Transient stability analysis with phase plane of high-order derivatives of angle dynamics

Transient stability is of essential concern in power systems. This paper provides a graphical method with high-order derivatives of voltage phase angle dynamics for transient stability analysis. Using a Single Machine Infinite Bus system, criteria are defined for determining unstable equilibrium points using the first, second, and third order derivatives of phase angle difference. To intuitively show stability characteristics, a new phase plane is defined with the first and second order derivatives. With measurement data from phasor measurement units, bus voltage phase angle and frequency dynamics are used for field application. Applications of the proposed method for transient stability evaluation and prediction are discussed. Simulations show that the proposed method provides an intuitive approach for transient stability analysis and is useful in field applications.