Small-Signal Stability Criterion for Inertial and Primary Frequency Droop Control of MTDC Grids Connected to Asynchronous AC Systems

Droop control strategy is widely used for exchanging frequency support amongst asynchronous AC areas through multiterminal DC (MTDC) grid. We provide analytical constraints on inertial and primary frequency droop coefficients as sufficient conditions of small-signal stability when both of the droop controls are active. To this end, a reduced-order model of the system is presented followed by salient observations leading up to the formulation of a stability theorem. The theorem is proved based on two lemmas, where the first lemma derives the sufficient condition for ensuring negative real parts of the eigenvalues of a matrix using the continuity argument of its eigenvalues with respect to its elements. The second lemma expresses the system matrix as rank-1 perturbation of a diagonal matrix, which greatly simplifies the proof. Finally, the analytical stability region in droop coefficient space is compared with the numerically-obtained stability region from the full-order model of an example test system.