Wind Turbine Output Air-Density Correction

ScopeA power curve is warranted at sea level and 59 degF, and a machine on a high plain on a hot afternoon is breathing air a quarter thinner. A site at 5,200 ft at 95 degF runs 0.05908 lb/cu ft, which is 77.2% of the reference density -- so a curve promising 2,200 kW is really promising 1,699 kW at that condition. THE DIAGNOSTIC USE IS THE PRACTICAL ONE. A machine reading 1,850 kW there is at 84% of the raw curve, which looks like a fault, and at 109% of the density-corrected curve, which is not one. The correction is what distinguishes physics from a problem, and skipping it condemns every high-altitude site in the country to look broken on the hottest afternoons -- which is precisely when the grid wants the power most. POWER IS LINEAR IN DENSITY AND CUBIC IN SPEED, so the two corrections are applied differently and must not be mixed up. The IEC convention is worth knowing because it is what a performance test uses: rather than scaling power it scales the measured WIND SPEED by the cube root of the density ratio, so 20 mph on that afternoon reads as 18.35 mph against the standard curve. The two agree where power is roughly cubic in speed and diverge near rated, where the machine is power-limited and density affects only where rated is reached, not the rated value -- which is also the limit of the linear form: applying it to rated power is wrong. SEASON MOVES IT AS MUCH AS ALTITUDE. The same site on a 20 degF winter morning runs 0.06831 lb/cu ft, 116% of the summer value, so the same wind makes 16% more power on density alone. A density correction using the ISA barometric relation, the same one the HVAC air-density calculator uses, so the two agree about the air at a site -- against a different reference, because a power curve is warranted at 59 degF where standard HVAC air is 70 degF. A measured barometric pressure beats an elevation estimate, and humidity has a small further effect not modelled. Pitch-regulated and stall-regulated machines respond differently and the manufacturer method governs. It does not evaluate whether a machine meets its warranted curve, which is a formal measurement to IEC 61400-12 with defined sectors, filtering, and uncertainty. The turbine manufacturer power curve, its stated reference conditions and correction method, and IEC 61400-12 govern.

Formula or tablethe ISA barometric relation: density = reference density x 518.67 / (459.67 + degF) x (1 - 6.8754e-6 x elevation) raised to 5.2559; power scales LINEARLY with the density ratio below rated, and the IEC method instead scales the measured wind speed by the cube root of that ratio.

Source and editionThe ISA barometric density relation by name against the IEC/ISO reference of 0.0765 lb/cu ft at 59 degF and sea level, with the IEC 61400-12 cube-root wind-speed correction named. The turbine manufacturer's power curve, its stated reference conditions and correction method, and IEC 61400-12 govern.

Free accessA density ratio from the site's own elevation and temperature; no manufacturer power curve is reproduced.

What governsEstimate. AHJ and licensed professional govern.

API field nameselevation_ft, air_temp_f, reference_density_pcf, measured_power_kw, curve_power_kw, wind_speed_mph, alt_air_temp_f, site_density_pcf, density_ratio, corrected_curve_power_kw, iec_speed_factor, iec_corrected_wind_mph, alt_density_pcf

• Linear in density, cubic in speed and the linear form does not apply above ratedturbine physics
• A performance test scales the speed by the cube root of the density ratio, not the powerIEC 61400-12
• Measured pressure beats an elevation estimate and humidity has a small further effect not modelledIEC 61400-12