Working data · pending review

15-minute input horizon and 15-minute prediction horizon

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both the input horizon and prediction horizon were set to 15 min. To ensure fair comparison, all baseline models were re-implemented in our PyTorch codebase according to the architectural specifications described in their original publications and we
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RMSE, MAE and R2 for prediction; separate robustness/efficiency metrics

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To comprehensively evaluate the multi-step forecasting perfor­ mance, Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R2) are selected. Let N denote the number of test samples, K represent the prediction horizon steps (where K=15 in this study), yi,jdenote the actual photovoltaic power for the i-th sample at the j-
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Physics-guided visual encoder/MCMD and GRU time-series encoder with ProCA regularization

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This study aims to predict the photovoltaic power sequence ̂Pt+1:t+k for the next k time steps based on historical sky image sequences It−m+1:t and photovoltaic time-series data Pt−m+1:t. Here, t represents the current time, and m represent
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adopts a gated recurrent unit (GRU) [24] as the core sequence modeling network because it provides a favorable balance between temporal modeling capability and computational efficiency for ultra-short-term PV forecasting. Compared with LSTM, GRU employs a simpler gating mechanism and fewer parameters, which i
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Historical sky-image sequence and historical photovoltaic power time series

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This study aims to predict the photovoltaic power sequence ̂Pt+1:t+k for the next k time steps based on historical sky image sequences It−m+1:t and photovoltaic time-series data Pt−m+1:t. Here, t represents the current time, and m represents the length of the historical sequence. This process can be modeled as a function mapping relationship: ̂ Pt+
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Photovoltaic power sequence

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This study aims to predict the photovoltaic power sequence ̂Pt+1:t+k for the next k time steps based on historical sky image sequences It−m+1:t and photovoltaic time-series data Pt−m+1:t. Here, t represents the current time, and m represents the length of the historical sequence. This process can be modeled as a function mapping relationship: ̂ Pt+
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2, 6 and 10 minutes

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2. To assess the performance of the model 2, 6, and 10 min forecast- ing horizons by scoring its quantitative statistical performance using the Smart Persistence Model (SPM)-based FS metric and the qualitative performance of the model using the Ramp Events (RE)-based Balanced Precision (BP) metric.
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Forecast skill (FS) and Balanced Precision (BP); abstract uses Balanced Accuracy terminology

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using the Smart Persistence Model (SPM)-based FS metric and the qualitative performance of the model using the Ramp Events (RE)-based Balanced Precision (BP) metric. 3. To show contradictions in the quantitative and qualitative pe
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balanced accuracy of ramp events by 9.43% and 3.91% on the 2-min and 6-min scales, respectively. However, based on the results, it can be concluded that for the single picture-digital bimodal model, the spatial informati
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CNN and ViT image backbones; gated late fusion and Transformer early fusion

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To present two new approaches for picture–numerical bimodal model interaction. Namely, an improvement of the later feature- level fusion method by means of a gate architecture and a new early feature-level fusion method based on the Transformer architecture. 2. To assess the performance of the model 2, 6, and 10 min forecast- ing horizons by scoring its quantitative statistical performance using the Smart Persistence
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ViT represents the image backbone network based on Transformer architecture proposed here as the alternative to the use of a CNN. The terms appended to CNN and ViT define the approach taken to fusion where -L represents late feature-level fusion architecture, -LG represents extra gate architec- ture, and -E represents feature-level fusion architecture. More detailed models architecture is presented in Appendix B. 2.3. Evaluation matrix Two criteria were used to evaluate the p
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Sky images plus station irradiance/weather, solar geometry and modeled clear-sky irradiance

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Inputs to each of the models comprised a set of time synchronised data that included clear sky irradiance (global horizontal irradiance, direct normal irradiance, diffuse horizontal irradiance), measured ir- radiance (GHI, DNI, DHI), weather data (dry bulb air temperature, humidity, relative air pressure, wind speed, and wind direction) mea- sured at ground base stations, and solar geometry (solar zenith and solar azimuth angles). Data alignment and quality control The initial stage of data pre- processing involved image compression, alignment of images to nu- merical data, quality control, and data normalisation. The Folsom dataset provides
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Clear-sky index (CSI) as model target, converted to irradiance forecast

