Power system instability prediction from the solution pattern of differential Riccati equations

Power system stability characteristics are typically evaluated in terms of small‐ and large‐signal (transient) stability. Access to the time‐varying A‐matrix of a state‐space‐based power systems model during transient conditions can be utilized to apply linear time‐varying system concepts for large‐signal stability analysis. In linear time‐varying system analysis, the differential Riccati equation (DRE) plays a vital role when the power system is subjected to a severe disturbance. The Möbius transformation is proposed in this paper to solve the DRE with singularity issues. It is shown that the solution of the DREs follows a specific mathematical pattern when the power system is stable but does not follow this pattern when the system progresses toward instability. The proposed method can be used in large‐signal stability analysis to predict instability and make the stability analysis more efficient. Additionally, the vector‐DRE is proposed to generalize the index in a large‐scale power system. Results show that analyzing the corresponding Riccati equation's behaviour can help researchers predict a power system's performance and improve the control and management of the system.