基于雅可比矩阵逆预处理的快速潮流计算方法

随着电网规模变大，利用稳定双共轭梯度法（Bi-CGSTAB）求解潮流计算中的修正方程组时，收敛速度会变得很慢。通过寻找合适的预处理矩阵是解决问题的关键。研究了雅可比矩阵预处理方法，针对牛顿法求解潮流过程中雅可比矩阵的变化特性，提出将第一次外迭代的雅可比矩阵逆作为预处理矩阵，并与稳定双共轭梯度法相结合，提高潮流计算的收敛速度。借助InterPSS电力系统仿真软件，对IEEE118、IEEE162、IEEE300和一个欧洲大陆真实电力系统进行仿真计算，验证了在处理大规模电网时，所提方法相对稀疏近似逆预处理具备更好的有效性。     

基于GaBP算法的快速潮流计算方法

研究在潮流迭代求解过程中雅可比矩阵方程组的迭代求解方法及其收敛性。首先利用PQ分解法进行潮流迭代求解,并针对求解过程中雅可比矩阵对称且对角占优的特性,对雅可比矩阵方程组采用高斯置信传播算法(GaBP)进行求解,再结合Steffensen加速迭代法以提高GaBP算法的收敛性。对IEEE118、IEEE300节点标准系统和两个波兰互联大规模电力系统进行仿真计算后结果表明：随着系统规模的增长,使用Steffensen加速迭代法进行加速的GaBP算法相对于基于不完全LU的预处理广义极小残余方法(GMRES)具有更好的收敛性,为大规模电力系统潮流计算的快速求解提供了一种新思路。     

基于牛顿-拉夫逊电力系统潮流计算的改进算法

牛顿-拉夫逊法是求解非线性代数方程有效的迭代计算方法,广泛应用于现代电力系统安全分析、故障诊断与控制的潮流计算中。为提高牛顿-拉夫逊潮流计算方法的快速性和收敛精度,本文提出一种改进的牛顿-拉夫逊潮流计算法,并通过IEEE14和IEEE30节点测试系统分析表明与传统方法相比该方法所具有的优点。     

改进牛顿法大规模电力系统潮流计算

电网互联导致电力系统规模不断扩大,对牛顿法进行潮流计算提出了更高的要求。探讨5种改进牛顿法应用到大规模电力系统潮流计算中。经IEEE 300、Poland多个互联的大规模电力系统共6个算例分析表明,算法1和算法2改善了初值范围,同样的迭代次数下,收敛精度较经典牛顿法高,但计算时间较经典的牛顿法并未明显提高;算法3和算法4提高潮流计算的速度和收敛精度。经UCTE 1254病态系统测试,算法3较算法5能高效地处理病态潮流问题,因而更适合于大规模电力系统潮流计算。     

具优势对称部分的非对称非线性问题的不精确Newton分裂算法

本文讨论了处理具优势对称部分的非对称非线性问题的不精确Newton方法.利用矩阵分裂技术,建立了求解此类问题的一类不精确Newton分裂极小参量法、不精确Newton分裂对称LQ法(简记:Newton-SMINRES,Newton-SSYMMLQ),并在合理的假设下,证明了算法的收敛性.数值计算表明:Newton-SMINRES,Newton-SSYMMLQ算法的收敛行为要好于一般求解非线性方程组的Newton-Krylov子空间方法:Newton-BiCGSTAB,Newton-GMRES和Newton-MINRES等算法.     

最优潮流问题的解耦半光滑牛顿型算法

提出一种求解最优潮流（OPF）问题的新算法--解耦半光滑牛顿型算法.该算法是对作者的投影半光滑Newton算法的改进和提高,它除了保持原算法不必识别不等式约束、对界约束的特殊处理以减少讨论问题的维数等优点外,其显著的特点是结合了电力系统固有的弱耦合性质,构造了求解OPF问题的一类解耦半光滑牛顿算法.解耦算法可达到加快计算速度、提高计算效率的目的.IEEE多个算例的数值实验以及与其他方法的比较均显示了新算法具有良好的计算效果.     

