Forecasting accuracy in highly uncertain environments is challenging due to the stochastic nature of systems. Deterministic forecasting provides only point estimates and cannot capture potential outcomes. Therefore, probabilistic forecasting has gained significant attention due to its ability to quantify uncertainty, where one of the approaches is to express it as a prediction interval (PI), that explicitly shows upper and lower bounds of predictions associated with a confidence level. High-quality PI is characterized by a high PI coverage probability (PICP) and a narrow PI width. In many real-world applications, the PI width is generally used in risk management to prepare resources that improve reliability and effectively manage uncertainty. A wider PI width results in higher costs for backup resources as decision-making processes often focus on the worst-case scenarios arising with large PI widths under extreme conditions. This study aims to reduce the large PI width from the PI estimation method by proposing a new PI loss function that penalizes the average of the large PI widths more heavily. The proposed formulation is compatible with gradient-based algorithms, the standard approach to training neural networks (NNs), and integrating state-of-the-art NNs and existing deep learning techniques. Experiments with the synthetic dataset reveal that our formulation significantly reduces the large PI width while effectively maintaining the PICP to achieve the desired probability. The practical implementation of our proposed loss function is demonstrated in solar irradiance forecasting, highlighting its effectiveness in minimizing the large PI width in data with high uncertainty and showcasing its compatibility with more complex neural network models. Therefore, reducing large PI widths from our method can lead to significant cost savings by over-allocation of reserve resources.
We report a data-parsimonious machine learning model for short-term forecasting of solar irradiance. The model inputs include sky camera images that are reduced to scalar features to meet data transmission constraints. The output irradiance values are transformed to focus on unknown short-term dynamics. Inspired by control theory, a noise input is used to reflect unmeasured variables and is shown to improve model predictions, often considerably. Five years of data from the NREL Solar Radiation Research Laboratory were used to create three rolling train-validate sets and determine the best representations for time, the optimal span of input measurements, and the most impactful model input data (features). For the chosen test data, the model achieves a mean absolute error of 74.34 $W/m^2$ compared to a baseline 134.35 $W/m^2$ using the persistence of cloudiness model.
Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years, conventional neural networks often fail to address these two critical aspects simultaneously or even independently. Inspired by natural physical systems and established literature, input convex architectures are known to enhance computational efficiency in optimization tasks, whereas Lipschitz-constrained architectures improve robustness. However, combining these properties within a single model requires careful review, as inappropriate methods for enforcing one property can undermine the other. To overcome this, we introduce a novel network architecture, termed Input Convex Lipschitz Recurrent Neural Networks (ICLRNNs). This architecture seamlessly integrates the benefits of convexity and Lipschitz continuity, enabling fast and robust neural network-based modeling and optimization. The ICLRNN outperforms existing recurrent units in both computational efficiency and robustness. Additionally, it has been successfully applied to practical engineering scenarios, such as modeling and control of chemical process and the modeling and real-world solar irradiance prediction for solar PV system planning at LHT Holdings in Singapore. Source code is available at https://github.com/killingbear999/ICLRNN.
Solar power harbors immense potential in mitigating climate change by substantially reducing CO$_{2}$ emissions. Nonetheless, the inherent variability of solar irradiance poses a significant challenge for seamlessly integrating solar power into the electrical grid. While the majority of prior research has centered on employing purely time series-based methodologies for solar forecasting, only a limited number of studies have taken into account factors such as cloud cover or the surrounding physical context. In this paper, we put forth a deep learning architecture designed to harness spatio-temporal context using satellite data, to attain highly accurate \textit{day-ahead} time-series forecasting for any given station, with a particular emphasis on forecasting Global Horizontal Irradiance (GHI). We also suggest a methodology to extract a distribution for each time step prediction, which can serve as a very valuable measure of uncertainty attached to the forecast. When evaluating models, we propose a testing scheme in which we separate particularly difficult examples from easy ones, in order to capture the model performances in crucial situations, which in the case of this study are the days suffering from varying cloudy conditions. Furthermore, we present a new multi-modal dataset gathering satellite imagery over a large zone and time series for solar irradiance and other related physical variables from multiple geographically diverse solar stations. Our approach exhibits robust performance in solar irradiance forecasting, including zero-shot generalization tests at unobserved solar stations, and holds great promise in promoting the effective integration of solar power into the grid.
This paper proposes an anticipative transformer-based model for short-term solar irradiance forecasting. Given a sequence of sky images, our proposed vision transformer encodes features of consecutive images, feeding into a transformer decoder to predict irradiance values associated with future unseen sky images. We show that our model effectively learns to attend only to relevant features in images in order to forecast irradiance. Moreover, the proposed anticipative transformer captures long-range dependencies between sky images to achieve a forecasting skill of 21.45 % on a 15 minute ahead prediction for a newly introduced dataset of all-sky images when compared to a smart persistence model.
For short-term solar irradiance forecasting, the traditional point forecasting methods are rendered less useful due to the non-stationary characteristic of solar power. The amount of operating reserves required to maintain reliable operation of the electric grid rises due to the variability of solar energy. The higher the uncertainty in the generation, the greater the operating-reserve requirements, which translates to an increased cost of operation. In this research work, we propose a unified architecture for multi-time-scale predictions for intra-day solar irradiance forecasting using recurrent neural networks (RNN) and long-short-term memory networks (LSTMs). This paper also lays out a framework for extending this modeling approach to intra-hour forecasting horizons thus, making it a multi-time-horizon forecasting approach, capable of predicting intra-hour as well as intra-day solar irradiance. We develop an end-to-end pipeline to effectuate the proposed architecture. The performance of the prediction model is tested and validated by the methodical implementation. The robustness of the approach is demonstrated with case studies conducted for geographically scattered sites across the United States. The predictions demonstrate that our proposed unified architecture-based approach is effective for multi-time-scale solar forecasts and achieves a lower root-mean-square prediction error when benchmarked against the best-performing methods documented in the literature that use separate models for each time-scale during the day. Our proposed method results in a 71.5% reduction in the mean RMSE averaged across all the test sites compared to the ML-based best-performing method reported in the literature. Additionally, the proposed method enables multi-time-horizon forecasts with real-time inputs, which have a significant potential for practical industry applications in the evolving grid.