Efficient dominant eigensystem computation using nodal equations

In this paper, alternative methods are developed for computing the smallest, the largest and a given subset of the largest eigenvalues associated with linear time‐invariant circuits. The proposed methods resort to the solution of DC or AC adjoint circuits, for which conventional nodal analysis can be adopted. Experimental results obtained with test cases comprising over 500 state variables show substantial computational savings with respect to standard algorithms, based on the system matrix A arising in the state‐space formulation. Copyright © 2008 John Wiley & Sons, Ltd.     

Time‐domain properties of reactive dual circuits

The present work explores some effects of the replacement of capacitors by inductors and vice versa in state and semistate models of lumped circuits. Such a replacement, when performed together with an inversion of the capacitance and inductance matrices, yields a transformation of the form λ→λ^?1 in the system spectra. In the semistate context, this covers in particular extremal cases in which null eigenvalues or infinite ones with higher index appear in the matrix pencil associated with the model; these cases describe certain pathological circuit configurations. This approach leads to a discussion of new properties of strictly passive circuits; specifically, from the known fact that the index of strictly passive circuits does not exceed two, we derive that the index of null eigenvalues in this setting cannot exceed one. This precludes in particular Takens‐Bogdanov degeneracies, defined by an index‐two double‐zero eigenvalue, in strictly passive circuits. Although the results are addressed in a linear context, they can be extended via linearization to non‐linear problems, as it is the case in the transformation of singularity‐induced bifurcation phenomena into steady bifurcations discussed at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Wave digital simulation of passive systems in linear state‐space form

This paper deals with wave digital modeling of passive state‐space models. The set of differential equations must be of linear state‐space form, but all parameters can be time‐variant and/or nonlinear. For such state‐space models, a canonical internally passive reference circuit is presented and used for deriving wave digital structures. In order to show the usability, special solutions for important basic linear time‐variant models are compared with wave digital simulation results. Moreover, the wave digital modeling of a nonlinear and time‐variant oscillator is discussed. Especially for a lossless oscillator an implementation is proposed, which preserves energy under finite‐arithmetic conditions. This is verified by comparing simulation results with the analytical solution of a gravity pendulum. Copyright © 2009 John Wiley & Sons, Ltd.     

An efficient algorithm for small signal stability analysis using the Arnoldi and S-matrix methods

This paper proposes an efficient algorithm for small signal stability analysis by means of the Arnoldi method with an S-matrix transformation. In the proposed algorithm, the Arnoldi method evaluates several eigenpairs of large-scale matrices with less execution time. The S-matrix transformation constructs dominant eigenvalues corresponding to low damped oscillation modes. The combined use of these techniques enables us to calculate exclusively the critical eigenvalues of large-scale power systems efficiently. The Arnoldi method has the specific feature that it can obtain eigenvalues successively from the outer part of their distribution. By making use of this characteristic, the spectral transformation can be simplified, thus improving calculation efficiency. The proposed method is also useful in understanding the shape of the spectrum by investigating all of the eigenvalues obtained, including nonconverged eigenvalues. The algorithm has been successfully applied to a large-scale power system which has 220 generating units and 3000 state variables. © 1998 Scripta Technica. Electr Eng Jpn, 121(4): 38–47, 1997     

Sparse approximate inverse preconditioning of deflated block‐GMRES algorithm for the fast monostatic RCS calculation

A sparse approximate inverse (SAI) preconditioning of deflated block‐generalized minimal residual (GMRES) algorithm is proposed to solve large dense linear systems with multiple right‐hand sides arising from monostatic radar cross section (RCS) calculations. The multilevel fast multipole method (MLFMM) is used to accelerate the matrix–vector product operations, and the SAI preconditioning technique is employed to speed up the convergence rate of block‐GMRES (BGMRES) iterations. The main purpose of this study is to show that the convergence rate of the SAI preconditioned BGMRES method can be significantly improved by deflating a few smallest eigenvalues. Numerical experiments indicate that the combined effect of the SAI preconditioning technique that clusters most of eigenvalues to one, coupled with the deflation technique that shifts the rest of the smallest eigenvalues in the spectrum, can be very beneficial in the MLFMM, thus reducing the overall simulation time substantially. Copyright © 2008 John Wiley & Sons, Ltd.     

