A Unified Analysis Method for Harmonic and Frequency/Voltage Stability of Inverter-Integrated Power Systems

The large-scale integration of inverter-based resources (IBRs) in power systems increases the risk of harmonic instability and frequency/voltage instability. Traditionally, these two types of stability are handled separately by multifarious methods, and the relationship between them has not been thoroughly investigated. This paper addresses this gap by proving the equivalence between harmonic stability and frequency/voltage stability. On this basis, a unified analysis method for the two types of stability is formulated using the locally measured $\boldsymbol{dq}$ admittance model. Several key advantages are offered by the proposed method over existing approaches: 1) It enables black-box analysis of both stability types, protecting intellectual property and proprietary information; 2) It allows for concurrent analysis of both stability types, avoiding the trade-off between enhancing one type of stability at the expense of the other; 3) It captures dynamic features across the full frequency range, demonstrating superior accuracy in inverter-integrated power systems; 4) It reveals that $\boldsymbol{d}$-axis and $\boldsymbol{q}$-axis subsystem harmonic stability correspond to frequency and voltage stability, respectively. Finally, a series of case studies involving heterogeneous generation units and non-linear loads validate the accuracy and effectiveness of the proposed method.