Fast Realization Of Order Reduction For Special Modes In Small Signal Stability Analysis Of Power System

Eigenvalue analysis method is one of the most widely used methods in small signal stability analysis. However, with the expansion of the scale of power system and the increasing number of generators, the order of state matrix has also increased. When the matrix order is quite high, not only the calculation time of QR algorithm is long, but also great errors maybe exist in the results of eigenvalues. Therefore, a lot of partial eigenvalue methods have been proposed, such as select modal analysis, subspace iteration, etc.The order reduction approach for special modes is also a partial eigenvalue method. With the effect of eigenvalues considered, an accurate expression for the order reduction of special modes is applied to the power system small signal stability analysis; while the improved algorithm of Rayleigh quotient inverse iteration is used, the order reduction approach for special modes has the advantage in computational precision. To consider the system scale of provincial grids in this thesis, the computational process and equation characteristic for order reduction are further analyzed to improve the calculation efficiency.First, the complex matrix in iteration operation is expressed as the realification expression. Based on that, the sparse technique is used. According to the number characteristic of electromechanical modes, the matrix construct of outer iteration expression is adjusted and the absolute values of diagonal elements get improved. So that the factor table formed from the sequence elimination approach can be used to solve the inverse matrix quickly. In inner iteration, sequence elimination and pivoting elimination are combined to consider both time and precision. Only non-zero elements and corresponding row and column numbers are stored to make sure of the sparse process in matrix operation.Second, it is found that the similar or same generator sets are participating in different oscillation modes of multi-machine system. Thus, the overall consideration of retained state variables is necessary when there are many electromechanical modes to analyze. With similar or same participating generators in some modes, the same retained state variables can be shared by these modes, which will reduce the calculation amount and simplify the order reduction analysis.Besides, the function of parallel computation in Open Multi-Processing (OpenMP) technique is also introduced. With special OpenMP compiler directives plugged in the original FORTRAN program code, compiler can realize parallel computation of order reduction automatically. The calculation efficiency has been further improved with the help of using multiprocessor.Related calculation program is compiled under Intel Visual FORTRAN11environment. The improved effect, such as sparse technique, retained generators shared by modes, and parallel computation, is analyzed by23-machine system,70-machine system and105-machine system.