Electrical Network Analysis Research Articles

Randomized flow model and centrality measure for electrical power transmission network analysis

Commonly used centrality measures identify the most important elements in networks of components, based on the assumption that flow occurs in the network only along the shortest paths. This is not so in real networks, where different operational rules drive the flow. For this reason, a different model of flow in a network is considered here: rather than along shortest paths only, it is assumed that contributions come essentially from all paths between nodes, as simulated by random walks. Centrality measures can then be coherently defined. An example of application to an electrical power transmission system is presented.

Minimum cycle bases

We consider the problem of computing exact or approximate minimum cycle bases of an undirected (or directed) graph G with m edges, n vertices and nonnegative edge weights. In this problem, a {0, 1} (−1,0,1}) incidence vector is associated with each cycle and the vector space over F 2 (Q) generated by these vectors is the cycle space of G . A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G . Cycle bases of low weight are useful in a number of contexts, for example, the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. There exists a set of Θ( mn ) cycles which is guaranteed to contain a minimum cycle basis. A minimum basis can be extracted by Gaussian elimination. The resulting algorithm [Horton 1987] was the first polynomial-time algorithm. Faster and more complicated algorithms have been found since then. We present a very simple method for extracting a minimum cycle basis from the candidate set with running time O ( m 2 n ), which improves the running time for sparse graphs. Furthermore, in the undirected case by using bit-packing we improve the running time also in the case of dense graphs. For undirected graphs we derive an O ( m 2 n /log n + n 2 m ) algorithm. For directed graphs we get an O ( m 3 n ) deterministic and an O ( m 2 n ) randomized algorithm. Our results improve the running times of both exact and approximate algorithms. Finally, we derive a smaller candidate set with size in Ω( m ) ∩ O ( mn ).

Cycle bases in graphs characterization, algorithms, complexity, and applications

Cycles in graphs play an important role in many applications, e.g., analysis of electrical networks, analysis of chemical and biological pathways, periodic scheduling, and graph drawing. From a mathematical point of view, cycles in graphs have a rich structure. Cycle bases are a compact description of the set of all cycles of a graph. In this paper, we survey the state of knowledge on cycle bases and also derive some new results. We introduce different kinds of cycle bases, characterize them in terms of their cycle matrix, and prove structural results and a priori length bounds. We provide polynomial algorithms for the minimum cycle basis problem for some of the classes and prove A P X -hardness for others. We also discuss three applications and show that they require different kinds of cycle bases.

New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over $\mathbb{F}_{2}$ generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k≥1, we give (2k−1)-approximation algorithms with expected running time O(kmn 1+2/k +mn (1+1/k)(ω−1)) and deterministic running time O(n 3+2/k ), respectively. Here ω is the best exponent of matrix multiplication. It is presently known that ω<2.376. Both algorithms are o(m ω ) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Θ(m ω ) bound. We also present a 2-approximation algorithm with expected running time $O(m^{\omega}\sqrt{n\log n})$ , a linear time 2-approximation algorithm for planar graphs and an O(n 3) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

Passivity and passification analysis of uncertain discrete‐time fuzzy systems

PurposePassivity theory is closely related to both electrical network and circuit analysis methods. The purpose of this paper is to try to establish some basic results on the uncertain discrete‐time fuzzy systems.Design/methodology/approachApplying the classical and effective Lyapunov function method and the powerful linear matrix inequality toolbox in MATLAB, the paper provides some sufficient conditions to verify the passivity of the uncertain discrete‐time fuzzy systems, or to passify such a system.FindingsFor uncertain discrete‐time fuzzy systems, its passivity can be easily verified numerically, and its passification can also be fulfilled.Practical implicationsA very effective and convenient criterion is provided to test the passivity of practical nonlinear discrete‐time system or to passify it.Originality/valueThis paper first treats this topic on uncertain discrete‐time fuzzy systems and obtains some important results.

Electric Power Network Decision Effects

Electric power networks pose design decision complexities characteristic of other large engineered systems. A great number of decisions must be made by many decision-makers, some decisions are made in a sequential manner over very long time periods, objectives compete, a large number of feasible solutions exist, and one decision-maker's actions can impact others, whose reactions in turn can affect the original decision-maker. This article addresses these issues, with a focus on the problem of determining when and how to consider decisions as an individual decision-maker vs. as part of a networked system. An electric power network analysis is presented, where local plant managers must decide when to replace existing power generation equipment (coal, oil, natural gas, nuclear, and hydropower) with an equivalent number of 12-megawatt natural gas–fueled microturbine generators. Competing objectives include cost, reliability, and environmental impact.

