Semistate models of electrical circuits including memristors

In this paper we present several semistate or differential‐algebraic models arising in nodal analysis of nonlinear circuits including memristors. The goal is to characterize the tractability index of these models under strict passivity assumptions, a key issue for the numerical simulation of circuit dynamics. We show that the main model, which combines memristors' fluxes and charges, is index two. From a technical point of view, this result is based on the use of a projector along the image of the leading matrix, in contrast to previous index analyses. For charge‐controlled memristors, the elimination of fluxes yields an index one system in topologically nondegenerate circuits, and an index two model otherwise. Analogous results are also proved to hold for flux‐controlled memristors. Our framework accommodates coupling effects among resistors, memristors, capacitors and inductors. Copyright © 2010 John Wiley & Sons, Ltd.     

Determination of initial conditions in active RLC networks

A new method is described of determining the initial values of state variables in active RLC networks. This method utilizes neither the conservation principle of charges and fluxes nor the theory of distributions. An RLC active network is assumed to be formed at t = 0 by joining or disconnecting the elements that are contained in it, this operation being performed by the use of a set of switches. The new method is based on the consideration of switches as independent sources, and the state equations are extended to cover this situation, and their solution at t = 0⁺ gives the initial conditions that have been sought. Further, the new method is applicable to any state-space formulation techniques used.     

一种基于回路电流法的有源配电网潮流算法

提出一种基于回路电流法的主动配电网三相潮流算法,并提出风机等多种分布式电源在该算法中的计算模型。首先建立配电网络对应的图,然后将基本回路电流、变压器原边支路电压、非恒阻抗负荷支路电压、分布式电源支路电压、异步电机正序负序电压、转差率作为未知量,列写回路KVL方程、变压器原副边电流方程、负荷功率平衡方程以及分布式电源相关方程,推导Jacobian矩阵,并利用牛顿法求解方程。该方法不需要PV节点转化为PQ节点的过程,也不需要将环路解列及复杂的节点编号,没有对Jacobian矩阵进行简化和近似,具有二阶收敛性。算例表明,所提方法计算速度快,能够处理所有常见的分布式电源,具有较强环路处理能力,且比前推回推法有更好的收敛性。     

Loop equation formulation for switched capacitor networks containing nullors

A method is given for determining the loop equations of an ideal active switched capacitance (SC) network containing switches, capacitors and nullors. These equations are obtained directly by row-column operations on the passive unswitched loop elastance matrix. the results are extended for the P- phase case. It is shown that the loop charges can be solved for and that the branch voltages can be obtained from the loop charges.     

A novel linear equivalent circuit of a transformer winding considering the frequency-dependence of the impedances

A new methodology for the representation of a transformer winding or any set of magnetically coupled coils by means of an equivalent circuit is presented in this paper. This circuit is suitable for the representation of the frequency-behavior of a system of coils at high frequencies and it consists of RL coupled circuit elements. The frequency-behavior representation of the actual impedances is accomplished by means of additional RL loops. Therefore, the circuit synthesis theory takes a step beyond the RL Foster or Cauer equivalent circuits, which were developed to represent only a single inductive element. Starting from the proposed equivalent circuit, the matrix equation of the system of coupled inductive branches is derived and their equivalence with the characteristic equations of the real system is proved. Finally, the method is applied to the modeling of transformer windings.     

Concurrent analogue fault simulation,the equation formulation aspect

Fault simulation is an essential tool for developing test patterns for circuits. Because the potential number of faults in a circuit is potentially very large, computational efficiency is an important consideration. In the digital domain, concurrent fault simulation is well‐established as an efficient tool. For analogue circuits, fault simulation is often performed by repeated insertion of possible faults and resimulation of the circuit. Consequently, methods for efficient concurrent analogue fault simulation are attracting attention. A review of existing methods of concurrent analogue fault simulation shows that most are based on a similar fundamental perturbation of the original fault‐free circuit equations, although the methods differ in the procedure applied after the circuit equations are formulated. We develop here a comprehensive set of element stamps, describing faulty elements, enabling effective and routine equation formulation for faulty circuits. These may be used no matter what method of fault simulation is later applied. These stamps are used in a new technique for concurrent analogue fault simulation, based on modified nodal analysis. A significant improvement in efficiency, compared with other methods, is demonstrated. Copyright © 2004 John Wiley & Sons, Ltd.     

