WIND SPEED MODEL BASED ON FRACTIONAL STOCHASTIC PROCESS

Abstract

Relevance. The urgent task of the technical and economic development of the Northern and Eastern regions of Russia is to provide reliable and efficient power supply to consumers, geographically located in remote, hard-to-reach areas. The use of wind power plants is a promising way to solve this problem. The primary task of the design and feasibility study of the use of wind power plants is to predict changes in wind speeds at the site of the power plant installation. The stochastic nature of the wind and its spatiotemporal variability explain the high complexity of this problem, for the solution of which the methods of mathematical modeling are used. The known models of wind speed based on Markov chains, autoregressive moving-average and other discrete models do not allow varying the time step, which does not allow their use for simulation of operating modes of wind turbines and wind energy systems. The article proposes a model of wind speed based on the stochastic differential equation which eliminates this drawback. The aim of the study is to construct wind speed model based on fractional Ornstein–Uhlenbeck process with a periodic long-term mean, which provides modeling of static and dynamic modes of operation of a wind power plant at different time intervals. Methods: mathematical and computer modeling using Matlab/Simulink software environment. Results. The proposed model, in contrast to the known SDE-based models, is able to produce autocorrelated wind speed trajectories with long-term dependence, daily and monthly variations to perform more detailed simulation of the operating modes of wind turbines at different time intervals with the required time step. The model was tested using the data of climatic observations of wind speed obtained from electronic archive of the All-Russian Institute of Hydrometeorological Information. The model adequacy was evaluated by comparing characteristics of simulated wind speed trajectories with actual observations collected at 518 weather stations located on territory of Russia.

Keywords

• wind energy
• wind speed modeling
• stochastic differential equations
• fractional brownian motion
• time series