Método para calcular el grado de fluctuación de la curva de demanda de potencia eléctrica usando dimensión fractal

dc.contributorAngulo García, Fabiola
dc.contributorOsorio Lema, Mauricio
dc.creatorTabares Ospina, Hector Anibal
dc.date.accessioned2021-07-08T15:33:30Z
dc.date.available2021-07-08T15:33:30Z
dc.date.created2021-07-08T15:33:30Z
dc.date.issued2021-06-29
dc.identifierhttps://repositorio.unal.edu.co/handle/unal/79777
dc.identifierUniversidad Nacional de Colombia
dc.identifierRepositorio Institucional Universidad Nacional de Colombia
dc.identifierhttps://repositorio.unal.edu.co/
dc.description.abstractEl objeto de estudio en esta tesis doctoral es la geometría fractal no lineal, que despierta el interés por su patrón gráfico fractal de formación. No obstante, la topología de los conjuntos resultantes son meras curiosidades matemáticas sin ninguna utilidad. Por lo tanto, en la primera parte de esta tesis se propone su acople con la potencia eléctrica en circuitos de corriente alterna, gracias a que ambos están defi nidos en el campo complejo. El acople resulta útil para comprobar que la potencia eléctrica alterna (resistiva, inductiva o capacitiva), también puede ser descrita mediante conjuntos fractales de Julia. Así mismo, se comprueba que las curvas de demanda de potencia eléctrica también pueden ser descritas mediante diagramas de órbitas y atractores en el plano complejo del conjunto de Mandelbrot. En la segunda parte de esta tesis, el concepto de dimensión fractal es usado para medir el grado de variación o fluctuación de las curvas demanda de potencia eléctrica. Se trata de una nueva unidad de medida con la que se caracteriza la variabilidad de la carga eléctrica, que complementa los estudios de carga en una red de distribución de potencia eléctrica. La tercera y última parte de esta tesis, versa sobre el desarrollo e implementación de un algoritmo para calcular la dimensión fractal e integración numérica de una función continua fluctuante. Las tres partes de la tesis están relacionados entre sí y con su aplicación en la ingeniería eléctrica. (Tomado de la fuente)
dc.description.abstractThe object of study in this doctoral thesis is nonlinear fractal geometry, which arouses interest due to its fractal graphic pattern of formation. However, the topology of the resulting sets are mere mathematical curiosities without any use. Therefore, in the rst part of this thesis, its coupling with electrical power in alternating current circuits is proposed, thanks to the fact that both are de fined in the complex field. The coupling is useful to verify that the alternating electrical power (resistive, inductive or capacitive), can also be described by means of Julia fractal sets. Likewise, it is found that the electrical power demand curves can also be described by means of orbits and attractors diagrams in the complex plane of the Mandelbrot set. In the second part of this thesis, the concept of fractal dimension is used to measure the degree of variation or fluctuation of the electrical power demand curves. It is a new unit of measurement with which the variability of the electrical load is characterized, which complements the load studies in an electrical power distribution network. In the third and last part of this thesis deals with the development and implementation of an algorithm to calculate the fractal dimension and numerical integration of a fluctuating continuous function. The three parts of the thesis are related to each other and to its application in electrical engineering. (Tomado de la fuente)
dc.languagespa
dc.publisherUniversidad Nacional de Colombia
dc.publisherMedellín - Minas - Doctorado en Ingeniería - Sistemas Energéticos
dc.publisherDepartamento de Ingeniería Eléctrica y Automática
dc.publisherFacultad de Minas
dc.publisherMedellín
dc.publisherUniversidad Nacional de Colombia - Sede Medellín
dc.relation[Barnsley et al., 1988] Barnsley, M., Devaney, R., Mandelbrot, B., Peitgen, H., Saupe, D., and Voss, R. (1988). The Science of Fractal Images. H.-O. Peitgen D. Saupe, eds.
dc.relation[Besicovitch, 1929] Besicovitch, A. (1929). On linear sets of points of fractional dimension. Mathematische Annalen, 101:161-193.
dc.relation[Binimelis, 2011] Binimelis, M. (2011). Una nueva manera de ver el mundo. RDA, Barcelona.
dc.relation[Borjon, 2002] Borjon, J. (2002). Caos, Orden Y Desorden En El Sistema Monetario Y Financiero Internacional. ed. Y. Valdes., New York.
dc.relation[Cantor, 1884] Cantor, C. (1884). On the power of perfect set of points. Acta Mathematica, 4:381-392.
dc.relation[Cayley, 1879] Cayley, A. (1879). The newton{fourier imaginary problem. The Newton-Fourier Imaginary Problem, 2:97.
dc.relation[Chapra and Canale, 2006] Chapra, S. and Canale, R. (2006). Numerical methods for engineers. The McGraw-Hill Companies, México.