FEM analysis of electromagnetic transients in linear networks

AbstractThis paper describes a new general solution method when modeling electromagnetic transients in single networks with linear lossy transmission lines in the time domain using the finite element method. Based on FEM and the generalized trapezoidal rule a novel numerical procedure for the system of the telegraph equations is presented. The presented technique enables to make a simple algorithm for the analysis of electrical network with linear lossy transmission lines. The proposed method for electrical network transient's analysis including lossy transmission lines in time domain has been successfully tested and compared to the analytical solution. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Fluid Layer Trapped Between a Plane, Circular Membrane and an Axisymmetrically Curved, Smooth Backing Wall: Analytical Model of the Dynamic Behaviour

Current electrostatic transducers are designed with a planar perforated backing electrode while nowadays some authors suggest that a non planar backing wall would enhance their performances. Accurate analytic results for these new shapes of backing electrode are not available until now whereas current applications (metrology, miniaturisation) arise which need more refined modelling. Therefore the present paper aims at providing an analytical description of the strong coupling between a fluid layer trapped between an axisymmetrically curved smooth backing wall and a circularvibrating membrane (the thickness of the fluid layer depends on the radial coordinate) using modelling wherein viscosity, heat conduction, inertia and compressibility of the fluid are considered, beyond realistic boundary conditions (no slip condition and no temperature variations near the walls). Solutions are given as the sum of an expansion on eigenfunctions of the membrane in vacua and an extended power series (using Frobenius method) to overcome the limitations of a standard electrical equivalent network analysis in the frequency range of interest (up to 100kHz for circular membranes approximately one millimetre in diameter). The results obtained provide tools for optimising the design of such small electrostatic transducers.

Minimizing Effective Resistance of a Graph

The effective resistance between two nodes of a weighted graph is the electrical resistance seen between the nodes of a resistor network with branch conductances given by the edge weights. The effective resistance comes up in many applications and fields in addition to electrical network analysis, including, for example, Markov chains and continuous-time averaging networks. In this paper we study the problem of allocating edge weights on a given graph in order to minimize the total effective resistance, i.e., the sum of the resistances between all pairs of nodes. We show that this is a convex optimization problem and can be solved efficiently either numerically or, in some cases, analytically. We show that optimal allocation of the edge weights can reduce the total effective resistance of the graph (compared to uniform weights) by a factor that grows unboundedly with the size of the graph. We show that among all graphs with $n$ nodes, the path has the largest value of optimal total effective resistance and the complete graph has the least.

An $\tilde{O}(m^{2}n)$ Algorithm for Minimum Cycle Basis of Graphs

We consider the problem of computing a minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over $\mathbb{F}_{2}$ generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Minimum cycle basis are useful in a number of contexts, e.g. the analysis of electrical networks and structural engineering. The previous best algorithm for computing a minimum cycle basis has running time O(m ω n), where ω is the best exponent of matrix multiplication. It is presently known that ω<2.376. We exhibit an O(m 2 n+mn 2log n) algorithm. When the edge weights are integers, we have an O(m 2 n) algorithm. For unweighted graphs which are reasonably dense, our algorithm runs in O(m ω ) time. For any ε>0, we also design an 1+ε approximation algorithm. The running time of this algorithm is O((m ω /ε)log (W/ε)) for reasonably dense graphs, where W is the largest edge weight.

Pervasive Grid for Large-Scale Power Systems Contingency Analysis

Optimal control and management of power systems require extensive analyses of phenomena that can compromise their operation in order to evaluate their impact on the security and reliability levels of the electrical networks. For complex networks, this process, known as power systems contingencies analysis, requires large computational efforts, whereas computation times should be less than a few minutes for the information to be useful. Even though many architectures based on conventional parallel and distributed systems have been widely proposed in the literature, they are characterized by low extensibility, reusability, and scalability, and so, they require a sensible hardware upgrade when more computational resources are necessary. This event is not infrequent in power systems where the constant growth of the electrical network complexity and the need for larger security and reliability levels of the plant infrastructures lead to the need of more detailed contingency analysis in shorter times. To address this problem, this paper proposes a pervasive grid approach to define a user-friendly software infrastructure for data acquisition from electrical networks and for data processing in order to simulate possible contingencies in a real electrical network. The grid infrastructure adopts a brokering service, based on an economy-driven model, to satisfy the quality of service constraints specified by the user (i.e., a time deadline to simulate the contingencies). This paper also discusses the deployment of the infrastructure on a network of heterogeneous clusters and PCs to compute the contingency analysis of a realistic electrical network. The experimental results obtained demonstrate the effectiveness of the proposed solution and the potential role of grid computing in supporting intensive computations in power systems

A distributed simulation based approach for detailed and decentralized power system transient stability analysis

This paper presents a distributed computing approach for piecewise transient stability (T/S) analysis of large-scale electrical networks using Diakoptics and large change sensitivity (LCS) concepts. Detailed T/S analysis in a secure and federative manner based on geographically decomposition using local computational resources is the greatest benefit realized by this method of analysis. In this way, with the minimum communications between subnetworks the same results as the conventional untorn T/S analysis can be achieved. Since the bottleneck in distributed computation is low speed network communication, a new latency exploitation technique is introduced for numerically solving system differential equations. The technique uses different step size in each subnetwork to decrease the number of numerical operations and data communications for a given total simulation time. The proposed distributed T/S method is implemented successfully across computer networks and its performance is studied using a 14 bus IEEE test system and some various large-scale networks up to 3000 buses. The presented results are compared with those obtained from conventional untorn T/S simulation.

