弱节点排序参与因子的等价判据与比较

将降阶潮流雅可比矩阵的最小奇异值(最小特征值)指标与节点电压/无功灵敏度指标相结合,给出了按参与因子进行弱节点排序的等价判据,即最小奇异值(最小特征值)对节点灵敏度的偏导数,拓展了参与因子应用于弱节点排序的物理意义。在IEEE 30节点系统上的仿真表明:降阶潮流雅可比矩阵得出的特征参与因子和奇异参与因子相等,因此对弱节点排序的作用完全相同。对于降阶潮流雅可比矩阵和由潮流雅可比矩阵的对称部分得到的对称降阶潮流雅可比矩阵,按灵敏度和参与因子得到的若干个关键弱节点相同,但排序略有差异。为简化有关计算,建议采用对称降阶潮流雅可比矩阵。     

潮流雅可比矩阵的对称性指标

针对潮流雅可比矩阵的对称性问题,根据零对角元素实矩阵与其对称及反对称矩阵奇异值之间的关系构造实矩阵的对称指标。指标间的比较不仅包括2-范数（最大奇异值）和F-范数的比较,同时也包括奇异值加权和的比较。这些指标同样适用于复矩阵。IEEE 30系统算例表明了其有效性。     

潮流Jacobian矩阵的正规性指标

为衡量潮流Jacobian矩阵的正规程度,根据正规矩阵的定义,正规矩阵Schur分解的特点,正规矩阵的奇异值与特征值的关系,以及正规矩阵的(反)Hermite部分的奇异值与正规矩阵的特征值实部(虚部)的关系,采用F-范数,2-范数或加权和的形式,建立了衡量矩阵正规程度的指标。在IEEE 30系统上进行的仿真表明:根据矩阵的奇异值和特征值得到的加权和指标应首先考虑,由矩阵的Schur分解得出的各指标大体相同。并对潮流Jacobian矩阵的正规程度与对称程度的关系进行了探讨。     

电压稳定分析中降阶潮流雅可比矩阵的研究

基于降阶潮流雅可比矩阵的V-Q灵敏度、模态分析等静态分析方法在分析电压稳定方面得到了广泛应用,但降阶雅可比矩阵涉及到系统潮流雅可比矩阵的子矩阵Pq可逆的问题,针对此问题,该文首先结合数学矩阵理论及电力系统的实际情况就矩阵Pq是可逆矩阵给出明确的证明,为基于降阶雅可比矩阵的应用提供理论支持。最后以新英格兰39节点系统作为算例,通过分析计算矩阵Pq的行列式、模最小特征值及条件数来验证矩阵Pq的可逆性,为电压稳定分析提供理论基础。     

衡量节点电压稳定的奇异值法和稳定指标

提出了衡量节点电压稳定的奇异值法，与衡量系统电压稳定的奇异值法相比，具有物理概念明确、计算量小的特点；通过对几种具有一定普遍性稳定指标的分析，总结了这一类指标的特点；讨论了最小奇异值表示的电压稳定裕度指标和物理量表示的电压稳定裕度指标间的关系；最后，就雅可比矩阵奇异、负荷功率极限和电压失稳临界值间的关系进行了探讨     

衡量节点电压稳定的奇异值和稳定指标

提出了衡量节点电压稳定的奇异值法，与衡量系统电压稳定的奇异值法相比，具有物理概念明确，计算量小的特点；通过对几种具有一定普遍性稳定指标的分析，总结了这一类指标的特点，讨论最小奇异值表示的电压稳定裕度指标和物理量表示的电压稳定裕度指标间的关系；最后，就雅可比矩阵奇异，负荷功率极限和电压失稳临值间的关系进行了探讨。     

基于预估/校正技术的改进奇异值指标

潮流雅可比矩阵最小奇异值可用来评估系统电压稳定裕度.但这种方法受到发电机无功出力越限的影响,给出的结果不够精确.该文致力于改进这一裕度指标,为此提出了利用预估/校正技术的算法来快速找到系统中电压崩溃点之前发电机无功越限信息,并利用这些信息修正潮流雅可比矩阵,使得其阶数不再受到发电机无功越限的影响,从而改进了最小奇异值裕度指标的线性性.给出了一个IEEE-14节点网络算例并得到预期结果.最后给出了结论,即利用预估/校正技术有效地克服了最小奇异值指标的阶跃性,提高了潮流雅可比矩阵最小奇异值作为裕度指标的可靠性.     

