A Hydrostatic Transmission (HST) offers a variable ratio transmission for wind turbines that has a higher power to weight ratio than traditional gearboxes, and requires less maintenance. In a conventional turbine, when the wind speed increases above the rated speed, the blade pitch is controlled to dissipate excess energy and regulate the turbine at rated power. An energy storage system allows the turbine to temporarily operate above rated power, and capture the traditionally dissipated energy in an accumulator. When the wind speed drops below the rated speed, the energy in the accumulator is released, increasing the delivered power This paper presents a high-fidelity mathematical model of the hydraulic hybrid wind turbine transmission. Simulation results for a series of step changes and for turbulent wind speed are investigated for a 60 kW turbine. Using a realistic turbulent wind data sample, energy production increased by 4% with a 52 liter accumulator with significantly smoother output power to the grid.