Spectral Impedance-Based Probabilistic Wideband Oscillatory Stability Analysis and Visualization

Probabilistic oscillatory stability analysis (POSA) is a crucial tool for evaluating the oscillatory instability risks of power systems with uncertainties. Conventional eigenvalue-based POSA mainly focuses on low-frequency oscillations at specific and isolated frequencies and thus cannot effectively identify or address the risks of emerging wideband oscillations. To tackle the limitations of conventional POSA, a spectral impedance-based POSA method is proposed in this paper. The proposed method combines a powerful cumulant-based method and an emerging frequency response gradient-enabled impedance-based stability criterion (FRGISC). Firstly, probabilistic distributions of uncertainties, e.g., wind speed, are modeled. Secondly, a spectral impedance of power system can be measured at a concerned operating condition. A group of impedance-based margin index values can be determined based on the FRGISC without solving eigenvalues. Then, probability density functions (PDFs) and cumulative distribution functions (CDFs) of the impedance-based margin index and frequency of concerned oscillation modes are derived by the cumulant-based method. Finally, comprehensive CDF curves including the CDFs of margin and frequency are proposed to form a spectrum to visualize the potential risks of wideband oscillations and instability probability for reasonable decision-making. The effectiveness of the proposed method is verified in a modified IEEE 68-bus power system with 3 wind farms.