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Methodology for the characterization of the electrical power demand curve, by means of fractal orbit diagrams on the complex plane of Mandelbrot set

  • * Corresponding author: Hector A. Tabares-Ospina

    * Corresponding author: Hector A. Tabares-Ospina 

Agencia de Educación Superior de Medellín (SAPIENCIA)

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  • The present article proposes a new geometric space in the complex plane of the Mandelbrot set, framed in the diagram of orbits and attractors, to characterize the dynamics of the curves of the demand of daily electrical power, with the purpose of discovering other observations enabling the elevation of new theoretical approaches. The result shows a different method to evaluate the dynamics of the electric power demand curve, using fractal orbital diagrams. This method is a new contribution that extends universal knowledge about the dynamics of complex systems and fractal geometry. Finally, the reader is informed that the data series used in this article was used in a previous publication, but using a different fractal technique to describe its dynamics.

    Mathematics Subject Classification: Primary: 62P30; Secondary: 97M50.

    Citation:

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  • Figure 1.  Graphical representation of the Mandelbrot set

    Figure 2.  Relationship between Mandelbrot set and orbital diagrams

    Figure 3.  Algorithm with the steps used to obtain the fractal of the power demand

    Figure 4.  The typical demand curves of active and reactive electric power

    Figure 5.  Electric power demand curve plotted in the first quadrant of the complex plane of Mandelbrot set

    Figure 6.  Representation of orbit diagram of power demand in the first quadrant of the complex plane of M set

    Table 1.  Daily load demand represented by hour

    Hour $ P $ $ Q $ $ P_{pu} $ $ Q_{pu} $ $ NumOrbs $
    $ 00:00:00 $ $ 889 $ $ 371 $ $ 0.222 $ $ 0.092 $ $ 5 $
    $ 01:00:00 $ $ 834 $ $ 405 $ $ 0.287 $ $ 0.101 $ $ 5 $
    $ 02:00:00 $ $ 792 $ $ 337 $ $ 0.197 $ $ 0.082 $ $ 5 $
    $ 03:00:00 $ $ 790 $ $ 324 $ $ 0.199 $ $ 0.081 $ $ 5 $
    $ 04:00:00 $ $ 804 $ $ 323 $ $ 0.201 $ $ 0.080 $ $ 3 $
    $ 05:00:00 $ $ 925 $ $ 355 $ $ 0.231 $ $ 0.088 $ $ 5 $
    $ 06:00:00 $ $ 1041 $ $ 482 $ $ 0.260 $ $ 0.120 $ $ 9 $
    $ 07:00:00 $ $ 1105 $ $ 556 $ $ 0.276 $ $ 0.139 $ $ 9 $
    $ 08:00:00 $ $ 1191 $ $ 610 $ $ 0.297 $ $ 0.152 $ $ 18 $
    $ 09:00:00 $ $ 1256 $ $ 704 $ $ 0.314 $ $ 0.176 $ $ 30 $
    $ 10:00:00 $ $ 1309 $ $ 744 $ $ 0.327 $ $ 0.186 $ $ 32 $
    $ 11:00:00 $ $ 1366 $ $ 775 $ $ 0.341 $ $ 0.193 $ $ 50 $
    $ 12:00:00 $ $ 1385 $ $ 793 $ $ 0.346 $ $ 0.198 $ $ 53 $
    $ 13:00:00 $ $ 1356 $ $ 774 $ $ 0.339 $ $ 0.193 $ $ 44 $
    $ 14:00:00 $ $ 1337 $ $ 759 $ $ 0.334 $ $ 0.189 $ $ 38 $
    $ 15:00:00 $ $ 1350 $ $ 774 $ $ 0.337 $ $ 0.193 $ $ 41 $
    $ 16:00:00 $ $ 1336 $ $ 773 $ $ 0.334 $ $ 0.193 $ $ 41 $
    $ 17:00:00 $ $ 1312 $ $ 749 $ $ 0.328 $ $ 0.187 $ $ 41 $
    $ 18:00:00 $ $ 1287 $ $ 687 $ $ 0.321 $ $ 0.171 $ $ 41 $
    $ 19:00:00 $ $ 1420 $ $ 683 $ $ 0.355 $ $ 0.170 $ $ 89 $
    $ 20:00:00 $ $ 1389 $ $ 660 $ $ 0.351 $ $ 0.167 $ $ 89 $
    $ 21:00:00 $ $ 1311 $ $ 605 $ $ 0.327 $ $ 0.151 $ $ 41 $
    $ 22:00:00 $ $ 1175 $ $ 544 $ $ 0.293 $ $ 0.136 $ $ 18 $
    $ 23:00:00 $ $ 1030 $ $ 489 $ $ 0.257 $ $ 0.122 $ $ 14 $
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