基于预估/校正技术的改进奇异值指标

潮流雅可比矩阵最小奇异值可用来评估系统电压稳定裕度。但这种方法受到发电机无功出力越限的影响,给出的结果不够精确。该文致力于改进这一裕度指标,为此提出了利用预估/校正技术的算法来快速找到系统中电压崩溃点之前发电机无功越限信息,并利用这些信息修正潮流雅可比矩阵,使得其阶数不再受到发电机无功越限的影响,从而改进了最小奇异值裕度指标的线性性。给出了一个IEEE-14节点网络算例并得到预期结果。最后给出了结论,即利用预估/校正技术有效地克服了最小奇异值指标的阶跃性,提高了潮流雅可比矩阵最小奇异值作为裕度指标的可靠性。     

潮流雅可比矩阵中有功/相角子矩阵的分析

探讨了潮流雅可比矩阵中有功/相角子矩阵的性质，给出了该矩阵可逆的充分条件及其奇异的必要条件。这些理论结果不仅可以澄清对该矩阵性质的模糊理解，而且可以为基于降阶潮流雅可比矩阵的应用提供坚实的数学基础。IEEE 14节点算例的仿真结果说明了该理论分析的正确性。     

用奇异值分解法对二级电压控制效果的分析

选取系统潮流雅可比矩阵的最小奇异值作为电力系统稳定裕度的相对量度,利用奇异值分解 法分析与评价二级电压控制对电力系统稳定性的影响。对两机系统在负荷微增、接 地短路故障以及重负荷微小扰动下分别进行了时域仿真,结果表明,二级电压控制通过重新 配置区域无功,使系统结构得到一定改善,增大了潮流雅可比矩阵的最小奇异值,也即增加 了系统的稳定裕度,从而提高了系统的稳定性。因此,二级电压控制是延缓电力系统电压崩 溃的有效手段。     

Fast calculation of a voltage stability index

The minimum singular value of the power flow Jacobian matrix has been used as a static voltage stability index, indicating the distance between the studied operating point and the steady-state voltage stability limit. A fast method to calculate the minimum singular value and the corresponding (left and right) singular vectors is presented. The main advantages of the algorithm are the small amount of computation time needed, and that it only requires information available from an ordinary program for power flow calculations. The proposed method fully utilizes the sparsity of the power flow Jacobian matrix and the memory requirements for the computation are low. These advantages are preserved when applied to various submatrices of the Jacobian matrix. The algorithm was applied to small test systems and to a large system with over 1000 nodes, with satisfactory results     

Voltage stability indices for stressed power systems

The use of static voltage stability indices based on a singular value decomposition of the power flow Jacobian matrix and matrices derived from the Jacobian matrix is discussed. It is shown that such indices, together with the singular vectors, contain substantial and important information about the proximity to voltage instability and also about critical buses and disturbances from a voltage instability point of view. This is done by a theoretical analysis of the linear power flow equations and an analysis from model power systems as well as realistic power systems (1033 nodes). It is argued that indices based on these matrices are useful for the system analyst in planning and operations planning     

Fast calculation of a voltage stability index of power systems

The minimum singular value of the Jacobian matrix of the load flow equation may have been preferred as an indicator of voltage collapse when the static voltage stability of power systems is studied. In this paper, the authors propose a highly efficient algorithm to calculate the smallest singular value of a Jacobian matrix of the load flow equation by employing the noniterative characteristic of an incremental condition estimation (ICE) method and the sparsity characteristic of large scale power networks. Both theoretical bases and computation costs of the algorithm are also detailed in the context. Finally, a practical application example is also given for demonstration     

多运行方式下恢复交直流系统潮流可行域的控制策略

电力市场化后,电力系统将运行在更加接近稳定约束边界的状态。当系统按正常网架运行时,由节点负荷和发电机出力确定的运行方式随时都在变化,系统可能在某些运行方式下出现不满足稳定约束条件的情况。针对一系列预想故障,提出了一种多运行方式下交直流互联系统静态电压稳定的预防控制策略,以使系统在所有的运行方式下对N-1情况都运行在潮流可行域范围内。以潮流雅可比矩阵的最小模特征值确定系统的最严重预想故障,根据节点注入无功对最小模特征值的参与因子,挑选出在恢复潮流可行域的优化计算中需要切除负荷和调整发电机出力的节点,并配合调整直流变量恢复系统至可行域范围内。算例分析表明所提方法是有效的。     

