A novel probabilistic wind speed forecasting based on combination of the adaptive ensemble of on-line sequential ORELM (Outlier Robust Extreme Learning Machine) and TVMCF (time-varying mixture copula function)

•A novel online ensemble model for deterministic wind speed forecasting.•Online multiple model selection and ordered aggregation that track the time-adaptive characteristic of wind speed.•Adaptive variational mode decomposition is used to decomposed the original wind speed.•Non-special predictive distributions of wind speed are established using TVMCF model.•Accurate deterministic forecasts and high quality of probabilistic prediction intervals can be generated. The uncertainty and nonstationary of wind speed have compelled the power system operators and researchers to search for more accurate and reliable techniques to implement wind speed forecasting (WSF). In allusion to this phenomenon, this paper presents an adaptive ensemble of model for the probabilistic WSF, which is based on combination of the adaptive ensemble of on-line sequential ORELM (OS-ORELM) and the time-varying mixture copula function (TVMCF) to perform multi-step WSF. An OS-ORELM with forgetting mechanism based on Cook’s distance (λCDFF OS-ORELM) serves as a basic WSF model and an on-line ensemble using ordered aggregation (OEOA) technique is employed to improve the prediction performance. In the data pre-processing period, the Bernaola Galvan algorithm (BGA) is employed to partition the raw wind speed series into segments and the adaptive variational mode decomposition (AVMD) is used to decompose each segment into sub-series with different sub-band. Each transformed sub-series is well-modeled with the application of λCDFF OS-ORELM-OEOA, which is optimized by modified crisscross optimization algorithm (CSO). Eventual forecast results are obtained through aggregate calculation. Then the probabilistic prediction intervals (PIs) of wind speed are established in a TVMCF framework by modeling the conditional forecasting error. Case studies using the real wind speed data from the National Renewable Energy Laboratory (NREL) demonstrate that the proposed model can not only improves point forecasts compared with benchmark methods, but also constructs higher quality of probabilistic PIs.