Trajectory-Based Nonlinear Indices for Real-Time Monitoring and Quantification of Short-Term Voltage Stability

Abstract

Existing short term voltage stability (STVS) methods typically address either voltage oscillations or delayed voltage recovery; however, the coexistence of both phenomena has not been adequately covered in the literature. Moreover, existing real-time STVS assessment methods often provide only binary stability classifications. This paper proposes novel indices that enable early detection and quantify the degree of stability. The proposed method decomposes post-fault voltage trajectories using Empirical Mode Decomposition (EMD) into residual and oscillatory components. It then employs Lyapunov Exponents (LEs) to characterize the dynamic behavior of each component and evaluates the stability degree using Kullback Leibler (KL) divergence by comparing the LEs of each component with those of a predefined critical signal. The proposed indices assess oscillatory stability significantly faster than the traditional LE method applied directly to the original signal. Specifically, they detect stability within 0.6 seconds after a fault, compared to approximately 10 seconds for the conventional LE approach. In addition, the delayed-recovery index can identify generator trips caused by over-excitation limits within 3 seconds, well before the actual trip occurs at approximately 20 seconds, thereby providing operators and controllers sufficient time to take preventive actions. Furthermore, thresholds are derived to distinguish between stable and unstable cases, offering a graded measure of the stability margin. Simulation studies on the Nordic test system under varying load conditions demonstrate the effectiveness of the proposed indices.