Location of Harmonic Distortions in Electrical Systems using Compressed Sensing
Article Sidebar
Main Article Content
This article is a study of the state of the art, where the advantages and disadvantages of the different classical digital signal processing techniques used to identify harmonic frequencies that distort the voltage and current waveforms of an electrical network are analyzed. Taking as a reference the classical techniques that determine the harmonic distortion of an electrical signal, an alternative is proposed for the detection of harmonic frequencies in an electrical waveform, based on compressed sensing algorithms; this technique extracts an efficient and reduced sample of the signal under study, this sample is transformed to the frequency domain by means of a transformation base which, for the present case study is the discrete cosine transform (DCT). The reduced signal in the frequency domain is subjected to a non-linear optimization process, which classifies the coefficients, extracts the most representative ones and makes the least representative ones zero. It is here where the harmonic frequencies, immersed in the electrical waveform come to light in a clear and precise way, with which the harmonic distortion (THD) is calculated. This article shows an example of the compressed sensing technique for the detection of harmonic frequencies in a theoretical sinusoidal signal which is contaminated by third and fifth order harmonics, the optimized coefficient vector is extracted, and the harmonic frequencies are identified.
(1) Mishra M. Power quality disturbance detection and classification using signal processing and soft computing techniques: A comprehensive review. Int Trans Electr Energy Syst. 2019;29(8):1–42. https://doi.org/10.1002/2050-7038.12008.
(2) Donoho DL. Compressed sensing. IEEE Trans Inf Theory. 2006;52(4):1289–306. https://doi.org/10.1109/TIT.2006.871582.
(3) Duarte MF, Baraniuk RG. Spectral compressive sensing. Appl Comput Harmon Anal 2013;35(1):111–29. http://dx.doi.org/10.1016/j.acha.2012.08.003.
(4) Kahane JP. Compressed sensing from a harmonic analysis point of view. Anal Math. 2016;42(1):19–29. https://doi.org/10.1007/s10476-016-0102-4.
(5) Baraniuk RG, Goldstein T, Sankaranarayanan AC, Studer C, Veeraraghavan A, Wakin MB. Compressive video sensing: Algorithms, architectures, and applications. IEEE Signal Process Mag. 2017;34(1):52–66. https://doi.org/10.1109/MSP.2016.2602099.
(6) Baraniuk RG. Compressive sensing. Handb Math Methods Imaging Vol 1, Second Ed. 2015;24(4):118–21. https://doi.org/10.1109/MSP.2007.4286571.
(7) Palczynska B, Masnicki R, Mindykowski J. Compressive sensing approach to harmonics detection in the ship electrical network. Sensors (Switzerland). 2020;20(9):1–18. https://doi.org/10.3390/s20092744.
(8) Maechler P, Studer C, Bellasi DE, Maleki A, Burg A, Felber N, et al. VLSI design of approximate message passing for signal restoration and compressive sensing. IEEE J Emerg Sel Top Circuits Syst. 2012;2(3):579–90. https://doi.org/10.1109/JETCAS.2012.2214636.
(9) Tobias S, Everson HT. Trends in Signal Processing Education. SPOTLIGHT. 2012;29(1):180–2. https://doi.org/10.1109/MSP.2011.943132.
(10) Baraniuk RG, Candes E, Nowak R, Vetterli M. Compressive sampling. IEEE Signal Process Mag. 2008;25(2):12–3. https://doi.org/10.1109/MSP.2008.915557.
(11) Baraniuk RG, Candes E, Elad M, Ma Y. Applications of sparse representation and compressive sensing. Proc IEEE. 2010;98(6):906–9. https://doi.org/10.1109/JPROC.2010.2047424.
(12) Granados-Lieberman D, Romero-Troncoso RJ, Osornio-Rios RA, Garcia-Perez A, Cabal-Yepez E. Techniques and methodologies for power quality analysis and disturbances classification in power systems: A review. IET Gener Transm Distrib. 2011;5(4):519–29. https://doi.org/10.1049/iet-gtd.2010.0466.
(13) Aharon M, Elad M, Bruckstein A. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process. 2006;54(11):4311–22. https://doi.org/10.1109/TSP.2006.881199.
(14) Mukherjee N, Chattopadhyaya A, Chattopadhyay S, Sengupta S. Discrete-Wavelet-Transform and Stockwell-Transform-Based Statistical Parameters Estimation for Fault Analysis in Grid-Connected Wind Power System. IEEE Syst J. 2020;14(3):4320–8. https://doi.org/10.1109/JSYST.2020.2984132.
(15) Zhao S, Wang C, Bian X. Research on harmonic detection based on wavelet threshold and FFT algorithm. Syst Sci Control Eng. 2018;6(3):339–45. https://doi.org/10.1080/21642583.2018.1558420.
(16) Jia K, Feng T, Zhao Q, Wang C, Bi T. High frequency transient sparse measurement-based fault location for complex DC distribution networks. IEEE Trans Smart Grid. 2020;11(1):312–22. https://ieeexplore.ieee.org/document/8731742
(17) Wang F, Li R, Wang Z, Zhang J. Compressed Blind Signal Reconstruction Model and Algorithm. Circuits, Syst Signal Process. 2016;35:3192–219. https://doi.org/10.1007/s00034-015-0189-z.
(18) Mercorelli P. Denoising and harmonic detection using nonorthogonal wavelet packets in industrial applications. J Syst Sci Complex. 2007;20:325–43. https://doi.org/10.1007/s11424-007-9028-z.
