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The accurate prediction of wind speed is important in satisfying the demands of power grids. However, the prediction of wind speed is challenging because of its randomness and volatility, especially in multi-step cases. This study proposes a novel multi-step wind speed prediction model combining a Weather Research and Forecasting (WRF) simulation and an error correction strategy. First, the WRF model is adopted to predict the wind speed. Variational Mode Decomposition (VMD) is then employed to mine features of the predicted wind speed using the WRF model. The Principal Component Analysis (PCA) method is next used to extract the main components and remove illusive components. Using these principal components and prediction error as the training dataset, Long Short-Term Memory (LSTM) is applied for error correction. The WRF-VMD-PCA-LSTM model is thus developed for the multi-step prediction of wind speed. In a case study of a wind farm located in Sichuan Province, China, the proposed WRF-VMD-PCA-LSTM model outperforms models to which it is compared. The results reveal that the VMD-PCA method effectively extracts features hidden in the numerical WRF output. The proposed model effectively improves the accuracy of multi-step wind speed prediction. • Features hidden in the numerical weather prediction output are extracted by a hybrid VMD-PCA method. • Propose an error correction strategy to improve the prediction accuracy of numerical weather prediction. • The proposed model is effective in multi-step wind speed prediction. [ABSTRACT FROM AUTHOR]

Carbon price forecasting is an important component of a sound carbon price market mechanism. The accurate prediction of carbon prices is an active topic of research. However, many previous studies have focused on the application of a single model, ignoring the application of combination strategies. In this study, a hybrid forecasting system that includes error correction strategy and divide-conquer strategy is designed to predict the carbon price series accurately. Specifically, the main framework of this article comprises four modules. Data preprocessing module of the divide and conquer strategy is proposed. Next, the optimization module uses a multi-objective grasshopper optimization algorithm to enhance the performance of the prediction module. Then, the error correction module predicts the error sequence and corrects the model results. To verify the performance of the established hybrid forecasting system, experiments were performed using two real carbon price series from China and European Union emissions trading schemes, and the results showed that the mean absolute percentage errors of the system were 2.7793% and 0.6720%, respectively, which are better than the other benchmark methods considered. Moreover, it was proved that the designed forecasting system provides a new, effective, and feasible solution for carbon price forecasting. • An advanced preprocessing strategy is applied to process the signal. • ORELM model is improved by multi-objective optimization strategy. • Datasets for different regions are used in the experiment. • Multiple evaluation metrics for testing system performance. [ABSTRACT FROM AUTHOR]