Synthesizing variant impedances in SPICE. A fast solution for powerelectronics and electric power systems simulations

The Simulation Program with Integrated Circuit Emphasis (SPICE) is a program widely used to simulate electric circuits. Characteristics such as versatility, large component libraries, integration of schematic edition, simulation and analyses have made it popular. As many students use this program early on, there is a natural tendency to continue using it in power electronics, electrical drives and electric power system courses. SPICE was initially developed to simulate integrated circuits. Therefore, sometimes the program parameters and components must be adapted to power circuits and systems. For example, the tolerances and component parameters have to be changed. Variant impedances frequently are present in electrical/electronic circuits. For example, an incandescent bulb is a power-variant resistance. A thermistor is a resistance that varies according to the temperature. An ideal thyristor controlled reactor (TCR), used to control voltage in electric power systems, is a variable inductance that changes its value depending on a control signal. A thyristor controlled series capacitor (TCSC) or a static reactive power compensator are ideally modeled as variable capacitances. Simulating such circuits requires defining the sub-circuits that, at their terminals, behave like the desired variant impedance     

A matrix pencil approach to the local stability analysis of non‐linear circuits

This paper addresses local stability issues in non‐linear circuits via matrix pencil theory. The limitations of the state–space approach in circuit modelling have led to semistate formulations, currently framed within the context of differential‐algebraic equations (DAEs). Stability results for these DAE models can be stated in terms of matrix pencils, avoiding the need for state–space reductions which are not advisable in actual circuit simulation problems. The stability results here presented are applied to electrical circuits containing non‐linear devices such as Josephson junctions or MOS transistors. Copyright © 2004 John Wiley & Sons, Ltd.     

Teaching Introductory Circuits Using the Theory of Distributions and the Convolution Algebra

In this paper we describe what we believe to be an innovation in the teaching of electrical engineering, that is the use of the theory of distributions and the convolution algebra in an introductory circuits course. Teaching the course in this way eliminates the contradiction in the usual defmition of the unit impulse, permits immittance to be defined in the time domain, and facilitates passage from the time domain to the frequency domain. The theory goes far beyond the case of basic circuits and applies to any linear time invariant system. Using distributions, the product of convolution becomes a powerful tool in solving circuit equations; the initial conditions are introduced automatically. It is the authors' belief that in a number of years most linear circuits and systems courses will be taught following the approach presented here.     

A general tool for circuit analysis based on wavelet transform

This paper deals with a generalized method for the time‐domain solution of electrical networks. The aim is to explore a new technique for the numerical simulation of circuits considering linear, time‐varying and non‐linear cases. By using the wavelet transform of the electrical quantities, differentiation and integration in the time domain are replaced by matrix multiplication. Then, the classical circuit differential equations obtained by mesh‐current, node‐voltage or state variables methods are transformed in algebraic equations. The numerical efficiency of wavelets makes the method effective for a fast and reliable numerical circuit simulation. Comparisons with analytical solutions and PSPICE simulations are presented in order to evaluate the numerical characteristics of the proposed method. Copyright © 2000 John Wiley & Sons, Ltd.     

A wavelet‐based piecewise approach for steady‐state analysis of power electronics circuits

Simulation of steady‐state waveforms is important to the design of power electronics circuits, as it reveals the maximum voltage and current stresses being imposed upon specific devices and components. This paper proposes an improved approach to finding steady‐state waveforms of power electronics circuits based on wavelet approximation. The proposed method exploits the time‐domain piecewise property of power electronics circuits in order to improve the accuracy and computational efficiency. Instead of applying one wavelet approximation to the whole period, several wavelet approximations are applied in a piecewise manner to fit the entire waveform. This wavelet‐based piecewise approximation approach can provide very accurate and efficient solution, with much less number of wavelet terms, for approximating steady‐state waveforms of power electronics circuits. Copyright © 2006 John Wiley & Sons, Ltd.     

Hyperchaotic behaviour of two bi‐directionally coupled Chua's circuits

In this paper, a non‐linear bi‐directional coupling of two Chua's circuits is presented. The coupling is obtained by using polynomial functions that are symmetric with respect to the state variables of the two Chua's circuits. Both a transverse and a tangent system are studied to ensure a global validity of the results in the state space. First, it is shown that the transverse system is an autonomous Chua's circuit, which directly allows the evaluation of the conditions on its chaotic behaviour, i.e. the absence of synchronization between the coupled circuits. Moreover, it is demonstrated that the tangent system is also a Chua's circuit, forced by the transverse system; therefore, its dynamics is ruled by a time‐dependent equation. Thus, the calculus of conditional Lyapunov exponents is necessary in order to exclude antisynchronization along the tangent manifold. The properties of the transverse and tangent systems simplify the study of the coupled Chua's circuits and the determination of the conditions on their hyperchaotic behaviour. In particular, it is shown that hyperchaotic behaviour occurs for proper values of the coupling strength between the two Chua's circuits. Finally, numerical examples are given and discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Non‐linear circuit modelling via nodal methods

We discuss in this paper several interrelated nodal methods for setting up the equations of non‐linear, lumped electrical circuits. A rather exhaustive framework is presented, aimed at surveying different approaches and terminologies in a comprehensive manner. This framework includes charge‐oriented, conventional, and hybrid systems. Special attention is paid to so‐called augmented node analysis (ANA) models, which somehow articulate the tableau and modified node analysis (MNA) approaches to non‐linear circuit modelling. We use a differential–algebraic formalism and, extending previous results proved in the MNA context, we provide index‐1 conditions for augmented systems, which are shown to be transferred to tableau models. This approach gives, in particular, precise conditions for the feasibility of certain state‐space reductions. We work with very general assumptions on device characteristics; in particular, our approach comprises a wide range of resistive devices, going beyond voltage‐controlled ones. Copyright © 2005 John Wiley & Sons, Ltd.     

