For understanding the stableness of power quality evaluation (PQE), i.e., the sensitivity of the evaluation result to the variances of index parameter, this paper introduces the conception and approach of sensitivity analysis for PQE. The traditional close value method (CVM) is modified by defining the absolute optimal alternative and the absolute worst alternative, and replacing the Euclidean distance of close value formula with the Hamming distance. Based on the improved CVM, in the process of sensitivity analysis the paper deduces the necessary and sufficient condition (NSC) about the priority between two alternatives, and then concludes a set of NSCs of the index attribute value and weight of power quality. Finally, the numerical example shows that the sensitivity of index parameters and evaluated alternatives can be effectively calculated through the proposed method, which provides the reference for the decision-maker to control the indexes with high sensitive and the decision-making of alternatives.