dc.relation[Chen and Huang, 2019] Chen, L. and Huang, Y. (2019). Modeling growth curve of fractal dimension of urban form of beijing. Physica A., 523:1038-1056.
dc.relation[Coloner et al., 2018] Coloner, J., Naranjo, A., Janvier, V., and Mossi, T. (2018). Evaluation of fractal dimension e ectiveness for damage detection in retinal background. J. Comput. Appl. Math., 337:341-353.
dc.relation[Cui and Yng, 2009] Cui, H. and Yng, L. (2009). Short-term electricity price forecast based on improved fractal theory. Technical report, International Conference on Computer Engineering and Technology.
dc.relation[Dandan et al., 2017] Dandan, Y., Meifeng, D., Yu, S., and Weiyi, S. (2017). Average weighted receiving time on the non-homogeneous double-weighted fractal networks. Phys. A Stat. Mech. Its Appl, 473:390-402.
dc.relation[Davis and Baylis, 1995] Davis, M. and Baylis, J. (1995). The nature and power of mathematics.The Mathematical Gazette, 2:79.
dc.relation[Devaney, 1990] Devaney, R. (1990). Chaos, fractals, and dynamics: Computer experiments in modern mathematics. Addison-Wesley, ed., Massachusetts.
dc.relation[Fatou, 1920] Fatou, P. (1920). Sur les equations fonctionelles. Bull. Sci. Math, France, 48:208-314.
dc.relation[Feigenbaum, 1991] Feigenbaum, A. (1991). Total quality control. McGraw-Hill, ed., New York.
dc.relation[Garcia et al., 2018] Garcia, T., Tamura Ozaki, G., Castoldi, R., Koike, T., Trindade Camargo, R., and F., S. C. (2018). Fractal dimension in the evaluation of di erent treatments of muscular injury in rats. Tissue and Cell, 54:120-126.
dc.relation[Gun-Baek et al., 2017] Gun-Baek, S., Hye-Rim, S., and Gang-Gyoo, J. (2017). Enhancement of the box-counting algorithm for fractal dimension estimation. Pattern Recognition Letters, 98:53-58.
dc.relation[Guosheng et al., 2019] Guosheng, F., Weimin, X., Feng, Y., Yi, Y., and Yuan, W. (2019). Surface fractal dimension of bentonite a ected by long-term corrosion in alkaline solution. Appl. Clay Sci., 175:94-101.
dc.relation[Hausdorff, 1919] Hausdorff, F. (1919). Der wertvorrat einer bilinearform. Mathematische Zeitschrift, 3:314-316.
dc.relation[Hernández et al., 2018] Hernández, J., Mejía-Rosales, S., and Gama Goicochea, A. (2018). Fractal properties of biophysical models of pericellular brushes can be used to di erentiate between cancerous and normal cervical epithelial cells. Colloids and Surfaces B: Biointerfaces, 170:572-577.
dc.relation[Hénon, 1976] Hénon, M. (1976). A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics, 50:69-77.
dc.relation[Jelica et al., 2018] Jelica, D., Taljegard, M., Thorson, L., and Johnsson, F. (2018). Hourly electricity demand from an electric road system a swedish case study. Applied Energy, 228:141-148.
dc.relation[Jian. et al., 2009] Jian., QianDu., and CaixinSum. (2009). An improved box-counting method for image fractal dimension estimation. Pattern Recognition, 42:2460-2469.
dc.relation[Jiménez et al., 2019] Jiménez, J., Anzola, A., and Jimenez-Triana, J. (2019). Pedestrian counting estimation based on fractal dimension. 5:1-20.
dc.relation[Jinyan et al., 2017] Jinyan, Y., Yanggrong, L., and Hongyong, C. (2017). Box-counting dimensions and upper semicontinuities of bi-spatial attractors for stochastic degenerate parabolic equations on an unbounded domain. Journal of Mathematical Analysis and Applications, 450:1180-1207.
dc.relation[Julia, 1918] Julia, G. (1918). Memoire sur literacion des fonctions rationelles. J. Math. Pures et App, 8:47-245.
dc.relation[Junfeng et al., 2017] Junfeng, X., Zengyun, J., and Xin, L. (2017). An application of box counting method for measuring phase fraction. Measurement, 100:297-300.
dc.relation[Katok, 1996] Katok, A. andHasselblatt, B. (1996). Introduction to the modern theory of dynamical systems. In Cambridge University Press., Cambridge.
dc.relation[Koch, 1904] Koch, H. (1904). Sur une courbe continue sans tangente, obtenue par une construction g eometrique elementaire. Arkiv For Matematik Astronomi Och Fysik, 1:681- 704.