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Clear sky index (CSI), i.e. the solar irradiance as a percentage of the clear sky irradiance, was chosen as the target for forecasts rather than the GHI, reflecting consensus within the solar forecasting community around its ability to improve the accuracy of solar irradiance forecasts made using numerical regression algorithms [44], including those that involve image–numerical multi-modality approaches. Additionally, use of C
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Next 10 minutes

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The task is to forecast 𝐘𝑡+10 for the next ten minutes with known inputs 𝐗𝑡−20 ∶𝐗𝑡, 𝐙𝑡−20, 𝐙𝑡−10, 𝐙𝑡for the last twenty minutes, in Eq. (1). 𝐘𝑡+10 = 𝑓(𝐗𝑡−20 ∶𝐗𝑡, 𝐙𝑡−20, 𝐙𝑡−10, 𝐙𝑡|𝜃) (1) The main reason for different sample rates is that the
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RMSE and MAE; 11.6% is RMSE improvement over the best base learner, not the metric name

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evaluation metrics, RMSE and MAE. It can be found that the 3D-CNN performs best in RMSE in base learners, while the RMSE of the proposed method improves by 11.6%. The ConvLSTM performs best in MAE in base learners, and the MAE of the proposed method improves by 21.2%. Moreover, the worst is MM, where the proposed method tuned up by 35.9% and 38.8%, respectively. Fig. 17 shows the residual distribution of each model. It can be seen that although the RMSE of 3D-CNN is small, the center of bias is more deviated from 0
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Stacked ensemble of six base learners, ridge meta-regression and HMM weather-state fine-tuning

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trained six base learners are used as weak regressors in ensemble learning to train a meta-learner, a linear ridge regressor. Specifically, the pre-trained models are used to obtain the respective results on the second training set. Then, these results are treated as the input of the ridge regression model, which is trained to obtain the final GHI. Thirdly, a HMM is trained to predict the future weather states. CSI is used as the observation sequence on training set. Finally, the weather states obtained by the HMM, together with the model’s performance weights, are used to fine-tune the linear coefficients of the Ridge regression. This following section contains three par
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Ground ASI images plus GHI/station meteorology; CSI and clear-sky values are derived

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The data for this experiment is from Nrel [30]. The ground-based clouds are from the EKO All-Sky Imager (ASI-16) product, with 10 min intervals in a large-volume database. Fig. 1 shows four categories of cloud images based on projection and exposure, where the projection means the images without surface buildings part. The GHI and eight meteorological variables are selected, two types of wind speed (WIND6, WIND19), barometric pressure (PR), DNI, aerosols (AOD), humidity (RH), cloud cover (CC) and temperature (TEMP). In Eq. (2), the ideal clear sky value (Iclr) and CSI are obtained [31]. 𝐼0 =1368 ∗(1 + 0.033 ∗𝑐𝑜𝑠(2 ∗𝜋∗𝐷𝑂𝑌∕365)), 𝑏=0.664 + 0.163∕exp(−1829∕8000), 𝐼𝑐𝑙𝑟=𝑏⋅𝐼0 ⋅exp (−0.09 ⋅𝐴𝑀⋅(𝑇𝐿𝐾−1)) , 𝐶𝑆𝐼=𝐷𝐻𝐼∕𝐼𝑐𝑙𝑟, (2) where 𝑇𝐿𝐾is Link
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Some parameters like solar momentum, the location of clouds and occlusions are measured by PV station, which were combined with meteorological variables for forecasting GHI [12]. However, these numerical features of clouds do not provide a comprehensive representation of cloud dynamics com- pared with ground-based cloud images. To overcom
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Global horizontal irradiance (GHI)

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The multi-modal intra-hour irradiance forecasting contains inputs from two modalities. One is the meteorological data 𝑥𝑚 𝑛and the GHI 𝑦𝑛with 1 min interval, where 𝑛denotes the time step and 𝑚represents the dimension of variables. The other is the ground-based cloud images 𝑧𝑘 𝑛′ with 10 min interval, where 𝑘re
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30 minutes

