Probabilistic Frequency Stability Analysis of Power Systems With Grid‐Forming and Grid‐Following Wind Power Generation: A Quantum Algorithm Approach

ABSTRACT

High wind power penetration makes probabilistic frequency stability sensitive to wind speed uncertainty and converter control modes in systems combining grid forming (GFM) and grid following (GFL) wind generation. Model‐driven Monte Carlo simulation preserves physical dynamics but requires repeated time domain solutions. This paper proposes a quantum ordinary differential equation (ODE) method for probabilistic frequency stability that propagates each sample through the mixed GFM/GFL frequency response model. Weibull wind speeds are converted by maximum power point tracking into uncertain active power references. The resulting differential algebraic equations  are analytically reconstructed as ODEs under explicit assumptions. Simulations show close agreement with the classical solution in deterministic trajectories, bus level frequency nadir, and rate of change of frequency (RoCoF). For the IEEE 39‐bus system, the active source bus trajectory RMSE is Hz, and the maximum nadir error is Hz. Across the 1000‐sample studies, the absolute errors in the mean and variance of the equivalent centre of inertia RoCoF remain below Hz/s and (Hz/s), respectively. These results demonstrate the numerical feasibility of the proposed framework for probabilistic frequency stability assessment.