A Power Series Formulation of the Betz's Criterion and Equation in a Wind Turbine

摘要

This work presents a mathematical power series expansion method to derive the functional form of Betz limit equation which is then used to calculate the Betz limit. The method assumes that the ratio of the upstream wind velocity, v_u , at the entrance of the rotor blades in m/s and the downstream wind velocity, v_d, at the exit of the rotor blades in m/s by is of order 3 deduced from the expression of power that can be extracted from wind. The technique further assumes that Betz equation can be written in a power series. It is shown that in calculating the Betz limit either from the formal method or the series method used here, the accuracy of the result improves when the calculations are carried out to more than three decimal places using Excel Spreadsheet, otherwise there is a blurred demarcation between the correct minimum and maximum as presented in the tables of results.