dc.relation[Kumar and Chaubey, 2012] Kumar, R. and Chaubey, N. (2012). On the design of treetype ultra wideband fractal antenna for ds-cdma system. J. Microwaves, Optoelectron. Electromagn. Appl., 11:107-121.
dc.relation[Lindberg et al., 2019a] Lindberg, K., Bakker, S., and Sartori, I. (2019a). Modelling electric and heat load profiles of non-residential buildings for use in long-term aggregate load forecasts. Utilities Policy, 58:63-88.
dc.relation[Lindberg et al., 2019b] Lindberg, K., Seljom, P., Madsen, H., Fisher, D., and Korpas, M. (2019b). Long-term electricity load forecasting: Current and future trends. Utilities Policy, 58:102-119.
dc.relation[Lorenz, 1963] Lorenz, E. (1963). Deterministic nonperiodic flow. J. Atmos. Sci., 20:130-141.
dc.relation[Losa, 2012] Losa, G. (2012). Fractals and their contribution to biology and medicine. Medicographia, 34:365-374.
dc.relation[Mamun-Ur-Rashid et al., 2017] Mamun-Ur-Rashid, S., Hossain, M., and Parvin, M. (2017). Numerical integration schemes for unequal data spacing. Am. J. Appl. Math., 2:48-56.
dc.relation[Mandelbrot, 1967] Mandelbrot, B. (1967). How long is the coast of britain? Statistical Self-Similarity and Fractional Dimension, 156:636-638.
dc.relation[Mandelbrot and HudsonStrogatz, 2004] Mandelbrot, B. and HudsonStrogatz, R. (2004). Practical Optimization. Ruin and Reward, Profile Books, London.
dc.relation[Martos et al., 2017] Martos, E., Lapuerta, F., Exp osito, M., and Sanmiguel-Rojas, J. (2017). Overestimation of the fractal dimension from projections of soot agglomerates. Powder Technol., 311:528-536.
dc.relation[Mathews and Fink, 2000] Mathews, J. and Fink, K. (2000). Numerical methods using MATLAB. P. HALL, ed., Madrid.
dc.relation[Milicic, 2018] Mili ci c, S. (2018). Box-counting dimensions of generalised fractal nests. Chaos, Solitons and Fractals, 113:125-134.
dc.relation[Moon et al., 2018] Moon, H., Youngjun, P., Jeong, C., and Lee, J. (2018). Forecasting electricity demand of electric vehicles by analyzing consumers charging patterns. Transportation Research Part D, 62:64-79.
dc.relation[Moon et al., 2014] Moon, P., Muday, J., Raynor, S., Schirillo, J., Boydston, C., Fairbanks, M., and Taylor, R. (2014). Fractal images induce fractal pupil dilations and constrictions. International Journal of Psychophysiology, 93(3):316-321.
dc.relation[Motlagh et al., 2019] Motlagh, C., Berry, A., and ONeil, L. (2019). Clustering of residential electricity customers using load time series. Applied Energy, 58:102-119.
dc.relation[Navascu es, 2013] Navascu es, M. (2013). Numerical integration of a ne fractal functions. J. Comput. Appl. Math., 252:169-176.
dc.relation[Pashminehazar et al., 2019] Pashminehazar, E., Kharaghani, R., and Tsotsas, A. (2019). Determination of fractal dimension and prefactor of agglomerates with irregular structure. Powder Technol., 343:765-774.
dc.relation[Poincar e, 1892] Poincar e, H. (1892). Les methodes nouvelles de la mecanique celeste. GAUTHIER-VILLARS ET FILS, Paris.
dc.relation[Popovic et al., 2018] Popovic, N., Radunovic, M., Badnjar, J., and Popovic, T. (2018). Fractal dimension and lacunarity analysis of retinal microvascular morphology in hypertension and diabetes. Microvascular Research, 118:36-43.
dc.relation[Ranjan et al., 2019] Ranjan, S., Mishra, J., and Palai, G. (2019). Analysing roughness of surface through fractal dimension: A review. Image and Vision Computing, 89:21-34.
dc.relation[Rezaee, 2019] Rezaee, A. (2019). Optimisation of demand response in electric power systems, a review. Renewable and Sustainable Energy Reviews, 103:308-319.
dc.relation[Rodriguez et al., 2016] Rodriguez, V., Prieto, B., Correa, H., Soracipa, M., Mendez, P., Bernal, C., Hoyos, O., Valero, A., and Velasco, R. (2016). Nueva metodologia de evaluacion del holter basada en los sistemas dinamicos y la geometria fractal: confirmacion de su aplicabilidad a nivel clínico. Rev. La Univ. Ind. Santander. Salud., 48:27-36.
dc.relation[Salvo and Piacquadio, 2017] Salvo, G. and Piacquadio, M. (2017). Multifractal analysis of electricity demand as a tool for spatial forecasting. Energy for Sustainable Development, 38:67-76.
