Fractal representation of the power daily demand based on topological properties of Julia sets
In a power system, the load demand considers two components such as the real power (P) because of resistive elements, and the reactive power (Q) because inductive or capacitive elements. This paper presents a graphical representation of the electric power demand based on the topological properties of the Julia Sets, with the purpose of observing the different graphic patterns and relationship with the hourly load consumptions. An algorithm that iterates complex numbers related to power is used to represent each fractal diagram of the load demand. The results show some representative patterns related to each value of the power consumption and similar behaviour in the fractal diagrams, which allows to understand consumption behaviours from the different hours of the day. This study allows to make a relation among the different consumptions of the day to create relationships that lead to the prediction of different behaviour patterns of the curves.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Geometrical representation of real and reactive powers of load demand by orbit diagrams in the Mandelbrot set
This paper presents the geometrical representation of the load demand by using orbits diagrams in the Mandelbrot set, to identify changing behaviors during a day period of the real and reactive powers. To perform this, d…
Topological properties of fractal Julia sets related to the signs and magnitudes of the real and reactive powers
In AC electrical systems, the power depends on the real power (P) due to resistive elements and the reactive power (Q) due to the inductive and capacitive elements, which are commonly studied by using phasor and scalar m…
Techniques for multifractal spectrum estimation in financial time series
Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimat…
Time SeriesTime Series AnalysisShape-aware Sampling Matters in the Modeling of Multi-Class Tubular Structures
Accurate multi-class tubular modeling is critical for precise lesion localization and optimal treatment planning. Deep learning methods enable automated shape modeling by prioritizing volumetric overlap accuracy. However…
On the Limitations of Fractal Dimension as a Measure of Generalization
Bounding and predicting the generalization gap of overparameterized neural networks remains a central open problem in theoretical machine learning. There is a recent and growing body of literature that proposes the frame…
Generalization BoundsLearning TheoryModel OptimizationTopological Data Analysis