SolarNet: A Deep Convolutional Neural Networkfor Solar Forecasting via Sky Images

Cong Feng, Jie ZhangThe University of Texas at Dallas{cong.feng1, jiezhang}@utdallas.edu

Abstract—The exponential growth of solar energy poses chal-lenges to power systems, mostly due to its uncertain and variablecharacteristics. Hence, solar forecasting, especially short-termsolar forecasting (STSF), has been adopted to assist power systemoperations. The STSF takes inputs from various sources, amongwhich sky image-based STSF is not yet well-studied. In this paper,a deep convolutional neural network (CNN) model, called theSolarNet, is developed to forecast the 10-min ahead GHI by onlyusing sky images without numerical measurements and extrafeature engineering. The SolarNet, composed of 21 convolutional,max-pooling, and fully-connected layers, learns latent patternsbetween sky images and global horizontal irradiance (GHI) inan end-to-end manner. Numerical results based on ten years datashow that the developed SolarNet outperforms the benchmarkingpersistence of cloudiness model and machine learning models byup to 11.88% under various weather conditions.

Index Terms—Deep learning, CNN, solar forecasting, skyimage processing

I. INTRODUCTION

Solar energy, especially solar photovoltaics (PV), has beenwitnessed an aggressive increase in the last decade. A totalof 94.2 GW PV was installed in 2018 worldwide and thisexponential growth is foreseen and projected in future decades.Nevertheless, integrating large amounts of PV into power sys-tems is challenging, mostly due to the uncertain characteristicsof PV generation. To deal with this issue, the importanceof solar forecasting has been emphasized in power systemoperations. For example, balancing authorities, such as theCalifornia Independent System Operator (CAISO), use solarpower forecasts in their daily operations [1]. PV plant outputforecasting is used to help plant operators bid in the energymarkets [2]. Therefore, improving solar forecasting accuracyis crucial and has been paid efforts in the literature.

A large collection of methods have been developed forshort-term solar forecasting (STSF), where machine learning(ML) methods are one of the most popular categories. For ex-ample, a set of benchmarking ML models, including Gaussianprocesses and support vector regression (SVR) models, weredeveloped in Ref. [3] for irradiance forecasting. The ensemblelearning with artificial neural networks (ANNs), SVR models,gradient boosting machines (GBMs), and a random forest (RF)model was used to provide short-term solar forecasts (STSFs)

This work was supported by the National Renewable Energy Laboratoryunder Subcontract No. ZDJ-8-82257-01 (under the U.S. Department of EnergyPrime Contract No. DE-AC36-08GO28308).

The authors would also like to thank the NVIDIA Corporation for donatingthe TITAN V GPU for this work.

with similar hour or similar weather downsampling [4], [5].A detailed ML review can be found in Ref. [6]. Moreover,deep learning (DL) approaches show potentials to furtherenhance the STSF accuracy, therefore, is being researched inrecent years. For example, a long short-term memory network(LSTM) was used for STSF and improved the accuracy by42.9% over ANN [7]. Wang et al. [8] compared three DLconfigurations and found that the combination of an LSTM anda convolutional neural network (CNN) outperformed others.However, compared to ML methods, the investigation of DLin STSF is far from comprehensive.

Heavily relying on the data, ML and DL methods predictSTSFs from various input sources, such as groud numeri-cal measurements, satellite-based information, and sky imagefeatures. Among different measuring instruments, total skyimagers (TSIs, also known as sky cameras) show unique-ness in STSF over others for its cost-effectiveness and dataformat. Therefore, TSIs have been widely used as inputs toML and DL models. However, the existing TSI-based STSFhas nonnegligible drawbacks. For example, some STSF usedhuman crafted features from TSIs, such as pixel-based features[9], whose optimality and impact are suspicious. DL encodingtechniques were introduced to address this problem, but mostof them were extracted from the classification-based models,such as in Refs. [10] and [11]. Limited work has examined topredict STSFs directly from TSIs.

To bridge the gaps in STSF, we propose a DL-based STSFnetwork, named the SolarNet, which provides STSFs by onlyusing TSIs. In such a way, we seek to explore the effectivenessof TSIs in STSF without the help of other measurements.The contributions of this paper include: (i) extracting TSI-based features for STSF through an end-to-end representationlearning, (ii) utilizing a state-of-the-art DL configuration, and(iii) achieving significant forecasting accuracy improvementover benchmark models.

The remainder of this paper is organized as follows. Sec-tion II formulates the TSI-based solar forecasting problem andintroduces the developed SolarNet. The case study dataset,DL training details, and benchmark models are described inSection III. Section IV discusses the results. Conclusions aremade in Section V.

II. THE SOLARNET

In this section, we first formulate the TSI-based solarforecasting problem. Then, different layer types (i.e., basic

blocks of the SolarNet) in the DL model are mathematicallydescribed. At last, the overall framework of the developedSolarNet is introduced.

A. Problem Formulation

In this paper, we seek to forecast the global horizontalirradiance (GHI), y ∈ RN×1, directly from the latest TSI,X ∈ RN×W×H×D, without numerical measurements andfeature engineering by a CNN:

y = F (X,W) (1)

where N , W , H , D are sample size, image width, imageheight, and image channel amount, respectively; y and y arethe actual and forecast GHI; X is the image input; W isthe trainable parameters in the developed CNN model. Toperform STSF, optimal parameters should be obtained firstin the training stage. Since STSF is a regression problem, weuse mean absolute error (MAE) as the loss function:

J(W) = − 1

N

N∑n=1

|yn − yn| (2)

where n is the sample index; y and y are forecast andactual GHI values at a certain time, respectively. Then, theobjective in the training process is to optimize the parametersby minimizing the loss function in an end-to-end manner (i.e.,from images to GHI values).

B. Deep Learning Layers

To build a DL model, different types of layers are required.The layers in the SolarNet include convolutional layers, pool-ing layers, and fully-connected layers (also known as denselayers).

