Slow Inter-area Electro-mechanical Oscillations Revisited: Structural Property of Complex Multi-area Electric Power Systems

This paper introduces a physically-intuitive notion of inter-area dynamics in systems comprising multiple interconnected energy conversion modules. The ideas build on an earlier general approach to setting their structural properties by modeling first stand-alone modular dynamics starting from the fundamental relations between energy stored in modules (components, areas), and constraining explicitly their Tellegen's quantities, power and rate of change of power, in particular. 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. 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 rate of change of intVars associated with the two 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.