A practical guide to multidimensional wave digital algorithms using an example of fluid dynamics

The wave digital concept for numerical integration of partial differential equations leads to algorithms with highly advantageous features as robustness, full localness and massive parallelism. However, the required synthesis of an internally multidimensionally passive reference circuit, from which the algorithm is derived, usually demands an in‐depth knowledge of circuit theory and a high level of intuition. In this practical guide, a step‐by‐step approach for the synthesis of such reference circuits is introduced to relax these requirements, using the nonlinear fluid dynamic equations as a nontrivial example. General implementation issues for the wave digital algorithm are discussed as well as applying arbitrary passive linear multistep methods in place of the commonly used trapezoidal rule. As an example, we take the well‐known numerically critical shock tube problem, the solution of which is problematic when the trapezoidal rule is used as unwanted oscillations occur. These oscillations are suppressed when using the second‐order accurate Gear method instead. Copyright © 2010 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.     

Nonlinear partial differential equation modeling and adaptive fault-tolerant vibration control of flexible rotatable manipulator in three-dimensional space

In this article, we investigate the problem of nonlinear modeling and adaptive boundary vibration control with actuator failure for a flexible rotatable manipulator in three-dimensional space, which is made up of a rotatable base and a flexible manipulator. In order to accurately reflect the characteristics of the distributed parameters, the Hamilton principle is introduced to derive the dynamic model expressed by partial differential equations (PDEs). Based on the model, an innovative boundary control scheme is proposed to eliminate the deflection and vibration simultaneously, and to guarantee that the rotatable base and the flexible manipulator can track the desired angle respectively. The adaptive law is developed to estimate the loss of the actuator. The effectiveness of the designed controller is verified from both theoretical analysis and numerical simulation.     

服务于变电站数字化设计的二次设备建模技术研究

针对变电站二次回路设计采用CAD图纸表达方式无法机器获得设计内容的问题,提出一套完整的变电站二次回路数字化设计流程;并研究服务于数字化设计的变电站二次设备及回路的建模方案.从二次回路数字化设计需求着手,分析不同部门对二次回路建模的需求,二次设备建模关注设备的物理属性和连接属性.在建模方案中,定义智能建模的范围、建模对象...     

On the design of multiband transmission functions synthesized by one wave digital lattice structure

In this contribution, the design of multiband transmission functions is considered. Independent and arbitrary number of bands can be designed. Moreover, the whole transmission function is synthesized by one wave digital lattice structure. The approximation process starts by extracting the scattering matrix properties of multiband reference lattice structures. Consequently, the approximation problem reduces to generating a polynomial Q of degree n, which is the degree of the filter. The degree n is depending on the number of the designed bands. Hence, if the number of bands is even, n will be odd, and if the number of bands is odd, n will be even. The polynomial Q will approximate the difference phase function of the two branch polynomials. It is composed of two subpolynomials, one of them is Hurwitz and the other is anti‐Hurwitz. The degrees of these subpolynomials differ by odd number if the number of bands is even and differ by even number if the number of bands is odd. Q is generated according to iterative interpolation and using explicit recursive formulas. After obtaining Q, the two subpolynomials are calculated and the two branch all‐pass functions are constructed. Consequently, the filter is synthesized in the digital frequency domain. The method is applied through an illustrative example. Copyright © 2011 John Wiley & Sons, Ltd.     

Extremum seeking for unknown scalar maps in cascade with a class of parabolic partial differential equations

We present a generalization of the scalar gradient extremum seeking (ES) algorithm, which maximizes static maps in the presence of infinite-dimensional dynamics described by parabolic partial differential equations (PDEs). The PDE dynamics contains reaction-advection-diffusion (RAD) like terms. Basically, the effects of the PDE dynamics in the additive dither signals are canceled out using the trajectory generation paradigm. Moreover, the inclusion of a boundary control for the PDE process stabilizes the closed-loop feedback system. By properly demodulating the map output corresponding to the manner in which it is perturbed, the ES algorithm maximizes the output of the unknown map. In particular, our parabolic PDE compensator employs the same perturbation-based (averaging-based) estimate for the Hessian of the function to be maximized applied in the previous publications free of PDEs. We prove local stability of the algorithm, real-time maximization of the map and convergence to a small neighborhood of the desired (unknown) extremum by means of backstepping transformation, Lyapunov functional and the theory of averaging in infinite dimensions. Finally, we present the generalization to the scalar Newton-based ES algorithm, which maximizes the map's higher derivatives in the presence of RAD-like dynamics. By modifying the demodulating signals, the ES algorithm maximizes the nth derivative only through measurements of the own map. The Newton-based ES approach removes the dependence of the convergence rate on the unknown Hessian of the higher derivative, an effort to improve performance and remove limitations of standard gradient-based ES. Numerical examples support the theoretical results.     