1) Convolutional Layers: Convolutional layers are the keycomponents in CNN models. Generally, convolution oper-ations are performed to the input tensor by filters in thefilter bank (also known as kernels), which are expressed asZl = Wl ∗Xl + bl, and detailed as:

z′lw(l+1),h(l+1),d(l+1) =ωl

wl,hl,dl,d(l+1) × xlwl,hl,dl+

blw(l+1),h(l+1),d(l+1)

(3)

where X, W, b, and Z are the input tensor, parameter tensor,bias tensor, and output tensor in the lth layer, respectively; ∗is a convolution operator; z, ω, x, and b are elements in theoutput, parameter, input, and bias tensors, respectively; w, h,and d are element location indices. Please note that the channelnumber, Dl+1, of the next layer equals to the filter numberof the previous layer. After the convolution operations, thefeature maps are activated by an element-wise rectified linearunit (ReLU) to add nonlinearity, as:

zlw(l+1),h(l+1),d(l+1) = max(0, z′lw(l+1),h(l+1),d(l+1)) (4)

2) Pooling Layers: To achieve more translation invarianceduring the spatial representation learning, pooling layers areused to perform max-pooling over a 2×2 pixel window withstride 2. In such a way, the convoluted feature maps are sub-sampled by the non-overlapping pooling windows by a factorof 2, which can be expressed as:

zlw(l+1),h(l+1),dl = max{xl|xl := xl

wl:wl+ Wl

Wl+1 ,hl:hl+ Hl

Hl+1 ,dl}

(5)where x is a subset of a feature map.

3) Fully-connected Layers: The convolutional and max-pooling layers are powerful in extracting informative featuresfrom the TSIs, but can not directly solve the regressionproblem. Therefore, the fully-connected layers are introducedin the model to learn the latent patterns between the TSIfeature maps and the GHI values. All the inputs are transmittedto the output in fully-connected layers, as:

Zl = Wl ·Xl + bl (6)

C. The Overall SolarNet FrameworkAs shown in Fig. 1, the developed SolarNet is composed

of 21 layers, including 13 convolutional layers, 5 max-poolinglayers, and three fully-connected layers. The configuration ofthe SolarNet is inspired by the well-known VGG16 network(VGG16) [12]. The SolarNet contains 5 feature learning blocks(FLBs), each of which stacks 2 or 3 convolutional layers anda max-pooling layer, which is shown in the upper part ofFig. 1. The SolarNet utilizes small filters with a size of 3×3 toextract more receptive fields from the input tensors. The filternumber of the next FLB is doubled to extract more abstractand informative features. However, the VGG16 is designed forclassification problems. To solve a deep regression problem,the last three dense layers use linear activation functionsinstead of ReLU functions. In dense layers, 20% of neurons arerandomly dropped to avoid over-fitting. The SolarNet forecastsGHI directly from TSIs without any feature engineering andany numerical inputs.

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Conv+ReLUMax-poolingDense+Linear

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2:3⇥

3⇥

64<latexit sha1_base64="gLI5xrHzRxAV00WAr1kJ/jmkSlk=">AAACAHicbZDLSsNAFIYnXmu9RV24cDPYCq5KUkVFXBS6cVnBXqANZTKdtEMnkzBzIpTQja/ixoUibn0Md76N0zaItv4w8PGfczhzfj8WXIPjfFlLyyura+u5jfzm1vbOrr2339BRoiir00hEquUTzQSXrA4cBGvFipHQF6zpD6uTevOBKc0jeQ+jmHkh6UsecErAWF37sFq+Pit2gIdMF3/g4rxrF5ySMxVeBDeDAspU69qfnV5Ek5BJoIJo3XadGLyUKOBUsHG+k2gWEzokfdY2KInZ46XTA8b4xDg9HETKPAl46v6eSEmo9Sj0TWdIYKDnaxPzv1o7geDKS7mME2CSzhYFicAQ4UkauMcVoyBGBghV3PwV0wFRhILJLG9CcOdPXoRGueQ6JfeuXKjcZHHk0BE6RqfIRZeogm5RDdURRWP0hF7Qq/VoPVtv1vusdcnKZg7QH1kf380LlJQ=</latexit><latexit sha1_base64="gLI5xrHzRxAV00WAr1kJ/jmkSlk=">AAACAHicbZDLSsNAFIYnXmu9RV24cDPYCq5KUkVFXBS6cVnBXqANZTKdtEMnkzBzIpTQja/ixoUibn0Md76N0zaItv4w8PGfczhzfj8WXIPjfFlLyyura+u5jfzm1vbOrr2339BRoiir00hEquUTzQSXrA4cBGvFipHQF6zpD6uTevOBKc0jeQ+jmHkh6UsecErAWF37sFq+Pit2gIdMF3/g4rxrF5ySMxVeBDeDAspU69qfnV5Ek5BJoIJo3XadGLyUKOBUsHG+k2gWEzokfdY2KInZ46XTA8b4xDg9HETKPAl46v6eSEmo9Sj0TWdIYKDnaxPzv1o7geDKS7mME2CSzhYFicAQ4UkauMcVoyBGBghV3PwV0wFRhILJLG9CcOdPXoRGueQ6JfeuXKjcZHHk0BE6RqfIRZeogm5RDdURRWP0hF7Qq/VoPVtv1vusdcnKZg7QH1kf380LlJQ=</latexit><latexit sha1_base64="gLI5xrHzRxAV00WAr1kJ/jmkSlk=">AAACAHicbZDLSsNAFIYnXmu9RV24cDPYCq5KUkVFXBS6cVnBXqANZTKdtEMnkzBzIpTQja/ixoUibn0Md76N0zaItv4w8PGfczhzfj8WXIPjfFlLyyura+u5jfzm1vbOrr2339BRoiir00hEquUTzQSXrA4cBGvFipHQF6zpD6uTevOBKc0jeQ+jmHkh6UsecErAWF37sFq+Pit2gIdMF3/g4rxrF5ySMxVeBDeDAspU69qfnV5Ek5BJoIJo3XadGLyUKOBUsHG+k2gWEzokfdY2KInZ46XTA8b4xDg9HETKPAl46v6eSEmo9Sj0TWdIYKDnaxPzv1o7geDKS7mME2CSzhYFicAQ4UkauMcVoyBGBghV3PwV0wFRhILJLG9CcOdPXoRGueQ6JfeuXKjcZHHk0BE6RqfIRZeogm5RDdURRWP0hF7Qq/VoPVtv1vusdcnKZg7QH1kf380LlJQ=</latexit><latexit sha1_base64="gLI5xrHzRxAV00WAr1kJ/jmkSlk=">AAACAHicbZDLSsNAFIYnXmu9RV24cDPYCq5KUkVFXBS6cVnBXqANZTKdtEMnkzBzIpTQja/ixoUibn0Md76N0zaItv4w8PGfczhzfj8WXIPjfFlLyyura+u5jfzm1vbOrr2339BRoiir00hEquUTzQSXrA4cBGvFipHQF6zpD6uTevOBKc0jeQ+jmHkh6UsecErAWF37sFq+Pit2gIdMF3/g4rxrF5ySMxVeBDeDAspU69qfnV5Ek5BJoIJo3XadGLyUKOBUsHG+k2gWEzokfdY2KInZ46XTA8b4xDg9HETKPAl46v6eSEmo9Sj0TWdIYKDnaxPzv1o7geDKS7mME2CSzhYFicAQ4UkauMcVoyBGBghV3PwV0wFRhILJLG9CcOdPXoRGueQ6JfeuXKjcZHHk0BE6RqfIRZeogm5RDdURRWP0hF7Qq/VoPVtv1vusdcnKZg7QH1kf380LlJQ=</latexit>

