Fractal representation of the power 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.

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TOPOLOGICAL PROPERTIES OF FRACTAL JULIA SETS RELATED TO THE SIGNS OF REAL AND REACTIVE ELECTRIC POWERS

Fractals ◽

10.1142/s0218348x1950066x ◽

2019 ◽

Vol 27 (04) ◽

pp. 1950066 ◽

Cited By ~ 2

Author(s):

HÉCTOR A. TABARES-OSPINA ◽

JOHN E. CANDELO-BECERRA

Keyword(s):

Reactive Power ◽

Julia Sets ◽

Electrical Circuit ◽

Topological Properties ◽

Real Power ◽

The Real ◽

Complex Power ◽

Complex Planes ◽

The Mathematical Model ◽

Clear Relation

This paper focuses on applying fractal Julia sets to observe the topological properties related to the signs of the real and reactive electric powers. To perform this, different power combinations were used to represent the fractal diagrams with an algorithm that considers the mathematical model of Julia sets. The study considers three cases: the first study considers the change of real power when the reactive power is fixed; the second study deals with the change of the reactive power when the real power is fixed; and finally, the third study contemplates that both real and reactive powers change. Furthermore, the fractal diagrams of the power in the four quadrants of the complex plane are studied to identify the topological properties for each sign. A qualitative analysis of the diagrams helps identify that complex power loads present some fractal graphic patterns with respect to the signs considered in the different quadrants of the complex planes. The diagrams represented in the complex planes save a relation in the forms and structure with other points studied, concluding that the power is related to other figures in other quadrants. Thus, this result allows a new study of the behavior of power in an electrical circuit by showing a clear relation of the different fractal diagrams obtained by the Julia sets.

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

Fractals ◽

10.1142/s0218348x20500036 ◽

2019 ◽

Vol 28 (01) ◽

pp. 2050003 ◽

Cited By ~ 1

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.

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Voltage Instability Analysis for Electrical Power System Using Voltage Stabilty Margin and Modal Analysis

Indonesian Journal of Electrical Engineering and Computer Science ◽

10.11591/ijeecs.v3.i3.pp655-662 ◽

2016 ◽

Vol 3 (3) ◽

pp. 655 ◽

Cited By ~ 4

Author(s):

Ahmad Fateh Mohamad Nor ◽

Marizan Sulaiman ◽

Aida Fazliana Abdul Kadir ◽

Rosli Omar

Keyword(s):

Power System ◽

Modal Analysis ◽

Electric Power ◽

Reactive Power ◽

Research Work ◽

Load Flow ◽

Electric Power System ◽

Instability Analysis ◽

Real Power ◽

Voltage Instability

Voltage instability analysis in electric power system is one of the most important factors in order to maintain the equilibrium of the power system. A power system is said to be unstable if the system is not able to maintain the voltage at all buses in the system remain unchanged after the system is being subjected to a disturbance.The research work presented in this paper is about the analysis of voltage instability of electric power system by using voltage stability margin (VSM), load real power (P) margin, reactive power (Q) margin, reactive power-voltage (QV) and real power-voltage (PV) modal analysis. IEEE 30-bus system has been chosen as the power system. The load flow analysis are simulated by using Power World Simulator software version 16. Both QV and PV modal analysis were done by using MATLAB application software.

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Understanding the Reactive Power Problem and a Mechanical Solution Using Peaking or Retired Generators

Volume 1: Fuels and Combustion, Material Handling, Emissions; Steam Generators; Heat Exchangers and Cooling Systems; Turbines, Generators and Auxiliaries; Plant Operations and Maintenance; Reliability, Availability and Maintainability (RAM); Plant Systems, Structures, Components and Materials Issues ◽

10.1115/power2014-32101 ◽

2014 ◽

Cited By ~ 1

Author(s):

Randall M. Attix ◽

D. M. Chamberlin

Keyword(s):

Electric Power ◽

Delivery System ◽

Reactive Power ◽

Power Delivery ◽

Prime Mover ◽

Power Circuit ◽

Real Power ◽

Circuit Components ◽

Inherent Nature ◽

Power Problem

Reactive power is an unwanted but unavoidable part of alternating current electric power delivery systems. Governed by the laws of physics, it occurs due to the inherent nature of the components of these systems. This article develops an understanding of reactive power and the control of it to reduce its adverse effects and to improve the efficiency of an electric power delivery system. The article begins by identifying and representing electric power circuit components, real power, and reactive power. These are then mathematically shown how they interact and affect the power delivery system. Control and mitigation of the effects of reactive power are then developed with emphasis on mechanical solutions using rotating machines. In particular, peaking or retired generators are identified for use as rotating condensers as well as new installations. A description of the gear type synchronous self-synchronizing (SSS) overrunning clutches used to connect and dis-connect a generator from the peaking prime mover or the retired generator from a starting system is included.

