scholarly journals Analog simulator of integro-differential equations with classical memristors

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
G. Alvarado Barrios ◽  
J. C. Retamal ◽  
E. Solano ◽  
M. Sanz
Keyword(s):  
Differential Equations ◽  
Error Control ◽  
Hydraulic Properties ◽  
Analog Computer ◽  
Operational Amplifiers ◽  
Electrical Network ◽  
Volterra Equations ◽  
Electrical Networks ◽  
State Variable ◽  
Nonlinear Volterra Equations

Abstract An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. We study the performance of these analog computers by simulating integro-differential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to 13% relative error for relevant timescales.

Computer Programming

SIMULATION ◽  
1965 ◽  
Vol 4 (5) ◽  
pp. 317-323 ◽  
Author(s):  
Joseph L. Hammond
Keyword(s):  
Differential Equations ◽  
Computer Program ◽  
Ordinary Differential Equations ◽  
Computer Programming ◽  
Characteristic Root ◽  
Analog Computer ◽  
State Variables ◽  
State Variable ◽  
Forcing Function ◽  
Derivatives Of

State variable techniques are reviewed and applied to analog computer programming. The concise rep resentation for ordinary differential equations made possible by this technique is used to formulate a gen eral program for all such equations. It is shown that an analog computer program based on state variables will not have redundant integrators. The fact that the use of state variables facilitates the choice of variables internal to an analog com puter program is illustrated by two techniques, namely, (1) a technique for avoiding derivatives of the forcing function in programming a large class of ordinary differential equations, and (2) a technique for simulating certain systems in such a way that the effect of each characteristic root is placed in evi dence.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

scholarly journals Optimal feeder reconfiguration in distributed generation environment under time-varying loading condition

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Yanrenthung Odyuo ◽  
Dipu Sarkar ◽  
Lilika Sumi
Keyword(s):  
Graph Theory ◽  
Distributed Generation ◽  
Spanning Tree ◽  
Voltage Stability ◽  
Electrical Network ◽  
List Type ◽  
Network Reconfiguration ◽  
Time Varying ◽  
Electrical Networks ◽  
Tree Algorithm

Abstract The development and planning of optimal network reconfiguration strategies for electrical networks is greatly improved with proper application of graph theory techniques. This paper investigates the application of Kruskal's maximal spanning tree algorithm in finding the optimal radial networks for different loading scenarios from an interconnected meshed electrical network integrated with distributed generation (DG). The work is done with an objective to assess the prowess of Kruskal's algorithm to compute, obtain or derive an optimal radial network (optimal maximal spanning tree) that gives improved voltage stability and highest loss minimization from among all the possible radial networks obtainable from the DG-integrated mesh network for different time-varying loading scenarios. The proposed technique has been demonstrated on a multiple test systems considering time-varying load levels to investigate the performance and effectiveness of the suggested method. For interconnected electrical networks with the presence of distributed generation, it was found that application of Kruskal's algorithm quickly computes optimal radial configurations that gives the least amount of power losses and better voltage stability even under varying load conditions. Article Highlights Investigated network reconfiguration strategies for electrical networks with the presence of Distributed Generation for time-varying loading conditions. Investigated the application of graph theory techniques in electrical networks for developing and planning reconfiguration strategies. Applied Kruskal’s maximal spanning tree algorithm to obtain the optimal radial electrical networks for different loading scenarios from DG-integrated meshed electrical network.

scholarly journals Predicting the influence of the non-sinusoidal network mode on power transformers

2019 ◽  
Vol 114 ◽  
pp. 04005
Author(s):  
Ngo Van Cuong ◽  
Lidiia I. Kovernikova
Keyword(s):  
Service Life ◽  
Electric Power ◽  
Power Quality ◽  
Electrical Equipment ◽  
Operating Conditions ◽  
Transformer Oil ◽  
Power Transformers ◽  
Electrical Network ◽  
Electrical Networks ◽  
Current Harmonics

The parameters of electrical network modes often do not meet the requirements of Russian GOST 32144-2013 and the guidelines of Vietnam. In the actual operating conditions while there is the non-sinusoidal mode in electrical networks voltage and current harmonics are present. Harmonics result in overheating and damage of power transformers since they cause additional active power losses. Additional losses lead to the additional heat release, accelerating the process of insulating paper, transformer oil and magnetic structure deterioration consequently shortening the service life of a power transformer. In this regard there arises a need to develop certain scientific methods that would help demonstrate that low power quality, for instance could lead to a decrease in the electrical equipment service life. Currently we see a development of automated systems for continuous monitoring of power quality indices and mode parameters of electrical networks. These systems could be supplemented by characteristics calculating programs that give out a warning upon detection of the adverse influence of voltage and current harmonics on various electrical equipment of both electric power providers and electric power consumers. A software program presented in the article may be used to predict the influence of voltage and current harmonics on power transformers.

Study of the influence of overvoltage on the quality of electricity in energy systems.

2020 ◽  
Vol 23 (2) ◽  
pp. 52-58
Author(s):  
S. SKRYPNYK ◽  
Keyword(s):  
Power Supply ◽  
Fire Hazard ◽  
Lightning Discharge ◽  
Quality Standard ◽  
Normal Operation ◽  
Electrical Network ◽  
Modern World ◽  
Electrical Networks ◽  
The World

Our world with its high technologies has long been deeply dependent on the quality of electricity supply. In most countries of the world there are national power grids that combine the entire set of generating capacity and loads. This network provides the operation of household appliances, lighting, heating, refrigeration, air conditioning and transport, as well as the functioning of the state apparatus, industry, finance, trade, health services and utilities across the country. Without this utility, namely electricity, the modern world simply could not live at its current pace. Sophisticated technological improvements are firmly rooted in our lives and workplaces, and with the advent of e-commerce began the process of continuous transformation of the way individuals interact with the rest of the world. But with the achievement of intelligent technologies, an uninterrupted power supply is required, the parameters of which exactly meet the established standards. These standards maintain our energy security and create a reliable power system, that is maintaining the system in a trouble-free state. Overvoltage is the deviation of the rated voltage from the value of the corresponding quality standard (frequency, sinusoidal voltage and compliance of harmonics). Overvoltage in terms of fire hazard is one of the most dangerous emergency modes of electrical equipment, which causes conditions that in most cases are sufficient for the occurrence of fire hazards (exceeding the allowable voltage leads to disruption of normal operation or possible ignition). Against the background of deteriorating engineering systems, increased power consumption and poor maintenance, power supply of electrical installations, the main causes of overvoltage in electrical networks are thunderstorms (atmospheric overvoltage), switching switches, uneven phase load in electrical networks, etc. The physical picture of internal overvoltage is due to oscillatory transients from the initial to the established voltage distributions in the conductive sections due to the different situation in the electrical circuit. In the conditions of operation of electric networks planned, mode or emergency situations are possible. Therefore, the ranges of overvoltage are determined by the range from several hundred volts to tens and hundreds of kilovolts, and depend on the types of overvoltage. Atmospheric overvoltage is considered to be one of the most dangerous types of emergency modes of operation of the electrical network. This overvoltage occurs as a result of lightning discharge during precipitation by concentrating electricity on the surface of the object, the introduction of potential through engineering networks and

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