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     

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。     

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     

基于ZM综合负荷模型地区电网静态电压稳定分析

提出一种适用于地区电网静态电压稳定分析计算的改进奇异值分解法.该方法在形成雅可比矩阵时,考虑了ZM综合负荷模型的稳态特性对电压稳定的影响,通过对扩展雅可比矩阵进行奇异值分析,得到弱稳定节点和静稳裕度.通过算例仿真验证了该方法的有效性和合理性,算例结果表明考虑动态设备的稳态特性后的分析结果更能反映电网的真实状态,从而有利于电压稳定控制决策.     

一种快速的定雅可比潮流算法

完美地组合了电流注入型潮流算法和保留二阶项的快速潮流算法的优点,弥补了二者的不足之处,提出了一种快速的定雅可比潮流算法。该算法修正方程式的雅可比矩阵是通过对电流注入型潮流算法PQ节点的雅可比矩阵进行改造而得来的,是一个对称的常数雅可比矩阵。修正方程式的常数项是在保留潮流方程式非线性项的基础上进行简化改进而获得的,是一个非常简单的修正公式,在迭代过程中完全不需要进行节点电压的修正和节点功率的计算。这些处理,既保证了算法的收敛性,又大大提高了计算速度。详细论述了该算法的原理及用法。最后将它与牛顿法、定雅可比牛顿算法、PQ分解法、快速解耦法（FDLF）等潮流算法在多个算例上进行了收敛性能和收敛速度的比较,结果证明该算法收敛速度远大于牛顿法和定雅可比牛顿算法,收敛能力与定雅可比牛顿算法相当,算法适用能力比PQ分解法和快速解耦法强。     

计及负荷特性的电压稳定安全指标快速计算

本文提出了计算电力系统电压稳定安全指标的新算法，该算法计及了负荷特性的影响，采用参数随运行状态变化的负荷模型，以负荷中动态荷部分的有功功率最大作为临界点判据，并在网络求解中负荷采用导纳模型来克服临界点附近潮流收敛的困难。本文还给出了７节点系统和３１节点系统的算例。     

A METHOD FOR TRACING PV CURVE FOR VOLTAGE STABILITY ANALYSIS WITH VOLTAGE DEPENDENT LOADS

ABSTRACT

A new method for construction of PV-curve has been developed using one of the load bus voltage as a parameter. This regularizes the power flow solution around maximum loading point. In conventional load flow solution it is observed that main cause of numerical instability is that the load is specified at each node directly, so that the singular point occurs at maximum loading point. It is important that, instead of specifying the load externally, to be obtained as a solution of the power flow equation. The size of modified Jacobian is the same as of the conventional load flow Jacobian. The method is capable of handling Q- limits on PV - buses. Loads have been assumed to be voltage dependent. PV- curves have been traced with and without voltage dependent loads. The results of applying the proposed technique to two test systems verify its roubstness and feasibility.     

配电网电压稳定的分布式评估方法

提出了一种分布式评估配电网静态电压稳定性的方法。基于Distflow潮流模型建立包括平衡节点在内的配电网潮流方程组,对方程组求导后得到雅克比矩阵;利用Shur补对上述雅克比矩阵进行降阶,降阶雅克比矩阵的行列式作为配电网电压稳定性的评估指标;进一步研究发现,降阶雅克比矩阵属于对角占优阵,行列式的值约等于对角元的乘积,且其对角元可以由配电网每个节点进行分布式计算。在IEEE 33节点配电网系统中验证了所提方法的可行性和有效性。     

Power injection model of STATCOM with control and operating limit for power flow and voltage stability analysis

This paper presents a power injection model (PIM) of STATCOM for power flow and voltage stability analysis. In this model, PWM control and phase control strategies of STATCOM are handled, and the operating limit is enforced. The NR formulation has the same structure before and after the limit enforcement, and the Jacobian matrix adds only one dimension. This model can also take into account the steady-state losses of STATCOM if desired, and hence more accurately predict the active and reactive power injections. The singular value decomposition (SVD) based method is then extended to study the effect of STATCOM on power systems voltage stability. IEEE 300-bus and 30-bus systems are used to verify the effectiveness and performance of this model and the effect of load changes at all the buses simultaneously on voltage stability has also been studied with the STATCOM.     

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。     

基于牛顿法的配电网络Zbus潮流计算方法

根据配电网的特点,在比较各类算法的基础上提出了一种新的基于牛顿法的配电网潮流算法。该算法从Zbus算法出发,对网络方程进行虚实部分解,形成的雅可比矩阵与节点导纳矩阵有极大的相似性,迭代中雅可比矩阵仅有少部分对角元素需要修改。算法通过修改雅可比矩阵元素来处理PV节点,还能够处理几种不同类型的负荷模型。理论分析和计算表明该算法性能优良,是配电网络潮流分析的有效方法。     

临近电压稳定极限的潮流和静稳极限算法

本文提出重负荷节点电纳模型的常规潮流算法，改变了临界点附近雅可比矩阵的最小模特征值，解决了重负荷条件下潮流计算的收敛困难问题。利用该算法可以很方便地解出临近电压稳定极限的重负荷潮流和电压静稳极限。通过矩阵扰动的理论证明并用实例验证了它的有效性和适用性，从而为电压稳定的研究提供了一种简便、有效的算法。     

