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

2020 ◽  
Vol 25 (5) ◽  
pp. 1895-1905
Author(s):  
Héctor A. Tabares-Ospina ◽  
◽  
Mauricio Osorio ◽  
Keyword(s):  
Complex Plane ◽  
Demand Curve ◽  
Electrical Power ◽  
Mandelbrot Set ◽  
Power Demand

A NEW METHODOLOGY TO ANALYZE THE DYNAMIC OF DAILY POWER DEMAND WITH ATTRACTORS INTO THE MANDELBROT SET

Fractals ◽  
2019 ◽  
Vol 28 (01) ◽  
pp. 2050003 ◽  
Author(s):  
HÉCTOR A. TABARES-OSPINA ◽  
FABIOLA ANGULO ◽  
MAURICIO OSORIO
Keyword(s):  
Complex Plane ◽  
Reactive Power ◽  
Electrical Power ◽  
Mandelbrot Set ◽  
Power Demand ◽  
Load Curve ◽  
Load Demand ◽  
Fractal Space ◽  
Time Series Plot ◽  
Geometric Space

The time series plot of electricity daily load demand is seasonal as shown by its regular repetitive pattern during the same period each year. Its behavior is determined by phase-space diagrams that are able to identify any of the following states of the series: fixed point, periodic, or chaotic. The first two deal with predictable systems. This paper focuses on presenting a new methodology to analyze the dynamics of the series in reference by using the curve formed by attractors that move in the complex plane over the Mandelbrot set according to the law dictated by the load curve. Because electrical power is a variable, it is also defined in the complex plane with the components of active power on the real axis and reactive power on the imaginary axis. Therefore, electrical power facilitates a new field of analysis in Mandelbrot fractal space. The obtained temporal curve confirms that the profile of the electric power demand is also mapped with the new fractal geometric space of the Mandelbrot set, thus providing a new contribution that extends knowledge about the dynamics of systems in fractal geometry.

scholarly journals A Characterization of the Dynamics of Schröder’s Method for Polynomials with Two Roots

2021 ◽  
Vol 5 (1) ◽  
pp. 25
Author(s):  
Víctor Galilea ◽  
José M. Gutiérrez
Keyword(s):  
Nonlinear Equations ◽  
Complex Plane ◽  
Iterative Process ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Schröder’S Method

The purpose of this work is to give a first approach to the dynamical behavior of Schröder’s method, a well-known iterative process for solving nonlinear equations. In this context, we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schröder’s method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We conclude our study with a graphical gallery that allow us to compare the basins of attraction of Newton’s and Schröder’s method applied to some given polynomials.

scholarly journals A Fuzzy Logic Model for Hourly Electrical Power Demand Modeling

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 448
Author(s):  
Marco Antonio Islas ◽  
José de Jesús Rubio ◽  
Samantha Muñiz ◽  
Genaro Ochoa ◽  
Jaime Pacheco ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
New England ◽  
Electrical Power ◽  
Logic Model ◽  
Power Demand ◽  
Demand Modeling ◽  
Mapping Model ◽  
Fuzzy Logic Model ◽  
Radial Basis

In this article, a fuzzy logic model is proposed for more precise hourly electrical power demand modeling in New England. The issue that exists when considering hourly electrical power demand modeling is that these types of plants have a large amount of data. In order to obtain a more precise model of plants with a large amount of data, the main characteristics of the proposed fuzzy logic model are as follows: (1) it is in accordance with the conditions under which a fuzzy logic model and a radial basis mapping model are equivalent to obtain a new scheme, (2) it uses a combination of the descending gradient and the mini-lots approach to avoid applying the descending gradient to all data.

scholarly journals Power Generation In Nigeria: The Past, Present And The Future

2020 ◽  
pp. 1-8
Author(s):  
Adeoye Samuel ◽  
◽  
Oladimeji TT ◽  
Keyword(s):  
Power Generation ◽  
Renewable Energy ◽  
Renewable Energy Sources ◽  
Electrical Power ◽  
Electrical Energy ◽  
Power Imbalance ◽  
Power Demand ◽  
Electrical Power System ◽  
Hydro Power ◽  
The Future

The goal of power sector in Nigeria is to efficiently and reliably transmit electrical power to all parts of the country which are made up of thirty-six states of the federation and the federal capital territory. The constituents of electrical power system are the generation, transmission, distribution and the utilization of electrical energy. There is gross power imbalance between the generation and the required power demand which has culminated into a defective economy in the last three decades. This paper therefore examines the power imbalance between the generation and power demand by the consumers and therefore stresses the need to harness the opportunity of renewable energy generation close to the gap between the power generation and power demand. This will help in transmitting and distributing efficient, effective, reliable power to consumers and improve both human and capital development. The availability of renewable energy sources such as sun, wind and small hydro power will be explored for the future of power generation in the country to fill in the gap between power generation and demand in Nigeria

scholarly journals Caracterización en línea de la dinámica temporal de señales para el monitoreo del sistema eléctrico de potencia