05/02086 Frequency domain transient analysis of electrical networks including non-linear conditions

05/02086 Frequency domain transient analysis of electrical networks including non-linear conditions

Analysis of nonlinear electric networks by means of differential algebraic equations solvers

In this article, we introduce a mixed method for the application of nonlinear electric networks in order to establish a system description, which can be easily formulated and simulated with the aid of the so-called differential algebraic equations (DAE) solvers of the mathematical software such as OCTAVE [3], SCILAB [4] or MATLAB [5]. The method has the advantage that it finds a system description of a nonlinear network relatively easily. As examples an electronic flipflop circuit and a three-phase current converter are analyzed.

Frequency domain transient analysis of electrical networks including non-linear conditions

This paper describes a method for the analysis of electromagnetic transients in multiphase transmission networks using the Numerical Laplace Transform. The proposed procedure is based on the superposition principle and is applied to switching and non-linear elements modeling. Switching operations are modeled as initial condition problems by means of injected current sources. In the case of non-linear elements, a piece-wise linear approximation is made, which reduces the problem to a sequence of switching operations. Several applications and comparisons with results obtained with the EMTDC and ATP programs are presented.

Gain-sensitivity analysis for cascaded two-ports and application to distributed-parameter amplifiers

Enhancement of a gain-sensitivity analysis of electrical networks is presented by computing gain sensitivities with respect to network parameters. A simple and versatile method. The so-called chain-sensitivity matrix is presented and compared with the current method in the literature, gain factorization, for the gain sensitivities of the cascaded networks. Analytical formulas are derived to calculate gain sensitivities of the T and Π types of distributed-parameter amplifiers with respect to the physical length l and characteristic impedance Z0, rather than using a time-intensive computer-based perturbation method. The numerical results of the T- and Π-type amplifiers for the design targets of noise figure Freq = 0,46 dB (⇔ 1, 12) input VSWR Vireq = 1, power gain GTreq = 12 dB (⇔ 15, 86) and the bandwidth B = 2 GHz − 11 GHz are given in comparison to each other. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14: 462–474, 2004.

Reaction Route Graphs. I. Theory and Algorithm

A theory and algorithm for reaction route (RR) network analysis is developed in analogy with electrical networks and is based on the combined use of RR theory, graph theory, and Kirchhoff's laws. The result is a powerful new approach of “RR graphs” that is useful in not only topological representation of complex reactions and mechanisms but, when combined with techniques of electrical network analysis, is able to provide revealing insights into the mechanism as well as the kinetics of the overall reactions involving multiple elementary reaction steps including the effect of topological constraints. Unlike existing graph theory approaches of reaction networks, the approach developed here is suitable for linear as well as nonlinear kinetic mechanisms and for single and multiple overall reactions. The theoretical approach for the case of a single overall reaction involving minimal kinetic mechanisms (unit stoichiometric numbers) is developed in Part I of this series followed by its application to examples of...

HYPERNION NUMBERS AND THEIR USE IN THE ANALYSIS OF NETWORKS DRIVEN BY NONSINUSOIDAL SOURCES

A method of using hypercomplex numbers for the analysis of linear electric circuits with nonsinusoidal voltages and currents has been proposed. Similar to the complex number method for circuits with sinusoidal voltages and currents, the proposed method reduces the analysis of nonsinusoidal circuits to the analysis of direct-current circuits. A special system of hypercomplex numbers, called hypernions, has been created in order to obtain a new efficient method for analyzing nonsinusoidal networks. This system is interesting in that it expands the concept of numbers and attaches meaning to equations and transformations involving discontinuous functions and makes it possible to describe various non-Euclidean spaces. It is shown that the proposed method of analysis of linear nonsinusoidal electric networks makes it possible to carry out numerical calculations for complex circuits by using standard software.

Analysis of linear networks in the Walsh transformation basis

The paper shows the possibility of analysis of linear electric networks in the basis of the Walsh functions.

Dynamic harmonic evolution using the extended harmonic domain

A novel methodology is presented in this paper for conducting transient and steady-state analysis of electric networks containing nonlinearities and switching plants components. The method is termed the extended harmonic domain (EHD) method as may be seen as an extension of the harmonic domain (HD) method used in steady-state analysis. It is shown in the paper that EHD is a natural approach for conducting dynamic and steady-state studies of the evolution of harmonics in power circuits containing nonlinear components and flexible AC transmission systems (FACTS) devices. It is also shown in the paper that EHD provides a suitable basis for extending the well-known steady-state power quality indices to the transient range. To illustrate the use of the theory, a three-phase linear circuit and a three-phase PWM-STATCOM are modeled using EHD. The results are compared against those provided by industry standard tools as PSCAD/EMTDC and Matlab.