###### Abstract  
The integration of renewable energy sources into modern power systems requires simulations with smaller step sizes, larger network models and the incorporation of complex nonlinear component models. These features make it more difficult to meet computation time requirements in real-time simulations and have motivated the development of high-performance LU decomposition methods. Since nonlinear component models cause numerical variations in the system matrix between simulation steps, this paper places a particular focus on the recomputation of LU decomposition, i.e., on the refactorisation step. The main contribution is the adoption of a factorisation path algorithm for _partial refactorisation_, which takes into account that only a subset of matrix entries change their values. The approach is integrated into the modern LU decomposition method NICSLU and benchmarked against the methods SuperLU and KLU. A performance analysis was carried out considering benchmark as well as real power systems. The results show the significant speedup of refactorisation computation times in use cases involving system matrices of different sizes, a variety of sparsity patterns and different ratios of numerically varying matrix entries. Consequently, the presented high-performance LU decomposition method can assist in meeting computation time requirements in real-time simulations of modern power systems. direct linear solvers; matrix decomposition; high-performance computing; power system simulation 202123300212300  
To reduce the computational effort while maintaining a high level of accuracy, recent research has aimed to change the modelling paradigm behind the simulation by considering time-varying phasors that shift the original frequency spectrum and omit predominant carrier frequencies [1]. Thus, the calculation of time-varying phasors according to shifted frequency analysis (SFA) instead of instantaneous waveform values in the EMT domain can enable the use of larger simulation step sizes and alleviate restrictions on the computation times [2]. Complementary to a potential change of the modelling paradigm, our study aimed to speed up the computation times required in each simulation step by applying a high-performance LU decomposition method. Previous research works have shown that the application of high-performance LU decomposition methods, particularly those designed to operate on sparse matrices of power system simulations, can lead to a significant speedup of computation times [3]. Hence, in this work, we considered the application of different LU decomposition methods in real-time simulations and carried out a corresponding performance analysis. Furthermore, we particularly focus on improving the computational efficiency when simulating power system components with nonlinear models. Nonlinear component models may cause numerically varying entries in the system matrix, i.e., either time-varying or iteratively varying matrix entries. This requires recomputing the LU decomposition of the system matrix once or multiple times during each simulation step. In this case, the symbolic pattern (i.e., the matrix sparsity structure) remains constant, whereas numerical variations occur for a subset of matrix entries. If subsequent recomputations of the matrix LU decomposition are required, repeating computation steps depending on a constant symbolic pattern can be omitted in the _preprocessing_ and _factorisation_ steps. The remaining computation steps account for numerical variations in the matrix and are combined in the so-called _refactorisation_ step. Performing a refactorisation step after numerical variations in the matrix occur can significantly speed up computation times and lead to computationally efficient solutions of systems with nonlinear component models. During the refactorisation step, we aim to exploit the fact that the number of varying matrix entries is usually small compared to the overall number of nonzero entries in the sparse system matrix.