Abstract
Current limiting turns the closed loop of a grid-forming converter into a mode-switching system. For projection-based (feedback-optimization) limiting, this paper shows that conventional linearization fails at the constraint boundary in two distinct ways, and that dynamic mode decomposition (DMD) of trajectories of a nonlinear averaged-dq model recovers the physically consistent spectra. At unconstrained operating points, the Jacobian of the smooth primal–dual field is evaluated where that field is not stationary, and it contains a spurious lightly damped mode belonging to neither the projected nor the unprojected formulation. At constrained operating points, the dual flow pins the constraint whenever the multiplier is active and, because the current predictor is exact in steady state, a backstop limiter sharing the projection limit places the raw current reference on the limiter kink; the constrained equilibria are then non-isolated and path-dependent, and the two well-conditioned one-sided Jacobians differ by an order-one amount. Audited against branch-consistent and one-sided linearizations and certified by out-of-sample reconstruction, DMD recovers the correct spectra over a two-parameter operating map and flags the non-linearizable points. A matched comparison with saturation and virtual-impedance baselines attributes the loss of the network resonance to hard clipping of the bridge current, which instead exposes a lightly damped filter resonance; a backstop above the projection limit restores unique, linearizable equilibria at the price of retaining the resonance. Sensitivities to identification settings, grid strength, controller gains, control delay, and measurement noise are quantified, and a three-converter microgrid study shows a sustained oscillation where a shared threshold admits no equilibrium.