To overcome the blind zone in the evaluation method of the operation status of the traditional distribution network caused by the high penetration of distributed power, this paper studies the state quantitative evaluation method of distribution network voltage quality which takes the random characteristics of distributed generation into account. In this paper, a method based on the invariant and Gram-Charlier series to calculate the probability power flow is introduced, and the evaluation system including the average over-limit probability of system voltage, the voltage confidence interval of node voltage and the maximum over-limit probability of node voltage is established. Then taking the distributed photovoltaic as the representative, the probabilistic model whose active output follows Beta distribution is proposed and an improved index of photovoltaic permeability that includes the photovoltaic fluctuation characteristics is defined so as to quantitatively evaluate the influence of different photovoltaic permeability on the voltage quality of the distribution network. Finally, the feasibility of this algorithm for the assessment of voltage quality status of distribution network is verified. This work is supported by Science and Technology Project of China Southern Power Grid Co., Ltd (No. 031200KK52160003).