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.     

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。     

注入式有源谐波电阻谐振抑制方法

微电网的电压等级逐步向中压发展。为了补偿微网中大量无功功率的传输,在中压配电网中一般加设无功补偿电容。无功补偿电容有可能导致电网谐波电流放大,严重的谐振问题会危及配电网的安全。首先,利用谐振模态分析法对中压配网的谐振进行分析;然后,基于注入式结构的有源谐波电阻AHR(active harmonic resistance),建立电压控制电流源方式下有源谐波电阻的阻抗模型,分析其对谐振阻尼的作用。仿真和实验结果证明了所提出的谐振分析与抑制方法对谐振有明确的预测与阻尼作用,可以有效保障系统的正常运行。     

Transient analysis of nonuniform lossy transmission lines with frequency dependent parameters

An s-domain method for transient analysis of lossy, frequency dependent nonuniform transmission lines having parameters arbitrary varying with space is presented. Nonuniform line is divided into adequate number of sections which are then assumed uniform. The terminal equation for the nonuniform line is calculated by using the terminal equations of the uniform line sections. By using the boundary conditions, total response in s-domain is obtained. Fast inverse Laplace transform is used for frequency to time domain conversion. In one of the examples, the step response of an open ended nonuniform line is obtained and the results are compared with those obtained by lattice-diagram technique. The effect of number of sections is investigated and it is concluded that for sufficiently large number of sections, the results approach to the analytical solutions which can be obtained only for very special nonuniform lines. In the second example, the method is applied for the calculation of transmission tower lightning surge response.     

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.     

电磁继电器接触系统振动特性的建模与仿真分析

接触系统作为电磁继电器的功能执行部件，是继电器整体的重要组成部分。其接触系统的固有频率与响应振幅特性直接影响电磁继电器的接触可靠性。研究电磁继电器接触系统的耐振动问题是动态接触(碰撞)条件下的非线性问题，以往研究工作很少。文章通过引入局部接触刚度的概念，根据振动力学理论，建立了接触系统的等效数学模型，将接触系统等效成两自由度的线性系统进行模态、谐响应分析，分析与研究了影响接触系统振动特性的主要因素，提出了高频正弦振动条件下接触系统保证接触的合理判据，以此验证接触系统抗振性能。最后，以某型号电磁继电器的接触系统为例，运用ANSYS有限元软件，仿真分析了由尺寸参数及接触点位置参数改变引起的振动特性，仿真结果验证了该模型及理论分析的正确性。研究结论对于电磁继电器接触系统的参数设计具有指导意义，对提高带有机械触点的开关电器的抗振性设计具有一定的参考价值。     

基于多特征目标函数PCA-ILP的非侵入式负荷分解方法

非侵入式负荷监测（non-intrusive load monitoring, NILM）能够在不影响用户正常用电的前提下,低成本地获取用电信息,实现用电设备的类型识别和负荷分解,而大量智能电表的安装也为用户进行NIML提供了数据与技术支撑。首先,在研究常见家用电器的功率特征、电流波形及其频域谐波特征的基础上,采用主成分分析方法（principal components analysis, PCA）对高维谐波特征空间进行降维,提取主要谐波信息,与基本功率特征结合形成多特征目标函数。然后,基于整数线性规划（integer linear programming, ILP）模型,提出了考虑多特征目标函数的PCA-ILP的NILM方法。算例分析表明,所提方法对不同信噪比（signal to noise ratio, SNR）下的不同家用电器应用场景均具有良好的负荷分解效果。     

电力系统串联谐波谐振的特性分析与灵敏度计算

分析电力系统谐波背景下模态分析与谐波谐振关联的机理,根据回路阻抗矩阵,绘制矩阵特征值频谱和串联谐波谐振下的关键模态导纳。根据串联谐振及谐波激励的自身特点,提出使用虚拟支路对系统拓扑结构进行修正处理,对网络进行谐波谐振模态分析,将模态分析结果与系统导纳频谱扫描结果进行比较,验证谐波谐振频率计算方法的可行性和准确性。定义灵敏度矩阵,通过基本回路矩阵确定系统元件与回路阻抗矩阵元素间的关联性,推导关键模态下特征值对各网络元件电气参数的灵敏度,通过标准化处理,提高了各支路元件灵敏度的可比性。对IEEE30母线系统进行仿真分析,得出串联谐振对元件的灵敏度影响程度和串联谐振的定位及传播范围。     

