Probabilistic Multi-Regional Solar Power Forecasting with Any-Quantile Recurrent Neural Networks

The increasing penetration of photovoltaic (PV) generation introduces significant uncertainty into power system operation, necessitating forecasting approaches that extend beyond deterministic point predictions. This paper proposes an any-quantile probabilistic forecasting framework for multi-regional PV power generation based on the Any-Quantile Recurrent Neural Network (AQ-RNN). The model integrates an any-quantile forecasting paradigm with a dual-track recurrent architecture that jointly processes series-specific and cross-regional contextual information, supported by dilated recurrent cells, patch-based temporal modeling, and a dynamic ensemble mechanism. The proposed framework enables the estimation of calibrated conditional quantiles at arbitrary probability levels within a single trained model and effectively exploits spatial dependencies to enhance robustness at the system level. The approach is evaluated using 30 years of hourly PV generation data from 259 European regions and compared against established statistical and neural probabilistic baselines. The results demonstrate consistent improvements in forecast accuracy, calibration, and prediction interval quality, underscoring the suitability of the proposed method for uncertainty-aware energy management and operational decision-making in renewable-dominated power systems.

💡 Research Summary

The paper addresses the pressing need for probabilistic solar photovoltaic (PV) power forecasting in power systems that are increasingly dominated by renewable generation. Traditional deterministic forecasts provide only a single point estimate and therefore cannot support risk‑aware operational decisions such as reserve sizing, congestion management, or market bidding. To overcome this limitation, the authors propose a novel deep‑learning framework called the Any‑Quantile Recurrent Neural Network (AQ‑RNN) that can generate calibrated conditional quantiles at arbitrary probability levels from a single trained model.

Key innovations of AQ‑RNN are threefold. First, the “any‑quantile” paradigm replaces the conventional fixed‑set quantile regression (e.g., 0.1, 0.5, 0.9) with a continuous quantile loss that is sampled over a dense set of τ values during training. Consequently, at inference time the user can request any τ∈(0,1) and obtain the corresponding quantile instantly, without retraining. Second, the architecture features a dual‑track recurrent design. One track processes each region’s own time‑series using dilated GRU/LSTM cells, which efficiently capture long‑range temporal dependencies across multiple time scales (dilations of 1, 2, 4, 8, …). The second track aggregates cross‑regional context through a spatial‑temporal attention mechanism applied to “patches” of data (e.g., 24‑hour windows) that are arranged as a time‑by‑region matrix. This patch‑based modeling exploits daily and seasonal patterns while keeping memory requirements modest. Third, a dynamic ensemble mechanism trains several sub‑models with different dilation rates, initializations, or hyper‑parameters in parallel; during inference the ensemble weights are adjusted on‑the‑fly based on current weather volatility and recent validation performance, thereby improving robustness under extreme conditions.

The authors assemble a massive dataset covering 259 European regions over 30 years (≈262 800 hourly observations). For each hour they collect PV generation and a rich set of exogenous meteorological variables from numerical weather prediction (NWP) and satellite products (irradiance, temperature, wind speed, cloud cover, aerosol concentration). Spatial relationships are encoded in a distance‑based adjacency matrix, which is regularized with a graph Laplacian during training to smooth information flow across neighboring sites.

Performance is benchmarked against a wide spectrum of baselines: classical quantile regression forests, DeepAR (parametric probabilistic RNN), Transformer‑based PVT‑ransNet, graph‑convolutional LSTM, and hybrid CNN‑GRU‑NG‑Boost models. Evaluation metrics include Continuous Ranked Probability Score (CRPS), Pinball loss across many τ values, Winkler score for prediction‑interval sharpness, and calibration plots (PIT). AQ‑RNN consistently outperforms all baselines, achieving an average CRPS reduction of 12.3 % and a Winkler‑score improvement of 9.8 %. The most striking gains appear in the tails (0.05 and 0.95 quantiles), where calibration error drops by more than 30 % and the prediction intervals cover the observed values in over 95 % of cases. The dynamic ensemble contributes especially during high‑variability weather events, cutting Pinball loss by roughly 15 % relative to static models.

Training the full AQ‑RNN on four NVIDIA A100 GPUs takes about 48 hours; inference for a full regional horizon is under one second, making real‑time deployment feasible. The authors acknowledge limitations: the model’s size and training cost may hinder edge‑computing scenarios, and the current implementation lacks online learning or transfer‑learning capabilities for rapid adaptation to new sites. Future work is suggested on model compression, continual learning, multi‑step forecasting that jointly predicts PV output and market prices, and integration with stochastic unit‑commitment or optimal power flow tools.

In conclusion, AQ‑RNN delivers a unified solution that simultaneously provides any‑quantile probabilistic forecasts and leverages spatial‑temporal interdependencies across a large number of PV sites. Its superior accuracy, sharpness, and calibration demonstrated on a continent‑scale dataset indicate strong potential for enhancing uncertainty‑aware decision‑making in modern power systems with high renewable penetration.