ECS-9610049 Zaborszky In previous work the mathematical structure of the large power system as differential-algebraic system with or without the presence of hard limits has been studied in the context of an overall taxonomy. Along with their mathematical structure, physical systems have a wide spread of physical structure ranging from unstructured to hierarchical or very strict structures. The large power system model has a very strong segmental (network) structure. The dynamic equations typically separate into segments (which are physically defined by the buses in the power system), tied together only through non-dynamic relations (in the network). This geographic structure becomes of great importance in questions related to control. In this project, along with completing certain aspects of the mathematical theory, the taxonomy theory will be studied for segmental systems in the context of control problems, specially in the control of power systems. In view of the power system's geographic structure many control problems can be addressed decentralized. For instance, the problem of stabilizing control can be formulated as tracking a moving target which has a single component for each segment and thus can be easily computed locally. The systemwide stability of such an observation decoupled control will be analyzed. The segmental structure of the power system also leads to various clustering approaches built on rudimentary clusters of observation decoupled single bus clusters. Clustered control schemes will be analyzed on the basis of the taxonomy theory. The convergence and accuracy of various control approaches will be studied and the most desirable approaches for various circumstances-such as fast, medium and slow control (tasks) will be sought. The fast control objectives are mostly connected to preserving the stability of the power system. We have formulated it as a problem of tracking a moving target vector. This objective readily breaks up into interconnected segmen tal problems and identifies the stable equilibrium point when the tracking is successful (note that it is not practical to identify the equilibrium on the time scale of the disturbances fact conveniently ignored in most of the literature). However, the equilibrium is found precisely at the end of successful tracking. This invites the design of effective approximate tracking schemes which lead in this case to precise results. It is important, however, to find such tracking schemes and establish precisely their convergence. This will be done in the project. The medium fast control for the problems of the automatic generation control (ACC) readily settles into a three layer segmented scheme both for the traditional AGC (equipment at individual buses, segments called Areas for individual power companies connected with tie lines and nationwide setting of desired frequency by NERC) and the new deregulated scheme (generating stations, national transmission company and distribution companies). Although needs are different, the structural similarity implies connections in the theory. These will be analyzed and the most desirable schemes sought. Clustering of the large system will be the basis of this work involving thorough and precise analysis and technique development. New taxonomy concepts such as observability region and controllability region within the state-parameter space will be defined and analyzed at the thoroughness and precision corresponding to our earlier Taxonomy work. The ongoing development of the power system away from local power companies and regulation connected AGC control to layers of generation, transmission and distribution companies based on a real time commodity trading nationally makes this proposed study quite important and potentially very useful. At present the final shape of the reorganized system which will eventually dictate the structure of its control needs is not yet emerging. Hence the flexibility of the taxonomy approach which can accommodate a grea t variety of needs and structure will make it an ideal vehicle for searching for the most desirable structures and objectives.
