Source--Grid Coupling in Power System Oscillations: Observational Equivalence, Feedback Detectability, and Modal Interaction

The research explores the distinction between forced and natural oscillations in power systems by incorporating the directionality of source-grid coupling into dynamical models. The study investigates when prescribed forcing and autonomous sources are observationally equivalent, and whether grid measurements can detect feedback from the source to the grid. The findings indicate that matched interface signals lead to exact equivalence under specific conditions defined by the deterministic grid problem and measurement map. Bidirectional feedback allows for interaction between source-grid eigenvalues in an augmented model. A reduced two-mode model suggests that this interaction depends on both loop coupling and modal separation. The framework establishes source-grid coupling directionality as a dynamical boundary for feedback inference, noting that weak feedback might remain unresolved. Simulation results on a two-area system demonstrate the feasibility of detecting feedback within a calibrated source family, although source-model mismatch can obscure the presence of feedback. A large system study on a WECC 243-bus system confirms the feasibility of feedback detection without requiring an exact candidate selection for the source.

The work probes the fundamental ambiguity in interpreting power system dynamics by formalizing the role of coupling directionality. The core tension lies between mathematical equivalence (matched signals) and physical observability (detectability via measurements). The implication for system assessment is that standard separation into 'forced' versus 'natural' modes may be insufficient when feedback paths exist; the system state requires modeling the causality of energy flow, not just the magnitude of oscillation. The limitation identified—where source-model mismatch confounds feedback detection—suggests that observational equivalence in measurement space does not automatically translate to physical certainty regarding the underlying causal structure. This suggests that grid monitoring must integrate a framework where coupling directionality is an explicit dynamical variable rather than an external assumption, pushing research toward defining necessary and sufficient conditions for inferring bidirectional causality from unilateral measurements. The finding on large systems suggests that practical monitoring can achieve this demarcation even without perfect knowledge of the source dynamics, highlighting the resilience of observational techniques despite underlying model imperfections.