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8. Experimental Analysis: Half an hour (30 Minutes) solar irradiance forecasting 8.1. Dataset, data Pre-processing, and evaluation metrics T
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R2, MBE, MAE, RMSE, MAPE

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The MBE and MAE values further support the model’s strength with minimal bias and slight overestimation during cloudy weather, typical of solar irradiance models. Also, the RMSE and MAPE indicate the model’s high accuracy with a low error rate, especially for fair-weather days. Figs. 21 and 22 illustrate the performance of the model on both sunny and cloudy
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Results of the experiment in Table 12 highlight that on sunny days, the prediction errors are low with a very high R2 value of 0.979. This underlines the efficiency of our model in predicting solar irradiance for clear weather conditions and fits qui
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Hybrid Transformer and RNN, dual image/numerical input

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This experiment utilises a dual-input approach of image and nu­ merical data with a hybrid architecture of a transformer and RNN approach. Image data allows the model to capture spatial patterns and dynamics such as cloud movement
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Sky images plus numerical atmospheric data (temperature, humidity, solar angles); NWP origin not established

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Numerical data provides precise, quantitative measures of atmospheric conditions, including tempera­ ture, humidity, and solar angles, which are crucial for fine-tuning the forecasts. The choice of architecture sits on the strengths of each architecture. Transformers are known for their parallel processing power, which can be used to manage spatial dependencies in ima
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Solar irradiance / GHI

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forecast of solar irradiance (SI) with high accuracy, specifically an R2 of 0.979 on sunny days and 0.976 on cloudy days, showing robust performance under different weather conditions. The findings emphasise the practical implications of deep learning models in enhancing energy production, improving
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1–9 minutes, at one-minute resolution

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Monthly summary statistics for the cloud speed persistence forecast is­ sued at forecast horizons 1 – 9 min at min resolution for the entire power plant. The 𝑅𝑀𝑆𝐸, 𝑀𝐴𝐸, 𝑀𝐵𝐸, and skill score were calculated according to Eq. (6)–Eq. (9). plant in Nevada, USA with an overall skill s
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RMSE, MAE, MBE and RMSE-based forecast skill

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the mean absolute error 𝑀𝐴𝐸 and the mean bias error 𝑀𝐵𝐸 which is defined as: 𝑅𝑀𝑆𝐸= 1 𝑃𝑛𝑜𝑚 √ √ √ √1 𝑁 𝑡𝑁 ∑ 𝑡=𝑡1 (̂𝑃𝑡−𝑃𝑡 )2 (6) and 𝑀𝐴𝐸= 1 𝑃𝑛𝑜𝑚 1 𝑁 𝑡𝑁 ∑ 𝑡=𝑡1
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Skill score = 1 −𝑅𝑀𝑆𝐸∕𝑅𝑀𝑆𝐸∗ (9) where 𝑅𝑀𝑆𝐸 and 𝑅𝑀𝑆𝐸∗ are the root-mean squared errors calculated using Eq. (6) for the cloud-speed persistence forecas
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Cloud-speed persistence with physically derived cloud motion vectors

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2.3 . Cloud speed persistence forecast The estimated CMVs are used to issue a cloud speed persistence fore­ cast for the power output from the PV power plant. To issue the forecast, a clear-sky index map is generated at time 𝑡{𝑘𝑖,𝑡 }𝑁 𝑖=1 and shifted so that {(𝑥𝑖,𝑡, 𝑦𝑖,
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String-level PV power/energy-yield histories; CMVs derived from these histories

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A novel method is proposed to estimate cloud motion vectors (CMVs) from endogenous photovoltaic (PV) power plant energy yield time-series data. The method is tested using three months of 1-min mean aggregated power output data collected from 8000+ string-sets in a 150+ MWp PV power plant. The CMVs are used as input to a cloud speed persistence PV power forecast which is benchmarked against a smart persistence PV power forecast. Forecasts issued for the entire power
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Photovoltaic plant power output

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CMVs enable cloud-speed persistence forecasting of PV power output. • Plant-level forecasts achieve a skill score of 0.16 at a 1-min ho
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