This paper presents a new concept called the ''Control Sensitivity Ind
ex'' or CSI, for the stability analysis of HVdc converters connected t
o weak ac systems. The CSI for a particular control mode can be define
d as the ratio of incremental changes in the two system variables that
are most relevant to that control mode. The index provides valuable i
nformation on the stability of the system and, unlike other approaches
, aids in the design of the controller. It also plays an important rol
e in defining non-linear gains for the controller. This paper offers a
generalized formulation of CSI and demonstrates its application throu
gh an analysis of the CSI for three modes of HVdc control. The conclus
ions drawn from the analysis are confirmed by a detailed electromagnet
ic transients simulation of the ac/dc system, The paper concludes that
the CSI can be used to improve the controller design and, for an inve
rter in a weak ac system, the conventional voltage control mode is mor
e stable than the conventional gamma control mode.