Wind Turbine Power Output

Wind Turbine Power Output

A wind turbine converts a fraction of the kinetic energy passing through its swept rotor area into mechanical (and then electrical) power. That fraction — the power coefficient Cp — is capped by the Betz limit around 0.59, but real turbines run somewhat lower once mechanical and aerodynamic losses are included.Because power output scales with the cube of wind speed, small differences in average site wind speed translate into large differences in expected energy production, which is exactly why wind resource assessment is such a critical (and expensive) part of any wind project’s feasibility study.

The power output is P = ½·ρ·A·v³·Cp, air density times swept area times wind speed cubed times the power coefficient, halved. where ρ is air density, A is the rotor swept area, v is wind speed, and Cp is the turbine’s power coefficient.

The rotor sweeps out a circular area as it spins, and that area is what the wind flows through to deliver energy to the blades.

Applying the wind power equation to that swept area converts the available kinetic energy flux into the mechanical power the turbine actually extracts at its given power coefficient.

Results

An output around 2.1 MW at a strong 12 m/s wind speed is consistent with a utility-scale turbine of this rotor size near its rated capacity. Because the cubic term dominates, cutting the wind speed in half would drop this output to roughly an eighth of its value — which is why turbine siting on the windiest available location matters so much more than most other design choices.

Assumptions & limitations

• Power coefficient Cp assumed constant across wind speeds (real turbines vary Cp with tip-speed ratio).
• Steady, uniform wind speed across the entire swept area.
• Mechanical-to-electrical generator conversion losses not included beyond Cp.

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