Eigenvalue Computation Techniques for Small-Signal Stability Analysis of Large-Scale New-Type Power Systems: A Review and Outlook
The escalating 'double-high' penetration of power electronics in new-type power systems has rendered conventional electromechanical transient small-signal stability analysis inadequate, necessitating electromagnetic transient (EMT) small-signal stability assessment. Eigenvalue analysis, grounded in rigorous theoretical foundations, is widely applied but faces two critical bottlenecks when scaled to large systems: the construction of EMT linearized state-space equations and the solution of high-order state-matrix eigenvalues. This review examines the urgent demand for EMT model eigenvalue analysis in large-scale new-type power systems. It systematically surveys research status and challenges across three domains: equilibrium-point modeling of EMT models, linearized state-space modeling, and efficient computation of critical eigenvalues. For equilibrium-point modeling, the paper evaluates Park transformation, double Park transformation, shifted frequency analysis (SFA), time-scale transformation, and Floquet-theory-based trajectory linearization. For linearized state-space modeling, it assesses component-level and network-level linearization strategies. For eigenvalue computation, it reviews partial eigenvalue algorithms, sparse matrix techniques, and model-order reduction methods. Key challenges include the inability of Park transformation to handle asymmetric or single-phase systems, the computational burden of Floquet transition matrix eigendecomposition, and the poor scalability of dense eigenvalue solvers for systems exceeding thousands of states. The paper concludes by identifying future research directions, including structure-preserving linearization, GPU-accelerated sparse eigenvalue algorithms, and data-driven model reduction, to enable practical EMT small-signal stability analysis for systems with 18.4 billion kW of installed renewable capacity by 2030.