P1:

3⇥

3,2

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3⇥

3,2

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C4:

3⇥

3⇥

128

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3⇥

3⇥

128

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3⇥

3⇥

128

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3⇥

3⇥

128

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3⇥

3⇥

512

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3⇥

3⇥

512

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3⇥

3⇥

512

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3⇥

3⇥

512

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:3⇥

3⇥512

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:3⇥

3⇥512

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P3:

3⇥

3,2

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3⇥

3,2

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C12

:3⇥

3⇥512

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:3⇥

3⇥512

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:3⇥

3⇥512

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:3⇥

3⇥512

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:3⇥

3⇥512

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:3⇥

3⇥512

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P4:

3⇥

3,2

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3⇥

3,2

<latexit sha1_base64="6ROZUJvzRCSc4vJfOPknH0mT8r8=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3ERTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPnrORqw==</latexit><latexit sha1_base64="6ROZUJvzRCSc4vJfOPknH0mT8r8=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3ERTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPnrORqw==</latexit><latexit sha1_base64="6ROZUJvzRCSc4vJfOPknH0mT8r8=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3ERTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPnrORqw==</latexit><latexit sha1_base64="6ROZUJvzRCSc4vJfOPknH0mT8r8=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3ERTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPnrORqw==</latexit> P5:

3⇥

3,2

<latexit sha1_base64="FAVtAABhs7Ia8QbscWjQTy4/TIQ=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3QRTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPoEWRrA==</latexit><latexit sha1_base64="FAVtAABhs7Ia8QbscWjQTy4/TIQ=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3QRTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPoEWRrA==</latexit><latexit sha1_base64="FAVtAABhs7Ia8QbscWjQTy4/TIQ=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3QRTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPoEWRrA==</latexit><latexit sha1_base64="FAVtAABhs7Ia8QbscWjQTy4/TIQ=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3QRTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPoEWRrA==</latexit>P5:

3⇥

3,2

<latexit sha1_base64="FAVtAABhs7Ia8QbscWjQTy4/TIQ=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3QRTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPoEWRrA==</latexit><latexit sha1_base64="FAVtAABhs7Ia8QbscWjQTy4/TIQ=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3QRTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPoEWRrA==</latexit><latexit sha1_base64="FAVtAABhs7Ia8QbscWjQTy4/TIQ=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3QRTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPoEWRrA==</latexit><latexit sha1_base64="FAVtAABhs7Ia8QbscWjQTy4/TIQ=">AAAB+XicbVDLSgNBEOz1GeNr1aOXwUTwIGE3QRTxEPDiMYJ5QBLC7GQ2GTL7YKY3EJb8iRcPinj1T7z5N06SPWhiQUNR1U13lxdLodFxvq219Y3Nre3cTn53b//g0D46bugoUYzXWSQj1fKo5lKEvI4CJW/FitPAk7zpje5nfnPMlRZR+ISTmHcDOgiFLxhFI/Vsu3Z1SyrFDoqA62LlstyzC07JmYOsEjcjBchQ69lfnX7EkoCHyCTVuu06MXZTqlAwyaf5TqJ5TNmIDnjb0JCaRd10fvmUnBulT/xImQqRzNXfEykNtJ4EnukMKA71sjcT//PaCfo33VSEcYI8ZItFfiIJRmQWA+kLxRnKiSGUKWFuJWxIFWVowsqbENzll1dJo1xynZL7WC5U77I4cnAKZ3ABLlxDFR6gBnVgMIZneIU3K7VerHfrY9G6ZmUzJ/AH1ucPoEWRrA==</latexit>

C6:

