【文章內(nèi)容簡介】 ntives to encourage investments in their puteraided online management. The important consequence of this situation is that these reallife works require systematic integration of monitoring, puting, and control for improved performance. Without such integration, which would facilitate timely use of online critical information, managing these systems is simply too plex and leads to plex operating failures, such as blackouts in electric power grids. While specific technologies are beginning to be available for effective online gathering of realtime data in such systems and the case for their use is being made [2], it remains critically important to develop methodologies for differentiating between the information necessary to make decisions in order to prevent undesired performance, on one side, and excessive data gathering, on the other. Such methodologies are not available at present, and this creates a major obstacle to enhancing the performance of electric power grids. Assumptions underlying today39。s operat ion of hierarchical systems Complex power grids are currently operated as hierarchical systems under strong assumptions concerning temporal and spatial separation. Both temporal and spatial simplifications are fundamentally based on APPLIED MATHEMATICS FOR POWER SYSTEMS weak interconnections between the subworks potentially achieved through the work design. Consequently, the supporting models for subworks and the work as a whole exhibit general properties of monotone dynamic systems 131. At the equilibrium, monotone systems decrease the magnitude of their state response when the magnitude of the disturbance increases. For example, when electric demand increases, voltage decreases. This must be accounted for when designing the controllers. Controllers then need to have gains that decrease the demand in order to bring voltage up. Temporal separation in hierarchical work systems is further induced by: (1) the operation of fast controllers to stabilize the system dynamics by controlling the local outputs of the individual ponents。 and (2) slower adjustments of the setpoints of these controllers for each subwork to achieve stationary performance. Further adjustments of the stationary interactions between the subworks are made through offline agreements and with no online information about the equipment status outside one39。s own subwork [3]. The class of monotone systems lends itself to many convenient simplifications of the monitoring and control logic, as well as to the supporting puter algorithms. To start with, monotone systems are effectively controlled in a distributed way, because the effects of each disturbance can be pensated locally for the operating conditions for which the work design is done [4]. In addition, no qualitative change in their logic is needed to ensure stabilization as the operating conditions vary, as long as their system response remains monotone. That is, as long as a linearized matrix of such system preserves the Metzlermatrix properties over the range of operating conditions of interest, at least the sign in the controllers39。 logic is correct, and the system is stabilizable without requiring fast munications between the ponents. The same properties favorable to decentralized regulation are seen in the models characterizing equilibria of monotone electric power work systems 15, 61. This property of localized response to the inputs/disturbances of both the dynamic responses of these systems and their equilibria has served as the basis for: (1) deposition of the system as a whole into subworks。 (2) deposition of the subworks for slow regulation。 and (3) fast stabilization of the local primary controllers on the individual equipment ponents. Much of the stateoftheart theoretical work for largescale work systems relies on this property. In linear control theory, the monotone work property is known as the blockdiagonal dominance property of the system matrix or as the property of weak interconnections between the subworks. Fundamentally, this is the same property which allows for: (1) robust decentralized staAutomating Operation of Large Electric Power Systems 111 bilization。 (2) aggregation into subsystems。 and (3) their decentralized control without requiring systemwide topdown coordination. Similarly, puter algorithms for deposing the work into subworks for parallel puting are based on the same property。 more recently, the ideas of amorphous puting have drawn on the same property. Implications of violating monotone response As the electric power grids are operated away from the conditions for which they were initially designed, they may lose the properties of monotone works. Consequently, the layeredmanaged system may fail to meet its objectives. The variations in system conditions are generally caused by both significant variations in operating conditions and/or by the major equipment failures. There is no blackandwhite line between the effects of these two, ., one cannot say that the system remains monotone for any changes in operating conditions as long as there is notopological change in the work caused by the equipment failures, and, viceversa, that any topological change would cause violations of system properties favorable to its deposition. As a matter of fact, it is well documented that often qualitative changes occur as the controllers reach their limits and the degree of controllability gets lost [7]. It is plausible that similar problems may take place if a critical measurement bees unavailable, and the system is less observable. Independent of the actual root causes of such changes in qualitative response of an electric power system, when weak interconnection conditions generally cease to hold, the hierarchical depositionbased operation may result in very unpredictable events. It i