Comparison of different multi-parameters probability density models for wind resources assessment

Abstract

Accurate wind resource assessment lies on the precise information provided by a probability distribution function (PDF). Therefore, it is an essential prerequisite to find the most appropriate PDF to model the wind speed data at the planning stage. Earlier, researchers have compared several distributions of 1, 2-parameters such as Rayleigh, Gamma, Exponential, Normal family, Weibull distributions, etc. Among these, 2-paramters Weibull distribution was a widely acceptable distribution for wind speed data modeling. However, its comparison with a multi-parameter (3 and 4 parameters) distribution has rarely been studied. In this paper, the Weibull distribution has been compared with four new distributions, which have rarely been studied for wind speed data modeling previously. They are 2-parameter Nakagami and Rician distribution, 4-parameter Johnson SB distribution, and 5-parameter Generalized Hyperbolic distribution. The sites selected for the case study are Trivandrum, Ahmedabad, Calcutta, Jaipur, New Delhi, and Port Blair of India. The result indicates that the Generalized Hyperbolic and Johnson distributions are ranked 1st and 2nd; Weibull and Nakagami distributions perform equally well and are ranked 3rd and 4th among the five compared distributions for five Indian stations. However, for one station (Ahmedabad), which is less skewed and has low kurtosis, the performance of Weibull distribution is better than those of the other distributions. The achieved results reveal that the skewness and kurtosis are equally important as the mean and standard deviation of wind speed data, which may influence the accuracy of the distribution. Wind behavior is stochastic, and a single distribution cannot be accepted as a universally accepted distribution for all locations of India.

Evaluation of Nakagami and Birnbaum-Saunders probability distribution for wind speed and power estimation

“…The findings of Alavi, Mohammadi, and Mostafaeipour (2016) and Gugliani (2020) suggest that the Nakagami distribution is similar to the Weibull distribution in different terrains. Although Haq et al (2021) do not explicitly mention this in their conclusion, their data suggests that the Nakagami and Weibull distributions have similar performance.…”

“…In addition, the applicability of the Birnbaum-Saunders distribution has been tested in a wide range of fields, including water quality, air pollution, economics, agriculture, engineering, and medicine (Gomes, Ferreira, and Leiva 2013;Leiva, Sanhueza, and Angulo 2009). Recently, a few researchers have also applied the Nakagami (Alavi, Mohammadi, and Mostafaeipour 2016;Aries, Boudia, and Ounis 2018;Gugliani 2020;Haq et al 2021;Idriss et al 2020) and Birnbaum-Saunders (Jia et al 2020;Mahbudi, Jamalizadeh, and Farnoosh 2020;Mohammadi, Alavi, and McGowan 2017) distributions to wind applications. However, the performance of a probability distribution function should be evaluated across different terrain, altitude, and locations.…”

A review of sensitivity analysis practices in wind resource assessment

“…WRA starts with statistically modelling the WS. WS time series (WSTS) is fitted with a distribution model (DM), most commonly with the two-parameter Weibull (W2) distribution (1) [23][24][25] [26][27], although other DMs are possible [28][27] [29][30] [31].…”