dc.relation[Sierpinski, 1915] Sierpinski, W. (1915). Sur une courbe dont tout point est un point de ramification. Comptes Rendus, 160:302-305.
dc.relation[Silva and Florindo, 2019] Silva, P. and Florindo, J. (2019). A statistical descriptor for texture images based on the box counting fractal dimension. 528:1-13.
dc.relation[Soumya et al., 2018] Soumya, N., Jibitesh, M., Asimanada, K., and Gopinath, P. (2018). Fractal dimension of rgb color images. Elsevier-Optik, 162:196-205.
dc.relation[Strogatz, 2018] Strogatz, S. (2018). Nonlinear Dynamics and Chaos. Perseus Books Publisher, New York.
dc.relation[Swain et al., 2019] Swain, R., Roy, S., Mukherjee, P., and Sawkar, B. (2019). Fractal dimension and its translation into a model of gold spatial proxy. Ore Geol. Rev., 110:1-10.
dc.relation[Tabares-Ospina et al., 2020a] Tabares-Ospina, H., Angulo, F., and Osorio, M. (2020a). New method to calculate the energy and fractal dimension of the daily electrical load. Fractals, 28:2050135 (12 pages).
dc.relation[Tabares-Ospina et al., 2020b] Tabares-Ospina, H., Angulo, F., and Osorio, M. (2020b). A new methodology to analyze the dynamic of daily power demand with attractors into the mandelbrot set. Fractals, 28:2050003 (9 pages).
dc.relation[Tabares-Ospina et al., 2019] Tabares-Ospina, H., Candelo-Becerra, J., and Hoyos-Velasco, F. (2019). Fractal representation of the power demand based on topological properties of julia sets. Int. J. Electr. Comput. Eng., 4:31-38.
dc.relation[Tabares-Ospina and Osorio, 2020a] Tabares-Ospina, H. and Osorio, M. (2020a). Characterization of the resistive and inductive loads of an energy distribution systems with julia fractal sets. Fractals, 28:2050082 (9 pages).
dc.relation[Tabares-Ospina and Osorio, 2020b] Tabares-Ospina, H. and Osorio, M. (2020b). Methodology for the characterization of the electrical power demand curve, by means of fractal orbit diagrams on the complex plane of mandelbrot set. Discrete and Continuous Dynamical Systems Series B, 25:1895-1905.
dc.relation[Tabares-Ospina and Osorio, 2021] Tabares-Ospina, H. and Osorio, M. (2021). Algorithm to calculate the fractal dimension and numerical integration of fluctuating continuous functions. Fractals, tal:X-Y.
dc.relation[Wem et al., 2019] Wem, L., Zhou, K., and Yang, S. (2019). A shape-based clustering method for pattern recognition of residential electricity consumption. Journal of Cleaner Production, 212:475-488.
dc.relation[Willis, 2002] Willis, H. (2002). Spatial Electric Load Forecasting. M. Dekker, ed., New York.
dc.relation[Yang et al., 2019] Yang, F., Zhang, X., Ma, R., Yang, S., and Wand, X. (2019). Fractal dimension of concrete meso-structure based on x-ray computed tomography. Powder Technol., 350:91-99.
dc.relation[Yilmaz et al., 2019] Yilmaz, S., Chambers, J., and Patel, M. (2019). Comparison of clustering approaches for domestic electricity load profile characterisation - implications for demand side management. Energy, 180:665-677.
dc.relation[Yongfu, 2018] Yongfu, X. (2018). Fractal dimension of demolition waste fragmentation and its implication of compactness. Powder Technol., 339:922-929.
dc.relation[Yuan-jia and Ming-Yue, 2018] Yuan-jia, M. and Ming-Yue, Z. (2018). Fractal and multifractal features of the broadband power line communication signals. Comput. Electr. Eng, 72:566-576.
dc.relation[Zaletel et al., 2015] Zaletel, I., Ristanovic, D., Stefanovic, B., and Puska s, N. (2015). Modified richardsons method versus the box-counting method in neuroscience. Journal of Neuroscience Methods, 242:93-96.
dc.relation[Zhai, 2015] Zhai, M. (2015). A new method for short-term load forecasting based on fractal interpretation and wavelet analysis. International Journal of Electrical Power Energy Systems, 69:241-245.
dc.relation[Zhao et al., 2016] Zhao, Z., Zhu, J., and Xia, B. (2016). Multi-fractal fluctuation features of thermal power coal price in china. Energy, 117:10-18.
dc.rightsAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.titleMétodo para calcular el grado de fluctuación de la curva de demanda de potencia eléctrica usando dimensión fractal
dc.typeTrabajo de grado - Doctorado


Este ítem pertenece a la siguiente institución