In DC power systems dominated by power electronic devices, constant power loads (CPLs) and saturation components significantly impact large-signal stability. During the large-signal stability analysis process, the presence of multiple state variables and high-order system poses substantial challenges. To address this, considering the complete control dynamics, this paper proposes an equivalent single-machine (ESM) model of the droop-based DC power systems to reduce the complexity of the large-signal analysis. Building on the proposed ESM model, considering the dynamics of CPL and saturation constraints, a region of attraction (ROA) estimation algorithm based on sum of squares (SOS) programming is proposed, which significantly reduces the conservativeness compared with other existing methods. Furthermore, a control parameter optimization algorithm based on SOS programming is proposed with the aim of expanding the ROA. Furthermgre, with the aim of expanding the ROA, controller sythesis is conducted with proposed control parameter optimization algorithm based on SOS programming. Ultimately, simulation experiments validate the accuracy of the proposed ESM model and the proposed ROA estimation algorithm, as well as the effectiveness of the control parameter optimization algorithm.