逆矩阵的应用

矩阵作为高等代数这一伟大数学图腾重要分支的一大重要部分，在我们的生活，学习，工作，更是在人类的进步中发挥了卓越的工具作用。可逆矩阵是矩阵知识的一个基础支流，作为矩阵乘法的逆运算，是矩阵的一种重要运算，在解决矩阵问题中起着重要的作用。因而矩阵的逆，在解决实际问题时，往往可以起到事半功倍的效果。本文将重点阐述矩阵的逆在通讯领域中的简单应用。     

基于照度矩阵的照度计算方法研究

本文简述了照明系统设计中照度计算的常见方法，定义了照度矩阵，平均照度矩阵，均差照度矩阵和参照度矩阵，并阐述了照度矩阵来计算照度的方法，该方法使照度计算更为准确，使照明设计更加灵活方便。     

(p+q)端口回转器综合阻抗和导纳矩阵

将非对称正定阻抗和导纳矩阵参数分解成对称矩阵和斜对称矩阵，证明了分解的对称矩阵与非对称矩阵的正定性相同，然后用（ｐ＋ｑ）端口回转器分别实现对称矩阵和斜对称矩阵后串联或者并联两矩阵的网络即得非对称正定阻抗和导纳矩阵的网络，解决了以往不能综合非对称正定阻抗和导纳矩阵的问题．     

衡量潮流雅可比矩阵及其降阶阵不对称性和奇异性的指标

依据：①矩阵与其(反)对称部分范数间的关系；②矩阵的1-范数与 -范数之间的关系；③矩阵特征值的绝对值的最大值与其最大奇异值之间的关系；④矩阵特征值的绝对值最大值和矩阵特征值的绝对值的最小值之比与矩阵的谱条件数之间的关系；⑤对最大奇异值，对应的奇异参与因子之和与1之间的关系，构造了衡量矩阵不对称性的指标，并依据：①矩阵特征值的绝对值最小值与最小奇异值之间的关系：②对最小奇异值而言，对应的奇异参与因子之和与1之间的关系，构造了衡量矩阵奇异性的指标。应用IEEE30系统算例和潮流雅可比矩阵及其相应的降阶雅可比矩阵对上述指标进行了分析，得出了潮流雅可比矩阵及其相应的降阶矩阵的谱条件数排序由相应的矩阵最小奇异值排序决定的结论。     

矩阵变换器在风力发电系统中的应用研究

风力发电是一种重要的新能源技术。介绍了应用于新型风力发电系统的矩阵变换器，详细分析了具有9个双向开关的传统矩阵变换器与改进的双桥结构矩阵变换器，以及各自的优缺点。通过分析比较得出，双桥结构矩阵变换器控制策略简单，对于不同负载，开关数目可以减少。其中，具有15个开关的双桥矩阵变换器以其经济性和控制的成熟性，适用于新型的风力发电系统。最后，详细介绍了该双桥式矩阵变换器箝位电路的工作原理和参数设计。     

同步电机电感矩阵分析方法

分析交流同步电机内部的故障时，通常以单个线圈或线圈组为单位写电机的数学模型，因此计算时需要求解复杂的时变系数矩阵微分方程。该文以绕组单个线圈电感表达式的分析为基础，结合电机定子线圈的空间分布，得到了同步电机电感矩阵的对称结构。通过分析这种对称结构，文中尝试构造了一个变换矩阵。通过变换矩阵的作用，可以将时变的电感矩阵转变为常系数矩阵，从而大大方便电机内部故障的仿真计算。文中还给出了各个互感矩阵的变换结果，然后举例说明了电机电感矩阵与系统电流电压方程的联接方法，并解释了仿真分析步骤。通过分析和计算进一步提出，在继电保护的整定计算应用中，可以适当简化电感系数的求解，便于仿真方法的工程应用，并给出了简化前后的仿真结果。     