3⇥

3⇥

256

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3⇥

3⇥

256

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3⇥

3⇥

256

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3⇥

3⇥

256

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3⇥

3⇥

256

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3⇥

3⇥

256

<latexit sha1_base64="pjsgUXPLRDGuSobTLE1rPLxLlw8=">AAACAXicbZDLSgMxFIbPeK31NupGcBNsBVdlpqIVcVHoxmUFe4F2KJk0bUMzmSHJCGWoG1/FjQtF3PoW7nwb03YQbf0h8PGfczg5vx9xprTjfFlLyyura+uZjezm1vbOrr23X1dhLAmtkZCHsuljRTkTtKaZ5rQZSYoDn9OGP6xM6o17KhULxZ0eRdQLcF+wHiNYG6tjH1ZKV2f5tmYBVfkfKJ5fdOycU3CmQovgppCDVNWO/dnuhiQOqNCEY6VarhNpL8FSM8LpONuOFY0wGeI+bRkU2CzykukFY3RinC7qhdI8odHU/T2R4ECpUeCbzgDrgZqvTcz/aq1Y9y69hIko1lSQ2aJezJEO0SQO1GWSEs1HBjCRzPwVkQGWmGgTWtaE4M6fvAj1YsF1Cu5tMVe+TuPIwBEcwym4UIIy3EAVakDgAZ7gBV6tR+vZerPeZ61LVjpzAH9kfXwDTpuU1g==</latexit><latexit sha1_base64="pjsgUXPLRDGuSobTLE1rPLxLlw8=">AAACAXicbZDLSgMxFIbPeK31NupGcBNsBVdlpqIVcVHoxmUFe4F2KJk0bUMzmSHJCGWoG1/FjQtF3PoW7nwb03YQbf0h8PGfczg5vx9xprTjfFlLyyura+uZjezm1vbOrr23X1dhLAmtkZCHsuljRTkTtKaZ5rQZSYoDn9OGP6xM6o17KhULxZ0eRdQLcF+wHiNYG6tjH1ZKV2f5tmYBVfkfKJ5fdOycU3CmQovgppCDVNWO/dnuhiQOqNCEY6VarhNpL8FSM8LpONuOFY0wGeI+bRkU2CzykukFY3RinC7qhdI8odHU/T2R4ECpUeCbzgDrgZqvTcz/aq1Y9y69hIko1lSQ2aJezJEO0SQO1GWSEs1HBjCRzPwVkQGWmGgTWtaE4M6fvAj1YsF1Cu5tMVe+TuPIwBEcwym4UIIy3EAVakDgAZ7gBV6tR+vZerPeZ61LVjpzAH9kfXwDTpuU1g==</latexit><latexit sha1_base64="pjsgUXPLRDGuSobTLE1rPLxLlw8=">AAACAXicbZDLSgMxFIbPeK31NupGcBNsBVdlpqIVcVHoxmUFe4F2KJk0bUMzmSHJCGWoG1/FjQtF3PoW7nwb03YQbf0h8PGfczg5vx9xprTjfFlLyyura+uZjezm1vbOrr23X1dhLAmtkZCHsuljRTkTtKaZ5rQZSYoDn9OGP6xM6o17KhULxZ0eRdQLcF+wHiNYG6tjH1ZKV2f5tmYBVfkfKJ5fdOycU3CmQovgppCDVNWO/dnuhiQOqNCEY6VarhNpL8FSM8LpONuOFY0wGeI+bRkU2CzykukFY3RinC7qhdI8odHU/T2R4ECpUeCbzgDrgZqvTcz/aq1Y9y69hIko1lSQ2aJezJEO0SQO1GWSEs1HBjCRzPwVkQGWmGgTWtaE4M6fvAj1YsF1Cu5tMVe+TuPIwBEcwym4UIIy3EAVakDgAZ7gBV6tR+vZerPeZ61LVjpzAH9kfXwDTpuU1g==</latexit><latexit sha1_base64="pjsgUXPLRDGuSobTLE1rPLxLlw8=">AAACAXicbZDLSgMxFIbPeK31NupGcBNsBVdlpqIVcVHoxmUFe4F2KJk0bUMzmSHJCGWoG1/FjQtF3PoW7nwb03YQbf0h8PGfczg5vx9xprTjfFlLyyura+uZjezm1vbOrr23X1dhLAmtkZCHsuljRTkTtKaZ5rQZSYoDn9OGP6xM6o17KhULxZ0eRdQLcF+wHiNYG6tjH1ZKV2f5tmYBVfkfKJ5fdOycU3CmQovgppCDVNWO/dnuhiQOqNCEY6VarhNpL8FSM8LpONuOFY0wGeI+bRkU2CzykukFY3RinC7qhdI8odHU/T2R4ECpUeCbzgDrgZqvTcz/aq1Y9y69hIko1lSQ2aJezJEO0SQO1GWSEs1HBjCRzPwVkQGWmGgTWtaE4M6fvAj1YsF1Cu5tMVe+TuPIwBEcwym4UIIy3EAVakDgAZ7gBV6tR+vZerPeZ61LVjpzAH9kfXwDTpuU1g==</latexit>

P2:

