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Parameter estimation of weibull probability distribution by seven methods – a wind regime of the city of nitra, Slovakia

Pobočíková Ivana, Sedliačková Zuzana, Michalková Mária, Jurášová Daniela

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 3

63--73

Slovakia currently has a relatively large unused potential in the area of electricity production from solar radiation and wind as renewable sources. The conversion of the wind’s mechanical energy into electrical energy depends, among other things, on the wind speed and its turbulence. Perhaps the most widely used probability distribution for a wind speed model is the Weibull distribution. In the article, we deal with the comparison of seven methods for estimating the parameters of this distribution – maximum likelihood method, method of moments, empirical method, empirical method of Lysen, power density method, least squares method and weighted least squares method – on wind speed records from the city of Nitra for the period of 2005-2021. The vicinity of this city is one of the places identified as a suitable location for the installation of wind turbines. The performance of individual estimation methods is evaluated based on the indicators – the coefficient of determination R 2 and the root mean square error RMSE. Based on these values, the most accurate method is the weighted least squares method, although all other methods achieved similarly good results.

Time series analysis of fossil fuels consumption in slovakia by arima model

Michalková Mária, Pobočíková Ivana

Acta Mechanica et Automatica

2023

Vol. 17, no. 1

35--43

According to the Green Deal, the carbon neutrality of the European Union (EU) should be reached partly by the transition from fossil fuels to alternative renewable sources. However, fossil fuels still play an essential role in energy production, and are widely used in the world with no alternative to be completely replaced with, so far. In recent years, we have observed the rapidly growing prices of commodities such as oil or gas. The analysis of past fossil fuels consumption might contribute significantly to the responsible formulation of the energy policy of each country, reflected in policies of related organisations and the industrial sector. Over the years, a number of papers have been published on modelling production and consumption of fossil and renewable energy sources on the level of national economics, industrial sectors and households, exploiting and comparing a variety of approaches. In this paper, we model the consumption of fossil fuels (gas and coal) in Slovakia based on the annual data during the years 1965–2020. To our knowledge, no such model, which analyses historical data and provides forecasts for future consumption of gas and coal, respectively, in Slovakia, is currently available in the literature. For building the model, we have used the Box–Jenkins methodology. Because of the presence of trend in the data, we have considered the autoregressive integrated moving average (ARIMA (p,d,q)) model. By fitting models with various combinations of parameters p, d, q, the best fitting model has been chosen based on the value of Akaike’s information criterion. According to this, the model for coal consumption is ARIMA(0, 2, 1) and for gas consumption it is ARIMA(2, 2, 2).