Analytic Expressions for Maximum Wind Turbine Average Power in a Rayleigh Wind Regime

Average or expectation values for annual power of a wind turbine in a Rayleigh wind regime are calculated and plotted as a function of cut-out wind speed. This wind speed is expressed in multiples of the annual average wind speed at the turbine installation site. To provide a common basis for comparison of all real and imagined turbines, the Rayleigh-Betz wind machine is postulated. This machineis an ideal wind machine operating with the ideal Betz power coefficient of 0.593 in a Rayleigh probabillty wind regime. All other average annual powers are expressed in fractions of that power. Cases considered include: 1) an ideal machine with finite power and finite cutout speed, 2) real machines operating in variable speed mode at their maximum power coefficient, and 3) real machinesoperating at constant speed.