矩阵行最简式的唯一性

分析了具有等价行向量组的两矩阵之间行向量组、列向量组及矩阵所对应的齐线性方程组的解之间关系，通过对行最简式定义的分析，得出两个结论：１．行最简式相同是矩阵行向量组等价的充要条件，２．矩阵行最简式是唯一的。使得对向量组等价性的研究转化为只需对矩阵作行初等变换即可实现，得到了研究向量组等价性的一种简洁、有效的方法，同时使得行最简式在矩阵研究中变得更为重要。     

交流电网相序变换的数学原理

给出了循环矩阵和对称循环矩阵的特征值和特征向量的4个基本定理：构成了含三相在内的多相交流电网相序变换的统一数学原理。该原理表明：相阻抗矩阵抽象为循环矩阵时，对称分量法是唯一的相序变换方法；相阻抗矩阵简化为对称循环矩阵时，存在无穷多的相序变换方法。     

交流电网相序变换的数学原理

给出了循环矩阵和对称循环矩阵的特征值和特征向量的4个基本定理：构成了含三相在内的多相交流电网相序变换的统一数学原理。该原理表明：相阻抗矩阵抽象为循环矩阵时，对称分量法是唯一的相序变换方法；相阻抗矩阵简化为对称循环矩阵时，存在无穷多的相序变换方法。     

矩阵方程A^TXA=B的中心对称解及其最佳逼近

利用矩阵的广义奇异值分解，得到了线性矩阵方程A^TXA＝B有中心对称解的充分必要条件及其通解的表达式。另外，导出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式。     

小波分解和高次小波差分的奇异点

提出小波变换矩阵B [n×n],它可将数字采样数列F[n]分解为Haar小波级数的系数C[n],其中n是 2的整数次幂 ,小波变换逆矩阵B- 1=BT,所以小波变换矩阵的方法能十分方便地进行小波分解C =B·F和小波重构F =BT·C。如令某些C[k]=0 ,其中k从 1到n/2 ,然后令高次小波差分为C1[k]=C[k]-C[k - 1],它能为原函数F[n]指出它的奇异变化点 ,文中作了图示举例     

基于历史数据潮流确定策略的实用化研究

对基于历史数据潮流确定策略的实用化进行了研究，针对该方法内存占用量大的缺点进行了改进。提出了对灵敏度阵进行简化的方法，对不同规模IEEE标准测试系统的试算表明：计算精度完全满足工程要求、且系统规模越大、简化效果越明显，在保证精度的前提下，最多可节省内存空间80%。     

APPLICATION OF WAVELETS TO THE ANALYSIS OF ARBITRARY THIN-WIRE LOOP ANTENNAS AND SCATTERERS

An analysis of arbitrary thin-wire loop antennas and scatterers using periodic orthogonal wavelets is presented. The periodic orthogonal wavelet expansion is applied to solve the thin-wire version of the electric-field integral equation (EFIE). The curved solution domains are mapped into the definition domain [0, 1] of the periodic wavelets. The unknown current over each loop wire is expanded in terms of a basis derived from a periodic orthogonal wavelet through the maps between the curved integration domains and the interval [0,1]. The integral equation under study is converted into a sparse matrix equation by this technique. Numerical examples are provided for a variety of thin-wire loop antennas and scatterers. © 1997 John Wiley & Sons, Ltd.     

用于开关电源的EMI滤波器设计

给出了用转移矩阵【A】参数法分析电源EMI滤波器插入损耗的具体方法,介绍了电源EMI滤波器的几种基本结构。通过分析LISN网络和EMI噪声的特性,分别对共差模等效电路进行分析与设计。结合所要通过的EMC标准计算所需的插入损耗,选择合适的元器件构造电源EMI滤波器,最后通过试验验证了设计方法的正确性。     

