Fast Formation Of State Matrix In Small Signal Stability Analysis Of Power System

Small signal stability analysis is one of the problems in power system stabilityanalysis. Small signal stability analysis of power system typically uses eigenvalueanalysis method. How to quickly and accurately form the state matrix is an importantstep in eigenvalue analysis method. Computation requirement for forming the statematrix in small signal stability analysis of power systems is rapidly increased with theexpansion of system scale. By analyzing the forming process of state matrix,reconstructing the related formulas, introducing reduced-order matrix inversion, andother approaches, improvement in computing speed is achieved in this paper.First, according to the Plug-in Modeling Technique, the first-order transmissionblock equation, correlation matrix equation and the first derivative equations aremixed; and the state matrix expression is obtained by further reconstruction andtransformation. Compared with the original method, the calculation steps are simplerafter the reconstruction. The back substitution process in matrix inversion isapproximate saved. The elimination process can introduce parallel calculation. Insome extent, the computation efficiency is improved.Second, part of the matrix inversion and multiplication is time-consuming duringthe formation of the state matrix. Partitioning and descending order is used in matrixinversion. Large matrix can be converted into several small matrixes. Eliminationinverse method is directly calculated on the original matrix, the memory use is lesser.Triple form is used in matrix storage. Only non-zero elements are stored to simplifythe process of matrix operations. Parallel computation technique in OpenMulti-Processing (OpenMP) is used in processing cycle and independent programsections. A task can be cracked into multiple non-interfering sub-tasks. The givenproblem can be solved efficient and rapidly.Finally, the program is compiled on the platform of Visual Studio2008.Programming language is Intel Visual FORTRAN11. Comparison and analysis ontwo different scales of power systems shows the effectiveness of proposed method.