基于静态电压稳定性指标的等价性研究

基于连续潮流分析方法,依据三种电压稳定指标(V-Q灵敏度、模态分析母线参与因子及负荷裕度灵敏度),在电力系统电压稳定崩溃点时的数量大小,识别对电压稳定有重要影响的负荷节点,找出这三种指标的等价性关系。利用上述方法对IEEE14节点算例系统和新英格兰10机39节点算例系统进行了分析,理论和算例都说明了在电压崩溃点处V-Q灵敏度、参与因子指标及负荷裕度灵敏度指标是互相吻合的。     

AN EFFICIENT CONTINUATION POWER FLOW METHOD FOR VOLTAGE STABILITY ANALYSIS

ABSTRACT

This paper presents an efficient continuation power flow-method for determining voltage stability limit of interconnected power systems. Decoupled power-flow solutions are extremely popular because of lesser storage and faster solution speed as compared to coupled power flow solution. However, it is generally believed that decoupling cannot be used near critical loading conditions. This paper shows that decoupled power-flow solution is possible even under such adverse operating conditions, it is achieved by judiciously incorporating the effects of non-negligible off diagonal submatrices through a subiteration scheme. The load parameter is included in both sets of equations. Bus angle (other than slack bus) and load parameter are used as continuation parameters for solving real & reactive power equations respectively. Results for 5-bus, 14-bus and a practical 91 -bus test systems have been obtained with the coupled and proposed decoupled versions of continuation power-flow to demonstrate the validity and efficiency of the proposed algorithm.     

Direct calculation of voltage-stability limit of electric power systems

On-line monitoring of voltage-stability conditions is a new requirement for the energy management systems of the electric power industry. Preferred by the utility engineers and dispatchers is an index which represents explicitly the margins to a voltage-stability limit (collapse point) expressed in a physical unit ordinarily used. For example, such indices are the system load and voltage-voltage-stability-margins (SVVSM) between the present operating point and a voltage collapse point. However, long computer time is required to calculate accurately the voltage collapse point by the conventional method because many multiple load-flow solutions are required. This paper presents a new algorithm to calculate directly, exactly, and rapidly the voltage-stability limit. The algorithm uses the load-flow equations and the explicit expressions of the voltage collapse root conditions are expressed as dR/dV = 0, where R is active or reactive power node injection, and modifying the conventional N-R load-flow program, and is not affected numerically by singular Jacobians. The proposed algorithm is verified through calculating the voltage stability limit of a 176-node power system.     

基于扩展潮流模型的电力系统电压稳定分析

提出一种追踪系统PV曲线并判断其电压崩溃类型的改进算法。它采用扩展潮流模型，应用连续潮流方法。给出新的发电机电流极限约束的直接处理算法，解决了计及发电机电流约束时，潮流难于收敛和不易精确求出电压崩溃点的问题；对不易精确求得的极限诱导分岔点，通过在连续潮流法的校正步骤中将关键的极限约束方程作为附加方程来快速而精确地求解。New-England 39节点系统和IEEE118节点系统算例表明该模型和算法的有效性和合理性。     

基于负荷模糊聚类的电压稳定概率评估

在对研究时段内多个负荷水平进行模糊C均值聚类的基础上,采用多维正态分布抽样技术,提出了一种同时计及节点负荷相关性和负荷预测不确定性的电压稳定概率评估方法。通过对负荷样本多次抽样后进行连续潮流计算及模态分析,可以获得系统功率极值、母线与支路参与因子的统计信息,以及系统在给定负荷水平下电压失稳的概率,从概率角度指出具有潜在电压稳定问题的区域,实现对系统电压稳定性的概率评估。通过对IEEE57节点系统进行分析计算,验证了算法的可行性和有效性,并就模糊聚类数、负荷预测不确定性和节点负荷相关性对电压稳定评估结果的影响进行了比较和分析。     

基于最优乘子潮流确定静态电压稳定临界点

给出了一种基于最优乘子潮流求静态电压稳定临界点的新方法.与连续潮流或直接法求解电压崩溃点不同,该方法从潮流的可行域外出发,利用潮流迭代过程中最优乘子的值和最小二乘解提供的信息,沿注入功率变化的方向逼近电压崩溃点.给出了判别和计算鞍结型和约束诱导型分岔点的方法,分析了逼近过程中的各种可能情况.对多个算例测试的结果表明:所提出的方法通过几次迭代即可收敛于静态电压稳定临界点,计算结果与应用连续潮流和直接法一致.     

