Inclusion of Load and Renewable Dynamics in ODE-Based Power System Models

Determine explicit modeling methodologies to incorporate the dynamics of loads and renewable energy resources within ordinary differential equation (ODE)-based power system models used for model order reduction in power networks, so that these models can represent load and renewable dynamics without neglecting the algebraic constraints that appear in nonlinear differential-algebraic equation (NDAE) formulations.

Background

The paper highlights a common practice in power system model order reduction: simplifying the network to ordinary differential equation (ODE) models that omit algebraic constraints. While such ODE-based approaches facilitate the application of linear systems theory, they can fail to capture critical aspects of power system behavior. In particular, the authors emphasize that algebraic variables—representing network voltage and current phasors—are highly nonlinear and central to system behavior, making direct elimination or explicit substitution infeasible in nonlinear differential-algebraic equation (NDAE) settings.

Within this context, the authors explicitly note that it remains unclear how to include the dynamics of loads and renewable resources in ODE-based models. This unresolved issue motivates their development of structure-preserving NDAE reduction methods that avoid conversion to ODEs and can jointly reduce dynamic and algebraic variables, but it also leaves open the broader question of whether and how ODE-based models could be extended to capture these dynamics.