应用矩阵块对角占优理论,讨论了块α-对角占优矩阵之间的蕴含关系,并得到了条件最弱的块严格α1-双对角占优的两个等价表征,并作为应用给出了块H矩阵新的判定准则,最后用数值例子说明结果的有效性.

Applying the theorem of block diagonally dominant matrices, we discuss the relations between blockα-diagonally dominant matrices. We give two equivalence representations for strictly double blockα1-diagonally dominant matrices. As its application, we obtain some criteria for block H-matrices. In the end, the efficiency of the proposed criteria is showed by a numerical example.

电力系统全过程动态仿真能够将机电暂态、中期和长期动态过程有机地统一起来进行数字仿真,仿真过程中需要多次求解大型稀疏线性方程组。该方程组由电力系统设备模型的微分—代数方程式差分后的代数方程和输电网络模型的代数方程形成,其快速求解算法是电力系统全过程动态仿真的难点之一。文中提出一种利用仿真中矩阵结构特点的分块快速直接求解算法,并开发实现了大型电力系统线性方程组稀疏求解器(ESS)。该算法首先将稀疏矩阵分为4个分块矩阵,然后将其中规模最大的对角块进一步细分为多个更小的对角分块矩阵,并利用部分小分块具有相同结构的特点进行矩阵LU符号分解和数值分解,最后根据分块矩阵进行前代和回代求解计算。与现有其他求解器进行的算例对比表明,ESS具有较为明显的整体求解速度优势,特别是在矩阵LU分解方面。

Power system whole process dynamic simulation is such a method in which the electro-mechanical transient,medium-and long-term dynamic phenomena are organically unified.During the whole process of dynamic simulation,it is one of the key steps to solve sparse systems of linear equations composed of two kinds of equations:difference equations from dynamic equipment and algebraic equations from power network.Because of its very high order and large numbers of solving,the algorithm for fast solving is very important for this kind of dynamic simulation.This paper proposes a new method based on the block matrix for fast solving this linear equation and has developed an electric sparse solver (ESS).It first divides the sparse matrix into four big blocks.Many decoupled diagonal smaller blocks which are related to the equipment on buses in the power system are further divided from the largest diagonal block.Next,by utilizing the same structure among these small blocks,these diagonal blocks are s

对于传统的电力系统广义Hamilton实现，判定Hamilton函数Hessian矩阵的正定性是保证系统Lyapunov意义下稳定的充分条件，而复杂电力系统中此Hessian矩阵通常为高维分块矩阵，其正定性判定较为困难。基于二次型和块对角占优的思想，推导出判断高阶分块矩阵正定性的一般方法，利用矩阵分块理论并结合矩阵块的行或列的性质来实现。计算过程简单，大大减小了计算量。运用电力系统暂态能量函数方法有助于控制的设计和研究，并使用上述方法判断系统在平衡点处Hessian 矩阵的正定性。在四机系统中进行 Simulink 仿真，证明了所推导判据的准确性和控制策略的有效性，简化了广义Hamilton系统实现的Hessian矩阵正定性的判断过程。

The positive definiteness judgment of Hessian matrix of Hamilton function is a sufficient condition to guarantee the system stability in the Lyapunov sense for the generalized Hamiltonian realization of the traditional power system.However,the Hessian matrices of complex power system are usually high-dimension blocked matrices and the judgments of positive definiteness are very difficult.The general method to judge the positive definiteness of high-order blocked matrix is derived based on the idea of quadratic form and block diagonal dominance,and it can be realized by using the characteristics of the blocked rows or columns of matrix and blocked matrix theory.The calculating process will be simpler,and it greatly reduces the amount of calculations.At the same time, it will be conducive to the research and design of the control by means of the transient energy function method of power system,and the positive definiteness of Hessian matrix at the equilibrium point is judged by the above

煤层气开采过程中通常采用数值模拟方法进行生产指标预测,其中的数值模型普遍采用三维全隐式差分法求解,模型涉及的参数变量多,求解难度大,计算复杂。根据煤层气的储气特征、吸附特征和解吸机理建立了反映煤层气解吸、扩散及渗流过程的气、水两相流动煤层气羽状水平井三维数学模型,模型考虑了煤层非均质各向异性的影响,运用块中心差分格式,对气、水相偏微分方程进行空间差分和时间差分,采用交替隐式(ADI)法求解,实现了煤层气羽状水平井开发数值模拟计算。交替方向格式可以把二维问题转化成一维问题,对x,y两个方向的迭代矩阵均为三对角矩阵,结构相同,易于编程计算。所建立的差分格式具有计算量小,稳定性好等优点,数值试验的结果表明效果良好。

The numerical simulation is an effective method to confirm CBM exploitation scheme and evaluate recovery factor. Present widely used 3D full implicit difference method is hard to compute and get solution. According to CBM storage and adsorption character-istics, as well as desorption mechanisms have modeled gas, water two phases flow CBM pinnate horizontal well 3D mathematical model can reflect CBM desorption, diffusion and seepage processes. The model has considered impacts from anisotropic coal seams, using block-centered finite difference scheme carried out spatial and temporal differences on gas, water phases partial differential equation, through ADI to get solution, realized CBM pinnate horizontal well exploitation numerical simulation computing. The alternating direc-tion scheme can transform two-dimensional problem into one-dimensional problem, to x, y two direction iterative matrixes are all tri-diagonal matrixes with same configuration, thus easy to programming computation. T

为了消除或降低多用户MIMO系统下行链路存在的共信道干扰(CCI),提出一种结合功率分配的基于最大化信漏噪比(SLNR)的预编码算法。首先,根据SLNR算法求出最优预编码矩阵,再结合最优功率分配算法,借助拉格朗日乘数法,优化分配每个用户的发送功率,从而提高系统和容量以及降低误码率(BER)性能。为了简化计算复杂度,还提出了SLNR算法结合次优化功率分配算法。仿真表明,所提出的算法比块对角化(BD)算法和最小均方误差准则(MMSE)算法在系统和容量以及误码率性能上都有所改善。

To eliminate or reduce the Co-Channel Interference ( CCI) between users,a precoding algorithm combined with power alloca-tion,based on maximizing Signal to Leakage and Noise Radio ( SLNR) ,is proposed for the downlink of multi-user MIMO system. On the basis of SLNR,find the optimal precoding matrix,and then with the aid of Lagrange multiplier method,coupled with the optimal pow-er allocation algorithm,allocate every user’ s transmitted power optimally,in order to improve the system sum capacity and reduce Bit Er-ror Rate (BER) performance. Suboptimal power allocation algorithm,combined with SLNR is proposed to simplify the computational complexity. The simulation results show that the proposed algorithm can make system has better performance on the system sum capacity and BER than BD and MMSE algorithm.