Coherence, vector Liapunov functions and large-scale power systems

Large-scale power systems considered in this paper can be decomposed into their coherent part of the reduced dimension and the non-coherent one. The coherence property of the former is used for the first hierarchical level aggregation of the system. A new system is obtained with essentially reduced order, which is then aggregated on the second hierarchical level by applying the vector Liapunov function concept of Bellman. A new vector Liapunov function aggregation form is developed to suit the properties of the coherent large-scale power systems, which require also usage of new comparison functions. As a result, a one-shoot stability test on the higher hierarchical level is established. The criterion is stated in terms of negative definiteness of a symmetric aggregation matrix of the order equal to the number of subsystems of the reduced order system. Essential order reduction is achieved. The theory developed in the paper is illustrated by an example.