CAJ | 학술논문

提出了一种求取大规模电力系统关键特征值的 Krylov-Schur 方法。该方法与隐式重启Arnoldi(IRA)方法在数学上是等价的，但消除了 IRA 方法的数值不稳定性，且对收敛特征值的锁定容易实现，使得后续计算可以在更低阶的子空间进行，节省了计算量。借助 Cayley 变换将关键特征值映射为主导特征值可便于Krylov-Schur方法求解，使用增广状态矩阵进行相应的稀疏运算可提高计算效益。对2940阶和5727阶电力系统关键特征值的计算结果表明，所提方法高效、可靠。
제출료일충구취대규모전력계통관건특정치적 Krylov-Schur 방법。해방법여은식중계Arnoldi(IRA)방법재수학상시등개적，단소제료 IRA 방법적수치불은정성，차대수렴특정치적쇄정용역실현，사득후속계산가이재경저계적자공간진행，절성료계산량。차조 Cayley 변환장관건특정치영사위주도특정치가편우Krylov-Schur방법구해，사용증엄상태구진진행상응적희소운산가제고계산효익。대2940계화5727계전력계통관건특정치적계산결과표명，소제방법고효、가고。
An efficient method called the Krylov-Schur method for computing critical eigenvalues of large-scale power systems is proposed.The Krylov-Schur method is equivalent to implicitly restarted Arnoldi(IRA)method mathematically but offers two advantages.First,the numerical instability of the IRA algorithm is avoided.Second,it is easier to lock converged eigenvalues, by which subsequent computation can be carried out on subspaces with lower dimensions in less operations.By using Cayley transformation,the critical eigenvalues are mapped onto extreme eigenvalues for calculation by Krylov-Schur method.The sparsity of augmented state matrix is used to improve the efficiency of the algorithm.The proposed method has been tested on systems with orders of 2 940 and 5 727.The results show that Krylov-Schur method is highly efficient and reliable.