Power mismatches of zero injection nodes have significant impact on the security estimation of the power system. In this paper, a novel state estimation method for the power system is proposed to reduce the power mismatches of zero injection nodes, in which zero injection constraints are added in the form of equality constraints in the bilinear WLAV(Weighted Least Absolute Value). Based on the IEEE standard system, a case study on a provincial system is performed using this method. The results demonstrate that this method can not only ensure the existing high computational efficiency of bilinear WLAV based on interior point method, but also reduce the power mismatches of zero injection nodes. Meanwhile, its robustness is improved to a certain degree.