A Bayesian Deep Learning Technique for Multi-Step Ahead Solar Generation Forecasting

Abstract: In this paper, we propose an improved Bayesian bidirectional long-short term memory (BiLSTM) neural networks for multi-step ahead (MSA) solar generation forecasting. The proposed technique applies alpha-beta divergence for a more appropriate consideration of outliers in the solar generation data and resulting variability of the weight parameter distribution in the neural network. The proposed method is examined on highly granular solar generation data from Ausgrid using probabilistic evaluation metrics such as Pinball loss and Winkler score. Moreover, a comparative analysis between MSA and the single-step ahead (SSA) forecasting is provided to test the effectiveness of the proposed method on variable forecasting horizons. The numerical results clearly demonstrate that the proposed Bayesian BiLSTM with alpha-beta divergence outperforms standard Bayesian BiLSTM and other benchmark methods for MSA forecasting in terms of error performance.

• The paper introduces an enhanced Bayesian BiLSTM model with alpha-beta divergence for multi-step solar generation forecasting, effectively reducing error metrics.
• It improves uncertainty quantification with a robust divergence scheme, achieving significantly lower RMSE, MAE, Pinball loss, and Winkler scores in experiments.
• The approach demonstrates efficient convergence using TensorFlow on Ausgrid data, offering promising implications for smart grid energy predictions.

Bayesian Deep Learning for Solar Generation Forecasting

The paper introduces an improved Bayesian BiLSTM technique incorporating alpha-beta divergence for MSA solar generation forecasting. The proposed method addresses limitations in standard BDL techniques, particularly in handling outliers and variability in solar generation data, by employing a more robust divergence scheme for approximating the posterior distribution of weight parameters. The effectiveness of the technique is demonstrated through comparative analysis using granular solar generation data from Ausgrid, evaluated with probabilistic metrics such as Pinball loss and Winkler score.

Methodology

The core of the proposed approach lies in enhancing the Bayesian inference within a BiLSTM framework. The standard LSTM cell, crucial for processing time-series data, is extended bidirectionally to capture temporal dependencies more effectively. The innovation centers on the optimization of weight parameters within the BDL model, where the posterior distribution is approximated using VI. Traditional BDL methods rely on KL divergence, which tends to underestimate posterior variance, especially in datasets with high variability. To mitigate this, the authors integrate alpha-beta divergence ($D_{\alpha\beta}$), offering a more scalable alternative that provides greater flexibility in parameter selection. The $D_{\alpha\beta}$ is defined as:

$$D_{\alpha\beta}(p||q) = \left( \frac{\alpha+\beta-1}{\beta(\alpha+\beta)} - \frac{\alpha + \beta -1}{\alpha\beta}-\frac{1}{\alpha (\alpha+\beta)} + \frac{1}{\alpha} \right) \times \mathbb{E}[\log (\theta)]$$

This improved divergence technique allows for a more accurate quantification of uncertainties, leading to more reliable probabilistic forecasts. The method employs a DIRMO approach to generate MSA forecasts for one day ahead solar generation, specifically 48-time steps (half-hourly intervals).

Implementation and Evaluation

The improved Bayesian BiLSTM technique is implemented using TensorFlow and evaluated on a solar generation dataset from Ausgrid, comprising data from 300 rooftop PV panels. The dataset is divided into training (9 months) and testing (3 months) sets. The performance of the proposed method is assessed using both deterministic (RMSE, MAE) and probabilistic (Pinball loss, Winkler score) error metrics.

The results demonstrate that the improved Bayesian BiLSTM outperforms standard BDL methods and benchmark point forecasting techniques, such as RNN, LSTM, and BiLSTM. Specifically, the proposed method achieves the lowest RMSE and MAE values, indicating superior accuracy in deterministic forecasting. Moreover, it exhibits significantly lower Pinball loss and Winkler scores, demonstrating enhanced probabilistic estimation.

Results and Discussion

The numerical results indicate a significant improvement in forecasting accuracy and uncertainty quantification. The Pinball and Winkler scores for the improved Bayesian BiLSTM are more than 10 times lower than those of standard Bayesian methods, attributable to the alpha-beta divergence's ability to manage uncertainties effectively. While BiLSTM models typically require additional computation time, the improved Bayesian BiLSTM converges more efficiently due to the more accurate divergence technique.

The paper includes graphical illustrations comparing the solar generation forecasts of the improved and standard Bayesian BiLSTM methods. These visualizations highlight the tighter PI bounds achieved by the proposed method, indicating more precise future generation probabilities. The study also investigates the impact of different forecasting time horizons, showing that the improved method is more robust in generating MSA forecasts.

Conclusion

The research presents a compelling case for the use of improved Bayesian BiLSTM with alpha-beta divergence for MSA solar generation forecasting. The method demonstrates superior performance in both deterministic and probabilistic forecasting, offering a promising solution for enhancing energy generation predictions in smart grid systems. Future research directions include exploring Bayesian BiLSTM for multidimensional energy forecasting problems.