Correlation-segregated joint pdf for stochastic assessment of synthetic inertia in wind turbines

The increasing integration of inverter-based resources (IBRs) into power systems is creating significant challenges for maintaining frequency response and stability. To address these concerns, recent research has explored leveraging the fast-response characteristics of IBRs, particularly by implementing synthetic inertia through advanced control algorithms. Although synthetic inertia from IBRs is promising for enhancing real-time system inertia and operation strategies, a noticeable gap remains in effectively integrating synthetic inertia considerations into long-term generation expansion planning. To bridge this gap, this study proposes a novel probabilistic approach using correlation-segregated joint probability density functions (PDFs) for the stochastic assessment and optimization of wind turbine synthetic inertia contributions. Specifically, wind turbine datasets are categorized based on their probabilistic correlation strength using rank correlation, enabling precise scenario generation for inertia evaluation. Unlike conventional methods, which uniformly allocate constant inertia values, the proposed method assigns individually optimized inertia constants to each wind turbine and allows varying inertia values across different output ranges. Simulation results from a real-world case study, utilizing actual wind speed and load data from a power system with high wind generation penetration, demonstrate that the proposed approach significantly reduces the likelihood of over- or under-estimating inertia resources compared to conventional methods. Moreover, the methodology can seamlessly integrate probabilistic inertia distributions derived from future wind farm sites, thus effectively supporting long-term generation expansion planning. Limitations and future directions, including explicit consideration of load-price interactions, are also discussed.