Speed distribution analysis based on maximum entropy principle and Weibull distribution function

Present study is aimed at constructing a probability distribution function using Maximum Entropy Principle and Weibull distribution function. A comparison between the two modeled function is given and error analysis is performed. For the purpose of study, 10 min averaged wind data measured at Keti Bandar, Pakistan for 21 months is used. Among many nonlinear equations as probability distribution functions with (N + 1) Lagrange multipliers and subject to moment constraints of the given set of wind speed data, a distribution function is selected for which entropy is maximized. Lagrange multipliers are determined for 5, 6, and 7 low order moments and corresponding entropies and probability distribution function are also determined. Goodness-of-fit is assured Kolmogorov–Smirnov (KS) test between the calculated cdfs of the theoretically function based on MaxEnt and recorded wind speed data. At 60 m, the monthly mean wind speed was varied between 5.18 and 8.15 m/s corresponding to the months of October and May with an overall mean of 6.6 m/s. On the other hand, the wind power density varied between a minimum of 82.8 W/m² and a maximum 334 W/m² for the months of October and May with an overall annual mean of 176.06 W/m². Test results indicate a good fit of the modeled function based on MaxEnt as KS test statistic, Q < critical value, Q₉₅ (∼10⁻²). R², RMSE, and χ² tests are also performed for testing goodness-of-fit of Weibull function. The study concluded that the MaxEnt based function is an alternative to Weibull based function.