A method to compute reactive power margins with respect to voltagecollapse

A method of computing the reactive power margin-i.e. the difference between the maximum reactive load and the corresponding base case value-for a given set of load buses of a power system is proposed. This margin is aimed at assessing the system robustness with respect to voltage collapse. The corresponding collapse point is directly obtained as the solution of an optimization problem with the load increase as the objective, the nonoptimized loads as equality constraints, and the generator reactive limits as inequality constraints. The CRIC electrical decoupling yields a voltage-only problem. The latter is solved using the Newton approach and a procedure is given to deal with the inequality constraints efficiently. A simple illustrative example and simulation results obtained on the Belgian 520-bus, 41-generator system are given     

一种计算最小负荷裕度的实用方法

最小负荷裕度能量度从当前运行点到电压失稳点的最恶劣的一种演化,为电压稳定预警提供更多信息。文中提出一种计算最小负荷裕度的实用方法。结合控制中心实际,得到一种负荷模式以及模式波动的表示形式,从而建立实用的连续潮流模型和求取最小负荷裕度的优化模型,推导了负荷裕度对于负荷模式的灵敏度,并采用序列线性规划法来快速、有效地求解最小负荷裕度。给出的期望负荷裕度和最小负荷裕度为电压稳定预警提供更丰富的规则信息。新英格兰10机39节点系统的仿真算例验证了所述方法的有效性。     

An economical generation direction for power system static voltage stability

This paper proposes an economical generation direction for static voltage stability. The proposed generation direction minimizes the total operating cost at any loading level, up to the point of collapse. The proposed approach, named as EGD approach, is based on the economic load dispatch with load flow. Two alternative methods to identify the economic generation direction are proposed. Economical generation direction is used in the continuation power flow process to obtain the static voltage stability margin. Static voltage stability margin with economical generation direction is compared with the margins resulting from other existing generation directions in the modified IEEE 14-bus test system under various system operating conditions. Cost of providing loading margin as well as PV curves and losses under different generation directions resulting from various generation direction approaches are also studied and compared. The proposed approach provides an alternative way for utilities to obtain the lowest total operating cost with voltage stability constraint by using any existing commercial software.     

基于禁忌算法的多目标无功优化

提出一种基于禁忌算法的多目标无功优化方法。在多目标优化中,包括了距离裕度和网损两项性能指标。首先在给定负荷增长方式的前提下,利用改进连续潮流法快速地找到电压崩溃点,进而求得当前运行点离崩溃点间的距离,并以此距离作为裕度指标,然后采用模糊集理论将裕度指标和网损指标两个目标优化问题转化为单目标优化问题,最后利用改进的禁忌算法对该单目标进行优化,使系统在满足约束的情形下既经济又安全地运行。文章在IEEE14节点系统上验证了该算法的优越性。     

负荷不确定性电网的电压稳定性评价方法

提出一种基于负荷不确定性电网的电压稳定性评价方法.在电网各节点及总负荷水平不确定、只能给出一个区间范围的情况下,首先定义了一种电压稳定性评价模型,采用边界定值法进行求解,找出一组最恶劣的负荷分布,使其在满足负荷取值范围的约束下离崩溃曲面的负荷距离最短.所述方法考虑了各节点和系统总负荷水平的不确定性,为电网的电压稳定性评估提供了一种新思路.在IEEE 14和IEEE 57节点系统中验证了所述算法的快速性和有效性.     

