Stability implications of drivetrain model–controller mismatch in variable-speed wind turbines: A comparative simulation study

Rigid one-mass drivetrain models simplify maximum power point tracking (MPPT) controller synthesis, but their use can create a model-controller mismatch when the implemented wind turbine has a flexible shaft. This study evaluates that mismatch using a nonlinear MATLAB/Simulink model of a 1.5 MW variable-speed horizontal-axis wind turbine. Three PI-based cases are compared: (A) a controller tuned with a one-mass model and applied to a two-mass plant, (B) a controller tuned with the two-mass plant, and (C) the matched controller supplemented by active torsional damping. The gains are selected from linearized one-mass and two-mass models using pole-placement and frequency-domain constraints, while identical saturation and anti-windup settings are retained. The controllers are tested for 60 s under a reproducible wind profile with a mean speed of 11.6 m/s, deterministic low- and medium-frequency components, a gust, and low-intensity random turbulence (sigma = 0.20 m/s; turbulence intensity approximately 1.7%). Under these specific conditions, the three cases yield 0.004125 MWh, a mean absolute generator-speed tracking error of 2.14 rad/s, a tracking-error standard deviation of 4.36 rad/s, and a maximum low-speed-shaft torque of 10.924 MN m. No amplified peak is observed near the calculated torsional frequency. The contribution is therefore a conditional counterexample and a reproducible benchmark showing that rigid-model tuning is not necessarily destabilizing for this parameter set. It is not a general proof of safety: the result is limited to the tested turbine, PI architecture, short simulation horizon, high inherent damping, and low turbulence level.