Hybrid-driven-based fuzzy secure filtering for nonlinear parabolic partial differential equation systems with cyber attacks

The problem of hybrid-driven fuzzy filtering for nonlinear semi-linear parabolic partial differential equation systems with dual cyber attacks is investigated. First, a Takagi-Sugeno (T-S) fuzzy model is employed to reconstruct the original nonlinear systems. Second, a hybrid-driven mechanism is applied for filter design to balance the systems' performance and the limited network resource consumption under dual cyber attacks composed of deception and denial of service attacks. Based on the Lyapunov direct method, sufficient conditions to guarantee the stability of the augmented system are obtained, and the parameters of the designed filter are earned with explicit form. Finally, a simulation example with robust analysis and comparative analysis is provided to illustrate the effectiveness of the proposed method.     

基于参数辨识的波浪发电场等效建模研究

提出了基于参数辨识的波浪发电场等效建模策略,将波浪发电场等效为单机模型。以阿基米德波浪摆(AWS)发电场内某一测点的实测波浪力作为输入,整个发电场稳态有功功率作为输出,采用粒子群算法(PSO)辨识单机等效模型中驱动系统的等效参数。在Matlab/Simulink中搭建了计及尾流和时滞的AWS波浪发电场详细模型,并利用多组实测波浪数据对等效建模策略进行了仿真验证。仿真结果表明,在不同实测数据下辨识得到的等效模型驱动参数相差不大,参数辨识结果平稳合理;对于某一组实测数据下辨识得到的等效驱动参数,在不同实测数据下获得的等效模型和详细模型功率曲线均基本一致。     

电力线路行波差动保护与电流差动保护的比较研究

线路电流差动保护的基础是线路的RL集中参数模型和电荷连续性。行波差动保护的基础是线路的分布参数模型和行波传输不变性。针对两类差动保护在电力线路上的应用进行了详细的理论和仿真对比研究。指出二者的根本区别在于行波差动保护考虑了线路的分布参数特性和空间传播特性,而电流差动保护把线路看成节点,完全忽略了分布参数特性和空间传播特性,差动电流是行波差动电流的退化形式。对于特高压长距离输电线路,行波差动保护相比于电流差动保护有明显的性能优势。对于高压和超高压输电线路,行波差动保护和电流差动保护性能无显著差别,电流差动保护可以胜任该类线路。     

山西电力神—太段数字微波电路收发信干扰的故障分析与处理

对神—太段微波电路收发信干扰的故障从理论上进行了深入、细致的分析和探讨 ,找出了故障症结 ,为今后类似故障的处理 ,提供了很好的实例。     

基于小波和高阶PDE的电缆局部放电去噪研究

局部放电(PD)试验是检测电力电缆绝缘性能的重要手段,由于试验现场电磁环境比较复杂,提取所得的PD信号已被噪声淹没。为得到较为真实的PD信号,提出了一种基于小波变换和高阶偏微分方程(PDE)相结合的去噪方法。利用小波变换提供较好的局部放电信号预处理和后处理平台,对低频子信号进行四阶PDE迭代去噪,同时采用效果评价指数信噪比(SNR)作为迭代终止条件。将该方法的去噪效果与传统的小波阀值去噪效果进行了比较,经过计算和仿真分析表明,文中方法能够较好的保留信号边缘与细节,比传统小波阀值去噪具有更优越的去噪性能。     

A novel interpretation of the hyperbolization method used to solve the parabolic neutron diffusion equations by means of the wave digital concept

In this paper, the neutron diffusion equations in two energy groups will be dealt with. The underlying parabolic differential equations as well as a hyperbolized version of them will be numerically solved with the wave digital concept. While the hyperbolization process avoids delay-free directed loops in the wave flow diagram, a direct implementation of the parabolic differential equations does not. However, an iteration method can be used to overcome these problems. This results under certain conditions in the same wave digital model. This way, it can be shown that the commonly used hyperbolization can be interpreted as the application of an iteration method. Copyright © 2006 John Wiley & Sons, Ltd.     

