Nonlinear dynamic networks

Abstract

The ultimate utility of the linear results in Chapters 4, 5 and 6 depends on their applicability to nonlinear systems. From physical laws or empirical evidence it is clear that time-scale properties are not restricted to linear systems. What classes of nonlinear models preserve their multi-time-scale behavior present in their linearized approximations? Which aggregate and local variables should be chosen to make this behavior explicit? This chapter answers such questions using coordinate-free characterization of singular perturbations and relating it to conservation and equilibrium properties. This results in an explicit singular perturbation model for which a time-scale modeling methodology is available. Applying this approach to the nonlinear electromechanical power system model, we have extended dynamic energy balance and coherency-based aggregation idea to this class of nonlinear dynamic networks. Further nonlinear generalizations of aggregation and coherency seem possible. Networks with both storage and non-storage nodes should be considered. Also important are storage elements involving nonlinearities and more complex dynamic behavior, such as more detailed models of synchronous machines.