Recursive Linearization of Higher-Order for Power System Models

A novel, general-purpose recursive linearization (RL) methodology for the analysis of small-signal stability that combines the use of chain rule-based techniques with perturbation theory is proposed. The method provides a straightforward and fast alternative to the linearization of complex systems described by ordinary differential equations (ODE) models that can be used to reduce the computational effort as well as to extend the applicability of perturbed Koopman mode analysis (PKMA) and the method of normal forms (MNF). First, the concept of recursive linearization is introduced to aid in the computation of higher-order approximations. Techniques for exploiting the structure of the expansions are then provided and relationships for computing second- and higher-order terms of the power series expansion of a real- or complex-valued nonlinear analytical model are developed. A synthetic nonlinear system is first used to illustrate the application of the RL method and provide computational complexity comparisons against perturbation-based methods. The application to multi-machine power systems is then considered to demonstrate that the RL has the accuracy of the analytic linearization (AL) method with less computational burden than the perturbation-based methods widely used in power systems analysis tools.