High‐order sensitivity invariants

The aim of the research reported in this paper is to extend the notion of invariant sensitivity sum, widely known for electrical networks, from first‐order sensitivities to high‐order sensitivities. The results are high‐order invariant sums of sensitivities of the first and the second kind, formulated for nonlinear lumped circuit, which consists of one‐port and two‐ports only. One‐ports are generalized resistances, capacitances, inductances, voltages, and current sources, whereas two‐ports are nonlinear generalizations of four types of controlled sources. It is observed that the invariant sums actually found for nonlinear lumped networks are generalizations of sums given earlier by authors for linear lumped networks. The article is illustrated by numerical sensitivity analysis of simple linear and nonlinear circuits. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficient estimation of adjoint‐variable S‐parameter sensitivities with time domain TLM

We present a novel algorithm for efficient estimation of S‐parameter sensitivities with the time‐domain transmission line modelling (TLM) method. The original electromagnetic structure is simulated using TLM to obtain the S‐parameters in the desired frequency band. For each port, an adjoint TLM simulation that runs backward in time is derived and solved. The sensitivities of the S‐parameters in the desired frequency band are estimated using only the original and adjoint simulations. For a structure with N_p ports and n designable parameters, our approach requires only N_p additional simulations regardless of n. This can be easily contrasted with the 2nN_p additional simulations required by the central difference approximation. Our algorithm is illustrated through the estimation of S‐parameter sensitivities with respect to the dimensions of waveguide discontinuities. Very good match is obtained between our sensitivity estimates and those obtained using central difference approximation. Copyright © 2005 John Wiley & Sons, Ltd.     

On models of fractal networks

A couple of iterative models for the theoretical study of fractal networks whose topologies are generated via iterated function systems is presented: a lumped‐parameter impedor‐oriented one and a two‐port‐network‐oriented one. With the former, the voltage and current patterns give a detailed understanding of the electromagnetic fields' self‐similar distribution throughout the network; on the other hand, model complexity exponentially increases with the prefractal iteration order. The latter ‘black‐box’ model only controls port‐oriented global parameters that are the ones commonly used in the integration of different electronic systems, and its complexity is independent of prefractal order. Sierpinski gasket and carpet topologies are reported as examples. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical synthesis of voltage‐mode even/odd‐nth‐order differential difference current conveyor and fully differential current conveyor II‐grounded resistor and capacitor universal filter structures

A complete definition of an odd/even‐nth‐order notch or band‐reject filter transfer function is presented. Based on the differences between the input voltage and (i) an nth‐order high‐pass; (ii) a traditional nth‐order notch; and (iii) an nth‐order all‐pass filtering transfer function, a systematic method has been proposed to derive a universal filter structure that can realize voltage‐mode odd/even‐nth‐order low‐pass, band‐pass, high‐pass, all‐pass and traditional notch filters. The intrinsic capability of voltage‐mode addition and subtraction of the two active elements, differential difference current conveyors and fully differential current conveyors, is used to advantage in the aforementioned synthesis procedure. Based upon the definition of an nth‐order notch or band‐reject filter transfer function proposed in this paper, the aforementioned universal one has been further extended to the newly defined nth‐order band rejection filter. The voltage and current tracking errors of the two active elements are compensated by varying the resistances of the proposed filter. Filtering feasibility, stability, component sensitivities, linear and dynamic ranges, power consumption, and noise are simulated using H‐Spice with 0.35 µm process. Compared to some of the recently reported universal biquads, the new one is shown to enjoy the lowest component sensitivities and the best output accuracy for all‐pass signals. Moreover, Monte Carlo and two‐tone tests for intermodulation linearity simulations are also investigated. Copyright © 2014 John Wiley & Sons, Ltd.     

Available energy of improper lossless LLTIP one‐ports

A method for evaluating the available energy of a class of black‐box circuit components is proposed. The class consists of those linear lumped time‐invariant passive one‐ports of any order that are improper and lossless. The approach requires the utilization of tools and techniques from the calculus of variations (Euler–Lagrange equations and natural transversality conditions) and involves rather demanding algebraic and integro‐differential manipulations. However, the final formula for the available energy has the simple structure of a quadratic form in the one‐port external state vector, relatively easy to use or to implement. The various steps of the approach developed are illustrated through examples. Furthermore, to evidence the difference between available energy and stored energy, two degenerate and one non‐degenerate open‐box one‐ports are discussed in some detail. Copyright © 2015 John Wiley & Sons, Ltd.     

Continuous howitt transformations and second order sensitivities

It is known that first order sensitivities can be updated for circuits which are generated by Howitt transformations. This result is extended to second order sensitivities, and a summed second-order sensitivity invariant is established.     

