Use of the Halphen distribution family for mean wind speed estimation with application to Eastern Canada

Abstract

We introduce the family of three-parameter heavy-tailed distributions, the Halphen distribution family (HDF), to model the mean wind speed for the purpose of wind energy estimation. The HDF has a number of properties favorable to model wind speed data, such as lower bound at zero (absence of location parameter), flexibility to cover a large range of shapes, and an explicit form of moment generating functions. We examined 126 stations in Eastern Canada (125 stations were heavy-tailed with positive excess kurtosis) and found that HDF provides fit superior to the most commonly used distribution for this purpose, the two-parameter Weibull distribution, in 100% of the stations according to the Akaike information criterion (AIC). HDF was compared against 4 two-parameter models (Gaussian, Weibull, Gamma, and inverse Gamma) and 3 three-parameter models (generalized extreme value, generalized Gamma and Burr). The most common best-fit distribution for the stations in the Eastern Canada case study is the HDF (46% according to AIC). The results of the case study show that wind observations cannot be fit by the Halphen inverse type B, but can be modelled by Halphen A and especially well by Halphen B (minimum of Kolmogorov-Smirnov statistic among candidate distributions). 87 stations exhibited class D tail behavior. No correlation between tail behavior class and best-fit distribution was observed. We encourage the use of Halphen A and Halphen B as candidate distributions for wind resource estimation studies that are based on mean wind speed estimation.