Wind power probabilistic forecasting considering meteorological conditions and spatiotemporal correlations: A hybrid method based on conditional normalizing flows and a two-stage R-vine copula

The low-carbon energy transition requires large-scale wind power integration, but the inherent uncertainty of wind power outputs threatens the safe and stable operation of power systems, making accurate probabilistic forecasting essential. This paper proposes a hybrid probabilistic forecasting method that combines conditional normalizing flows (CNF) with a two-stage R-vine copula to fit the joint probability distribution of multidimensional wind power outputs. Specifically, CNF is used to fit the conditional marginal distributions of wind power output under multivariate meteorological conditions, while the two-stage R-vine copula sequentially decouples temporal and spatial correlations to enable parallel computation. Case study results show that: (1) CNF reduces the deviation to within 2.5% under any number of meteorological condition dimensions, outperforming weighted kernel density estimation; (2) compared with independent modeling of single wind farms, joint modeling of multiple wind farms improves root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) by nearly 50%, with a cost-benefit ratio of 483.76; (3) compared with traditional vine copula methods, the proposed copula achieves lower Akaike information criterion and energy scores while reducing computing time by approximately 77% (≈2.5 h); (4) compared with mainstream deep learning models (spatiotemporal graph convolutional network), the proposed method achieves an RMSE of 4.35 MW, an MAE of 2.55 MW, and a MAPE of 6.35%; and (5) the time-first-then-space two-stage R-vine copula is suitable for small sample sizes with large data fluctuations, whereas the space-first-then-time version is suitable for large sample sizes with moderate or small fluctuations. Overall, the proposed method demonstrates advantages in accuracy, speed, and adaptability.