A simplified design-oriented analysis of switched-capacitor active filters

The method presented in this paper provides a simplified approach to obtain the z-domain equivalent circuit of an SC active filter by one-for-one substitution of each basic SC element with its z-domain equivalent admittance, if a specific terminal condition is met. Then, traditional circuit analysis techniques can be used to derive the z-domain transfer function of the filter. This method makes the analysis and the design of the SC active filter simple and similar to the S-domain method. Two application examples are given.     

非同步机电源接入电网后的谐振问题分析及抑制

随着非同步机电源在电网中的占比越来越大，有别于传统功角振荡的电网谐振不稳定问题逐渐显现。为此，文中提出了一种基于s域节点导纳矩阵的网络谐振分析方法，用以分析及抑制含非同步机电源电力系统的谐振问题。首先，介绍了两种非同步机电源的s域阻抗建模方法——小干扰线性化法和测试信号法，重点考虑了内环控制器和锁相环的影响。然后，给出了一套基于s域节点导纳矩阵的网络谐振结构分析方法，并提出了两个描述谐振模式的特征指标，用以确定其主要影响区域和敏感元件参数。最后，以某风电场并网系统为例，对该系统的谐振结构进行了分析，并针对其存在的谐振问题提出了相应的改善措施。分析表明，由于电力电子装置的负电阻效应，含非同步机电源的电力系统确实存在谐振不稳定的风险，需要加以抑制。     

A Computer-Aided Design Toolkit For Continuous/Discrete Systems Based On Continued Fractions

This paper presents new algorithms (1) to generate complete mathematical symbolic expressions of continued fraction expansion coefficients in the s-domain, (2) to determine their numeric values and (3) to perform continued fraction inversion in the s-domain. A software package in PASCAL and LISP to implement these algorithms is developed. In addition, a simple z-domain inversion algorithm used in the computer implementation of bilinear s-z transformation is also included in the software package. These algorithms play an important role in the analysis and synthesis of complex electrical networks and control systems. Especially, the s-domain expansion and inversion algorithms have potential applications in model simplification and system order reductions. the paper also shows that the package, as such, serves as a comprehensive computer-aided analysis and design (CAD) toolkit for both continuous and discrete systems. the software is interactive and runs on computers equipped with a PASCAL or LISP compiler. It is noted that the iterative implementation of these methods using the new continued fraction algorithms saves considerable memory space and processing time. Numerical examples and computer data are given to demonstrate the development of the new algorithms and the usefulness of the software toolkit in the CAD design of continuous and discrete systems.     

s-Domain analysis of lightning surges in three-phase systems using nonuniform single-phase line model

Surge response of the transmission tower in a three-phase transmission system is computed using s-domain nonuniform single-phase transmission line modelling. First, tower top voltage is obtained considering the tower and the ground wire by excluding the effect of the phase conductors, and then the induced voltages on the phase conductors as a result of the current flowing through the ground wire are computed using the magnetic coupling between the ground wire and the phase conductors. The first step of the analysis is the formulation of the system response in the s-domain, and the second step is the frequency to time domain conversion, which is carried out using fast inverse Laplace transform (FILT). The voltages on the phase conductors and the voltages across the tower insulators are computed, and some of the results obtained using s-domain analysis are compared with those obtaining using electromagnetic transients program (EMTP). The effect of frequency dependence of the line parameters is investigated.     

A Contribution to the Frequency Analysis and Transient Response of Power Transformer Windings

Abstract—This article proposes a new approach to study the frequency response and the transient analysis of power transformer windings. For improved accuracy, the suggested model includes, among other equivalent circuit elements, the mutual magnetic couplings between any winding turn and all others. This implies that the equivalent inductance of any considered turn will be a location-dependent parameter. Accordingly, the winding will be analyzed as a non-uniform transmission line. Through the application of a recursive circuit reduction technique, a closed-form Laplace s-domain analytical expression for the winding's input impedance can be obtained for any neutral treatment. The resulting expression can be used to determine the winding's series and parallel resonance frequencies. The s-domain expression for the input impedance, in connection with the numerical inverse Laplace transform, will be utilized for determination of the winding's time-domain transient response for any input voltage or current time waveform. Accuracy increases with the assumed number of winding sections, which can be even increased to the actual number of turns, limited only by the available computation resources. The results of case studies are in good agreement with those available in the literature using the time-domain solution of the simultaneous differential equations in the state variables.     