3⇥

3,2

<latexit sha1_base64="1L/vlXfxxdYWCTjhC5ki3Rh2e7Y=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LLaCBylJelDEQ8GLxwr2A9pQNttNu3SzCbuTQgn9J148KOLVf+LNf+O2zUFbHww83pthZl6QCK7Bcb6twsbm1vZOcbe0t39weGQfn7R0nCrKmjQWseoERDPBJWsCB8E6iWIkCgRrB+P7ud+eMKV5LJ9gmjA/IkPJQ04JGKlv2w3vFtcqPeAR05Xalde3y07VWQCvEzcnZZSj0be/eoOYphGTQAXRuus6CfgZUcCpYLNSL9UsIXRMhqxrqCRmkZ8tLp/hC6MMcBgrUxLwQv09kZFI62kUmM6IwEivenPxP6+bQnjjZ1wmKTBJl4vCVGCI8TwGPOCKURBTQwhV3NyK6YgoQsGEVTIhuKsvr5OWV3Wdqvvolet3eRxFdIbO0SVy0TWqowfUQE1E0QQ9o1f0ZmXWi/VufSxbC1Y+c4r+wPr8AZuPkak=</latexit><latexit sha1_base64="1L/vlXfxxdYWCTjhC5ki3Rh2e7Y=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LLaCBylJelDEQ8GLxwr2A9pQNttNu3SzCbuTQgn9J148KOLVf+LNf+O2zUFbHww83pthZl6QCK7Bcb6twsbm1vZOcbe0t39weGQfn7R0nCrKmjQWseoERDPBJWsCB8E6iWIkCgRrB+P7ud+eMKV5LJ9gmjA/IkPJQ04JGKlv2w3vFtcqPeAR05Xalde3y07VWQCvEzcnZZSj0be/eoOYphGTQAXRuus6CfgZUcCpYLNSL9UsIXRMhqxrqCRmkZ8tLp/hC6MMcBgrUxLwQv09kZFI62kUmM6IwEivenPxP6+bQnjjZ1wmKTBJl4vCVGCI8TwGPOCKURBTQwhV3NyK6YgoQsGEVTIhuKsvr5OWV3Wdqvvolet3eRxFdIbO0SVy0TWqowfUQE1E0QQ9o1f0ZmXWi/VufSxbC1Y+c4r+wPr8AZuPkak=</latexit><latexit sha1_base64="1L/vlXfxxdYWCTjhC5ki3Rh2e7Y=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LLaCBylJelDEQ8GLxwr2A9pQNttNu3SzCbuTQgn9J148KOLVf+LNf+O2zUFbHww83pthZl6QCK7Bcb6twsbm1vZOcbe0t39weGQfn7R0nCrKmjQWseoERDPBJWsCB8E6iWIkCgRrB+P7ud+eMKV5LJ9gmjA/IkPJQ04JGKlv2w3vFtcqPeAR05Xalde3y07VWQCvEzcnZZSj0be/eoOYphGTQAXRuus6CfgZUcCpYLNSL9UsIXRMhqxrqCRmkZ8tLp/hC6MMcBgrUxLwQv09kZFI62kUmM6IwEivenPxP6+bQnjjZ1wmKTBJl4vCVGCI8TwGPOCKURBTQwhV3NyK6YgoQsGEVTIhuKsvr5OWV3Wdqvvolet3eRxFdIbO0SVy0TWqowfUQE1E0QQ9o1f0ZmXWi/VufSxbC1Y+c4r+wPr8AZuPkak=</latexit><latexit sha1_base64="1L/vlXfxxdYWCTjhC5ki3Rh2e7Y=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LLaCBylJelDEQ8GLxwr2A9pQNttNu3SzCbuTQgn9J148KOLVf+LNf+O2zUFbHww83pthZl6QCK7Bcb6twsbm1vZOcbe0t39weGQfn7R0nCrKmjQWseoERDPBJWsCB8E6iWIkCgRrB+P7ud+eMKV5LJ9gmjA/IkPJQ04JGKlv2w3vFtcqPeAR05Xalde3y07VWQCvEzcnZZSj0be/eoOYphGTQAXRuus6CfgZUcCpYLNSL9UsIXRMhqxrqCRmkZ8tLp/hC6MMcBgrUxLwQv09kZFI62kUmM6IwEivenPxP6+bQnjjZ1wmKTBJl4vCVGCI8TwGPOCKURBTQwhV3NyK6YgoQsGEVTIhuKsvr5OWV3Wdqvvolet3eRxFdIbO0SVy0TWqowfUQE1E0QQ9o1f0ZmXWi/VufSxbC1Y+c4r+wPr8AZuPkak=</latexit>P2:

