Anti-Diagonal Mapping Relationship of dq-Admittance and Frequency–Voltage Stability

The increasing penetration of inverter-based resources (IBRs) aggravates harmonic, frequency and voltage instability in modern power systems. While harmonic stability has been extensively studied, the theoretical understanding of frequency–voltage stability remains limited. This letter investigates system frequency and voltage dynamics under power disturbances by the PQ/ωU transfer function, and uncovers the anti-diagonal mapping relationship between dq-admittance and frequency–voltage stability. The results reveal that a main diagonally dominant dq-admittance implies that the system frequency and voltage are primarily impacted by reactive and active power, respectively. Conversely, an anti-diagonally dominant dq-admittance indicates that frequency and voltage are more sensitive to active and reactive power, respectively. The proposed theory enables frequency–voltage stability assessment based on the dominance pattern of dq-admittance, providing a new perspective for understanding frequency and voltage dynamics. The analysis is validated using three representative IBR-based test systems.