Computational time efficiency analysis for resonance studies in transmission grids and microgrid clusters

The limitations of traditional methods for identifying resonance frequencies have driven the development of Resonance Mode Analysis (RMA) as a more effective alternative. Despite its potential, RMA faces challenges in computational efficiency, particularly in multi-terminal transmission grids. To address this, Rapid RMA, a power iteration (PI)-based approach for determining the dominant eigenvalue of the nodal impedance matrix, was introduced. However, the PI-based approach can exhibit slow convergence or fail under certain conditions. To overcome these limitations, recent advancements have proposed two new methodologies: Faster RMA, a modified shifted-inverse PI-based method, and Lanczos-based RMA, a non-Hermitian Lanczos method. This paper evaluates the computational performance of RMA-based methods using various software tools (including normal computation, parallel computation and sparse techniques) across three distinct hardware-computing systems. The study highlights practical differences in computational speed and efficiency for RMA applications under diverse scenarios. By emphasising the critical role of optimising computational tools, the paper examines how hardware and software configurations influence RMA performance, particularly in transmission grids and microgrid clusters, using MATLAB/Simulink simulations. Finally, the paper proposes an efficient RMA-based methodology that is adaptable to a wide range of grid configurations and computational environments. This approach is applied to stability studies using the positive-mode-damping stability criterion, thereby offering a robust framework for advancing harmonic resonance analysis in power systems.