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Performance Investigation of D-Q Model for PI and Fuzzy Controller Based UPFC

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.573.310 ◽

2014 ◽

Vol 573 ◽

pp. 310-316 ◽

Cited By ~ 1

Author(s):

K. Poun Raj ◽

V. Raja Sekaren ◽

S. Selvaperumal ◽

N. Mageswari

Keyword(s):

Transmission Line ◽

Power Flow ◽

Reactive Power ◽

Power Transmission ◽

Fuzzy Controller ◽

Voltage Drop ◽

Electrical Power ◽

Unified Power Flow Controller ◽

Power Demand ◽

Real Power

– The unified power flow controller (UPFC) is the most versatile and complex power electronic equipment that has emerged as the indispensable equipment for the control and optimization of power flow in electrical power transmission system. In this manuscript is investigated the control of real and reactive power flow through a transmission line with the use of UPFC at the sending end. Computer simulation using MATLAB Simulink is done and the behavior of the UPFC is studied. In the UPFC based control of transmission line parameter control systems, it is observed that whenever the SSSC sources some real power into the transmission line it is manifested as a voltage drop across the DC link. Reactive power demand is indicated as fall in the bus bar AC voltage. The fall of the DC link voltage is an indication of real power demand from the receiving end. Similarly a fall of the bus bar AC voltage is an indication of reactive power demand from the receiving end. Fuzzy Logic and PI controllers are used in this works, the control of DC voltage, AC voltage and power transfer.

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Factual Power Loss Diminution by Enhanced Frog Leaping Algorithm

Journal of Applied Science, Engineering, Technology, and Education ◽

10.35877/454ri.asci112 ◽

2020 ◽

Vol 3 (2) ◽

pp. 114-118

Author(s):

Kanagasabai Lenin

Keyword(s):

Local Search ◽

Power Loss ◽

Reactive Power ◽

Test System ◽

Premature Convergence ◽

Speed Of Convergence ◽

Real Power ◽

The Real ◽

Simulation Results ◽

Power Problem

This paper proposes Enhanced Frog Leaping Algorithm (EFLA) to solve the optimal reactive power problem. Frog leaping algorithm (FLA) replicates the procedure of frogs passing though the wetland and foraging deeds. Set of virtual frogs alienated into numerous groups known as “memeplexes”. Frog’s position’s turn out to be closer in every memeplex after few optimization runs and certainly, this crisis direct to premature convergence. In the proposed Enhanced Frog Leaping Algorithm (EFLA) the most excellent frog information is used to augment the local search in each memeplex and initiate to the exploration bound acceleration. To advance the speed of convergence two acceleration factors are introduced in the exploration plan formulation. Proposed Enhanced Frog Leaping Algorithm (EFLA) has been tested in standard IEEE 14,300 bus test system and simulation results show the projected algorithm reduced the real power loss considerably.

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Short-term electric power demand forecastingusing a hybrid model of SARIMA and SVR

IOP Conference Series Earth and Environmental Science ◽

10.1088/1755-1315/619/1/012035 ◽

2020 ◽

Vol 619 ◽

pp. 012035

Author(s):

QiheLou ◽

QiLyu ◽

Zhixiong Na ◽

Dayan Ma ◽

Xiaoguang Ma

Keyword(s):

Electric Power ◽

Hybrid Model ◽

Power Demand ◽

Short Term

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EIGENVALUES OF FIBONACCI STOCHASTIC ADDING MACHINE

Stochastics and Dynamics ◽

10.1142/s0219493710002966 ◽

2010 ◽

Vol 10 (02) ◽

pp. 291-313 ◽

Cited By ~ 6

Author(s):

A. MESSAOUDI ◽

D. SMANIA

Keyword(s):

Julia Set ◽

Transition Operator ◽

Complex Numbers ◽

Topological Properties

In this work, we compute the eigenvalues of the transition operator associated to the Fibonacci stochastic adding machine. In particular, we show that the eigenvalues are connected to the set [Formula: see text] of complex numbers z where (z2, z) belongs to the filled Julia set of a particular endomorphism of ℂ2. We also study some topological properties of the set [Formula: see text].

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