IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 2, MAY2005 973 Application of a New Sensitivity Analysis Framework for Voltage Contingency Ranking Nima Amjady, Member, IEEE, and Masoud Esmaili Abstract—In this paper, a new sensitivity analysis framework for voltage contingency ranking has been presented. The pro- posed sensitivity analysis is a combination of linear sensitivities and eigenvalue analysis. The sensitivity analysis framework can determine the voltage stability status of the power system due to the occurrence of each contingency. Moreover, stability margin or instability depth of the post-contingency state is determined in the framework. In other words, a severity index is obtained for each voltage contingency and so the contingencies can be ranked. This rank shows bottlenecks of the power system in the priority order, a property that is a key issue for both planners and operators of the power system. The proposed method can also evaluate islanding contingencies as well as the nonislanding ones. Moreover, the method can consider the generator contingencies in addition to the branch contingencies in a unique framework. The proposed method has been tested on the New Zealand test system and Iran’s power network. Obtained results, discussed comprehensively, confirm the validity of the developed approach. Index Terms—Contingency ranking, sensitivity analysis, voltage contingency. I. INTRODUCTION F OR the secure operation of a power system, all forms of security constraints must be met in any considered oper- ating point. These include static constraints such as thermal limits of circuits, as well as dynamic constraints such as voltage, transient, and small-signal stability limits. Violating these con- straints may result in severe consequences, even system wide blackout. In this paper, we focus on the voltage stability limit. Voltage instability is a load driven instability, which constitutes an important subset of power system instabilities. Nowadays, in many countries, the introduction of competitive supply and cor- responding organizational separation of supply, transmission, and system operation has resulted in more highly stressed and unpredictable operating conditions, more vulnerable networks, and an increased need to monitor the operational security level of the transmission system [1]. These conditions, brought on by natural load growth especially for developing countries coupled with a significant increase in long-distance transmission usage, often result in heavy transmission circuit loadings, depressed bus voltage magnitudes, and closer proximity to voltage insta- bility [1]. Manuscript received February 13, 2004; revised April 16, 2004. Paper no. TPWRS-00071-2004. N. Amjady is with the Department of Electrical Engineering, Semnan Uni- versity, Semnan, Iran (e-mail: amjady@tavanir.org.ir). M. Esmaili is with the National Dispatching Department, Tavanir Company, Tehran, Iran (e-mail: esmaili@iust.ac.ir). Digital Object Identifier 10.1109/TPWRS.2005.846088 As electric utilities attempt to maximize the usage of their transmission system capacities to transport real power, voltage collapse acts as a limiting factor [2]. IEEE definitions for voltage collapse, instability and security can be found in [3] and [4], where it is concluded that voltage collapse may be caused by a variety of single or multiple contingencies known as voltage contingencies [5] in which voltage stability of the power system is threatened. Voltage contingencies such as a sudden removal of real and reactive power generation, loss of transmission line or a transformer or an increase in the system load without an adequate increase in the reactive power can decrease voltage stability margin of the power system [6]. Thus, a key issue in voltage stability studies is to determine the severity of each voltage contingency, i.e., evaluate the risk level of each contin- gency. The ranking of insecure contingencies according to their severity is known as contingency ranking [6], which is vital for both operators and planners of the power system. In this paper, we focus on the problem of voltage contingency ranking. How- ever, contingency ranking for other kinds of stabilities such as transient stability and small signal stability is also important and was considered in the previous works [7], [8]. Early methods for voltage contingency ranking are based on the severity of MVA branch flow overloads [9], [10]. However, these methods cannot see other factors of voltage stability such as reactive power reserves [4] and so are not accurate. Others consider the severity of voltage violations due to contingencies [11], [12]. However, although voltages decline during voltage collapse, it is possible for a system to encounter it near nom- inal voltage levels [13]. The first and second order eigenvalue sensitivity analyzes have been proposed for voltage contingency ranking in [14] and [15], respectively. These sensitivity analyzes are based on the dominant eigenvalue, an eigenvalue with the least absolute value. It can be shown that severe voltage contin- gencies can change the dominant eigenvalue and singular value position [16]. In other words, the dominant value of the precon- tingency can be replaced by another one in post-contingency. Thus, monitoring the dominant eigenvalue/singular value of the base case in the sensitivity analysis can result in ranking errors for severe voltage contingencies. In [1], a probabilistic method is proposed for risk evaluation and contingency ranking. The method requires not only a large amount of data to compose probability distribution functions (PDFs) for each contingency but also high computation burden to combine PDFs. Thus, the implementation of the method in a practical power system with many possible voltage contin- gencies, from hundreds to thousands, is very time consuming. Besides, in [17], linear and quadratic estimates of voltage sta- bility margin change have been used for contingency ranking. 0885-8950/$20.00 © 2005 IEEE