Recursive linearization of Carleman-based nonlinear power system models

摘要

In the past few years, there has been a growing interest in developing higher-order small-signal model-based techniques like the method of Normal Forms (MNF) and the perturbed Koopman mode analysis (PKMA) technique to examine various aspects of system behavior. However, applying these methods to realistic system models is highly computationally demanding due to the size and complexity of the coefficient matrices or are not flexible enough to accommodate more complex system representations. In this research, we explore the use of a Carleman-based MNF, which allows us to obtain a closed-form system representation equivalent to that of the PKMA method. We start by introducing a general framework for deriving bilinear models from the series expansion of the nonlinear equations governing system behavior. Next, efficient recursive linearization (RL) procedures for the computation of the coefficient matrices related to the evolution of the higher-order terms in the Carleman-type models are proposed. Analytical equivalences between the Carleman-based MNF and PKMA are derived, and efficient algorithms are presented to compute the coefficient matrices. It is shown that the use of RL avoids using the Kronecker product, thus significantly reducing the computational burden. Applications to both synthetic and power system models show the usefulness of the proposed approach.