Integrating Covariant Lyapunov Vectors with Fourth-Order Generator Dynamics for Enhanced Transient Stability Assessment

Transient stability assessment (TSA) remains a fundamental requirement for secure power system operation, particularly under severe disturbances in converter-rich networks. Classical rotor-angle methods and energy-based measures provide useful stability margins but rely on simplified generator representations and post-fault trajectory characteristics, making them less effective for real-time predictive diagnostics. Recent efforts have explored Lyapunov exponents and Covariant Lyapunov Vectors (CLVs) to characterize nonlinear electromechanical dynamics. However, these studies have largely been restricted to second-order swing models and have not been rigorously linked to operational metrics such as Critical Clearing Time (CCT). This paper advances CLV-based TSA by integrating a fourth-order synchronous generator model with excitation system dynamics and variational-state evolution to extract dominant instability directions in tangent space. An IEEE 9-bus study demonstrates that CLV projections serve as a sensitive trajectory-based indicator, consistently detecting instability prior to rotor-angle divergence and yielding quantifiable early-warning times relative to CCT limits. The results establish CLVs as a mathematically grounded and practically complementary diagnostic for TSA, offering improved insight into electromechanical stress evolution in multi-machine networks.