Time domain and steady‐state sensitivity of periodic switched networks to element changes

Switched periodic networks are widely used in power engineering and sensitivities of their steady‐state to element changes are of interest to the designers. The paper develops a method to obtain steady‐state sensitivities for networks in which semiconductor and other switching devices are modelled as ideal short circuits without additional elements. Such modelling has the advantage that switching transients need not be calculated and correct initial conditions after switching are obtained with only four integration steps. It is also shown that sensitivities need not be calculated during the process of reaching the steady‐state. Once the steady‐state is available, integration over two additional periods is sufficient to provide time domain steady state sensitivity to the element changes. Copyright © 1999 John Wiley & Sons, Ltd.     

Square‐root domain wave filters

In this paper the wave method is used for designing high‐order square‐root domain filters, which emulate the topology of the corresponding LC ladder prototypes. This is achieved by transposing the signal flow graph that corresponds to the wave equivalent of the elementary two‐port subnetwork in the linear domain to the corresponding one in the square‐root domain, by employing an appropriate set of complementary operators. As the equivalents of the other reactive elements are derived from the wave equivalent of the elementary subnetwork, by interchanging the terminals of the appropriate wave signals and/or using inverters, an advantage offered by the proposed technique is the modularity of the derived filter configurations. As an example, a fifth‐order lowpass square‐root domain wave filter was designed and its behaviour was studied through simulation results in order to demonstrate the validity of the proposed design technique. Copyright © 2006 John Wiley & Sons, Ltd.     

基于灵敏度计算的电力系统参数可辨识性分析

对于简单电力系统建模中参数可辨识性问题,以往采用解析方法可以进行分析。但对于大规模电力系统,解析方法难以进行。文中发现了电力系统参数的可辨识性与灵敏度之间的关系。提出先根据灵敏度的相位来判断参数能否唯一辨识,再根据灵敏度的大小来选择可辨识的重点参数,最后采用蚁群算法优化重点参数。通过算例分析,证明了上述方法的可行性。     

Time‐domain sensitivity analysis of planar structures using first‐order one‐way wave‐equation boundaries

An efficient adjoint variable method technique is developed for time‐domain sensitivity analysis of planar structures with transmission‐line modeling complemented by a first‐order one‐way wave‐equation absorbing boundaries. A backward‐running adjoint simulation is derived and solved. The validity of the technique is illustrated through three microstrip circuits. The examples demonstrate the efficiency and accuracy of the technique in comparison with the classical finite‐difference approaches to the estimation of the response sensitivities. Copyright © 2007 John Wiley & Sons, Ltd.     

电力系统动态灵敏度计算的伴随方程方法

提出了计算电力系统动态灵敏度的一种新方法。针对电力系统的某一性能指标函数，构造了系统的伴随方程。伴随方程是一组与系统动态方程规模相同的微分代数方程组。通过求解一次伴随方程，即可计算该动态性能指标关于所有可调参数的动态灵敏度系数，因而其计算效率约为直接法的np倍(np倍为系统可调参数的个数)。同时，在求解伴随方程时采用了因子表重用技术，有效地提高了计算效率。采用该方法，只需在常规的暂态稳定分析计算之外附加很小的计算量，即可求得系统的动态灵敏度系数。文中讨论了与伴随方程方法相关的、动态系统的一些基本特性，以及伴随方程的构造方法，并且给出了伴随方程方法的算法流程和数值实例。     

利用改进Rayleigh商逆迭代法进行大系统特定模式降阶

对大系统特定模式进行降阶计算.依据特征值灵敏度对系统状态矩阵A重新排序,仅保留与特定模式强相关的发电机组,使矩阵维数得以降低.由于降阶后矩阵一般为复数形式,把矩阵虚部作为实部的修正量.以实部的特定特征值作为初值,用改进Rayleigh商逆迭代格式准确计算.算例分析验证了该方法的有效性.     

Passivity‐based control for stabilization,regulation and tracking purposes of a class of nonlinear systems

In this paper, a new passivity‐based control (PBC) scheme based on state feedback is proposed in order to solve tracking, regulation and stabilization problems for a class of multi‐input multi‐output (MIMO) nonlinear systems expressed in the normal form, with time‐invariant parameters and locally bounded reference weakly minimum phase. For the proposed control scheme two new different state feedbacks, one non‐adaptive for the case when the system parameters are assumed to be known and the other adaptive for the case of unknown parameters, are developed. For the adaptive case it is assumed that the unknown parameters appear linearly in the equations. Analysis of the transient behaviour of the proposed control schemes is presented through the simulation of two examples. Copyright © 2006 John Wiley & Sons, Ltd.     

