In this study of power grid structures, we propose a novel text-based matrix reordering and decomposition technique. Tailored for analysis of power grids, this method seamlessly decomposes the original grid matrix into two submatrices. Crucially, these submatrices maintain symmetric positive definiteness, thereby accelerating network solution processes without altering the original solution. The proposed technique is compatible with various solvers. In the experimental phase, we compare and analyze transient power grid analysis using second-order algorithms and the original Modified Nodal Analysis (MNA) algorithm, employing several representative solvers. Experimental results demonstrate a significant efficiency improvement with the second-order algorithm. Following the application of reordering and decomposition techniques, the solving speed of the second-order algorithm doubles that of the initial algorithm. For solvers lacking support for parallel computation, our approach offers an effective means of enhancing computational efficiency.