O-splines para analizar señales de oscilaciones de potencia
DOI:
https://doi.org/10.29105/ingenierias23.89-6Keywords:
Discrete Taylor Fourier Transform, dynamic phasor, electromechanical modes, complex envelope detection, filter banks, multiresolution analysis, oscillatory harmonics, O-splines, phase space, power oscillations, synchrophasor estimation, time-frequency separation, total phasor errorAbstract
A new family of splines and their derivatives is presented, which come from the low-pass differentiators of the Discrete Taylor-Fourier Transform (DTFT). They are called O-splines because their segments are spaced in steps of a cycle from the fundamental frequency. With them oscillatory power signals are analyzed. To illustrate their application and their progressive accuracy, they are applied to estimate voltage phasors, and to separate electromechanical modes of oscillation in a real power system. With them, the computational complexity of the DTFT is reduced, since only a subset of filters is applied. The estimated parameters offer much richer dynamic information than traditional methods. In particular, they provide a representation of states for
each oscillatory component, and detection of frequency modulated events. Its estimation performance is evaluated with a new error called Total Phasor Error. It is concluded that this multiresolution technique offers a series of solutions of gradual accuracy for the phasor estimation and the separation of oscillation modes. This new mathematical framework merges the area of phasor measurement with that of analysis of modes of oscillation in electrical power systems that have traditionally been separated in electrical engineering.
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J. G. Proakis and D. K. Manolakis, Digital Signal Processing, 4th ed. Upper Saddle River, N.J: Pearson, 2006.
M. A. Platas-Garza and J. A. De la O Serna, “Dynamic harmonic analysis through Taylor-Fourier transform,” IEEE Trans. Instrum. Meas., vol. 60, no. 3, pp. 804–813, 2011. [Online]. Available: http://dx.doi.org/10.1109/ TIM.2010.2064690 DOI: https://doi.org/10.1109/TIM.2010.2064690
J. A. de la O Serna, “Analyzing power oscillating signals with the o-splines of the discrete taylor–fourier transform,” IEEE Trans. Power Syst., vol. 33, no. 6, pp. 7087–7095, Nov 2018. DOI: https://doi.org/10.1109/TPWRS.2018.2832615
“IEEEstandardforsynchrophasormeasurementsforpowersystems,”IEEE Std C37.118.1-2011 (Revision of IEEE Std C37.118-2005), pp. 1–61, Dec 2011. DOI: https://doi.org/10.1159/000320901
A. G. Phadke and B. Kasztenny, “Synchronized phasor and frequency measurement under transient conditions,” IEEE Trans. Power Del., vol. 24, no. 1, pp. 89–95, Jan 2009. DOI: https://doi.org/10.1109/TPWRD.2008.2002665
R. Ghiga, K. Martin, Q. Wu, and A. Nielsen, “Phasor measurement unit test under interference conditions,” IEEE Trans. Power Del., vol. PP, no. 99, pp. 1–1, 2017, DOI:10.1109/TPWRD.2017.2691356. DOI: https://doi.org/10.1109/TPWRD.2017.2691356
D. Macii, D. Petri, and A. Zorat, “Accuracy analysis and enhancement of DFT-based synchrophasor estimators in off-nominal conditions,” IEEE Trans. Instrum. Meas., vol. 61, no. 10, pp. 2653–2664, Oct 2012. DOI: https://doi.org/10.1109/TIM.2012.2199197
M.Karimi-Ghartemani,B.T.Ooi,andA.Bakhshai,“Applicationofenhanced phase-locked loop system to the computation of synchrophasors,” IEEE Trans. Power Del., vol. 26, no. 1, pp. 22–32, Jan 2011. DOI: https://doi.org/10.1109/TPWRD.2010.2064341
I. Kamwa, A. K. Pradhan, and G. Joos, “Adaptive phasor and frequency- tracking schemes for wide-area protection and control,” IEEE Trans. Power Del., vol. 26, no. 2, pp. 744–753, April 2011. DOI: https://doi.org/10.1109/TPWRD.2009.2039152
J. S. Gasca and D. Trudnowski, “Identification of electromechanical modes in power systems,” IEEE Power and Energy Society, Task Force on Identificatioin of electromechanical modes, Tech. Rep., June 2012.
J. F. Hauer, C. J. Demeure, and L. L. Scharf, “Initial results in Prony analysis of power system response signals,” IEEE Trans. Power Syst., vol. 5, no. 1, pp. 80–89, Feb 1990. DOI: https://doi.org/10.1109/59.49090
J. Rommes, N. Martins, and F. Freitas, “Computing rightmost eigenvalues for small-signal stability assessment of large scale power systems,” in IEEE PES General Meeting, July 2010, pp. 1–1. DOI: https://doi.org/10.1109/PES.2010.5589670
J. W. Pierre, D. J. Trudnowski, and M. K. Donnelly, “Initial results in electromechanical mode identification from ambient data,” IEEE Trans. Power Syst., vol. 12, no. 3, pp. 1245–1251, Aug 1997. DOI: https://doi.org/10.1109/59.630467
A. R. Messina and V. Vittal, “Nonlinear, non-stationary analysis of interarea oscillations via Hilbert spectral analysis,” IEEE Trans. Power Syst., vol. 21, no. 3, pp. 1234–1241, Aug 2006. DOI: https://doi.org/10.1109/TPWRS.2006.876656
A. Q. Zhang, L. L. Zhang, M. S. Li, and Q. H. Wu, “Identification of dominant low frequency oscillation modes based on blind source separation,” IEEE Trans. Power Syst., vol. PP, no. 99, pp. 1–1, 2017.
J. A. De la O Serna, J. M. Ramirez, A. Zamora Mendez, and M. R. A. Paternina, “Identification of electromechanical modes based on the digital Taylor-Fourier Transform,” IEEE Trans. Power Syst., vol. 31, no. 1, pp. 206–215, 2016. [Online]. Available: http://dx.doi.org/10.1109/TPWRS.2015.2403290 DOI: https://doi.org/10.1109/TPWRS.2015.2403290
J. A. De la O Serna, “Synchrophasor measurement with polynomial phase- locked-loop Taylor-Fourier filters,” IEEE Trans. Instrum. Meas., vol. 64, no. 2, pp. 328–337, 2015. [Online]. Available: http://dx.doi.org/10.1109/ TIM.2014.2344333 DOI: https://doi.org/10.1109/TIM.2014.2344333
I. Daubechies, Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, 1992. [Online]. Available: http://epubs.siam.org/doi/abs/10.1 137/1.9781611970104 DOI: https://doi.org/10.1137/1.9781611970104
J. A. De la O Serna, “Dynamic phasor estimates for power system oscillations,” IEEE Trans. Instrum. Meas., vol. 56, no. 5, pp. 1648–1657, 2007. [Online]. Available: http://dx.doi.org/10.1109/TIM.2007.904546 DOI: https://doi.org/10.1109/TIM.2007.904546
M. A. Platas-Garza and J. A. De la O Serna, “Dynamic phasor and frequency estimates through maximally flat differentiators,” IEEE Trans. Instrum. Meas., vol. 59, no. 7, pp. 1803–1811, 2010. [Online]. Available: http://dx.doi. org/10.1109/TIM.2009.2030921 DOI: https://doi.org/10.1109/TIM.2009.2030921
M. Vetterli, K. Kovacevic, and V. K. Goyal, Foundations of Signal Processing, 3rd ed. Cambridge, UK: Cambridge University Press,2014, available at http:// www.fourierandwavelets.org/. DOI: https://doi.org/10.1017/CBO9781139839099
