Eigenvalue Patterns and Participation Analysis of Symmetric Renewable Energy Power Systems

State-space analysis is widely employed for examining power system dynamics but faces challenges in large-scale power systems integrated with numerous inverter-based resources (IBRs), where the significant increase of system states complicates modal analysis. Notably, renewable energy power systems often consist of multiple homogeneous generation units. This uniformity, termed symmetry in this paper, can facilitate the system stability analysis. Eigenvalue patterns and participation factors in three types of symmetric renewable energy power systems are investigated, including ideally-, quasi-, and group-symmetric systems. An ideally-symmetric (or quasi-symmetric) system comprises a group of identical (or similar) subsystems connected to an external grid. A system containing multiple such groups is termed group-symmetric. In these symmetric systems, two types of modes are defined to characterize different interactions: inner-group modes, which describe the interactions among subsystems within a single group, and group-grid modes, which describe the interactions between the groups and the external grid. A new concept termed group participation factor is also proposed to extend the use of conventional participation factors for repeated and close modes. In addition, the invariance properties of the inner-group modes and group-grid modes are discussed. The findings provide insights for stability analysis and targeted optimization in power systems. Theoretical advances are validated through numerical results and electromagnetic transient (EMT) simulations on example power systems of varied types and scales.