Multi-Scale Photovoltaic Power Forecasting with WDT–CRMABIL–Fusion: A Two-Stage Hybrid Deep Learning Framework

Palandi, Reza Khodabakhshi; Cristaldi, Loredana; Martiri, Luca

doi:10.3390/en19020455

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Open AccessArticle

Multi-Scale Photovoltaic Power Forecasting with WDT–CRMABIL–Fusion: A Two-Stage Hybrid Deep Learning Framework

by

Reza Khodabakhshi Palandi

^*

,

Loredana Cristaldi

and

Luca Martiri

Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria (DEIB), 20133 Milan, Italy

^*

Author to whom correspondence should be addressed.

Energies 2026, 19(2), 455; https://doi.org/10.3390/en19020455 (registering DOI)

Submission received: 10 December 2025 / Revised: 5 January 2026 / Accepted: 8 January 2026 / Published: 16 January 2026

(This article belongs to the Special Issue Exploring Energy Innovations: The Rise of Next-Generation Photovoltaic Modules)

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Abstract

Ultra-short-term photovoltaic (PV) power forecasts are vital for secure grid operation as solar penetration rises. We propose a two-stage hybrid framework, WDT–CRMABIL–Fusion. In Stage 1, we apply a three-level discrete wavelet transform to PV power and key meteorological series (shortwave radiation and panel irradiance). We then forecast the approximation and detail sub-series using specialized component predictors: a 1D-CNN with dual residual multi-head attention (feature-wise and time-wise) together with a BiLSTM. In Stage 2, a compact dense fusion network recombines the component forecasts into the final PV power trajectory. We use 5-minute data from a PV plant in Milan and evaluate 5-, 10-, and 15-minute horizons. The proposed approach outperforms strong baselines (DCC+LSTM, CNN+LSTM, CNN+BiLSTM, CRMABIL direct, and WDT+CRMABIL direct). For the 5-minute horizon, it achieves MAE = 1.60 W and RMSE = 4.21 W with

R^{2}

= 0.943 and CORR = 0.973, compared with the best benchmark (MAE = 3.87 W; RMSE = 7.89 W). The gains persist across K-means++ weather clusters (rainy/sunny/cloudy) and across seasons. By combining explicit multi-scale decomposition, attention-based sequence learning, and learned fusion, WDT–CRMABIL–Fusion provides accurate and robust ultra-short-term PV forecasts suitable for storage dispatch and reserve scheduling.

Keywords: photovoltaic power forecasting; ultra-short-term; wavelet decomposition; residual multi-head attention; BiLSTM; CNN; hybrid deep learning; fusion network; numerical weather prediction; grid stability

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MDPI and ACS Style

Palandi, R.K.; Cristaldi, L.; Martiri, L. Multi-Scale Photovoltaic Power Forecasting with WDT–CRMABIL–Fusion: A Two-Stage Hybrid Deep Learning Framework. Energies 2026, 19, 455. https://doi.org/10.3390/en19020455

AMA Style

Palandi RK, Cristaldi L, Martiri L. Multi-Scale Photovoltaic Power Forecasting with WDT–CRMABIL–Fusion: A Two-Stage Hybrid Deep Learning Framework. Energies. 2026; 19(2):455. https://doi.org/10.3390/en19020455

Chicago/Turabian Style

Palandi, Reza Khodabakhshi, Loredana Cristaldi, and Luca Martiri. 2026. "Multi-Scale Photovoltaic Power Forecasting with WDT–CRMABIL–Fusion: A Two-Stage Hybrid Deep Learning Framework" Energies 19, no. 2: 455. https://doi.org/10.3390/en19020455

APA Style

Palandi, R. K., Cristaldi, L., & Martiri, L. (2026). Multi-Scale Photovoltaic Power Forecasting with WDT–CRMABIL–Fusion: A Two-Stage Hybrid Deep Learning Framework. Energies, 19(2), 455. https://doi.org/10.3390/en19020455

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Multi-Scale Photovoltaic Power Forecasting with WDT–CRMABIL–Fusion: A Two-Stage Hybrid Deep Learning Framework

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