A new approach for estimating voltage collapse point based on quadratic approximation of PV-curves

The MW-distance to voltage collapse is a good indicator of voltage stability at a given operating condition in power systems. This indicator is determined using PV-curves obtained through continuation power flow (CPF) program. The CPF method performs several power flow runs requiring a large amount of computing time. This method is reliable for off-line voltage stability studies, but not very much suitable for real-time operation of today's stressed power systems. Given that, it is essential for system operators to have quick information about voltage stability, a new method is needed for a fast estimation of voltage collapse point. This is the main thrust of the presented paper. It is well known that PV-curves are approximately quadratic functions and become exactly quadratic in close neighborhood of the collapse point. Some authors used this fact and suggested methods that use two to three power flow solutions for a relatively quick, but approximate, calculation of the collapse point. The present paper, also based on quadratic approach, proposes a new method for the determination of voltage collapse that uses only one power flow solution and gives more accurate estimate of the collapse point when compared with other existing methods. Another advantage of the presented method is that the estimation becomes more accurate for stressed power systems. In addition, application of the presented method for performing the top/stable portion of the PV-curves provides an effective step-size that reduces the number of power flow runs. The method is tested using the New England 39-bus and the IEEE 300-bus test systems. The results confirm the effectiveness of the presented method.     

An improved load flow technique based on load current injection for modern distribution system

This paper presents load current injection based improved load flow (LF) technique for modern distribution system. The proposed LF technique is derived by promulgating the concept of conventional backward forward sweep technique. This proposed technique uses a single load current to bus voltage (LCBV) matrix to perform both the backward and the forward sweeps of power flow calculation in a single step. Utilizing the concept LCBV, the bus voltages can be determined, directly, from the load current injections. Due to the distinctive solution technique of the proposed approach, the time-consuming lower–upper factorization and forward–backward substitution or any derivative operation required in the traditional LF technique are no longer necessary. These unique features make the proposed technique faster in operation. The proposed approach is flexible enough to accommodate any sort of change in network structure due to reconfiguration. Along with the modeling of various equipments of distribution system (viz. distribution transformer, voltage regulator, voltage dependent loads, distributed generations, etc.), special treatments for weakly meshed system are also presented in this work. It is experimented on several test systems of varying complexities (viz. 28-, 69- and 30-bus balanced radial distribution system (RDS), 10-bus and IEEE 34-bus unbalanced RDS and 33- and 69-bus weakly meshed system) and the obtained results demonstrate the effectiveness of the proposed approach while comparing to the existing methodologies. Furthermore, it is revealed that the proposed algorithm is, computationally, faster, robust and more suitable for modern distribution network than the contemporary techniques available in the state-of-the-art literature.     

基于小波分析的动态电压稳定判据

对发生在到达传输能力极限之前的动态电压崩溃事件,尚缺乏很好的方法进行检测。针对这一问题,提出对负荷点的电压及基于同步相量测量计算的动态雅可比逆矩阵电压/无功灵敏度进行小波变换。由于小波变换在检测信号突变方面优势明显,可以迅速筛选电压崩溃过程中的异常变化量,因此可以使用这种方法监测母线状态达到检测电压崩溃的目的。该方法的有效性在包含异步电动机的IEEE 39母线系统的仿真中得到了验证。     

Multi-objective optimal reactive power flow including voltage security and demand profile classification

This paper proposes a method to optimize reactive power flow (ORPF) with regard to multiple objectives while maintaining system voltage security across a time-domain. Compromise programming is employed in the ORPF formulation, which is designed to minimize both losses and payment for the reactive power service in the framework of the UK daily balancing market. In coordination with ORPF, continuation power flow (CPF) is applied to evaluate and maintain the voltage security margin of the system. Prior to the optimisation procedure, the related control parameters can be grouped with the aid of a load classification method in order to simplify the control actions. During the optimisation, through the application of both ORPF and CPF, multi-objective optimisation can be achieved with voltage security at an acceptable level. The Ward and Hale 6-bus system and a 60-bus UK test system are presented to illustrate the application of the proposed modeling framework.     