3⇥

3,2

<latexit sha1_base64="1L/vlXfxxdYWCTjhC5ki3Rh2e7Y=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LLaCBylJelDEQ8GLxwr2A9pQNttNu3SzCbuTQgn9J148KOLVf+LNf+O2zUFbHww83pthZl6QCK7Bcb6twsbm1vZOcbe0t39weGQfn7R0nCrKmjQWseoERDPBJWsCB8E6iWIkCgRrB+P7ud+eMKV5LJ9gmjA/IkPJQ04JGKlv2w3vFtcqPeAR05Xalde3y07VWQCvEzcnZZSj0be/eoOYphGTQAXRuus6CfgZUcCpYLNSL9UsIXRMhqxrqCRmkZ8tLp/hC6MMcBgrUxLwQv09kZFI62kUmM6IwEivenPxP6+bQnjjZ1wmKTBJl4vCVGCI8TwGPOCKURBTQwhV3NyK6YgoQsGEVTIhuKsvr5OWV3Wdqvvolet3eRxFdIbO0SVy0TWqowfUQE1E0QQ9o1f0ZmXWi/VufSxbC1Y+c4r+wPr8AZuPkak=</latexit><latexit sha1_base64="1L/vlXfxxdYWCTjhC5ki3Rh2e7Y=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LLaCBylJelDEQ8GLxwr2A9pQNttNu3SzCbuTQgn9J148KOLVf+LNf+O2zUFbHww83pthZl6QCK7Bcb6twsbm1vZOcbe0t39weGQfn7R0nCrKmjQWseoERDPBJWsCB8E6iWIkCgRrB+P7ud+eMKV5LJ9gmjA/IkPJQ04JGKlv2w3vFtcqPeAR05Xalde3y07VWQCvEzcnZZSj0be/eoOYphGTQAXRuus6CfgZUcCpYLNSL9UsIXRMhqxrqCRmkZ8tLp/hC6MMcBgrUxLwQv09kZFI62kUmM6IwEivenPxP6+bQnjjZ1wmKTBJl4vCVGCI8TwGPOCKURBTQwhV3NyK6YgoQsGEVTIhuKsvr5OWV3Wdqvvolet3eRxFdIbO0SVy0TWqowfUQE1E0QQ9o1f0ZmXWi/VufSxbC1Y+c4r+wPr8AZuPkak=</latexit><latexit sha1_base64="1L/vlXfxxdYWCTjhC5ki3Rh2e7Y=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LLaCBylJelDEQ8GLxwr2A9pQNttNu3SzCbuTQgn9J148KOLVf+LNf+O2zUFbHww83pthZl6QCK7Bcb6twsbm1vZOcbe0t39weGQfn7R0nCrKmjQWseoERDPBJWsCB8E6iWIkCgRrB+P7ud+eMKV5LJ9gmjA/IkPJQ04JGKlv2w3vFtcqPeAR05Xalde3y07VWQCvEzcnZZSj0be/eoOYphGTQAXRuus6CfgZUcCpYLNSL9UsIXRMhqxrqCRmkZ8tLp/hC6MMcBgrUxLwQv09kZFI62kUmM6IwEivenPxP6+bQnjjZ1wmKTBJl4vCVGCI8TwGPOCKURBTQwhV3NyK6YgoQsGEVTIhuKsvr5OWV3Wdqvvolet3eRxFdIbO0SVy0TWqowfUQE1E0QQ9o1f0ZmXWi/VufSxbC1Y+c4r+wPr8AZuPkak=</latexit><latexit sha1_base64="1L/vlXfxxdYWCTjhC5ki3Rh2e7Y=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LLaCBylJelDEQ8GLxwr2A9pQNttNu3SzCbuTQgn9J148KOLVf+LNf+O2zUFbHww83pthZl6QCK7Bcb6twsbm1vZOcbe0t39weGQfn7R0nCrKmjQWseoERDPBJWsCB8E6iWIkCgRrB+P7ud+eMKV5LJ9gmjA/IkPJQ04JGKlv2w3vFtcqPeAR05Xalde3y07VWQCvEzcnZZSj0be/eoOYphGTQAXRuus6CfgZUcCpYLNSL9UsIXRMhqxrqCRmkZ8tLp/hC6MMcBgrUxLwQv09kZFI62kUmM6IwEivenPxP6+bQnjjZ1wmKTBJl4vCVGCI8TwGPOCKURBTQwhV3NyK6YgoQsGEVTIhuKsvr5OWV3Wdqvvolet3eRxFdIbO0SVy0TWqowfUQE1E0QQ9o1f0ZmXWi/VufSxbC1Y+c4r+wPr8AZuPkak=</latexit>

GHI

D2:

256

<latexit sha1_base64="1YE2iuJNyIvfFEve2zmv1B4WPKY=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKewu+EA8BPTgMYJ5QLKE2clsMmZ2ZpmZFcKSf/DiQRGv/o83/8ZJsgdNLGgoqrrp7goTzrRx3W+nsLK6tr5R3Cxtbe/s7pX3D5paporQBpFcqnaINeVM0IZhhtN2oiiOQ05b4ehm6reeqNJMigczTmgQ44FgESPYWKl561/5Z+e9csWtujOgZeLlpAI56r3yV7cvSRpTYQjHWnc8NzFBhpVhhNNJqZtqmmAywgPasVTgmOogm107QSdW6aNIKlvCoJn6eyLDsdbjOLSdMTZDvehNxf+8TmqiyyBjIkkNFWS+KEo5MhJNX0d9pigxfGwJJorZWxEZYoWJsQGVbAje4svLpOlXPbfq3fuV2nUeRxGO4BhOwYMLqMEd1KEBBB7hGV7hzZHOi/PufMxbC04+cwh/4Hz+AOKojfs=</latexit><latexit sha1_base64="1YE2iuJNyIvfFEve2zmv1B4WPKY=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKewu+EA8BPTgMYJ5QLKE2clsMmZ2ZpmZFcKSf/DiQRGv/o83/8ZJsgdNLGgoqrrp7goTzrRx3W+nsLK6tr5R3Cxtbe/s7pX3D5paporQBpFcqnaINeVM0IZhhtN2oiiOQ05b4ehm6reeqNJMigczTmgQ44FgESPYWKl561/5Z+e9csWtujOgZeLlpAI56r3yV7cvSRpTYQjHWnc8NzFBhpVhhNNJqZtqmmAywgPasVTgmOogm107QSdW6aNIKlvCoJn6eyLDsdbjOLSdMTZDvehNxf+8TmqiyyBjIkkNFWS+KEo5MhJNX0d9pigxfGwJJorZWxEZYoWJsQGVbAje4svLpOlXPbfq3fuV2nUeRxGO4BhOwYMLqMEd1KEBBB7hGV7hzZHOi/PufMxbC04+cwh/4Hz+AOKojfs=</latexit><latexit sha1_base64="1YE2iuJNyIvfFEve2zmv1B4WPKY=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKewu+EA8BPTgMYJ5QLKE2clsMmZ2ZpmZFcKSf/DiQRGv/o83/8ZJsgdNLGgoqrrp7goTzrRx3W+nsLK6tr5R3Cxtbe/s7pX3D5paporQBpFcqnaINeVM0IZhhtN2oiiOQ05b4ehm6reeqNJMigczTmgQ44FgESPYWKl561/5Z+e9csWtujOgZeLlpAI56r3yV7cvSRpTYQjHWnc8NzFBhpVhhNNJqZtqmmAywgPasVTgmOogm107QSdW6aNIKlvCoJn6eyLDsdbjOLSdMTZDvehNxf+8TmqiyyBjIkkNFWS+KEo5MhJNX0d9pigxfGwJJorZWxEZYoWJsQGVbAje4svLpOlXPbfq3fuV2nUeRxGO4BhOwYMLqMEd1KEBBB7hGV7hzZHOi/PufMxbC04+cwh/4Hz+AOKojfs=</latexit><latexit sha1_base64="1YE2iuJNyIvfFEve2zmv1B4WPKY=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKewu+EA8BPTgMYJ5QLKE2clsMmZ2ZpmZFcKSf/DiQRGv/o83/8ZJsgdNLGgoqrrp7goTzrRx3W+nsLK6tr5R3Cxtbe/s7pX3D5paporQBpFcqnaINeVM0IZhhtN2oiiOQ05b4ehm6reeqNJMigczTmgQ44FgESPYWKl561/5Z+e9csWtujOgZeLlpAI56r3yV7cvSRpTYQjHWnc8NzFBhpVhhNNJqZtqmmAywgPasVTgmOogm107QSdW6aNIKlvCoJn6eyLDsdbjOLSdMTZDvehNxf+8TmqiyyBjIkkNFWS+KEo5MhJNX0d9pigxfGwJJorZWxEZYoWJsQGVbAje4svLpOlXPbfq3fuV2nUeRxGO4BhOwYMLqMEd1KEBBB7hGV7hzZHOi/PufMxbC04+cwh/4Hz+AOKojfs=</latexit>D2:

