Eigenvalue-based analysis of small-signal dynamics and stability in DC grids

In this chapter, we discuss a modular approach for state-space modeling and eigenvalue-based analysis of small-signal dynamics in DC grids. We first introduce the requirements for state-space representation and linearization together with the fundamental properties of eigenvalues and corresponding tools for small-signal analysis, such as participation factors and parametric sensitivities. Then we utilize these methods for analysis of small-signal dynamics in a multiterminal DC system. We first define interfaces for subsystem models to enable a systematic development of state-space models for large-scale HVDC transmission systems. We outline a workflow for system-level modeling and analysis, including the steps for developing and interconnecting the state-space models of subsystems according to the specified interface definitions, as well as for calculating the steady-state operating point needed for the linearization. We select a meshed four-terminal high-voltage DC (HVDC) grid as an example. The subsystem modeling required for analyzing this configuration highlights the challenges related to the modeling of HVDC transmission systems covering large geographical areas, including the time-invariant representation of modular multilevel converter (MMC)-based HVDC terminals and the state-space modeling of long DC cables. Finally, we present examples of numerical results from eigenvalue-based assessment of small-signal stability and interactions in the studied system.