## 7 Conclusions  
In this paper, a VMD-NRBO-Transformer-BiLSTM short-term PV output prediction model is proposed for the PV output uncertainty problem. Through example tests, the model has better error evaluation indexes and better prediction effects than the general Transformer model, the Transformer model incorporating BiLSTM, and the Transformer-BiLSTM model utilizing VMD. The following conclusions are drawn:  
* The VMD method effectively mitigates the challenge of feature extraction caused by the volatility of photovoltaic output data. By removing high-frequency components from each decomposed mode and reconstructing the data using the remaining components, the resulting waveform becomes smoother while preserving key information. This process effectively filters out noise, thereby reducing its interference with the model's predictions. * Building on the Transformer encoder-decoder architecture, BiLSTM is employed to replace the attention layer in the original Transformer decoder, while residual connections are introduced to process the input sequence data. This approach preserves the encoder's information, enhances the model's capacity to capture and process relevant features, and effectively addresses the challenge of long-term dependencies in sequence data. * The NRBO algorithm overcomes the challenges associated with manually selecting hyperparameters for the network model, as well as the limitations of empirical selection methods in specific prediction scenarios. As a result, the model's prediction accuracy is significantly enhanced. The MAE, MAPE, MSE, and RMSE are reduced by 42.38%, 53.40%, 73.94%, and 48.94%, respectively, while the \(R^{2}\) score increases by 15.18%. Figure 13: Compass diagrams of error evaluation metrics for each model. (**a**) Compass plot of MAE for each model; (**b**) compass plot of MAPE for each model; (**c**) compass plot of MSE for each model; (**d**) compass plot of RMSE for each model; and (**e**) compass plot of 1-R\({}^{2}\) for each model. In addition, this paper only focuses on the accuracy of PV power generation prediction over the past few days. It has not yet considered the training of the model and prediction solving efficiency, as real-time fast prediction has not been further studied, and has not been further divided into prediction scenarios, which cannot guarantee the prediction effect of different weather and regions. It can be used to perform in-depth research on the universality of model application and real-time prediction in the future. Finally, for microgrid system operators, selecting a good prediction model, combining the advantages of each network and algorithm, and selecting the local PV output historical data for a large number of model training allows the prediction model to be deployed in advance to accurately predict distributed PV output, which is conducive to the accurate formulation of the microgrid scheduling plan. Conceptualization, X.F., R.W. and Y.Y. ; Data curation, Y.Y. ; Formal analysis, X.F. and R.W. ; Funding acquisition, R.W. ; Investigation, J.W. ; Methodology, X.F., R.W. and Y.Y. ; Project administration, X.F. and J.W. ; Resources, X.F. ; Software, X.F. and Y.Y. ; Supervision, J.W. ; Validation, J.W. ; Visualization, Y.Y. ; Writing--original draft, X.F., R.W. and Y.Y. ; Writing--review and editing, J.W. All authors have read and agreed to the published version of the manuscript. This research was funded by the State Grid Chongqing Electric Power Company Electric Power Science Research Institute, grant number SGCQDK00 DWJS2400091. Not applicable. Not applicable. Not applicable. Not applicable. The datasets presented in this article are not readily available because the data are part of an ongoing study. Requests to access the datasets should be directed to the corresponding author. We would like to thank [PERSON], [PERSON], and [PERSON] for their contributions to this paper and their very valuable help, without which we would not have been able to complete this paper.