Ultra-Short-Term Solar Power Forecasting

• Ultra-short-term solar power prediction is the forecasting of PV output at minute-level granularity to manage real-time grid dynamics.
• Techniques such as CEEMDAN, CNNs, iTransformers, and BiLSTMs are used to extract and model distinct high-frequency and low-frequency patterns.
• Fusion with multi-head attention and evidential quantile networks provides sharp uncertainty estimates for improved grid stability and operational decision-making.

Ultra-short-term solar power prediction refers to the forecasting of photovoltaic (PV) power output or solar irradiance at very short time horizons, typically ranging from seconds to several hours, with a particular emphasis on intra-hour to intra-minute granularity. Accurate ultra-short-term forecasts are essential for the management of power grids with high solar penetration, real-time energy dispatch, and grid stability under rapidly fluctuating weather conditions. The principal challenges in this domain arise from the inherent stochasticity in solar resource availability—principally due to cloud cover dynamics—and the need for fast, adaptive, and reliable prediction methodologies that can characterize uncertainty as well as point estimates.

1. Data Decomposition and Spatio-Temporal Feature Extraction

Advanced ultra-short-term solar power prediction frameworks frequently begin by decomposing the PV power time series to extract and separately model physically meaningful temporal patterns. A prominent approach leverages CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) to decompose the PV power series into high-frequency and low-frequency components. Each Intrinsic Mode Function (IMF) extracted through CEEMDAN is characterized by its dominant frequency (using FFT and power spectral density $S(k) = |X(k)|^2$) and frequency centroid

$$f_{\text{cen}, i} = \frac{\sum_{m=1}^{\lfloor N/2 \rfloor} f_{\text{pos}}(m) S_{\text{pos}}(m)}{\sum_{m=1}^{\lfloor N/2 \rfloor} S_{\text{pos}}(m)}$$

By grouping IMFs with $f_{\text{dom}, i} > f_{\text{high}}$ as high-frequency (rapid fluctuations) and $f_{\text{dom}, i} < f_{\text{high}}$ as low-frequency (trend/seasonal), these components are reconstructed into separate signals for downstream modeling. This facilitates independent capture of transient noise (e.g., due to clouds) and diurnal or slowly-varying trends, thereby enhancing overall generalization and reducing overfitting risk (Wang et al., 21 Sep 2025).

Feature extractors are tailored to the nature of each component: CNNs excel in capturing spatio-temporal features in high-frequency data, while transformer variants—such as iTransformers designed to model longer-term dependencies—are applied to low-frequency signals. Meteorological variables (irradiance, temperature, humidity, visibility) with high correlation to PV output are processed separately, often via bidirectional LSTMs (BiLSTMs), allowing direct integration of exogenous drivers.

2. Data Fusion, Attention, and Probabilistic Modeling

Following the extraction of component-wise features, a fusion step is employed—typically realized via a multi-head attention mechanism—to consolidate and weight spatio-temporal and meteorological predictors. This attention mechanism enables the model to adaptively prioritize salient features in both the recent history and across modalities.

To enable robust quantification of predictive uncertainty, the fused features are fed to an Evidential Quantile Network (EQN) or similar architecture, which simultaneously produces quantile forecasts and evidential confidence estimates. The training objective is a weighted composite loss:

$$\mathcal{L}_{\text{EQN}} = \lambda_1 \mathcal{L}_{\text{quantile}} + \lambda_2 \mathcal{L}_{\text{evidence}} + \lambda_3 \mathcal{L}_{\text{width}}$$

where the width penalty term explicitly discourages overly broad prediction intervals:

$$\mathcal{L}_{\text{width}} = \frac{1}{W} \sum_{k} w_k \cdot \frac{1}{N} \sum_{i=1}^N \max(\Delta q_{i, k} - \theta_k, 0)$$

with $w_k$ the quantile weight, $\Delta q_{i, k}$ the interval width, and $\theta_k$ the maximum allowed width for the $k^{th}$ quantile. This constraint ensures informative, sharp confidence intervals without sacrificing coverage (Wang et al., 21 Sep 2025).

