VSC-HVDC system robust stability analysis based on a modified mixed small gain and passivity theorem

In a VSC-HVDC system, when the input power to the converter is controlled to a positive constant, the converter acts a differential negative resistance - Po/i20, which may cause instability in case of a connected weak AC-grid. In order to analyze the robust stability of such a system, a modified mixed small gain and passivity theorem is proposed, which shows that the negative feedback interconnection of two linear time invariant stable subsystems (converter admittance and AC-grid impedance) is input to output stable if in certain frequency bands, both subsystems are passive and at least one of them is strictly passive; at the remaining frequency bands, the loop gain is to be strictly less than one. Under different AC-grid topologies, the stability sufficient conditions with respect to the AC-grid inductance are studied. It shows that for AC-grid consists of series RgLg-circuit, an introduced series capacitor can improve the system robustness but not for the shunt capacitor.