Tens and hundreds of thousands of disturbances occur annually in modern power systems. The overwhelming majority of them are eliminated by relay protection devices and other automatic systems and by the actions of the dispatching personnel. A small fraction of the emergencies (tens of cases in such large power interconnections as those in the United States and Canada, Europe, and the United Power System (UPS) of Russia) result in significant system failures, sometimes of a cascading nature. They are consequences of unusual primary disturbances, failures of automatic emergency control systems, protection device malfunctions, and errors by personnel, but do not cause extreme consequences for the power system and the consumers. Of these, only some rare failures-blackouts-become catastrophes with severe long-term consequences for the national economies and population. Recent blackouts in North America, Europe, Russia, and other countries require specialists once again to pay closer attention to the blackout phenomenon. It is often believed that the philosophy of preventing blackouts should be based on dispatching personnel training, wide-area system visibility,and better computer models for the analysis of the stability and security of power systems. The authors of this paper also think that in emergency situations of a cascading nature, automatic emergency control systems should play a major role. A confirmation for this statement is the fact that from 1975 to 2005 there were no blackouts in the UPS of Russia (where automatic emergency control systems are widely used). At the same time, the Moscow blackout demonstrated that the growing problems in the Russia's UPS (such as aging equipment and load growth) made it also vulnerable to major blackouts. This stresses again that the electrical power industry faces common global problems and that a global effort, cooperation, and exchange of the best practices are needed to prevent blackouts. This paper describes the Russian

This paper develops a novel concept and computational framework of the expected angle stability margin (EASM) in electrical power systems. This new integrated index provides a common transient (angle) stability characteristic over a set of possible system configurations and contingencies, disturbances and faults, and load demand levels. The EASM expresses a general transient stability "fitness" of the system for a variety of operating conditions. The set of contingencies covered by the index is selected on the basis of their probability, economical, social and system values of the corresponding system configurations. The EASM characteristic can be effectively used to assess the average level of transient stability in power systems. It also evaluates the impact of decision-making in power system reinforcement and expansion planning, and provides an objective for formal optimization procedures in combined stability/reliability studies. A computational scheme for EASM is developed and tested using the IEEE 25-bus test system.

A number of facts about quadratic load flow problems y=f(x)=0, x/spl isin/R/sub x//sup n/, y/spl isin/R/sub y//sup n/ is proved. The main results are the following: If any point x belongs to a straight line connecting a pair of distinct solutions in the state space R/sub x//sup n/, the Newton-Raphson iterative process goes along this line. If a loading process y(/spl beta/) reaches a singular point of the problem, the corresponding trajectory of state variables x(/spl beta/) in R/sub x//sup n/ tends to the right eigenvector nullifying the Jacobian matrix at the singular point. In any singular point of the quadratic problem, there are two solutions which merge at this point. The maximum number of solutions on any straight line in state the space R/sub x//sup n/ is two. Along a straight line through two distinct solutions of a quadratic problem, this problem can be reduced to a single scaler quadratic equation which locates these solutions. In addition, a number of other properties is reported. New proofs of them are given. There is a point of singularity in the middle of a straight line connecting a pair of distinct solutions in the state space R/sub x//sup n/. A vector co-linear to a straight line connecting a pair of distinct solutions in R/sub x//sup n/ nullifies the Jacobian matrix at the point of singularity in the middle of the line.