Compact model order reduction of weakly nonlinear systems by associated transform

We advance a recently proposed approach, called the associated transform, for computing slim projection matrices serving high‐order Volterra transfer functions in the context of weakly nonlinear model order reduction (NMOR). The innovation is to carry out an association of multivariate (Laplace) variables in high‐order multiple‐input multiple‐output transfer functions to generate univariate single‐s transfer functions. In contrast to conventional projection‐based NMOR which finds projection subspaces about every s_i in multivariate transfer functions, only that about a single s is required in the proposed approach. This leads to much more compact reduced‐order models without compromising accuracy. Specifically, the proposed NMOR procedure first converts the original set of Volterra transfer functions into a new set of linear transfer functions, which then allows direct utilization of linear MOR techniques for modeling weakly nonlinear systems with either single‐tone or multi‐tone inputs. An adaptive algorithm is also given to govern the selection of appropriate basis orders in different Volterra transfer functions. Numerical examples then verify the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Inversion of the nodal admittance matrix by the use of state equations

Previous methods^1–4 for inverting the nodal admittance matrix when the elements are rational functions of the Laplace transform variable s used pivotal techniques. Problems of numerical stability made this type of approach suitable only for quite small circuits. A new method based on diagonalizing the A-matrix of a set of state equations defining the circuit has greatly improved stability. The state equations are derived directly from the nodal equations using a newly developed algorithm. These equations are then used to compute the inverse of the nodal admittance matrix as a matrix of rational functions of s. An example is presented of the application of these methods to a system of 21 degrees of freedom.     

Optimum elimination of inadmissible operating states

This work contains a general analysis of an algorithm developed to determine a state of performance which guarantees the elimination of the network's operating states defined as inadmissible and optimizes the costs.The mathematical model formulated required an appropriate linear programming algorithm and a specific program to determine the sensitivity matrix.The experience obtained with the use of this linear method to solve the problem of optimum load flow shows that, compared with non-linear methods, it offers some advantages: on the one hand, the possibility of considering a greater number of constraints owing to the reduction of variables achieved by means of the sensitivity matrix and, on the other hand, the ability to detect incompatibility in the formulated constraints. In addition, this method offers greater guarantees of convergency, for the same quantity of functional constraints, than the nonlinear methods, because it does not use penalty functions.     

Multi-scale Kalman filters algorithm for GPS common-view observation data based on correlation structure of discrete wavelet coefficients

Global positioning system (GPS) common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients. Suppose that the GPS commonview observation data has the 1/f fractal characteristic, the algorithm of wavelet transform was used to estimate the Hurst parameter H of GPS clock difference data. When 0<H<1, the 1/f fractal characteristic of the GPS clock difference data is a Gaussian zero-mean and non-stationary stochastic process. Thus, the discrete wavelet coefficients can be discussed in the process of estimating multi-scale Kalman coefficients. Furthermore, the discrete clock difference can be estimated. The single-channel and multi-channel common-view observation data were processed respectively. Comparisons were made between the results obtained and the Circular T data. Simulation results show that the algorithm discussed in this paper is both feasible and effective. Translated from Journal of Jilin University (Engineering and Technology), 2006, 36(4): 599–603 [译自: 吉林大学学报 (工学版)]     

基于分治策略的分布式调度自动化系统 稳态监控网络拓扑分析

电网拓扑分析是电网调度自动化系统的一项基础性工作,是联通电网模型和电网分析的桥梁,为电网调度员潮流计算、防误操作等等提供必要的基础数据。随着电网建设,网架结构逐步扩大,亟需一种方法在充分利用计算机资源的基础上实现高效率的网络拓扑分析。提出了一种基于分治思想的电网网络拓扑分析算法,通过结合电网模型的特点以及成熟的图论算法予以实现。同时将面向高级应用服务和面向监控服务的拓扑功能解耦,在不影响电力潮流计算等应用功能的基础上提高调度自动化系统集成效率,最后应用该算法编写并行的分布式电网拓扑分析程序,并展望了其应用前景。     