面向磁流体动力学方程组的异构众核全隐求解器研究

磁流体动力学方程组被广泛应用于受控核聚变装置托卡马克、天体物理、磁流体发电等问题的研究中,其往往具有非线性、多尺度、多物理等特征,大规模数值难度较大.目前国际上对不可压缩流体问题的大规模数值求解主要采用全隐或半隐方法,但都是在同构的超级计算机而不是目前主流的异构众核系统上进行计算.论文面向国产神威"太湖之光"超级计算机,开展面向磁流体动力学方程组的异构众核全隐求解器研究.针对Newton-Krylov这类全隐求解器,提出了面向申威26010众核处理器的异构众核并行算法,并对其核心函数开展了众核并行和优化.对核心函数稀疏矩阵向量乘采用Matrix Free的方法来提升性能,对稀疏三角求解采用基于几何信息的异构众核并行算法,针对其访存密集的特点提出了存储格式、数据读取与计算依赖分离、核间寄存器通信等多种优化方法,对非线性残差计算等stencil类计算及10多个向量函数进行了异构众核并行,该异构众核并行算法可被其它应用软件重用.论文采用二维磁场重联问题进行测试,实验结果表明16进程时加速比可达13.6倍,能够支持高分辨率长时间模拟,并准确捕捉磁场重联现象.另外整体并行扩展性已经达到53万核,强可扩展性并行效率达到了33.8%,弱可扩展性并行效率达到了80.7%.     

求解周期三对角Toeplitz方程组的一种新修正算法

利用Sherman-Morrison-Woodbury公式导出了求解周期三对角Toeplitz方程组的一种新的修正算法.该算法的计算量比求解周期三对角方程组的追赶法要少,且可以并行计算.对新算法进行了可行性和稳定性分析.数值算例表明了新算法的有效性.     

轻负荷磁头气动力分析

本文采用微分离散有限差分法求解滑流条件下的修正雷诺方程.离散后的三对角线性代数方程组用ADI方法求解.本方法适用于任意几何形状、尺寸、姿态角的多轨窄式磁头滑块的气动力计算,并不受大压缩数的限制.计算结果包括即时给出的压强分布立体图.     

粒子群算法在求解方程组中的应用

提出了采用粒子群算法求解线性方程组和非线性方程组的智能算法。采用粒子群算法求解方程组具有形式简单、收敛迅速和容易理解等特点,且能在一次计算中多次发现方程组的解,可以解决非线性方程组多解的求解问题,为线性方程组和非线性方程组的求解提供了一种新的方法。     

几种Krylov迭代法在潮流计算中的对比

在潮流计算时,绝大部分时间都用在求解大规模稀疏线性方程组Ax=b上。众多文献中运用的迭代法并不统一,它们只注重预处理方法的改进。本文就针对几种流行的Krylov迭代法进行详细介绍,总结特性,并利用实验来分析它们总的FLOPS值和收敛效率。最后,通过评估算法的计算效率,得出一种比较适合潮流计算的Krylov迭代法。     

Exchange market algorithm based optimum reactive power dispatch

In this paper, an exchange market algorithm (EMA) approach is applied to solve highly non-linear power system optimal reactive power dispatch (ORPD) problems. ORPD is most vital optimization problems in power system study and are usually devised as optimal power flow (OPF) problem. The problem is formulated as nonlinear, non-convex constrained optimization problem with the presence of both continuous and discrete control variables. The EMA searches for optimal solution via two main phases; namely, balanced market and oscillation market. Each of the phases comprises of both exploration and exploitation, which makes the algorithm unique. This uniqueness of EMA is exploited in this paper to solve various vital objectives associated with ORPD problems. Programs are developed in MATLAB and tested on standard IEEE 30 and IEEE 118 bus systems. The results obtained using EMA are compared with other contemporary methods in the literature. Simulation results demonstrate the superiority of EMA in terms of its computational efficiency and robustness. Consumed function evaluation for each case study is mentioned in the convergence plot itself for better clarity. Parametric study is also performed on different case studies to obtain the suitable values of tuneable parameters.     

