Nowadays the voltage instability problems occur in the distribution grid due to the integration of more and more fluctuant distributed generators. This paper focuses on voltage stability of distribution networks with wind generation. A voltage stability index is presented, and calculated by an expanding Newton-Raphson power flow method in which the wind power generation nodes are modified according to the P-Q(V) character. In order to obtain the key components of fluctuant wind power, the Hilbert-Huang transform algorithm is utilized to reveal the inherent characteristics of wind power. The extrema extending method based on the mirror periodic is used in the empirical mode decomposition and can handle the end effects. According to the Hilbert spectrum and instantaneous energy of each intrinsic mode functions, the components with lower instantaneous frequency are selected to rebuild the wind power. The new rebuilt series consist of stationary and monotonic components which are smoother, and the rebuilt series can reflect the main fluctuant characteristic of the initial wind power data by comparing the index.