256

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512

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Output

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Figure 1. The overall structure of the SolarNet. Colors indicatedifferent layer types. The upper part is the modified VGG16,while the lower part shows the detailed hyperparameters ofeach layer.

III. EXPERIMENTAL SETUP

This section briefly introduces the dataset for case studies,the SolarNet training strategies, and the benchmark models.

A. Dataset Description

In this paper, the largest publicly available dataset withboth TSIs and numerical measurements, namely, the nationalrenewable energy laboratory (NREL) solar radiation researchlaboratory (SRRL) dataset, is used for case studies. TheSRRL has been collecting continuous solar measurements atNREL’s South Table Mountain Campus (longitude: 105.18◦

W, latitude 39.74◦ N, elevation 1,828.2 m), Golden, Coloradosince 1981. In addition to numerical measurements with a 1-min resolution, the SRRL dataset has two sets of total TSIstaken by a Yankee Total Sky Imager (TSI-800) and an EKOAll Sky Imager with a 10-min resolution. More information ofthe SRRL dataset can be found in a recent solar energy dataartical [13].

(a) An original sky im-age

(b) A binary ROImask

(c) A processed skyimage

Figure 2. Sky image pre-processing.

The numerical meteorological features, including GHI, di-rect normal irradiance, direct horizontal irradiance, tempera-ture, relative humidity, wind speed, and atmosphere pressure,are used (only GHI is used in the SolarNet as labels, whileothers are used in benchmarks). The calendar features, i.e.,month of the year and hour of the day, and the Ineichen andPerez clear sky GHI (denoted as CGHI, obtained from pvlibpackage in Python [14]) are also included. For the TSIs,the TSI-800 images are used in this study due to its longercoverage period. To match the resolution with TSIs, numericaldata are averaged every 10 min. The original TSIs have352×288 pixels, whose regions of interest (ROI) are extractedto avoid the hazy sky and obstacle presence. Therefore, a256×256 binary mask is applied to circularly cropping theTSIs by centering at their center pixels, as shown in Fig. 2.Both the TSIs and numerical data are normalized by themaximum values before being fed into the model (GHI isnormalized by the CGHI). To ensure a successful trainingprocess without over-fitting, ten years (i.e., from 2008-01-01to 2017-12-31) numerical and image data are downloaded andprocessed, where the first five years (i.e., from 2008-01-01to 2012-12-31) data are used for training, the following threeyears data (i.e., from 2013-01-01 to 2015-12-31) are used forvalidation, and the last two years data are used for testing(i.e., from 2016-01-01 to 2017-12-31). Meaningless data inthe early morning and late night have been discarded in the

dataset. Therefore, the sample sizes in the training, validation,and testing sets are 128,779, 78,505, and 52,665, respectively.In this study, the forecasting time horizon is one-step ahead(i.e., 10-min ahead).

B. Training Strategies

Having 14,846,273 parameters distributed in 21 layers, theSolarNet is trained with the mini-batch stochastic gradientdescent (SDG), for its convergence stability and efficiency.The parameters are initialized with the ImageNet pre-trainedweights to promote the convergence. During the trainingprocess, SDG minimizes the objective function J(W) in Eq. 2by updating the parameters in the opposite direction of its gra-dients with respect to the parameters. In the training process,the complete training dataset is passed forward and backward60 epochs, during which mini-batches with a batch size of 64(restricted by the GPU memory) are randomly generated toshuffle the data order. In each iteration, gradients are averagedover the mini-batch. The learning rate scheduling is used todampen training oscillations. Specifically, the learning ratestarts with 0.001 and is reduced by 50% once a plateau isreached for more than 10 epochs.

Table I. Machine learning benchmark models

Model Function/Algorithm Hyperparameter

ANN1 Resilient BP lr=0.01, max_epoch=1,000,min_delta=1×106, max_delta=50

ANN2 Momentum BP lr=0.01, max_epoch=1,000,momentum=0.9

ANN3 Standard BP lr=0.01, max_epoch=1,000

GBM1 Squared loss lr=0.01, ntrees=1,000,max_depth=20, bag_frac=0.5

GBM2 Laplace loss lr=0.01, ntrees=1,000,max_depth=20, bag_frac=0.5

GBM3 T-distribution loss lr=0.01, ntrees=1,000,max_depth=20, bag_frac=0.5, DF=4

RF CART aggregation ntrees=1,000, mtry=5

C. Benchmark Models

To compare with the developed SolarNet, the persistence ofcloudiness model [4] (denoted as PoC and also known as thesmart persistence or cloudiness-index persistence) and a col-lection of 7 ML models are built based on the numerical data(with the latest meteorological features). The ML models in-clude three ANNs with different back-propagation (BP), threeGBMs with different loss functions, and an RF model. Pleasenote that several ANNs, GBMs, and RF models were tested butonly the best ones are reported in the paper. The hyperparam-eters of the benchmark models are empirically determined andsummarized in Table I, including the learning rate (lr) andthe maximum number of epochs (max_epoch) in ANN1–ANN3; the minimum update value (min_delta) and themaximum update value (max_delta) in ANN1; the momen-tum (momentum) in ANN2; the number of boosting iterations(ntrees), maximum tree depth (max_depth), learning rate(lr), out-of-bag fraction (bag_frac) in GBM1–GBM3; thedegree of freedom (DF) in GBM3; and the number of trees

(ntrees) and the number of variables randomly sampled ascandidates at each split (mtry) in RF.

