Hierarchical Risk-Warning Method Integrating Transient Voltage Prediction Based on Koopman-Theory-Based Transient Voltage Trajectory Prediction and Stability Margin Quantification

This paper addresses the transient voltage stability problem in power systems with high penetration of renewable energy by proposing a hierarchical risk-warning method that integrates Koopman-theory-based transient voltage trajectory prediction and stability margin quantification. First, an online Koopman-theory-based transient voltage trajectory prediction model is constructed through the adaptive optimization of basis functions, a dynamic operator update mechanism, and multistage error correction, significantly enhancing prediction accuracy and generalization capability. Second, a piecewise-weighted quantitative index for transient voltage stability margins is proposed, achieving refined stability assessments ranging from individual nodes to the entire system. Finally, a risk-mapping function based on utility theory is established to convert continuous margin indices to discrete risk levels, forming a complete hierarchical warning system for the transient voltage risk. Simulation results demonstrate that the proposed method achieves precise voltage trajectory prediction and stable-state judgment across various scenarios, effectively identifies critical system weaknesses, and provides reliable technical support for the safety prevention and control of the power system’s transient voltage.