基于源-荷功率动态匹配的海上平台电力系统静态电压稳定分析

对海上平台电力系统进行静态电压稳定分析是保证其安全性、可靠性的前提.针对海上平台电力系统多平衡节点特征,基于透平发电机组和旋转负荷群的源-荷特性建立计及源-荷功率动态匹配特性的扩展连续潮流模型;针对海上平台电力系统的机组小容量特征和旋转负荷的生产要求,基于机组出力和节点电压的限值确立静态电压稳定分析边界约束;推导扩展连续潮流增广雅可比矩阵,提出基于牛顿-拉夫逊法的静态电压稳定分析方法.对某海上平台电力系统的静态电压稳定分析结果表明,与传统牛顿-拉夫逊法相比,所提方法不仅能找出随负荷增加的电压薄弱节点,且能给出各机组适应负荷增加的出力值.     

A second order method for contingency severity assessment withrespect to voltage collapse

The increase in power transfer among areas of interconnected systems, and the reduction of reactive power reserves, force system operators and planners to consider the contingency analysis also from the voltage/reactive point of view. In this paper, second order information derived from the singular value analysis of the Jacobian of load flow equations is used to obtain an effective ranking of contingencies with respect to the voltage collapse. Besides, a quantification of the risk associated to a contingency is provided by a procedure that calculates quasilinear indices useful both in planning and in operation. The effectiveness of the presented indices is supported by the analysis of the perturbation on the Italian power system in August 1994     

极限诱导分岔最小负荷裕度计算方法

由于极限诱导分岔点处的潮流雅可比矩阵非奇异,因此电压稳定裕度对参数灵敏度的计算存在困难。对此,采用分岔点处参数灵敏度计算的新方法,只需求解一个左端系数阵为扩展潮流雅可比矩阵的线性方程组,进而提出了包含极限诱导分岔点在内的静态电压稳定最小负荷裕度计算方法。该方法结合负荷增长模式及其波动形式,建立了连续潮流模型和求取最小负荷裕度的优化模型。IEEE 118节点系统的仿真算例验证了所述方法的简单有效性。     

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。     

具有PV节点的配电网常Jacobian矩阵潮流算法的分析比较

随着配电网实时监控要求的不断提高,有必要寻找一种既能建立常Jacobian系数矩阵以提升其收敛速度,又能满足病态条件下方程有解而不至于发散的潮流计算方法。该文基于牛顿-拉夫逊法的极坐标形式,从复功率方程出发,忽略功率方程迭代过程中影响相对较小的负荷功率,把PV节点电压的实部、虚部线性拟和为幅值,建立了完全常数项的Jacobian矩阵。对常Jacobian矩阵的适应性进行了详细的论证且得到了实际算例证实,证明本算法提高了计算效率并显著降低了内存需求;该算法无须解耦,不受R/X数值大小的影响,具有出色的收敛性     

含静止同步串联补偿器的电力系统电压稳定性奇异值分析法及指标计算

提出了一种静止同步串联补偿器(static synchronous series compensator,SSSC)混合模型,推导了电力系统中加入SSSC模型后的潮流方程。在潮流计算和奇异值分解的基础上,构建了基于SSSC混合模型和奇异值分解的电压稳定性弱节点判别指标及最危险负荷增长方式指标。利用奇异值分析法,深入分析了在负荷平均增长和最灵敏节点负荷增长2种情况下,SSSC对电力系统电压稳定性的影响。研究了采用弱节点判别指标和最危险负荷增长方式指标确定系统最薄弱节点和负荷增长最快节点的方式。证明了在系统最薄弱节点和负荷增长最灵敏节点线路中加入SSSC后能提高电力系统电压稳定性。对IEEE14节点系统进行了仿真计算,验证了所构建的SSSC混合模型以及2个电源稳定性分析指标的可行性、有效性和适用性。     

节点追加法形成Jacobian逆矩阵的潮流算法

电力网络是由一系列连接关系高度稀疏的节点构成。为了在潮流计算中充分利用这一特性以最大限度地采用稀疏技巧,文章提出一种通过节点追加法来形成Jacobian逆矩阵的潮流算法。该算法以一个节点为基础,逐次添加一个节点,直至网络中所有的节点都添加完毕,最终形成完整的Jacobian逆矩阵。给出了直角坐标和极坐标形式下该算法的推导公式,结果表明:在形成Jacobian逆矩阵的过程中可以充分利用Jacobian矩阵元素排列的高度稀疏特性。以IEEE-30节点系统为例验证了该算法的有效性。     

Control of voltage stability using sensitivity analysis

The effects of static compensation on the voltage stability boundary are investigated. For a class of voltage instabilities which correspond to static bifurcations of load flow equations, minimum singular values of the Jacobian matrix and total generated reactive power are calculated as indicators of stability margin, and sensitivity methods are used for reactive support allocation. Improvement in stability margin under progressive loading was investigated on a 39-bus test system for different allocations and amounts of reactive support with reactive generation capabilities taken into account