Solving the helmholtz equation using multiply propagated fields

Computer models in electromagnetics are based primarily either on integral or on differential equations. The former arise from source integrals using some appropriate Green's function whereas the latter originate from the Maxwell curl equations. Although requiring volume rather than surface sampling even for spatially homogeneous problems, in contrast to integral-equation (IE) models, differential-equation (DE) models are geneally a better choice for problems involving spatial inhomogeneities. This is because such problems require volumetric sampling using either approach, but the DE model produces a sparse matrix rather than the full matrix of the IE formulation. In this paper we describe a new approach based on using multiply propagated fields for numerically solving the banded matrix that results from discretizing the Helmholtz equation. A computer-time savings of N^1/2 and N^2/3 for two-dimensional (2-D) and three-dimensional (3-D) problems, respectively, is made possible, where N is the total number of field samples or unknowns. For even moderate-size problems where 100 samples per linear dimension are used (N₂ = 10,000 and N₃ = 1,000,000), the time savings can be of the order of 100 and 10,000 respectively. Another advantage of this procedure, which we call Helmholtz equation multiple propagator (HEMP), is that the radiation or closure condition needed to terminate the spatial solution mesh for exterior problems can be enforced rigorously with essentially no additional computational cost. The method is illustrated for a 2-D problem by application to plane-wave scattering from an infinite, metal, circular cylinder. Results are presented for the mode amplitudes of the scattered field, the induced surface current, and the bistatic far field as obtained from HEMP, and shown to be in good agreement with the analytical results. Although limited here to the simplest possible application in order to establish its feasibility, the approach's advantage would be its applicability to 2-D and 3-D problems involving inhomogeneous, penetrable objects.     

Finite‐model adaptive control using an LS‐like algorithm

Adaptive control problem of a class of discrete‐time nonlinear uncertain systems, of which the internal uncertainty can be characterized by a finite set of functions, is formulated and studied by using an least squares (LS)‐like algorithm to design the feedback control law. For the finite‐model adaptive control problem, this algorithm is proposed as an extension of counterpart of traditional LS algorithm. Stability in sense of pth mean for the closed‐loop system is proved under a so‐called linear growth assumption, which is shown to be necessary in general by a counter‐example constructed in this paper. The main results have been also applied to parametric cases, which demonstrate how to bridge the non‐parametric case and parametric case. Copyright © 2006 John Wiley & Sons, Ltd.     

Kernelized relative entropy for direct fault detection in industrial rotary kilns

The objective of this work is to use a 1‐dimensional signal that reflects the dissimilarity between multidimensional probability densities for detection. With the modified Kullback‐Leibler divergence, faults can be directly detected without any normality assumption or joint monitoring of related test statistics in different subspaces such as the T² and SPE in principal component analysis–based methods. To relieve the difficulty associated with asymptotic high‐dimensional density estimates, we have estimated the density ratio rather than the densities themselves. This can be done by approximating the density ratio with kernel basis functions and learn the weights from the available data. The developed algorithm is generic and can be applied to any industrial system as long as process historical data is available. As a case study, we apply this algorithm to a real rotary kiln in operation, which is an integral part of the cement manufacturing plant of Ain El Kebira, Algeria.     

Approximate formulae for numerical inversion of Laplace transforms

Most methods for the numerical calculation of inverse Laplace transformations f(t) = L⁻¹[F(s)] have serious limitations concerning the class of functions F(s) that can be inverted or the achievable accuracy. The procedures described in the paper can be used to invert rational as well as irrational or transcendental functions of the complex variable s. The required accuracy of the results can be enhanced without changing the algorithm, only at the cost of a longer computation time. The described methods were verified with many examples including transients in lumped/distributed systems with sections of lossy multiconductor transmission lines or with distributed RC elements. © 1998 John Wiley & Sons, Ltd.     

