The distribution network has complex network structure, various types of equipment, and a wide range of operating points, while distribution automation equipment cannot achieve full coverage. This paper proposes a partial state estimation of distribution network method based on a nonlinear dynamical system approach. The proposed method is globally convergent and can use sparse synchronized phasor measurements without the traditional requirement of network observability. For the application of voltage control or thermal limit control, enhancing the accuracy of the voltage amplitude or the voltage phase angle is required. Under this situation, we propose an enhanced formulation including the voltage amplitude measurement residual constraints and voltage phase angle measurement residual constraints. The calculations cases show the effectiveness of the proposed method.