Calculation of transient processes in electrical circuits using Chebyshev polynomials

Transient electromagnetic processes in electrical systems present a significant risk to machines and influence the reliability of relay protection; therefore, the investigation of these processes is important. Transient modeling in transformers is presently done by construction and solution of state equations for magnetoelectrical equivalent schemes that bring together the electric and magnetic circuits of these devices, taking into account the interaction with each other. Modeling of these processes can be quite long when using modern software. An aim of the given work is development of more fast-acting method of calculation of electromagnetic transients, using a polynomial approximation of the solution, and also development of scheme model of method that creates convenience for engineers in modeling. A method of calculation of transients in electric circuits is developed on the basis of expansion of the solution of state equations in series of orthogonal Chebyshev polynomials. A scheme interpretation of the developed method is offered. It is shown that, in the special equivalent scheme, Kirchhoff’s laws apply to images of currents and magnetic fluxes as vectors containing the values of coefficients of decomposition of these values by Chebyshev polynomials. The given method allows replacement of operations with instantaneous values of currents by operations with direct currents in the presented equivalent scheme. Transient calculation via the suggested method in a single-phase transformer processor is twice as fast as with well-known methods. The presented method is especially appropriate for transient calculation in magnetoelectrical circuits, since it allows the use of voltage sources controlled by the current derivative for easy calculation of the integrals of solutions.     

The relation of Tellegen's theorem to the continuous field equations revisited

Tellegen's theorem for networks is directly derived from Maywell's equations. As for general circuits including capacitors and inductances, non‐vanishing displacement currents and temporally varying magnetic fluxes are present, in the presented approach domains containing lumped elements are treated such that the utilization of an electric potential and of Kirchhoff's current law can be maintained in the considered field domain. The procedure works for the general form of Tellegen's theorem including nonlinear elements and relating topologically equal but otherwise different networks. Copyright © 2010 John Wiley & Sons, Ltd.     

海上风电场柔性直流输电变流器的无源性控制策略

由于海上风能并网直流输电变流器模型本身存在非线性强耦合特性,常规PI调节器控制方式需调节的参数较多,难以获得理想的动态特性.提出利用非线性系统无源性理论.将变流器两相同步旋转坐标系下的数学模型以拉格朗日方程形式表达,验证被控对象为严格无源系统,选取光滑可微的正定存储函数作为Lyapunov函数,满足控制系统在原点渐近稳...     

Eddy currents and electrical surface charges

In eddy current calculations, the displacement current in the non‐conducting space surrounding the eddy current region is usually neglected. This assumption enforces that the electric charge density and the accompanying normal components of the eddy current density on the surface of the eddy current region must vanish. If the field exiting source currents are not accompanied by charges this assumption may yield acceptable results for the eddy current distribution. However, if the field exiting source currents are accompanied by charges, this assumption may lead to totally wrong results for the current distribution in the eddy current region. An example is given which makes plain this point. To obtain correct results it is not necessary to employ the full set of Maxwell's equations capable to describe wave propagation phenomena also outside the eddy current region. It is shown in the paper that by replacing the displacement current density in the field describing equations by a specifically chosen current density function makes it possible to determine eddy currents and surface charges within the quasi‐stationary calculation scheme for arbitrary field exciting source currents which may or may not be accompanied by charges. The solution obtained in this way is shown to be unique. Copyright © 2003 John Wiley & Sons, Ltd.     

Multifrequency approach to fault diagnosis

This paper deals with multiple-fault diagnosis for linear analogue circuits. the proposed approach is based on multifrequency measurements of some voltage (transfer function) at the accessible output port and can be used for multiple-fault location. It uses certain algebraic invariant properties of the transfer function with respect to the set of faulty elements. Computationally this approach reduces checking the problem of multiple-fault diagnosis to one of the existence or non-existence of a common solution of two systems of linear equations; this amounts to the finding of the rank of a matrix. These linear equations are derived via symbolic representation of the measured voltage (transfer function) accessible for measurements. A numerical example of the application of such an approach is given.     

Two algorithms for obtaining sparse loop matrices

This paper deals with the problem of obtaining a linearly independent set of loop matrix equations, whose nonzero pattern is as sparse as possible. Unlike existing procedures, based on trees and associated fundamental loops, the two algorithms proposed in this paper attempt to find as short as possible loops by means of systematic breadth-first searches. Linear independence of the resulting loops is assured by forcing each loop to contain a characteristic branch that cannot belong to future or past loops, respectively. Such a branch plays the role of links in fundamental loops, providing more flexibility in the way loops are closed. Experimental results on benchmark systems show that the proposed methods yield loop matrices that are much sparser than those provided by existing methods.     

An interval method for finding all operating points of non-linear resistive circuits

A new method for finding the set of all d.c. operating points of non-linear electronic circuits is suggested. it is applicable in the case where the circuit equations are written in the hybrid-representation form. In the general case, the non-linear elements involved may be described by non-monotone continuous characteristics. The method suggested is based on interval analysis techniques. Unlike other non-interval methods, this approach guarantees that all operating points will be found within prescribed accuracy in a finite number of steps. The computational efficiency of the present method is illustrated by a numerical example.     