(19) Shao C, Li H. Identifying Single-Event Transient Location Based on Compressed Sensing. IEEE Trans Very Large Scale Integr Syst. 2018;26(4):768–77. https://doi.org/10.1109/TVLSI.2017.2778750.
(20) Duarte MF, Baraniuk RG. Kronecker compressive sensing. IEEE Trans Image Process. 2012;21(2):494–504. https://doi.org/10.1109/TIP.2011.2165289.
(21) Metzler CA, Maleki A, Baraniuk RG. From Denoising to Compressed Sensing. IEEE Trans Inf Theory. 2016;62(9):5117–44. https://doi.org/10.1109/TIT.2016.2556683.
(22) Gołowicz D, Kasprzak P, Kazimierczuk K. Enhancing compression level for more efficient compressed sensing and other lessons from NMR spectroscopy. Sensors (Switzerland). 2020;20(5):1–19. https://doi.org/10.3390/s20051325.
(23) Xiao J, Hu F, Shao Q, Li S. A low-complexity compressed sensing reconstruction method for heart signal biometric recognition. Sensors (Switzerland). 2019;19(23):5330. https://doi.org/10.3390/s19235330.
(24) Joshi P, Jain SK. An improved active power direction method for harmonic source identification. Trans Inst Meas Control. 2020;42(13):2569–77. https://doi.org/10.1177%2F0142331220932638.
(25) Candes EJ, Wakin MB. An Introduction To Compressive Sampling. IEEE Signal Process Mag. 2008;25(2):21–30. https://doi.org/10.1109/MSP.2007.914731.
(26) Ahmed N, Natarajan T, Rao KR. Discrete cosine transform. IEEE Transactions on Computers. 1974;C-23(1):90–93. https://doi.org/10.1109/T-C.1974.223784.
(27) Hegde C, Baraniuk RG. Signal recovery on incoherent manifolds. IEEE Trans Inf Theory. 2012;58(12):7204–14. https://doi.org/10.1109/ISIT.2012.6283066.
(28) Su T, Yang M, Jin T, Flesch RCC. Power harmonic and interharmonic detection method in renewable power based on Nuttall double-window all-phase FFT algorithm. IET Renew Power Gener. 2018;12(8):953–61. https://doi.org/10.1049/IET-RPG.2017.0115.
(29) Kerdjidj O, Ramzan N, Ghanem K, Amira A, Chouireb F. Fall detection and human activity classification using wearable sensors and compressed sensing. J Ambient Intell Humaniz Comput. 2020;11:349–61. http://dx.doi.org/10.1007/s12652-019-01214-4.
(30) Huang K, Xiang Z, Deng W, Tan X, Yang C. Reweighted Compressed Sensing-Based Smart Grids Topology Reconstruction with Application to Identification of Power Line Outage. IEEE Syst J. 2020;14(3):4329–39. https://doi.org/10.1109/JSYST.2019.2958869.
(31) Carta D, Muscas C, Pegoraro PA, Sulis S. Identification and Estimation of Harmonic Sources Based on Compressive Sensing. IEEE Trans Instrum Meas. 2019;68(1):95–104. https://doi.org/10.1109/TIM.2018.2838738.
(32) Jandan F, Khokhar S, Shaha SAA, Abbasi F. Recognition and classification of power quality disturbances by DWT-MRA and SVM classifier. Int J Adv Comput Sci Appl. 2019;10(3):368–77. https://dx.doi.org/10.14569/IJACSA.2019.0100348.
(33) Solis-Munoz FJ, Osornio-Rios RA, Romero-Troncoso RJ, Jaen-Cuellar AY. Differential evolution implementation for Power Quality Disturbances monitoring using OpenCL. Adv Electr Comput Eng. 2019;19(2):13–22. http://dx.doi.org/10.4316/AECE.2019.02002.
(34) Karafotis PA, Evangelopoulos VA, Georgilakis PS. Evaluation of harmonic contribution to unbalance in power systems under non-stationary conditions using wavelet packet transform. Electr Power Syst Res. 2020;178:1–9. https://doi.org/10.1016/j.epsr.2019.106026.
(35) Inga-Ortega J, Inga-Ortega E, Gómez C, Hincapié R. Electrical load curve reconstruction required for demand response using compressed sensing techniques; 2017 IEEE PES Innov Smart Grid Technol Conf - Lat Am ISGT Lat Am. Ecuador: IEEE; 2017. pp. 1-6. https://doi.org/10.1109/ISGT-LA.2017.8126731.
(36) He S, Li K, Zhang M. A real-time power quality disturbances classification using hybrid method based on s-transform and dynamics. IEEE Trans Instrum Meas. 2013;62(9):2465–75. https://doi.org/10.1109/TIM.2013.2258761.
(37) Baraniuk RG, Cevher V, Duarte MF, Hegde C. Model-based compressive sensing. IEEE Trans Inf Theory. 2010;56(4):1982–2001. https://doi.org/10.1109/TIT.2010.2040894.
- Luis Amaya Vásquez, Miguel Ángel Campaña Molina , Optimal Design of Electrical Distribution Networks Using Optimization Models , Ingeniería y Competitividad: Vol. 25 No. 1 (2023): Ingeniería y Competitividad.
Accepted 2021-10-28
Published 2022-01-15
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors grant the journal and Universidad del Valle the economic rights over accepted manuscripts, but may make any reuse they deem appropriate for professional, educational, academic or scientific reasons, in accordance with the terms of the license granted by the journal to all its articles.
Articles will be published under the Creative Commons 4.0 BY-NC-SA licence (Attribution-NonCommercial-ShareAlike).