Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures

Emilio Gómez-Lázaro,María Bueso,Mathieu Kessler,Bri-Mathias Hodge,Jie Zhang,Angel Molina-García,Sergio Martín-Martínez

doi:10.3390/en9020091

Abstract

The Weibull probability distribution has been widely applied to characterize wind speeds for wind energy resources. Wind power generation modeling is different, however, due in particular to power curve limitations, wind turbine control methods, and transmission system operation requirements. These differences are even greater for aggregated wind power generation in power systems with high wind penetration. Consequently, models based on one-Weibull component can provide poor characterizations for aggregated wind power generation. With this aim, the present paper focuses on discussing Weibull mixtures to characterize the probability density function (PDF) for aggregated wind power generation. PDFs of wind power data are firstly classified attending to hourly and seasonal patterns. The selection of the number of components in the mixture is analyzed through two well-known different criteria: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Finally, the optimal number of Weibull components for maximum likelihood is explored for the defined patterns, including the estimated weight, scale, and shape parameters. Results show that multi-Weibull models are more suitable to characterize aggregated wind power data due to the impact of distributed generation, variety of wind speed values and wind power curtailment.

Highlights

The growing integration of renewable resources into the electricity sector can be attributed to different factors, including deregulation of the electricity market, environmental goals, economic incentives, and technical maturity
The Spanish power system is a suitable example of a power system with high wind power penetration, accounting for over 800 wind farms and 20,000 wind turbines
Each year is divided into four quarters, from Q1 (January, February and March) to Q4 (October, November and December), according to similarities between monthly wind power generation due to seasonal effects

Summary

Introduction

The growing integration of renewable resources into the electricity sector can be attributed to different factors, including deregulation of the electricity market, environmental goals, economic incentives, and technical maturity. The share of energy consumption produced from renewable resources is currently considered a relevant short- and mid-term target in many countries. Among the different renewable resources, wind and solar power currently receive the most attention, with wind power the most prevalent in terms of installed capacity [1]. The amount of wind power generation integrated into power systems, together with other time-variable, non-dispatchable. Energies 2016, 9, 91 electricity generation, has been increasing exponentially during the past decade [2]. This increase can be identified in power systems with significant penetration of variable renewable generation, such as in Spain, where the share of wind power can’t be neglected from the supply–side. Spain is the world’s fourth biggest producer of wind power, with a year-end installed capacity of

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Results

Discussion

Conclusion