A method of analogue-digital multiple fault diagnosis

This paper develops an algorithm for multiple fault diagnosis of analogue-digital circuits. By sequentially partitioning the devices into those ‘assumed good’ and those ‘under test’, it is possible to develop a set of fault diagnosis equations which account for the special nature of digital components. A modified Newton-Raphson solution is then described which incorporates a digital state hypothesis testing scheme in the solution of the fault diagnosis equations for each partition. After solving for the input-output characteristics of the devices under test, a Boolean decision algorithm is used to analyse the test results of each partition and thus sequentially arrive at the set of faulty elements. A generic condition for diagnosability in terms of the circuit topology is given. Two examples are included to illustrate the technique.     

Block Diagrams: A Tutorial Alternative to Dynamical Analogies

Educational advantages and disadvantages of dynamical analogy and block-diagram models for interdisciplinary systems are discussed. If the system equations are known, a block-diagram is a useful tutorial alternative to the conventional dynamical analogy. It is easily drawn and yields a direct, graphical representation of the system equations with block elements that are not required to be physical elements of a specific discipline. Block diagrams illustrate system equations and processes quite differently from dynamical analogies and thereby provide new insights into system performance. They can also be used as alternative representations for linear circuits so that, in principle, it is possible to convert any dynamical analogy into a block diagram. A practical example is given wherein a combined electrical, mechanical, and acoustical system, normally studied using dynamical analogies, is modeled and analyzed with the aid of block diagrams Several interesting technical aspects of this specific, yet typical, interdisciplinary system are assessed.     

Coordination of directional relays without generating all circuits

A novel method is proposed for obtaining a minimum break point set for computer-aided coordination of directional relays in a power system. This very simple technique uses only fundamental circuits of the system graph for determining a minimum set of such break points. The procedure is very fast as it does not require generation of all circuits     

继电保护运行整定中计算分支系数的快速方法

目前电力系统继电保护整定计算软件中计算分支系数的常用方法是进行不同运行方式的故障计算,得到保护支路和配合支路的电流,从而得到分支系数。为了提高继电保护运行整定的速度和效率,根据序电流的分布只取决于该序网的结构而与其他序网无关,推导出了一种仅与序网的节点阻抗矩阵有关无需故障电流计算的分支系数的快速计算方法,并针对影响分支系数的不同因素介绍了一些加快措施。编程实践证明,该方法大大提高了继电保护运行整定的速度和效率。     

基于回路电流法的双抽头单相电机的网络方程

借助于异步电机的等值电路,采用了与传统的交轴磁场法和旋转磁场法不同的分析方法。该方法通用性强,适于分析定子绕组具有各种不同连接方式的异步电机的稳态运行性能,并能列写出便于计算机辅助计算矩阵方程。以定子绕组连接复杂的双抽头单相电机为例,该方法把该电机的定子电路分成了2个回路和6条支路,选择其中的1条支路作为基准支路,转子绕组向基准支路中的绕组折算,各支路绕组中的正序与逆序感应电势当作流控电压源进行处理,然后由回路电流法列写出了计算电机性能的网络方程,为验证计算结果,给出了1台双抽头单相电扇电机某些电流与电压的计算值,并与实测值作了比较,计算值与实测值的相互吻合说明了网络方程的正确性。     

用于提高输电能力的TCSC选址和定容方案

支路传输功率、节点电压等的越限是制约系统输电能力提高的重要因素,为此文章采用连续潮流模型,在临界运行点推导了输电能力对支路电抗灵敏度的数学表达式,提出根据此灵敏度排序结果确定可控串联补偿器(thyristor controlled series capacitor,TCSC)安装地点的新方法。该方法中,TCSC安装位置确定以后,将安装TCSC之前发生越界的不等式约束在其边界值处用等式形式表示出来,并设定为已知条件,将TCSC对其所要安装支路的补偿度设定为一个新的未知量,扩展常规潮流方程,以求取扩展潮流不匹配函数的最小值为目标,计算支路的最优补偿度。对IEEE30节点和IEEE118节点系统的仿真计算结果表明该文所提出的选址和定容方法是有效的。     

Elementary proofs of some classical stability criteria

Classical stability results and test on the stability of a given polynomial are proved and derived using a simple continuity property. The resulting proofs given of the Hermite-Bieler theorem and the Routh and Jury tests are elementary and full of insight. The proofs allow the instructor to present these fundamental topics of control theory to undergraduates in an elementary, rational, and meaningful way rather than as mere sets of rules and formulae