Model reduction of interconnected power systems via balanced state-space representation

Many model reduction methods have been developed for linear dynamical systems based on measures of controllability and observability. Although they provide an efficient way to retain the most relevant modes of the system, those approaches have not been used in practice for building dynamic equivalents of power systems. Indeed, this kind of reduction provides a state-space representation which does not preserve the structure of the physical system, i.e., differential equations for generators and their regulations and the algebraic equations that represent the network. The existing alternatives need information of the whole system to reduce part of it. This information may not always be available as it is the case for the studies of interconnection of two power systems. In such situations, when reducing one power system, full data for the other one cannot always be used. However, the reduction should be done such that when connecting the two simplified models, the important cross-border phenomena like, e.g., inter-area modes which involve machines of both sides are preserved. We propose here an approach based on a balanced representation of the power system to be reduced on one side of the border which contains sufficient information to preserve the overall cross-border behavior. The Synchronic Modal Equivalencing (SME) principles of constructing the equivalent are used in this new framework to obtain a structure-preserving reduced system considering that the modes of interest are those observed in the interconnection lines between the two power systems. Those modes are identified from a balanced realization of the power system to be reduced without using data from the power system on the other side of the border. Two examples are presented.