Virtual-Node-Enhanced Mirror-Equivalent Energy Framework for Online Transient Stability Assessment of EHV Transmission Lines

Online transient stability assessment (TSA) is essential for the secure operation of long-distance extra-high-voltage (EHV) transmission lines. Mirror-equivalent energy (MEE) methods depend on accurate center-of-oscillation (CoO) localization, but conventional two-terminal frequency interpolation may inadequately represent internal frequency variations in long EHV lines. Measurement noise can further affect weighted least-squares (WLS) state estimates and subsequent energy assessment. This paper proposes a virtual-node-enhanced MEE framework that reconstructs internal frequency responses using extended Kalman filter (EKF)-estimated generator states and a multi-section π-equivalent transmission-line model. The CoO is located through linear-regression analysis and used to construct the mirror-equivalent system and calculate the MEE index. The framework is evaluated using a PSS/E model of a 750 kV, 300 km double-circuit transmission line in the Northwest China Power Grid. In the representative stable and unstable cases of the studied system, virtual-node reconstruction reduces the absolute CoO location errors from 5.236 to 3.281 km and from 65.021 to 0.349 km, respectively, compared with two-terminal interpolation. In 200 paired Monte Carlo trials at SNRs of 40 and 30 dB, the EKF-based method produces smaller mean CoO location errors and no incorrect stability decisions, whereas the WLS-based method produces seven incorrect decisions. Additional simulations evaluate the framework under different pre-fault transfer powers, fault locations, fault types, and clearing times. These results demonstrate improved CoO localization accuracy and more reliable stability assessment under the tested conditions.