spectra & Noise Magnitudes<br />25<br />5%<br />Harmonics<br />10.0<br />Interharmonics<br />1.0<br />% of Nominal Voltage of Fundamental<br />.2%<br />.1<br />White Noise<br />.02%<br />.01<br />Sources: IEEE 519 & IEC 61000-2-2 & IEC 1000-2-1<br />
- 26. Interharmonic Limits<br />26<br />Limits<br />Standard<br />IEEE 519-1992<br />Not covered<br />IEC 1000-2-2<br />0.2% at ripple control frequencies<br />IEC 1000-2-4<br />0.2% for classes 1 & 2, up to 2.5% for class 3<br />EN 50160<br />Under consideration<br />All %’s are of nominal fundamental frequency<br />Survey of Interharmonics in Indian Power System Network, B.E. Kushare, et al.<br />
- 27. Proposed Interharmonic Limits<br />Current Standards* use 0.2%<br />Other Proposed Limits<br />Less than 1%, 3% or 5% depending on the voltage level.<br />Adopt limits correlated with Pst<br /> Develop appropriate limits for particular equipment and systems. <br />27<br />All %’s are of nominal fundamental frequency<br />*IEC 61000-2-2<br />Source: Survey of Interharmonics in Indian Power System. Network, B.E. Kushare, et al.<br />
- 28. Causes of Interharmonics<br />Asynchronous switching (i.e., not synchronized with the power system frequency); and<br />Rapid changes of the load current causing the generation of sideband components adjacent to the fundamental supply frequency and its harmonics; and <br />A combination of the above can occur at the same time in many kinds of equipment.<br />28<br />Source: Power Quality Application Guide: European Copper Institute, AGH University of <br />Science and Technology and Copper Development Association.<br />
- 29. Sources of Interharmonics<br />Includes at least:<br />PWM power electronic systems (Asynchronous Switching)<br />Arc Furnaces (Rapid Current Changes)<br />Cycloconverters (Asynchronous Switching)<br />29<br />Source: Power Quality Application Guide: European Copper Institute, AGH University of <br />Science and Technology and Copper Development Association.<br />
- 30. Cycloconverter<br />30<br />
- 31. Variable Speed Drives<br />31<br />DC-Link<br />Ld<br />Id<br />AC/DC<br />f1<br />f2<br />DC/AC<br />Converter 2<br />Converter 1<br />
- 32. Variable Speed Drives (cont.)<br />32<br />If the reactor and/or capacitor at the DC Link is infinite<br /> there will not be any DC ripple at the DC Link.<br />Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.<br />
- 33. An Arc Furnace is a Varying Load<br />33<br />
- 34. Varying Loads<br />34<br />Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.<br />
- 35. Modulated Power<br />35<br />Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.<br />
- 36. RMS Deviation from Interharmonics<br />36<br />36<br />Source: Power Quality Application Guide: European Copper Institute, AGH University of <br />Science and Technology and Copper Development Association.<br />0.2<br />0.15<br />% RMS Deviation Due to Interharmonics<br />0.1<br />0.05<br />0.0<br />0 50 100 150 200 <br /> Interharmonic Frequency<br />
- 37. Problems Caused by Interharmonics<br />Lamp Flicker;<br />Heating; and<br />Interharmonics vary with the operating conditions of the interharmonic producing load. This makes interharmonics more difficult to mitigate than harmonics.<br />37<br />
- 38. Lamp Flicker<br />38<br />58 Hz<br />42 Hz<br />Source : EPRI<br />Source: Interharmonics: basic concepts & techniques <br />for their detection & measurement, Chun Li, et al.<br />Human eye is sensitive to frequencies between about<br />8 Hz and 12 Hz<br />
- 39. Minimum Interharmonic Amplitude Causing Perceptible Flicker<br />39<br />Flickermeter<br />Source: Detection of Flicker Caused by Interharmonics<br />Taekhyun Kim, Student Member, IEEE, Edward J. Powers, Fellow, IEEE, W. Mack Grady, Fellow, IEEE, and<br />Ari Arapostathis, Fellow, IEEE<br />
- 40. Rolling Mill Case<br />40<br />Bus<br />Source: Leonardo Energy by Michele De Witte<br />40<br />
- 41. Harmonic Impedance at Resonance<br />41<br />Source: Harmonic Impedance Study for Southwest<br />Connecticut Phase II Alternatives by KEMA, Inc.<br />
- 42. Rolling Mill Case (cont.)<br />42<br />180<br />485<br />330<br />notch<br />notch<br />notch<br />Source: Leonardo Energy by Michele De Witte<br />
- 43. Interharmonic Conclusions<br />Interharmonics have always been around, they are just becoming more important and visible.<br />Power electronic advances are resulting in increasing levels of interharmonic distortion.<br />Traditional filter designs can result in resonances that make interharmonic problems worse.<br />Light flicker is the most common impact.<br />Measurement is difficult, but standards make them possible and the results comparable.<br />43<br />
- 44. IEC Groupings<br />Number of cycles to sample chosen to provide 5 Hz frequency bins<br />10 Cycles for 50 Hz Systems<br />12 Cycles for 60 Hz Systems<br />Grouping concept<br />Harmonic factors calculated as the square root of the sum of the squares of the harmonic bin and two adjacent bins.<br />Interharmonic factors calculated as the square root of the sum of the squares of the bins in between the harmonic bins (not including the bins directly adjacent to the harmonic bin).<br />44<br />Source: Power Quality Application Guide: European Copper Institute, AGH University of <br />Science and Technology and Copper Development Association.<br />
- 45. IEC 61000-4-7 (Groupings)<br />45<br />Harmonic subgroup<br />Harmonic group<br />Harmonic subgroup<br />The RMS value of the two<br /> harmonic components <br />immediately adjacent to<br />the fundamental .<br />The RMS value of the <br />fundamental and adjacent <br />Harmonic components<br />n<br />n+1<br />n+2<br />The time-window is 12 cycles at 60 Hz<br />and has 5 Hz resolution.<br />Source: Power Quality Application Guide: European Copper Institute, AGH University of <br />Science and Technology and Copper Development Association.<br />
- 46. IEC 61000-4-7 (Groupings) <br />46<br />The RMS value of all <br />interharmonics components <br />in the interval between two <br />consecutive harmonics.<br />The RMS value of all interharmonic<br />components in the interval<br />between two consecutive <br />harmonic frequencies, <br />excluding components <br />adjacent to the harmonic<br />frequencies<br />Interharmonic<br /> subgroup<br />Interharmonic<br /> group<br />n<br />n+1<br />n+2<br />Source: Power Quality Application Guide: European Copper Institute, AGH University of <br />Science and Technology and Copper Development Association.<br />
- 47. Options Using PX-5<br />47<br />
- 48. Show Harmonics Only (PX-5)<br />Harmonic Sub-Groups<br />Magnitude<br />Frequency (Hz)<br />0 60 120 180 240 300 360<br />1 3 5<br />48<br />
- 49. Show Harmonics & Interharmonics (PX-5)<br />Magnitude<br />Frequency (Hz)<br />0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125<br />1 2<br />49<br />
- 50. Harmonics Calculated Including Interharmonics (PX-5)<br />50<br />Harmonic<br />Sub-Groups<br />Interharmonic<br />Sub-Groups<br />Magnitude<br /> 0 5-55 55-65 70-110 115-125 130-170 175-185 <br /> 1 2 3<br />
- 51. Questions & Comments<br />51<br />

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