SYSTEM L0ADAB1LITY VERSUS BUS LOADABILITY FOR VOLTAGE INSTABILITY

ABSTRACT

The techniques used to evaluate the limiting point and hence the security margin between the operating point and the voltage collapse point are considered the most accurate method in static voltage instability studies. Two such approaches are compared: the system loadability ( and its associated sensitivity parameters ) versus the bus loadability at a predetermined set of buses. The mathematical models for the two approaches are unified and the same nonlinear optimization technique (Augmented Lagrangian Multipliers ) is used to solve the two problems in order to obtain comparable results. Three different systems are used in the comparison: a 20-bus, a 30-bus and a 57-bus systems.     

基于非参数估计的无功电压控制响应规则辨识

由于传统分析难以准确把握电压、无功之间复杂的非线性关系,使得调压措施给系统节点电压带来的电压偏移模糊不清,导致调压后系统中某些节点电压进一步恶化。且传统电压无功分析依赖于模型建立的精度,其负荷模型建立存在较大难度,因此有必要通过电压对无功的响应数据来研究两者之间的关联关系。提出一种基于Group-Lasso的多场景下电压无功关联度分析方法,挖掘系统负荷水平、无功激励与节点电压之间的函数关系。该方法能准确量化三者间的关联强弱,且所得函数表达式具有较强的泛化能力。通过IEEE 24、IEEE 118节点系统标准算例验证了所提思路与方法的有效性,为今后电压无功关联度分析提供了新的思路。     

一种电力系统最小负荷功率裕度的快速求取方法

本文以雅可比矩阵零奇异值对应的左奇异向量为负荷增长方向,从系统初始运行点出发,用改进连续潮流法搜索此方向上的电压崩溃点,再以该崩溃点雅可比矩阵零奇异值对应的左奇异向量作为新的负荷增长方向重新计算,直到负荷增长方向与崩溃点处崩溃点曲面的法线方向重合为止,从而得出了一种最危险的负荷增长方式和最小负荷功率裕度的快速求解方法,IEEE14节点系统实例计算验证了该方法的可行性。     

An approach for real power scheduling to improve system stability margins under normal and network contingencies

In the present day power system planning and operation, considerable interest is being shown in system security and stability analysis. Pattern of load sharing/generation scheduling that results in heavy flows tend to incur greater losses, threaten stability, security and ultimately making certain generation patterns undesirable. Generation schedules mainly based on economic criteria may lead to lower reserve margins and therefore diminished reliability is a serious concern for the systems. With increased loading of existing power transmission systems, the problem of voltage stability and voltage collapse has also become a major concern in power system planning and operation. While the voltage stability is more dependent on the reactive power sources/voltage profile in the system, it is also a function of real power flows. In this paper, network sensitivity between load voltages and source voltages to compute voltage stability index (L), is used as the basis to evaluate desirable load sharing for improving stability margins. The proposed method has been tested on typical sample systems and also on a practical 24-bus equivalent power system, and results are presented to illustrate the proposed approach.     

考虑双馈异步风电机组无功极限的静态电压稳定概率评估

风电机组中双馈异步发电机(DFIG)恒电压运行时具备一定无功调压能力。为了准确评估含DFIG风电机组的电力系统电压稳定性,得到更为精确的临界功率或负荷裕度的统计信息,构建了考虑DFIG风电机组恒电压运行的无功极限的静态电压稳定概率分析模型,并采用蒙特卡罗法结合内点法加以求解。模型中将风电场接入节点作为PV节点,考虑了风机网侧变换器的注入无功功率,分析了风速随机性和相关性对风电机组注入无功功率和系统电压稳定性的影响。IEEE 118和300节点标准系统的计算结果验证了所提模型和方法的有效性。