Nonlinear controllability of singularly perturbed models of power flow networks

A method based on differential geometric control theory is presented intended to provide insight into how the nodes of a power network can affect each other. In this preliminary report, we consider a simple model of a power system derived from singular perturbation of the power flow equations. It is shown that such a model is accessible, and that for simple chain topology the network is actually feedback linearizable. The result is illustrated numerically. This simple example is a precursor for more interesting models of networks. I. INTRODUCTION Dynamical analysis of large electric power networks is becoming increasingly important as power systems have be- come larger and more interconnected and are operated close to stability limits. Power networks are high dimensional dynamical systems composed of heterogeneous components governed by nonlinear evolution equations and subject to disturbances. These facts make them difficult to analyze. An important aspect of the dynamical behavior of power systems that is particularly difficult to codify is that directly related to its network structure. The connectvity implies that any change at one bus necessarily affects all busses, so that fundamental questions such as how power from a given bus is distributed in the network are quite subtle to deal with. Power networks can be represented as planar graphs, which are much-studied objects, however being neither regular nor random they fall into a category that is some- what resistant to conventional approaches. Power grids are typically modeled mesoscopically, meaning that they generally consist of tens to thousands of nodes, and their dynamics takes place in a state space with two to perhaps twenty dimensions per node. See below for a more detailed description of dynamical power grid models. In this paper we use geometric control theory to analyze the network- dependent structure in power systems. This paper begins the investigation by considering perhaps the simplest dynamics possible based on conventional power flow equations. See (2) for another application of control methods to power systems.