Networks, multipoles and multiports

Reibiger, Albrecht

doi:10.1109/ecctd.2013.6662191

Cited by 5 publications

(2 citation statements)

References 51 publications

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“…Multipoles are introduced as elements with ordered external terminals (poles) consisting of a network and a family of terminal classes. The terminal classes are disjoint subsets of the node set of the corresponding network [23]. The rest of the nodes (after extraction of poles) in the structure of each structural element are named internal nodes of this element.…”

Section: Basic Terms and Definitionsmentioning

confidence: 99%

Mathematical Modeling of the Dynamics of Linear Electrical Systems with Parallel Calculations

Cieślik

2021

Energies

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The dynamics of power systems is often analyzed using real-time simulators. The basic requirements of these simulators are the speed of obtaining the results and their accuracy. Known algorithms (backward Euler or trapezoidal rule) used in real-time simulations force the integration time step to be reduced to obtain the appropriate accuracy, which extends the time of obtaining the results. The acceleration of obtaining the results is achieved by using parallel calculations. The paper presents an algorithm for mathematical modeling of the dynamics of linear electrical systems, which works stably with a relatively large integration time step and with accuracy much better than other algorithms widely described in the literature. The algorithm takes into account the possibility of using parallel calculations. The proposed algorithm combines the advantages of known methods used in the analysis of electrical circuits, such as nodal analysis, multi-terminal electrical component theory, and transient states analysis methods. However, the main advantage over other algorithms is the use of the method based on average voltages in the integration step (AVIS method). The attention was focused on the presentation of the scientifically acceptable general principle offered to mathematical modeling of dynamics of linear electrical systems with parallel computations. However, the evidence of its effective application in the analysis of the dynamics of electric power and electromechanical systems was indicated in the works carried out by the team of authors from the Institute of Electrical Engineering UTP University of Science and Technology in Bydgoszcz (Poland).

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Section: Basic Terms and Definitionsmentioning

confidence: 99%

Mathematical Modeling of the Dynamics of Linear Electrical Systems with Parallel Calculations

Cieślik

2021

Energies

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“…The concept of the indefinite admittance matrix representation for the description of a linear multi-pole goes back to Shekal [8] and can also be transferred in a modified form to the description of the terminal behaviour of nonlinear multi-poles [9]. This concept can be applied to the analysis and parametrization of crossbar arrays for VMM.…”

Section: Indefinite Admittance Matrix Representation Of Crossbar Arraymentioning

confidence: 99%

Parametrization of resistive crossbar arrays for vector matrix multiplication

Haase

2019

Proceedings of the 9th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools

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Vector Matrix Multiplication (VMM) is a fundamental operation in machine learning algorithms focused on artificial neural networks and also many simulation codes. Implementations based on crossbar arrays provide a promising approach to perform this operation with an analogue circuit. In comparison to purely digital solutions, significant improvements in processing speed and power consumption can be expected when applying this approach. However, securing the accuracy is more difficult than in the digital case. Primary reasons include nonlinearities of essential resistive elements and non-zero resistances of wiring lines. Many publications have dealt with this topic in the recent years analysing the different influences in different ways. We provide a unified approach based on the well-known indefinite admittance matrix concept for the description of the terminal behaviour of analogue multi-poles for the parametrization of crossbar arrays and for the estimation of computational error limits. This paper describes work in progress. It illustrates the procedures through a number of examples using modelling and simulation capabilities of VHDL-AMS. This behavioural modelling language seems particularly suitable for investigations on tailored implementations using VMM. It combines the support of analogue mixed modelling and simulation with the facility to generate scalable architectures. Aspects of solving this task with Modelica are also discussed. Furthermore, it is also shown how symbolic methods might be used to consider resistances of wiring lines in the parametrization of crossbar arrays. CCS Concepts• Computing methodologies ➝ Model development and analysis

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Foundations of network theory

Reibiger

2011

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -Different axiomatizations of network theory are considered. Kirchhoff networks are regarded with priority. Multipole and multiport networks are introduced as alternative variants. Additionally, Minty and Paynter networks, which are always dualizable are discussed briefly. The latter are special cases of Kirchhoff as well as of multiport networks. This paper seeks to discuss these issues. Design/methodology/approach -The paper develops network theory inside of set theory, i.e. networks, multipoles, etc. are defined as objects of set theory. As such objects we use preferably ordered pairs, ordered triples, etc. The objects of network theory are then separated from the class of all these set theoretical objects by means of some defining conditions. These conditions are the axioms of our approaches to network theory. Findings -It is shown that all presented variants of axiomatizations can be developed on the basis of a uniform representation for the time functions for voltages and currents. All these variants allow interdisciplinary applications of network theory and they can be generalized to multidimensional networks. An interesting byproduct is the relationship between multiport networks, networks in Belevitch normal form, Paynter networks, and bond graphs. Originality/value -For applications it is essential that Kirchhoff and multipole networks are with respect to their modeling capability of equal value. But from the foundational point of view the multipole terminology has a number of crucial disadvantages compared with that based on Kirchhoff networks. This fact is important both for the conception of circuit simulation software packages and for the development of basic circuit theory curricula. IntroductionApart from the Faraday-Maxwell theory of electromagnetic fields, the theory of electrical networks is one of the basic disciplines of electrical engineering. The theory of networks is even the elder of the two theories. Its beginnings go back to the work of G.S. Ohm and G.R. Kirchhoff. Unlike field theoretic descriptions network theoretical models describe the processes taking place in an electrical circuit by finite families of time-functions.Kirchhoff's papers mark the start for the development of systematic methods for network analysis. He considered circuits composed exclusively of two-pole devices such as metallic resistors and galvanic elements connected by wires with negligible resistance values. He introduced a description of such circuits by means of oriented graphs and constitutive equations. In recent terminology, the circuit models created by him could be classified as resistive, uncoupled, time-invariant, and -except for independent voltage sources -as linear. On this basis, he has proved for the first time theorems on the number of linear independent loop and node equations. Additionally, he has developed combinatorial rules for the computation of symbolic solutions for networks of the class mentioned above. With his researches he has founded

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Networks, multipoles and multiports

Cited by 5 publications

References 51 publications

Mathematical Modeling of the Dynamics of Linear Electrical Systems with Parallel Calculations

Mathematical Modeling of the Dynamics of Linear Electrical Systems with Parallel Calculations

Parametrization of resistive crossbar arrays for vector matrix multiplication

Foundations of network theory

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