  This paper introduces a physically-intuitive notion of inter-area dynamics in
systems comprising multiple interconnected energy conversion modules. The idea
builds on an earlier general approach of setting their structural properties by
modeling internal dynamics in stand-alone modules (components, areas) using the
fundamental conservation laws between energy stored and generated, and then
constraining explicitly their Tellegen's quantities (power and rate of change
of power). In this paper we derive, by following the same principles, a
transformed state-space model for a general nonlinear system. Using this model
we show the existence of an area-level interaction variable, intVar, whose rate
of change depends solely on the area internal power imbalance and is
independent of the model complexity used for representing individual module
dynamics in the area. Given these structural properties of stand-alone modules,
we define in this paper for the first time an inter-area variable as the
difference of power wave incident to tie-line from Area I and the power
reflected into tie-lie from Area II. Notably, these power waves represent the
interaction variables associated with the two respective interconnected areas.
We illustrate these notions using a linearized case of two lossless
inter-connected areas, and show the existence of a new inter-area mode when the
areas get connected. We suggest that lessons learned in this paper open
possibilities for computationally-efficient modeling and control of inter-area
oscillations, and offer further the basis for modeling and control of dynamics
in changing systems comprising faster energy conversion processes.