数字式变压器差动保护误动分析

结合对一起主变差动保护误动原因的分析,介绍了CST31A型数字式变压器差动保护电流相位校正和幅值平衡补偿的基本原理,对误动原因进行了定性分析和定量计算,从技术和管理方面提出了防范措施。     

P级TA饱和对数字式比率制动特性差动保护的影响

长期以来，比率制动曲线的比率制动部分历来都和电流互感器（TA）的抗饱和能力联系在一起，认为只要有了比率制动特性，差动保护就不会误动，但事实并非如此，长期统计表明有些原因不明的误动或多或少地和TA的暂态饱和有关，通过对非TPY级TA饱和的变压器区外故障动模数据分析，得出比率制动特性差动保护在P级TA暂态饱和情况下可能会误动的结论。同时，还详细阐述了选择合理的出口判据次数，数字滤波算法，数据窗的长度能提高差动保护抗TA暂态饱和能力的影响。     

基于微分方程模型阻抗算法的综合应用

对解微分方程算法作了改进,方法是通过对传统微分方程算法在有限时段上进行积分变换,借助积分减少高频分量的影响。通过数字仿真计算验证了改进后算法的优良估计性能,将之与基于微分方程模型的最小二乘法、全波傅里叶算法作了比较。并根据各算法的估计性能特点,提出了一种具有反时限特性的距离保护算法的实现方案。     

基于气网动态精细化建模的区域电-气综合能源系统机会约束最优能流计算

随着国家能源转型和“双碳”目标的逐步实施,燃气发电在我国电力系统装机中占比不断提高,日益密切的电、气耦合关系使电-气综合能源系统受到更多关注。为此,研究了考虑气网动态精细化建模对含出力不确定的分布式新能源发电的区域电-气综合能源系统运行策略的影响。提出考虑管道气流方向灵活可变的气网动态复频域建模方法,提升了电-气最优能流的计算精度;采用机会约束建立分布式新能源发电不确定性对电网和气网运行影响的模型;算例测试结果表明气网动态精细化模型可有效提升区域电-气综合能源系统对运行不确定性的应对能力。     

基于TEV和超声波的开关柜局部放电便携式检测仪的研制

为了及时发现高压开关柜的绝缘缺陷,保障电网的安全运行,文中研制了一套开关柜局部放电便携式检测仪。该仪器采用内置式TEV传感器和超声波传感器联合检测,具有体积小、操作简单、能检测多种放电缺陷的优势。文章阐述了该仪器的总体设计结构和硬件电路实现;并在实验室搭建了仪器的性能及功能测试平台;最后,与国外某公司的产品进行了详细的对比测试和分析。结果表明,该检测仪的灵敏度与准确性较高,满足我国电力工业界对高压开关柜绝缘状态先进检测仪器的迫切需求。     

Fluctuation analysis of partial discharge pulse occurrence with an integral equation

This paper proposes an integral equation to describe the stochastic fluctuation of partial discharge (PD) occurrence under sinusoidal voltage stress based on a simple PD model. In the model, the stochastic behavior of PD fluctuation is assumed to arise from the fluctuation of the PD delay time after the inception voltage is built up across a discharge gap. For simplicity of calculation, the delay time is assumed to have an exponential distribution. Based on these assumptions, it is found that the proposed integral equation provides the basic characteristics such as the PD pulse distribution in the applied voltage phase angle domain. The authors have solved the equation numerically and demonstrate several ?–n distribution patterns with average delay times of 0.05 to 5 ms at low applied voltage. The solution is compared with PD characteristics obtained by Monte Carlo simulation based on the same PD model, and good agreement is found. © 2001 Scripta Technica, Electr Eng Jpn, 136(1): 16–28, 2001     

Optimal design of lattice wave digital fractional‐order Butterworth filter

This letter presents the design of digital fractional‐order Butterworth filter (DFOBF) of order (n+α) , where n is an integer, and α ∈ (0,1) , from the perspective of optimal realization. The magnitude–frequency characteristic of the DFOBF is optimally modeled using the computationally efficient lattice wave digital filters (LWDFs). Design examples for the third‐ and fifth‐order LWDF‐DFOBFs with various values of n, α_, and cut‐off frequencies are presented.     

On stochastic modelling of linear circuits

In this paper, the deterministic modelling of linear circuits is replaced by stochastic modelling by including variance in the parameters (resistance, inductance and capacitance). Our method is based on results from the theory of stochastic differential equations. This method is general in the following sense. Any electrical circuit that consists of resistances, inductances and capacitances can be modelled by ordinary differential equations, in which the parameters of the differential operators are the functions of circuit elements. The deterministic ordinary differential equation can be converted into a stochastic differential equation by adding noise to the input potential source and to the circuit elements. The noise added in the potential source is assumed to be a white noise and that added in the parameters is assumed to be a correlated process because these parameters change very slowly with time and hence must be modelled as a correlated process. In this paper, we model a series RLC circuit by using the proposed method. The stochastic differential equation that describes the concentration of charge in the capacitor of a series RLC circuit is solved. Numerical simulations in MATLAB are obtained using the Euler–Maruyama method. Copyright © 2008 John Wiley & Sons, Ltd.