2020 ◽  
pp. 26-34
Author(s):  
Francisco Román Lezama-Zárraga ◽  
Jorge de Jesús Chan-González ◽  
Meng Yen Shih ◽  
Roberto Carlos Canto-Canul
Keyword(s):  
Nonlinear Oscillations ◽  
Electrical Power ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Electrical Power System ◽  
Transient Phenomena ◽  
On Line ◽  
Measurement Units ◽  
Dynamic Phenomena

The characterization of dynamic phenomena is essential for monitoring the Electrical Power System subject to disturbances. This article proposes an On-line time systematic approach to analyze and characterize the temporal evolution of transient and nonlinear oscillations in these systems. Two methods are used; the first method is based on a local decomposition of the signal under study into orthogonal basis functions to obtain the dynamics of transient oscillations. Next, a second method is applied to those orthogonal basis functions to obtain analytical signals and characterize the instantaneous amplitude, phase and frequency attributes of the oscillations and determine a physical interpretation of the system’s behavior. The proposed methodology is a time-frequencyenergy analysis which can be applied to the timesynchronized Phasor Measurement Units measurements. The results demonstrate that the proposed methodology provide an accurate characterization of transient phenomena with non-stationary effects.

Characterization of Damping and Beating Effects Within the Aggregate Power Demand of Heterogeneous Thermostatically Controlled Loads

2015 ◽  
Author(s):  
Donald J. Docimo ◽  
Hosam K. Fathy
Keyword(s):  
Population Heterogeneity ◽  
Parameter Distribution ◽  
Population Parameter ◽  
Control Input ◽  
Power Demand ◽  
Response Dynamics ◽  
Parameter Heterogeneity ◽  
Thermostatically Controlled Loads ◽  
Aggregate Dynamics

This paper presents an analysis of the damping and beating effects within the aggregate power demand of heterogeneous thermostatically controlled loads (TCLs). Demand response using TCLs is an appealing method to enable higher levels of penetration of intermittent renewable resources into the electric grid. Previous literature covers the benefits of TCL population heterogeneity for control purposes, but the focus is solely on the damping observed in these systems. This work is, to the best of the authors’ knowledge, the first to characterize the combined damping and beating response of power demand versus the level of TCL population parameter heterogeneity. The forced aggregate dynamics of TCLs have been shown to be bilinear when set point temperature adjustment is used as a control input. This motivates the paper’s use of free response dynamics, which are linear, to characterize both the damping and beating phenomena. A stochastic parameter distribution is applied to the homogeneous power demand solution, furnishing an analytic expression for aggregate power demand. The resulting analysis shows that increasing parameter heterogeneity increases damping and shortens the beat period.

On Uniqueness of Dirichlet Series

2020 ◽  
Author(s):  
Bao Qin Li
Keyword(s):  
Analytic Continuation ◽  
Dirichlet Series ◽  
Finite Order ◽  
Half Plane ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Uniqueness Theorems

Abstract We give a characterization of the ratio of two Dirichelt series convergent in a right half-plane under an analytic condition, which is applicable to a uniqueness problem for Dirichlet series admitting analytic continuation in the complex plane as meromorphic functions of finite order; uniqueness theorems are given in terms of a-points of the functions.

Characterization of Piezoelectric Materials for Thermoacoustic Power Transduction

2008 ◽  
Author(s):  
A. Wekin ◽  
C. Richards ◽  
K. Matveev ◽  
M. Anderson
Keyword(s):  
Experimental Study ◽  
Piezoelectric Materials ◽  
Electrical Power ◽  
Power Production ◽  
Piezoelectric Transducers ◽  
Maximum Power ◽  
Small Scale ◽  
Thermoacoustic Engine ◽  
Thermoacoustic Engines

In this work an experimental study of the performance of piezoelectric transducers for power production from a small-scale thermoacoustic engine is presented. Four piezoelectric samples are identified and characterized. These samples are tested on a variable acoustic driver and electrical power produced is measured. Finally, the samples are tested on four experimental thermoacoustic engines to verify the results from the acoustic setup. The maximum power produced is 177 μW from a closed thermoacoustic engine coupled to a 15mm PZT disk.

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