基于RKNd算法的暂态稳定性快速数值计算方法

RKNd方法是一类新的数值积分方法。在相同级数条件下,RKNd方法可达到的最高代数阶比传统的Runge—Kutta方法以及Runge—Kutt—Nystrom方法均高,而且具有更高的计算效率。将RKNd方法引入电力系统暂态稳定性数值计算。以IEEEl45节点电力系统为例,通过数值实验将新方法与电力系统分析中常用的传统数值计算方法进行了对比分析。数值实验结果表明,RKNd方法在计算精度和计算效率等方面均具有明显的优势,N而更适合于电力系统暂态稳定性及相似问题的数值计算。     

Algebraic and Parametric Solvers for the Power Flow Problem: Towards Real-Time and Accuracy-Guaranteed Simulation of Electric Systems

The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration.     

基于Transformer的多任务暂态稳定评估

电力系统中的暂态功角稳定和暂态电压稳定对于系统安全运行至关重要,而可再生能源接入比例不断提高和核心设备的电力电子化使得传统的暂态稳定评估方法难以适用。因此,本文提出一种基于Transformer的多任务暂态稳定评估模型。该模型利用Transformer的自注意力机制打破传统循环神经网络的串行计算结构,并行计算暂态过程中各个时间点间的相互关系,快速高效的提取时序特征,并且采用门控多任务学习方法同时评估暂态电压和暂态功角稳定问题,提升模型计算精度和计算效率。本文在IEEE10机39节点系统以及含新能源系统中进行仿真和测试验证了本文提出方法的有效性。     

Evolving ant direction differential evolution for OPF with non-smooth cost functions

In this paper, an effective and reliable algorithm, termed as evolving ant direction differential evolution (EADDE) algorithm, for solving the optimal power flow problem with non-smooth and non-convex generator fuel cost characteristics is presented. In this method, suitable mutation operator for differential evolution (DE) is found by ant colony search. The genetic algorithm evolves the ant colony parameters and the Newton-Raphson method solves the power flow problem. The proposed algorithm has been examined on the standard IEEE 30-bus and IEEE 57-bus systems with three different objective functions. Different cases were considered to investigate the robustness of the proposed method in finding the global solution. The EADDE provides better results compared to classical DE and other methods recently reported in the literature as demonstrated by simulation results.     

多波前算法在电力系统分析计算中的应用

以IEEE检验系统为例,通过数值试验将多波前算法与电力系统分析中常用的稀疏三角分解技术进行对比分析。数值试验结果表明,在串行计算平台上,多波前算法相对于稀疏三角分解技术具有更好的计算效率,因而更适合于现代大规模电力系统的分析计算。此外,多波前算法更易于并行化,而且是一种适合于可重构计算系统的新方法。     

An ordinal optimization theory-based algorithm for large distributed power systems

In this paper, we propose an ordinal optimization (OO) theory-based algorithm to solve the yet to be explored distributed state estimation with continuous and discrete variables problems (DSECDP) of large distributed power systems. The proposed algorithm copes with a huge amount of computational complexity problem in large distributed systems and obtains a satisfactory solution with high probability based on the OO theory. There are two contributions made in this paper. First, we have developed an OO theory-based algorithm for DSECDP in a deregulated environment. Second, the proposed algorithm is implemented in a distributed power system to select a good enough discrete variable solution. We have tested the proposed algorithm for numerous examples on the IEEE 118-bus and 244-bus with four subsystems using a 4-PC network and compared the results with other competing approaches: Genetic Algorithm, Tabu Search, Ant Colony System and Simulated Annealing methods. The test results demonstrate the validity, robustness and excellent computational efficiency of the proposed algorithm in obtaining a good enough feasible solution.