Probabilistic Models for Wind Turbine and Wind Farm Performance

A Markov model for the performance of wind turbines is developed that accounts for component reliability and the effect of wind speed and turbine capacity on component reliability. The model is calibrated to the observed performance of offshore turbines in the north of Europe, and uses wind records obtained from the coast of the state of Maine in the northeast United States in simulation. Simulation results indicate availability of 0.91, with mean residence time in the operating state that is nearly exponential and has a mean of 42 days. Using a power curve typical for a 2.5 MW turbine, the capacity factor is found to be beta distributed and highly non-Gaussian. Noticeable seasonal variation in turbine and farm performance metrics are observed and result from seasonal fluctuations in the characteristics of the wind record. The input parameters to the Markov model, as defined in this paper, are limited to those for which field data are available for calibration. Nevertheless, the framework of the model is readily adaptable to include, for example: site specific conditions; turbine details; wake induced loading effects; component redundancies; and dependencies. An on-off model is introduced as an approximation to the stochastic process describing the operating state of a wind turbine, and from this on-off process an Ornstein–Uhlenbeck (O–U) process is developed as a model for the availability of a wind farm. The O–U model agrees well with Monte Carlo (MC) simulation of the Markov model and is accepted as a valid approximation. Using the O–U model in design and management of large wind farms will be advantageous because it can provide statistics of wind farm performance without resort to intensive large scale MC simulation.