Transient Stability in Oscillating Multi-Machine Systems Using Lyapunov Vectors

In wake of frequency stability challenges enhanced by the volatile renewable energy based generation, there is a renewed interest in the methods that can provide stability insights for broad range of operating conditions of the oscillating multi-machine systems, such as power system. With this perspective in sight, this work proposes an analysis of transient stability with emphasis on the Gram-Schmidt and covariant Lyapunov vectors. Numerical accuracy of these Lyapunov vectors is validated by comparison with Floquet exponents obtained from the Jacobian matrix leading to an increased confidence in their potential application. In addition, a study of global stability using Lyapunov exponents and of local stability by Lyapunov vectors is performed. The assumptions necessary for the derivation of energy functions are avoided resulting in a broader stability perspective that is also applicable on the operating point outside the stability manifold. The methods are evaluated for the IEEE 9 bus system.