Geometric measures of modal controllability and observability of power system models

The proximity of the subspaces spanned by the individual columns of the B matrix to the one-dimensional A^t-invariant subspaces can be used as measures of modal controllability of a linear model. These measures and their duals of modal observability are calculated in this paper for two representations of a multi-machine power system with 39 buses and 10 generators. The conditioning of the eigensystem is checked for the classical representation and the more detailed representation. The practical significance of the measures is demonstrated by showing their relation to coherency.     

偏远地区风电场并网系统串联谐振分析

针对偏远风电场并网时易被忽略的并网系统串联谐振问题,提出结合回路元件灵敏度的串联谐振模态分析法进行研究。虽然并联谐振在电力系统中所占比例较大,但串联谐振的危害亦不可忽略。偏远风电场因其送出线较长,并网结构薄弱,输电线路分布电容所带来的影响不容忽视。建立线路分布参数模型,并分析其阻抗特性,基于已建立的风电场并网模型,采用串联谐振模态分析法分析系统串联谐振现象,准确判断串联谐振频率的同时,给出串联回路电气元件的模态灵敏度值。最后,以某风电场为实例建立仿真模型,仿真结果验证了所采用分析方法的可行性。通过元件灵敏度值的计算,进一步阐述线路长度的改变对风电场并网系统串联谐振频率和幅值的影响规律,为风电场实际规划建设提供理论指导。     

输电网网架结构的谱聚类分析算法

互联电网的网架结构日趋复杂,对于电力系统运行管理和分析计算合理地进行电网分区是必要的,文中引入了谱图理论进行电网网架结构的分析,以获得恰当的电网分区。采用谱聚类算法首先需要为电网的网络拓扑结构建立图模型及其Laplace矩阵,然后通过分析可以得出电网结构相关的丰富信息,准确反映网架结构的连接特征,进而实现电网的区域划分。通过IEEE 118节点系统算例的应用表明,该算法能够帮助了解电网的拓扑结构特点,准确有效地确定电网分区。     

基于模态分析的全并联AT网动态谐波谐振研究

为防止牵引网谐波谐振引起的系统过电压,达到及时预防和抑制的目的,针对中国高速铁路全并联自耦变压器(auto-transformer,AT)供电方式,采用模态分析方法对系统的节点导纳矩阵进行分析处理,通过解耦与特征值求取确定其谐振信息。研究机车功率变化、机车位置移动等动态条件下的牵引网谐振规律。并针对谐振频率在某一区间或范围变化,引出谐振带的概念。通过与频谱分析法对比,证明模态分析方法能有效识别系统的谐振频率,并且可用于分析由动态运行的机车产生的动态谐波谐振。     

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.     

谐波分析及谐振评估软件的开发与应用

结合模态分析法和谐波潮流算法,基于C#和Matlab语言开发出一套谐波分析及谐振评估软件.除换一般的谐波分析功能外,软件还具有2个特色功能:通过频率扫描能搜索出系统中所有的谐振点,对谐振点进行模态分析,得到系统中发生谐振的严重区域,并以参与因子指标反映谐振在系统中的分布;对加入滤波器后的系统进行频率扫描,若系统谐振点次数与谐波源次数相近,则重新调整滤波器参数,经反复调整与扫描直至系统谐振点次数不与谐波源次数相近,实现滤波器参数的优化设计,解决由于其参数设计不恰当而引起的谐波谐振或谐波放大问题.算例仿真结果表明该方法对谐波谐振评估以及无源滤波器参数优化是正确、有效的.     