3. Benchmarking, Ablation, and Performance Metrics

Methodological rigor is maintained via a comprehensive suite of deterministic and probabilistic evaluation metrics, including normalized MAE (nMAE), normalized RMSE (nRMSE), coefficient of determination ($R^2$), Continuous Ranked Probability Score (CRPS), Absolute Coverage Error (ACE), and Winkler Score. Comparative and ablation studies are performed against baseline models such as LSTM-Quantile Regression, Mixture Density Network, XGBoost Quantile Regression, Beta Distribution NNs, and the Temporal Fusion Transformer.

Ablation experiments confirm that:

• The reconstruction of IMFs into dual frequency components yields significant gains in both deterministic and probabilistic forecasting accuracy.
• The use of specialized networks for each component stream (CNN for high-frequency, iTransformer for low-frequency, BiLSTM for meteorology) is superior to using a monolithic architecture.
• The explicit width control in the loss function results in tighter, more reliable predictive intervals.

Reported experiments on datasets from a rooftop PV installation in Hong Kong demonstrate that the proposed hybrid framework outperforms all baseline models across all metrics, with measurable improvements in both prediction sharpness and uncertainty quantification (Wang et al., 21 Sep 2025).

4. Advantages and Limitations Relative to Prior Art

The main advantages of this decomposed-attentive-probabilistic framework are as follows:

• Disentangling noise and signal: CEEMDAN-based decomposition isolates high-frequency stochastic disturbances due to cloud dynamics from stable seasonal or diurnal trends, allowing each to be modeled by an optimally chosen deep network.
• End-to-end adaptivity: Deep attention mechanisms ensure that the fusion process is data-driven and adaptive to changing statistical properties, rather than relying on static feature selection.
• Informative uncertainty quantification: The combination of quantile regression and explicit interval-width penalties enables both sharp and reliable probabilistic output—a requirement for grid operators needing risk-aware decision support in highly stochastic regimes.
• Improved generalization: By extracting features from physically interpretable components and limiting overfitting via regularization, the resulting model achieves strong performance across diverse settings and weather conditions.

However, potential challenges include:

• Choice of decomposition parameters: The CEEMDAN frequency threshold ($f_{\text{high}}$) must be tuned; performance may be sensitive to this hyperparameter.
• Interpretability: While each network operates on physically meaningful signals, the overall system complexity may complicate interpretation, especially in the attention-driven fusion layer.
• Resource requirements: The multi-stage, multi-architecture system may require substantial computational resources for training, though the paper notes competitive efficiency in practice.

5. Grid Operation and Distributed PV Integration

Accurate ultra-short-term forecasts directly facilitate grid stability, reduce reserve margin requirements, and enable high-penetration distributed PV integration. The provision of sharp probabilistic output (intervals and quantiles) allows for real-time scheduling and control decisions that are robust to forecast error. This forecasting paradigm is particularly relevant for distributed energy resource (DER) management systems, demand-side management, and energy market applications where deviations from schedule can result in financial penalties or reliability risks.

The demonstrated generalization of this framework across temporal resolutions and site types (from individual rooftops to broader urban contexts) provides a pathway toward scalable, real-time deployment in diverse grid environments with minimal loss of accuracy or reliability.

6. Technical Formulation Summary

Key components of the integrated methodology can be concisely represented as follows:

• Decomposition via CEEMDAN:

$$\text{PV}(t) \xrightarrow{\text{CEEMDAN}} \{\text{IMF}_1, \ldots, \text{IMF}_k\} \xrightarrow{\text{grouping by } f_{\text{dom}}, f_{\text{cen}}} \{\text{Low}, \text{High}\}$$

• Feature Extraction:

$$\text{High-freq} \to \text{CNN},\quad \text{Low-freq} \to \text{iTransformer},\quad \text{Meteorology} \to \text{BiLSTM}$$

• Fusion and Probabilistic Forecasting:

$\{\text{CNN}, \text{iTransformer}, \text{BiLSTM}\} \xrightarrow{\text{Multi-head Attention}} \text{EQN} \to \text{Quantile %%%%14%%%% Confidence}$

• Objective with Width Regularization:

$$\mathcal{L}_{\text{EQN}} = \lambda_1 \mathcal{L}_{\text{quantile}} + \lambda_2 \mathcal{L}_{\text{evidence}} + \lambda_3 \mathcal{L}_{\text{width}}$$

This architecture demonstrates a principled approach to integrating frequency decomposition, deep learning feature extractors, adaptive fusion, and probabilistic output—representing the state of the art for ultra-short-term solar power prediction (Wang et al., 21 Sep 2025).