Higher Order Recursive Linearization of Power Systems with Electronic Converters

The generation of electrical energy from renewable energy sources (RESs) has increased over the past few decades as part of efforts to reduce humanity's environmental impact. However, their integration into the power grid through electronic converters (ECs) has introduced several challenges, including reduced global system inertia, diminished stability margins, and issues affecting power system operation, planning, and reliability. Despite these challenges, a comprehensive nonlinear analysis of electric power systems with ECs has not yet been fully addressed. In this article, we analyze the nonlinear model of an electric power system with ECs using recursive linearization to derive higher-order linear models. Our analysis shows that the EC model is transformed into a differential-algebraic equation (DAE) representation, which limits the direct application of nonlinear analysis techniques such as normal forms and perturbed Koopman mode analysis. In contrast, by employing recursive linearization, we derive a Taylor series-based model and an extended Carleman-type model to explore alternative higher-order linear representations. These models are validated using a two-area power system with a wind power plant (WPP) and a 46-machine test system with three WPPs. Additionally, key observations and potential future research directions are discussed.