Wind farm layout optimization with uncertain wind condition

Due to the uncertainty of wind condition, the annual energy production (AEP) of a wind farm during operation time is varying from year to year and is difficult to be estimated. A risk management method based on conditional value-at-risk (CVaR) is introduced for increasing the robustness of the AEP under uncertain wind conditions. To implement the risk management in the wind farm layout optimization, uncertainty analysis method for the discretized wind distribution in the future is proposed, and the CVaR of the AEP as the objective function is calculated by the proposed normal approximation method with the uncertainty analysis results. The discrete probability distribution of future wind condition is denoted by the wind relative frequencies. The wind relative frequencies itself are treated as random variables. A Dirichlet-Multinomial distribution is applied to model the uncertainty of the wind relative frequencies in the future. The approximated normal distribution of AEP is established based on the probability distribution of the wind relative frequencies, and the CVaR can be calculated analytically based on the mean and variance of the normal distribution. The simulation verifies that the optimization method achieves a trade-off between maximizing the expected value of AEP with historical wind condition, and minimizing the potential variation of the AEP due to a changing wind condition in the future.