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     

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     

A New Computationally Efficient Index for Loadability Limit Studies

This paper presents the Load Increase Index, which is a new computationally efficient loadability limit index derived from the continuation power flow method. The continuation power flow is a well-known procedure for identifying the maximum loading point of a static power system network. The proposed index is a byproduct of the continuation power flow, and may be obtained with little extra computational effort while yielding considerable information about the distance to the critical loading point. This paper also presents the mathematical relationship of the proposed index to two other commonly used voltage stability indices: the smallest singular value of the loadflow Jacobian and the determinant of the loadflow Jacobian. The proposed index has been verified on numerous test systems of various sizes.     

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     

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.     

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。     

基于改进Chord法的电力系统连续潮流计算新方法

连续潮流计算是电力系统研究静态电压稳定和传输能力应用的重要工具,但临界点处的奇异性制约了连续潮流计算的应用和发展。因此,解决好临界点病态问题是更好应用连续潮流的关键。应用改进Chord法处理连续潮流问题中临界点处的计算,能够快速计算该点处的解,收敛速度快,达到二阶收敛。不用扩展原雅可比矩阵,因此不需要担心原系统中的非奇异点变为系统扩展雅可比矩阵的奇异点问题,使计算过程更为简单。应用线性化方法预测连续潮流计算方向,整个计算过程简洁方便。在计算及分析中与扩展潮流计算方法进行比较,体现了所提Chord法简洁、高效的优点。不同工况下,IEEE39和IEEE57节点系统仿真算例结果表明,所提模型和方法能够快速有效地计算连续潮流和临界点处的奇异解,有着很好的精确性和鲁棒性。     

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.     

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。     

计及TCSC的交直流系统静态电压稳定性分析

基于交直流系统潮流方程雅可比矩阵的特征结构分析法,提出了一种利用可控串联补偿器(thyristor controlled series compensator,TCSC)提高交直流系统静态电压稳定性的方法。该方法研究了交直流系统潮流方程雅可比矩阵的最小模特征值,以节点电压对无功功率变化的灵敏度为指标,结合参与因子,判断全电网中最有可能发生电压不稳定的节点或者区域,从而为系统无功功率补偿装置的配置提供决策依据。对美国西部5机14节点系统进行了仿真计算,验证了TCSC在交直流系统中提高静态电压稳定性的可行性、有效性和正确性。     

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.     

Using automatic code differentiation in power flow algorithms

First order derivative computations (Jacobian matrices) are required by power flow studies. In this paper the computation of the sparse Jacobian matrix is implemented using an automatic code differentiation tool for FORTRAN77 code. The user only programs the code for the computation of the numeric mismatch values of all equations. The automatic generation of the derivative code includes also the automatic consideration of inherent sparsity of the Jacobian of the power flow equations. This approach allows the coding as explicit equations of also complex features such as remote voltage and area interchange control, controlled quantity limits and the dynamic change from one equation set to another during the power flow iterations. The resulting power flow code is easy to enhance and to maintain, shows good execution speed and has been successfully applied to network systems as large as 2550 nodes     

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。     

电力系统频域电压稳定测度的研究

传统的电压稳定测度指标都把潮流方程邪念可比矩阵奇异点作为系统电压失稳的临界点,而不考虑系统发生Ｈｏｐｆ分叉的可能性,因而上应的测度指标不可避免地具有一定的冒进性。     

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。     

Constraints Violation Handling of GUPFC in Newton-Raphson Power Flow

Generalized Unified Power Flow Controller (GUPFC) is one of the newest Flexible AC transmission system (FACTS) devices based on voltage source converters. This paper presents a developed model of GUPFC based on power injection approach. The series converters of GUPFC is represented by injected complex loads as function of the specified powers flow, while the shunt converter is represented as a synchronous condenser that provides the reactive power compensation to control the bus voltage magnitude. The main advantage of the developed model is that the original structure and symmetry of the admittance and Jacobian matrices can still be kept avoiding the changes of the original Jacobian matrix. Consequently, the complexities of the load flow are reduced. This model includes simple strategies for handling the operating constraints of GUPFC, including the injected series and shunt voltages magnitude, currents of the series and shunt converters, and the real powers exchanged in the converters. The strategies are based on decreasing one or more values of specified values or by modifying the specified values as a function of the required constraint limits. The developed model and proposed strategies for handling violation of GUPFC operating constraints are tested on IEEE test systems such as 57-bus and 118-bus systems.     

基于降阶雅可比矩阵的电力系统状态估计可观测性分析方法

提出了一种新的基于降阶网络雅可比矩阵的电力系统状态估计可观测性分析方法。该方法利用潮流岛内未知状态量最多是一个复电压的特性,提出了潮流岛状态变量的概念,在降阶网络雅可比矩阵基础上成功地实现了基于潮流定解条件的潮流岛合并。该方法减少了未知状态变量的数量,从而简化了循环判断过程和便于程序设计。并通过实例对所提出的方法进行了有效性检验。     

基于PMU量测的配电网稀疏估计

同步相量量测技术的应用为配电网估计如潮流雅可比矩阵估计和电压/相角-功率灵敏度估计提供了重要技术基础。针对潮流雅可比矩阵的相关性、稀疏性和对称性,提出了一种基于同步相量测量单元量测数据的潮流雅可比矩阵和灵敏度矩阵的稀疏估计方法,在较少量测下,有效估计了雅可比矩阵和灵敏度矩阵。进一步针对量测过程中出现的不良数据,引入鲁棒性更大的加权最小二乘法,提高了算法的鲁棒性。最后,通过IEEE33节点配电系统验证了方法的可行性。     

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.     

Voltage stability evaluation using modal analysis

The authors discuss the voltage stability analysis of large power systems by using a modal analysis technique. The method computes, using a steady-state system model, a specified number of the smallest eigenvalues and the associated eigenvectors of a reduced Jacobian matrix. The eigenvalues, each of which is associated with a mode of voltage/reactive power variation, provide a relative measure of proximity to voltage instability. The eigenvectors are used to describe the mode shape and to provide information about the network elements and generators which participate in each mode. A simultaneous iteration method, which is well suited to applications involving large power systems, is used for selective calculation of appropriate eigenvalues. Results obtained using a 3700 bus test system are presented illustrating the applicability of the approach