arXiv:2608.04740v3 Announce Type: replace Abstract: As converter-interfaced units become dominant in power systems, understanding nonlinear stability phenomena involving discrete switching events becomes essential for secure operation. The limited overcurrent capability of grid-forming (GFM) inverters makes current limiting essential during large disturbances. Activation of a circular current limiter (CCL) can cause the operating equilibrium to disappear under certain circumstances. This paper develops an analytical framework to predict the grid-voltage boundaries for CCL activation and determine whether the operating equilibrium persists or disappears after activation. For CCL-based GFM inverters with frozen anti-windup, closed-form expressions for the activation boundaries are derived while accounting for the filter capacitor. A criterion is established to determine whether a saturated (i.e., current-limited) stable equilibrium point (satSEP) persists following limiter activation. A continuation method is also developed to trace equilibria across normal-control and current-limited operation. Power-angle analysis and dynamic-model continuation in single-inverter and modified 9-bus systems validate these predictions. Time-domain simulations further confirm the results. The results show that CCL activation can either cause immediate loss of the stable equilibrium or allow stable current-limited operation to continue until the equilibrium is lost as operating conditions change further.