基于灵敏度与相关性的综合负荷模型参数优化辨识策略

综合负荷建模及其参数辨识是电力系统分析研究的重点和难点之一。为了研究综合负荷模型参数对模型响应的影响以及参数之间的动态关联,提出一种基于参数灵敏度与相关性分析的综合负荷模型优化辨识策略。首先,对配电网集结等效的综合负荷模型进行解析灵敏度分析以及Hessian矩阵特征值表征的灵敏度分析;其次,通过Pearson相关系数判断参数一阶灵敏度之间的相关性,得到对输出响应作用相似的参数;然后,在遗传算法与Levenberg-Marquardt算法相结合的混合算法基础上,提出固定灵敏度小的参数,按比例简化辨识线性相关参数的优化辨识策略;最后,通过实测曲线及完整负荷模型的仿真,验证了该辨识策略的有效性。     

Constructing numerically stable Kalman filter‐based algorithms for gradient‐based adaptive filtering

This paper addresses the numerical aspects of adaptive filtering (AF) techniques for simultaneous state and parameters estimation arising in the design of dynamic positioning systems in many areas of research. The AF schemes consist of a recursive optimization procedure to identify the uncertain system parameters by minimizing an appropriate defined performance index and the application of the Kalman filter (KF) for dynamic positioning purpose. The use of gradient‐based optimization methods in the AF computational schemes yields to a set of the filter sensitivity equations and a set of matrix Riccati‐type sensitivity equations. The filter sensitivities evaluation is usually carried out by the conventional KF, which is known to be numerically unstable, and its derivatives with respect to unknown system parameters. Recently, a novel square‐root approach for the gradient‐based AF by the method of the maximum likelihood has been proposed. In this paper, we show that various square‐root AF schemes can be derived from only two main theoretical results. This elegant and simple computational technique replaces the standard methodology based on direct differentiation of the conventional KF equations (with their inherent numerical instability) by advanced square‐root filters (and its derivatives as well). As a result, it improves the robustness of the computations against round off errors and leads to accurate variants of the gradient‐based AFs. Additionally, such methods are ideal for simultaneous state estimation and parameter identification because all values are computed in parallel. The numerical experiments are given. Copyright © 2015 John Wiley & Sons, Ltd.     

电力系统关联性参数的辨识与评估

在模型参数辨识中,具有关联性的参数的不同组合可以得到同样的仿真结果,这将导致它们的辨识结果偏离真实值,因而需要对关联性参数进行识别和评估。根据关联性参数的轨迹灵敏度的线性相关性,研究关联性参数的辨识与评估问题。首先,利用参数轨迹灵敏度的拟合识别出哪些参数具有关联性;然后,给部分关联性参数赋默认值,估计出其他参数;最后,根据轨迹灵敏度的拟合系数,评估当赋给部分参数的默认值偏离真实值时,其他参数辨识结果偏离真实值的大小。算例结果表明该方法能对关联性参数进行正确的识别和鲁棒的估计,当默认值与真值相差不大,或者关联性参数之间的线性度较好时,关联性参数能得到有效的评估。     

A class of versatile circuits,made up of standard electrical components,are memristors

In this paper, we propose a whole class of memristor circuits. Each element from the class consists of the cascade connection between a static nonlinear two‐port and a dynamic one‐port. The class may be divided into two subclasses depending on the input variable (voltage or current). Within each of these subclasses, two further sets of memristor circuits may be distinguished according to which output voltage and current of the two‐port represents one of the system states. The simplest memristor circuits make only use of purely passive elementary components from circuit theory, an absolute novelty in this field of research. Thus they are suitable circuit primers for the introduction of the topic of memristors to undergraduate students. A sample circuit is built using discrete devices and its memristive nature is validated experimentally. In case the one‐port is purely passive, the proposed circuits feature volatile memristive behavior. Allowing active devices into the dynamic one‐port, non‐volatile dynamics may also emerge, as proved through concepts from the theory of nonlinear dynamics. Given the generality of the proposed class, the topology of the emulators may be adjusted so as to induce a large variety of dynamical behaviors, which may be exploited to accomplish new signal processing tasks, which conventional circuits are unable to perform. Copyright © 2015 John Wiley & Sons, Ltd.     

Self‐adjoint S‐parameter sensitivities for lossless homogeneous TLM problems

We present a novel efficient algorithm for the estimation of S‐parameter sensitivities in homogeneous and lossless transmission line modelling (TLM) problems. Our approach estimates S‐parameter adjoint‐based sensitivities without actually carrying out any adjoint simulation. By applying a transformation to the original TLM simulation we establish an isomorphism between the original and the adjoint problem. The unique properties of the TLM node in a lossless and homogeneous problem are also exploited in establishing the isomorphism. For an electromagnetic structure with N_p ports, only the N_p original simulations utilized in evaluating the S‐parameters are required to estimate their sensitivities as well. Our novel approach is illustrated through estimating S‐parameter sensitivities with respect to waveguide discontinuities. Good match is obtained between our sensitivity estimates and those calculated using finite differences at the response level. Copyright © 2005 John Wiley & Sons, Ltd.     

用特征值灵敏度法分析系统参数对小干扰稳定性的影响

电力系统小干扰分析中,特征值对参数的灵敏度定量地提供了参数影响的程度和趋势。该文以某电网的典型运行方式为基础,根据特征值对任意运行参数(如PQ节点功率、PV节点电压)和网络参数(如线路阻抗、变压器分接头)的灵敏度,分析了各个系统参数对电网小干扰稳定性的影响。依据分析结果,可以通过调整系统参数来改善系统的小干扰稳定性。