Comparison of modeling techniques in circuit variability analysis

Three nonlinear reduced‐order modeling approaches are compared in a case study of circuit variability analysis for deep submicron complementary metal‐oxide‐semiconductor technologies where variability of the electrical characteristics of a transistor can be significantly detrimental to circuit performance. The drain currents of 65 nm N‐type metal‐oxide‐semiconductor and P‐type metal‐oxide‐semiconductor transistors are modeled in terms of a few process parameters, terminal voltages, and temperature using Kriging‐based surrogate models, neural network‐based models, and support vector machine‐based models. The models are analyzed with respect to their accuracy, establishment time, size, and evaluation time. It is shown that Kriging‐based surrogate models and neural network‐based models can be generated with sufficient accuracy that they can be used in circuit variability analysis. Numerical experiments demonstrate that for smaller circuits, Kriging‐based surrogate modeling yields results faster than the neural network‐based models for the same accuracy whereas for larger circuits, neural network‐based models are preferred as, in all metrics, better performance is obtained. Within‐die variations for an XOR circuit are analyzed, and it is shown that the nonlinear reduced‐order models developed can more effectively capture the within‐die variations than the traditional process corner analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

基于JACOBI-DAVI DSON方法的小干扰稳定性分析中关键特征值计算

提出了一种大规模电力系统小干扰稳定性分析的有效方法。应用Jacobi-Davidson方法求取系统状态矩阵的关键特征子集。该方法在搜索子空间中挑选出想要的特征值和特征向量的近似值，然后用与当前近似特征向量正交的子空间上的修正方程的解扩展搜索子空间，从而得到想要的特征值和特征向量的更好近似。算法中使用了电力系统线性化模型中的增广状态矩阵进行相应面向稀疏的计算，可准确求解修正方程，以保证算法具有渐进二次收敛速度。将提出的方法在46机系统上进行了试验，结果表明该方法灵活，稳定性好，能有效地求出系统的关键特征子集。     

Circuit models for symmetric systems of linear equations

Electric circuit models are constructed for general symmetric systems of linear algebraic equations. The modelling procedure is based on the node‐voltage analysis of linear circuits under steady‐state conditions. These electric circuit models can, in principle, be physically realized and used for the solution of the systems of equations by simply measuring the electric voltage at the circuit nodes. Copyright © 2000 John Wiley & Sons, Ltd.     

电力系统特征值与状态变量对应关系分析

电力系统中特征值与状态变量之间的对应关系的分析对研究系统的详细动态特性具有十分重要的意义。文中首先对研究系统稳定问题的小扰动方法进行了分析,认为非线性动力系统的代数方程约束和各状态量之间的耦合关系是造成系统动态特性十分复杂的重要原因,进而利用同伦函数的概念给出了一种确定线性化系统中特征值与状态变量对应关系的方法。用此方法对简单电力系统做了分析,得出了令人满意的结果。     

A fast power loss calculation method for long real time thermal simulation of IGBT modules for a three‐phase inverter system

A fast power losses calculation method for long real time thermal simulation of IGBT module for a three‐phase inverter system is presented in this paper. The speed‐up is obtained by simplifying the representation of the three‐phase inverter at the system modelling stage. This allows the inverter system to be simulated predicting the effective voltages and currents whilst using large time‐step. An average power losses is calculated during each clock period, using a pre‐defined look‐up table, which stores the switching and on‐state losses generated by either direct measurement or automatically based upon compact models for the semiconductor devices. This simulation methodology brings together accurate models of the electrical systems performance, state of the art‐device compact models and a realistic simulation of the thermal performance in a usable period of CPU time and is suitable for a long real time thermal simulation of inverter power devices with arbitrary load. Thermal simulation results show that with the same IGBT characteristics applied, the proposed model can give the almost same thermal performance compared to the full physically based device modelling approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of a self‐regulated,self‐excited,brushless three‐phase synchronous generator,which includes the effect of core losses

This paper presents a novel analysis of a self‐regulated, self‐excited, brushless three‐phase synchronous generator, which includes the effect of core losses. The core losses are modeled by equivalent core loss resistances connected to additional windings on the generator's magnetic coupling model. A magnetic circuit is drawn from the magnetic coupling model, and an electrical equivalent circuit of the generator is derived by utilizing a duality between the magnetic and electric circuits. Using this equivalent circuit, the generator's steady‐state performance is theoretically predicted, and the results are verified through experiment. In addition, the power losses during power generation are analyzed quantitatively. The proposed analysis takes into account the nonlinearity of the exciting impedances due to magnetic saturation. © 2000 Scripta Technica, Electr Eng Jpn, 131(2): 51–60, 2000