New mutual coupling compensation method and its application in DOA estimation

A new mutual coupling compensation method based on a new mutual impedance matrix, as well as its application to dipole arrays, are proposed. This new mutual impedance matrix is deduced by electromotive force (EMF) method, based on the current distribution obtained by the characteristic basis function method. It appears in a concise and explicit formulation that facilitates the numerical calculation. The compensation performance is demonstrated and evaluated through its application in direction of arrival (DOA) estimation. Numerical results show that the proposed method exhibits excellent compensation performance compared with conventional mutual impedance matrix approaches. __________ Translated from Chinese Journal of Radio Science, 2007, 22(4): 541–545 [译自: 电波科学学报]     

Equivalence of stability criteria for time-delay systems

During the past few decades, there have been a number of new delay-dependent stability criteria based on linear matrix inequalities published in the literature. These criteria, to some extent, can reduce the conservativeness. In fact, some criteria are equivalence. In this paper, we aim to theoretically establish equivalence of two stability criteria. One was obtained by Sun et al. [Sun et al. In: Proceedings of IEEE Power &; Energy Society General Meeting. 2009, 1–7] and the other was given by Xu et al. [Xu et al. IEEE Transactions on Automatic Control, 2005, 50(3): 384–387]. Also, we theoretically establish equivalence of the robust stability criterion presented by Jia et al. [Jia et al. Automation of Electric Power Systems, 2010, 34(3): 6–11] and the one given by Xu et al. (2005).     

One-cycle Control and Its Applications in Power Quality Control and Renewable Power Generation （2）

PFC rectifiers serve the same purpose as the APFs do except at lower power levels. Articles [5,6,7,14] have shown numerous three-phase topologies for rectification. Those with a single capacitor output rail are two level converters suitable for low voltage and high current operation while the others with split rails over two capacitors are threelevel converters suitable for high voltage operation. Unified control of these rectifiers was established based on the One-Cycle Control method [-5,6,7]. In this paper, an example of a standard bridge rectifieris provided. Using a similar procedure as for the APF,a control key equation matrix is derived below.     

Hilbert不等式的推广

本文讨论了一个在不等式理论中占重要地位的不等式－Ｈｉｌｂｅｒｔ不等式。由于Ｈｉｂｅｒｔ不等式在解析函数论、单实变函数论等数学分支的广泛应用，人们对它进行了许多研究和推广。本文应用推广的Ｈｏｌｄｅｒ不等式给出Ｌｅｖｉｎ和Ｓｔｃｃｋｉｎ￣［６］及Ｌｅｖｉｎ￣［７］在许多数下Ｈｉｌｂｅｒｔ不等式的推广。     

Concatenated Alamouti codes using multi-level modulation and symbol mapping diversity technique

A family of space-time block codes (STBCs) for systems with even transmit antennas and any number of receive antennas is proposed. The new codeword matrix is constructed by concatenating Alamouti space-time codes to form a block diagonal matrix, and its dimension is equal to the number of transmit antennas. All Alamouti codes in the same codeword matrix have the same information; thus, full transmit diversity can be achieved over fading channels. To improve the spectral efficiency, multi-level modulations such as multi-quadrature amplitude modulation (M-QAM) are employed. The symbol mapping diversity is then exploited between transmissions of the same information from different antennas to improve the bit error rate (BER) performance. The proposed codes outperform the diagonal algebraic space-time (DAST) codes presented by Damen [Damen et al. IEEE Transactions on Information Theory, 2002, 48(3): 628–636] when they have the same spectral efficiency. Also, they outperform the 1/2-rate codes from complex orthogonal design. Moreover, compared to DAST codes, the proposed codes have a low decoding complexity because we only need to perform linear processing to achieve single-symbol maximum-likelihood (ML) decoding.     

Distribution Line Carrier Sensitivity Analysis Using Bus Impedance Matrix

In a previous paper[1] we described the use of a bus impedance matrix approach for determining the signal strength of distribution line carrier signals. The technique used bus impedance matrices to calculate transimpedances which are the ratios of the voltage at any point on the line to the current injected at any point on the line. In the current paper we apply sensitivity analysis to this bus impedance approach and show how simply new transimpedances can be obtained from the original values when changes in the distribution line are made.