• • China's renewable energy installed capacity reached 1.84 billion kW by end-2025, with projections to become the primary electricity supply source by 2030; this scale renders conventional electromechanical transient models inadequate because they neglect fast electromagnetic dynamics, directly driving the need for EMT eigenvalue analysis in systems with thousands of state variables.
• • Park transformation fails under asymmetric operating conditions by introducing negative-sequence double-frequency components and cannot extend to single-phase or multi-phase systems; double Park transformation resolves positive- and negative-sequence components but leaves zero-sequence components as AC quantities, fundamentally limiting its applicability to unbalanced systems.
• • Shifted frequency analysis (SFA) converts AC state variables into DC envelope signals under steady-state, enabling equilibrium-point linearization; however, when implemented with real matrices via time-scale transformation, the state matrix dimension doubles, increasing eigenvalue computation burden by approximately 2x compared to complex-space formulations.
• • Floquet-theory-based trajectory linearization eliminates time-periodicity by eigendecomposing the state transition matrix Φ(T,0), but the computational cost of this eigendecomposition scales as O(n³) for an n-dimensional system, making it impractical for large-scale MMC-based systems with thousands of states without sparse or partial eigenvalue techniques.