Fractional-Order Dynamic Modeling of Renewable-Dominant Power Systems Using Long-Memory Load and Generation Data

The large-scale rapid deployment of renewable generation and energy storage is transforming traditional power system dynamics through intermittency, reduced inertia, and pronounced long-range temporal dependence. Existing power system modeling frameworks are primarily based on short-memory assumptions and integer-order dynamics, which are unable to capture the persistence and oscillatory behavior of emerging renewable-dominant power systems. This structural mismatch leads to inaccurate system representation and degraded long-horizon prediction performance. Although fractional calculus has been applied to specific control and forecasting tasks in power systems, the joint system-level modeling of renewable generation and load demand using real-world data remains largely unexplored. In this paper, we develop a data-driven fractional-order dynamic modeling framework that explicitly incorporates long-memory effects into the governing equations through fractional differential equations based on the Caputo formulation. Using publicly available high-resolution datasets of load and renewable generation, empirical analysis reveals power-law decaying autocorrelations and dominant low-frequency spectral characteristics that motivate the use of fractional-order dynamics. Fractional orders and model parameters are jointly identified through prediction-error minimization to ensure consistency between modeled trajectories and observed persistence. The numerical results demonstrate that the proposed approach achieves a root–mean–square error of 3.12, compared to 5.64 and 4.98 for integer-order and finite-memory models, respectively, and reduces the normalized root–mean–square error from 0.156 and 0.132 to 0.087. Residual and spectral analyses further confirm that long-memory behavior is effectively captured by the proposed dynamics. The framework provides a scalable and physically interpretable foundation for the data-driven modeling of renewable-dominant power systems.