Performance analysis of the forgetting factor RLS algorithm

An analysis is given of the performance of the standard forgetting factor recursive least squares (RLS) algorithm when used for tracking time-varying linear regression models. Three basic results are obtained: (1) the ‘P-matrix’ in the algorithm remains bounded if and only if the (time-varying) covariance matrix of the regressors is uniformly non-singular; (2) if so, the parameter tracking error covariance matrix is of the order O(μ + γ²/μ), where μ = 1 - λ, λ is the forgetting factor and γ is a quantity reflecting the speed of the parameter variations; (3) this covariance matrix can be arbitrarily well approximated (for small enough μ) by an expression that is easy to compute.     

基于光伏阵列输出特性的GMPPT算法研究

针对局部阴影条件下光伏阵列的P-V曲线呈现多峰值的情况,在研究光伏阵列输出特性的基础上提出了一种全局最大功率点追踪GMPPT(global maximum power point tracking)算法。该算法由均匀光照和局部阴影条件下的两个最大功率点追踪算法构成。通过所提出的局部阴影检测手段判别光伏阵列所处的光照条件,从而决定使用哪个子算法。最后将该算法在Matlab中进行仿真验证。仿真结果表明在局部阴影条件下该算法能快速地追踪到全局最大功率点,且避免了对整条P-V曲线的扫描。在均匀光照条件下要比传统的最大功率点追踪算法(扰动观察法)更快地定位到最大功率点。     

Delay-dependent robust H ∞ controller design for a class of nonlinear uncertainty time-delay systems with input delay

Based on an appropriate Lyapunov function, this paper analyzes the design of a delay-dependent robust H _∞ state feedback control, with a focus on a class of nonlinear uncertainty linear time-delay systems with input delay using linear matrix inequalities. Under the condition that the nonlinear uncertain functions are gain bounded, a sufficient condition dependent on the delays of the state and input is presented for the existence of H _∞ controller. The proposed controller not only stabilized closed-loop uncertain systems but also guaranteed a prescribed H _∞ norm bound of closed-loop transfer matrix from the disturbance to controlled output. By solving a linear matrix inequation, we can obtain the robust H _∞ controller. An example is given to show the effectiveness of the proposed method. __________ Translated from Journal of Nanjing University of Aeronautics and Astronautics, 2007, 39(2): 159–163 [译自: 南京航空航天大学学报]     

Lossless 2-ports between non-reactive terminations

Lossless reciprocal 2-ports between terminations with even impedance functions are considered. They are the unifying concept for the synthesis of FDNR and leapfrog RC-active filters in their most general form. The scattering matrix of lossless reciprocal 2-ports with respect to such terminations is defined, its canonic form deduced and the transfer of active power discussed. This scattering matrix is related to the usual scattering matrix of the same 2-port but with respect to unit resistance terminations. In such a way the precise structure of the 2-port as an LC ladder can be deduced from properties of the original transfer function and the termination impedances and the LC synthesis can be performed by conventional methods and programs. An exhaustive enumeration of the different cases that may arise is given. It can give a general outlook on the different RC-active filters that may be obtained.     

基于高斯方法及Sherman-Morrison公式的暂态稳定性并行计算方法

并行计算是实现大规模电力系统暂态稳定性实时分析计算的有效途径。将s级2s阶的高斯方法和扩展的Sherman-Morrison矩阵求逆公式相结合,提出了一类新的暂态稳定性并行计算方法。该方法首先利用s级2s阶的高斯方法对微分-代数方程组进行多级离散,并利用严格的牛顿法对离散后的非线性方程组进行整体求解。在此基础上,按s个时间点将整体雅可比矩阵分裂成为一个分块对角矩阵和一个分块常系数矩阵。然后,以分裂后的分块对角矩阵为基础,利用扩展的Sherman-Morrison矩阵求逆公式将s个时间点上的计算任务进行“解耦”。所提方法在保持严格牛顿法的收敛性的同时具有很好的并行性。利用OpenMP并行计算技术在多核计算机上对2个不同的系统算例进行了测试,结果表明,所提出的并行方法可以获得较好的加速比以及并行效率。