基于模态分析和虚拟支路法的串联谐波谐振分析

串联谐振与并联谐振共同组成谐振问题的两个重要分支。模态分析为解决谐振问题提供了新思路。该文指出,由于串联谐振的发生与回路阻抗的密切关系,利用模态分析法(简称模态法)解串联谐振问题时应使用回路阻抗矩阵,而非节点阻抗矩阵。阐明分析串联谐振时,网络拓扑结构不断改变的实质。提出一种结合模态分析和"虚拟支路法"来分析网络回路阻抗矩阵以获得串联谐振频率及相关支路信息的方法。该方法继承模态法解谐波谐振问题的优点并对之是补充和完善,使模态分析与目前通用的频谱分析并列,成为可完整解决谐振问题的方法。测试系统研究和实际应用均证明该文所提出方法的正确性和适用性。研究结果可作为分析谐波谐振问题的基本方法,还可用于滤波器装置的谐振频率校验。     

Power system dynamic equivalence based on a new model reduction technique

Power system dynamic equivalents play an important role in the effort to reduce the computational burden of the transient stability analysis of power systems. This paper proposes a new efficient practical algorithm for forming linear dynamic equivalents for power systems based on modal analysis. The main feature of the proposed method is that the accuracy of the equivalent model is greatly improved by converting a coordinate system representing the subsystem from the R-J coordinate system of the main system to the reference generator D-Q coordinate system of the subsystem. The order reduction is based on aggregation of similar modes and elimination of the inferior modes without significant effect on the frequency response of the subsystem. Thus the equivalent obtained by the proposed method can be used for both steady-state and transient stability analysis studies. To verify the dynamic equivalent performance stability simulation results for a model power system composed of 16 generators also are shown.     

改进的HHT算法在电力系统谐波检测中的应用

使用改进的HHT方法检测电力系统谐波.由于HHT方法存在模态混叠现象,不能有效的得到各次谐波分量.采用预处理的方法,首先将一个信号通过一级低通滤波器得到一级高频成份和一级低频成份,一级高频成份进一步分解为二级高频成份和二级低频成份,如此类推直到满足分解完成条件.对各个频带进行EMD分解得到IMF分量,最后将所有的IMF...     

基于ANSYS的纯压电振子瞬态特性分析

基于ANSYS的电-结构耦合场,对矩形纯压电振子进行模态分析、谐响应分析和瞬态响应分析。通过模态分析和谐响应分析得到面内的一阶纵向振动和二阶弯曲振动的频率和振型以及两振型在振动方向上正交的理想频率;通过瞬态响应分析,得到在理想频率下各动力学参数随时间的变化曲线以及椭圆运动轨迹,得出振子从激振开始到振动达到平衡这一过程所经的时间和应力变化情况。该结果对超声波电动机性能和工作效率的提高有实际意义。     

基于模态分析的风电场并网谐波谐振研究

针对风电场并网时易发生的谐波谐振问题,采用模态分析法对风电场并网系统的节点导纳矩阵进行解耦处理,并通过特征值分解确定其谐振频率、谐振中心等相关信息。首先建立并网LCL逆变器等效诺顿模型和电网等效模型,基于已建立模型,采用模态分析法分析风电场并网谐振现象并给出各节点谐振参与因子、谐振中心等谐振信息。基于仿真平台PSCAD按照某99 MW风电场参数搭建实例仿真模型,在验证模态分析法可行性的同时,深入研究随着风电场集电线路长度和风机并网台数改变时的并网谐振各节点参与因子与谐振中心的变化规律。     

Measurement and analysis of harmonic distortion in power distribution systems

Power distribution systems often exhibit different harmonic behaviours at different locations. It is not usually possible to completely characterise the distortion at a particular site, however, due to insufficient data about the measured system and instrumentation inability to evaluate or register complete set of measurement quantities. In this paper existing power quality standards are analysed and new harmonic distortion indices are derived. A new index describing the total harmonic distortion in current measurements, TRD, is suggested in order to simplify and standardise harmonic measurements. Another index representing the increase of harmonic voltage distortion with TRD, equivalent harmonic impedance z_eq, is proposed as an efficient way of characterising a particular site. The framework described here can be used to predict future harmonic behaviour at any previously measured point. Finally, extensive harmonic measurements of a real distribution system were performed to prove the usefulness of the proposed indices.