Uniqueness and testability of grid-forming effective impedance in phase-jump compliance assessment

ENTSO-E technical reports on grid-forming capability describe converters as an internal voltage source behind an effective impedance z eff at the port. This paper examines the uniqueness and testability of the reported effective impedance in a Thevenin-type compliance representation. Since the internal voltage e is generally inaccessible, the transient difference method is often considered. The active power–frequency outer loop changes the internal-voltage phase during the early response. A sufficient error bound relates extraction accuracy to source motion, current excitation and control tuning. Even when e is exposed for direct back-calculation, the result depends on the dynamic compensation mechanism. Vector filtering removes the steady-state virtual-impedance contribution, while scalar compensation changes the reported impedance according to the internal-voltage extraction point and the operating point. The remaining inner-loop and physical-filter contributions are retained. Controller hardware-in-the-loop experiments quantify the impedance differences together with the port-level power and energy responses. Changing only the internal-voltage extraction point changes the reported impedance without changing the implemented control law. The reported z eff therefore requires a declared internal-voltage extraction point and test conditions, together with port-level support metrics.