IV. RESULTS AND DISCUSSION

The case studies are conducted on a workstation with anIntel Xeon(R) E5-2603 1.6GHz CPU and an NVIDIA TITANV GPU. The SolarNet and benchmark models are implementedusing the Keras library with Tensorflow backend andthe scikit-learn library in Python version 3.6. It took1241.32 mins to train the SolarNet and 8.60 mins to generateforecasts of the entire testing set (around 9.80 ms for a singleforecast). Considering the computational cost, the SolarNet isapplicable for solar nowcasting. The loss values of the trainingepochs are shown in Fig. 3, which reveals a successful training.

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A. Overall Accuracy

To quantify the overall performance of the SolarNet andbenchmarks, three error metrics are selected, which are themean bias error (MBE), root mean square error (RMSE), andforecasting RMSE skill score (FSS). These three metrics arewidely used in the solar forecasting society and can be foundin Ref. [15]. As listed in Table II, the developed SolarNet out-performs benchmarks consistently based on RMSE. The FSSof SolarNet is 11.88%, which is a significant improvement.Considering the MBE, the SolarNet underforecasts the GHIbut is still competitive compared to benchmarks.

Table II. GHI forecasting errors

Models RMSE [W/m2] MBE [W/m2] FSS [%]SolarNet 80.14 -2.78 11.88PoC 90.94 4.31 0 .00ANN1 101.74 -4.93 -11.87ANN2 85.61 7.15 5.86ANN3 97.71 -21.83 -7.44GBM1 87.47 -0.40 3.82GBM2 87.41 -0.73 3.89GBM3 89.12 -2.00 2.01RF 85.65 -1.35 5.82

Note: The maximum GHI in the testing dataset is 1,268.393 W/m2,while the maximum GHI in the entire dataset is 1,319.328 W/m2.

To compare the SolarNet with benchmarks (only the besttwo ML models and the PoC model are selected) in detail,joint and marginal distributions of the GHI observations andforecasts are shown in Fig. 4. Compared to benchmarks, theSolarNet forecasts are more consistent with actual GHI, since

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the hex bins concentrate more around the diagonal. Especially,the SolarNet shows better performance than the ANN2 and RFmodels in the mid- and high-irradiance conditions. However,the SolarNet forecasts in low-irradiance conditions need to befurther improved.

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Figure 5. Forecasting bias error statistics in CSI groups.The interquartile range box represents the middle 50% ofbias errors. The upper and lower bounds are maximum andminimum bias error, respectively, excluding the outliers.

B. Weather Effects

It is observed that the irradiance condition impacts SolarNetforecasts. Therefore, to dig into the weather effects, forecastsgenerated by the four models are grouped based on clear skyindex (CSI). Figure 5 shows the statistics of forecasting biaserror of the four models under various weather conditions.Generally, the SolarNet outperforms three best benchmarks inpartially cloudy and clear sky conditions, since it has smallerMBE when CSI ≥ 0.75. Nonetheless, the performance of

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Figure 6. Observed, forecast, CGHI time series, CSI time series, and TSIs of a typical day (i.e., 2017-05-29). Only hourlyimages are shown here, due to the space limitation.

SolarNet is not as good as the three best models in cloudyconditions, which is revealed by the large MBE and errorvariance (e.g., CSI=0.25 and CSHI=0.5).

The findings are supported by the GHI time series, CSI timeseries, and their corresponding TSIs. Figure 6 shows a typicalday with clear sky (i.e., 5am–10am), partially cloudy (i.e.,2pm and 5pm–7pm), and cloudy conditions (i.e., 11am–1pmand 3pm–4pm). It is found that the SolarNet forecast errors aresmall under the clear sky and partially cloudy conditions (CSI≥ 0.75). In contrast, forecast errors of the SolarNet are largeunder cloudy conditions (CSI < 0.75), which can be observedby the large deviations between the observed and actual GHI.

C. Discussion

This is the first version of SolarNet, which aims to inves-tigate the effectiveness of using only one image to forecast10-min ahead GHI. Nonetheless, the network is flexible to(i) provide STSFs with longer time horizons in a parallelapproach, (ii) incorporate features from multiple sources, suchas meteorological measurements, and (iii) be extended to 3DCNN to take TSI time series as inputs. Additionally, the impactof weather effects on the SolarNet forecasts also inspires usto include post-processing (e.g., solar zenith angle filtering),weather recognition techniques, and probabilistic forecastingto mitigate the negative effects under cloudy conditions in thefuture network.

V. CONCLUSION

This paper developed a 21-layer deep convolutional neuralnetwork (CNN), called the SolarNet, to forecast 10-min aheadglobal horizontal irradiance (GHI). The SolarNet used onlyone total sky image (TSI) as the input without any numericalmeasurements and extra feature engineering process. The So-larNet is trained based on an end-to-end manner, during whichthe latent relations between TSIs and GHI were capturedby the five feature learning blocks and three fully-connectedlayers. Numerical experiments based on ten years publiclyavailable data showed that the SolarNet significantly improvedthe forecasting performance compared with the persistence of

cloudiness model and machine learning models. The weathereffects and future directions were also discussed.

REFERENCES

[1] C. B. Martinez-Anido, B. Botor, A. R. Florita, C. Draxl, S. Lu, H. F.Hamann, and B.-M. Hodge, “The value of day-ahead solar powerforecasting improvement,” Solar Energy, vol. 129, pp. 192–203, 2016.

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