基于模态法的静态电压稳定性分析

提出了基于模态法的静态电压稳定性分析的新方法,通过建立模态法的静态电压稳定分析数学模型,求取潮流方程雅可比矩阵的最小特征值及其相对应的特征向量,以最小模特征值来间接评估系统的静态电压稳定裕度,并在此基础上提出了参与因子指标,计算各个节点在最小特征值下的节点参与因子来找出哪些节点或区域的电压稳定性较差.通过对某大型电网进行研究,得到其相应的电压薄弱区域,并与灵敏度分析法所得到的结果进行对比,结果基本一致,从而验证了本文方法的合理性与有效性。     

Reliable prediction of Hopf bifurcation in power systems

In this study, a new index for detection and prediction of oscillatory instabilities associated with HOPF bifurcation (HB) in power systems is proposed. Conventional indices could just predict HB in the heavy load conditions. The proposed index has a wider linear range and therefore prediction of system behavior at a wider range of load changes (even in lightly load condition) is provided. Consequently, the power system operators have more time to make the proper decisions to prevent HB. Conventional indices use critical eigenvalue pair of the state matrix to predict HB. This pair possesses biggest real parts among all eigenvalue pairs. However, sometimes this pair might not reach the imaginary axis before other eigenvalues. Therefore, they are not representative for HB eigenvalues which can lead to HB (This pair of eigenvalues could not be considered as HB eigenvalues). In this study, proposed index uses HB eigenvalue pair of state matrix to predict HB and two criteria are used to recognize HB eigenvalue pair. The first criterion is based on the proximity of the pairs of complex eigenvalue to the imaginary axis and the second criterion is based on the speed and the direction of the eigenvalues’ movement towards the imaginary axis. Also, in this study, Matrix Reciprocal Condition Number Estimate (MRCNE) instead of minimum singular value decomposition is used to determine proximity of matrix to singularity. This estimation causes faster calculation without missing considerable accuracy. In order to demonstrate the effectiveness and accuracy of the proposed index, the new method is tested on the IEEE-14 bus and WSCC-9 bus test systems and results are presented. Results indicate that the proposed index has wider linear range and could predict HB in lower load level.     

Efficient solution algorithms for computing fold points of power flow equations

Techniques for identifying fold points of power flow equations are fundamental to voltage stability analysis. This paper presents efficient methods for computing fold points of power flow equations. The proposed methods make use of two generalized extended systems for determining fold points of nonlinear systems, i.e., the Moore-Spence system and the minimally extended system. Block elimination (BE) techniques are used in the solution procedures for the two systems. Hence, the sparsity of Jacobian matrix of power flow equations can be fully exploited to enhance computational efficiency. Left and right singular vectors corresponding to the zero eigenvalue of Jacobian matrix of nonlinear power flow equations can be obtained simultaneously at the end of the iterations. Numerical examples of Ward & Hale 6-bus system and a real 1620-bus power system in China are presented to validate the methods.     

基于辅助变量的潮流方程二次转折分岔点的直接算法

对于一个含单参数的潮流方程组，二次转折分岔是最简单的且最为普遍存在的一种分岔。在二次转折分岔点处，系统的Jacobi矩阵为秩降1的奇异阵。为了克服Jacobi矩阵的奇异性，可采用Moore—Spence系统来确定转折分岔点。然而，Moore—Spence系统具有很高的维数，给计算工作带来不便。该文通过引入辅助变量和辅助方程，得到一个求解潮流方程的Moore—Spence扩展系统的矩阵降阶新算法。该算法克服了潮流方程在分岔点处的奇异性所造成的求解困难，同时也解决了Moore Spence方程的高维数问题。     

电力系统电压崩溃临界状态的近似算法

利用潮流方程的多解特性，用一个新的近似变量组成了一个新的Jacobian矩阵，间接地避免 了潮流方程的Jacobian矩阵在临界点奇异而带来的不收敛问题；提出了快速计算电压崩溃临 界状态的近似算法，为计算电压崩溃的临界运行状态及其裕度提供了一种快速计算方法。