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PVNet: A LRCN Architecture for Spatio-Temporal Photovoltaic PowerForecasting from Numerical Weather Prediction

Anonymous Authors1

Abstract

Photovoltaic (PV) power generation has emergedas one of the lead renewable energy sources. Yet,its production is characterized by high uncertainty,being dependent on weather conditions like solarirradiance and temperature. Predicting PV pro-duction, even in the 24 hour forecast, remains achallenge and leads energy providers to keep idle- often carbon emitting - plants. In this paper weintroduce a Long-Term Recurrent ConvolutionalNetwork using Numerical Weather Predictions(NWP) to predict, in turn, PV production in the24 hour and 48 hour forecast horizons. This net-work architecture fully leverages both temporaland spatial weather data, sampled over the wholegeographical area of interest. We train our modelon a NWP dataset from the National Oceanic andAtmospheric Administration (NOAA) to predictspatially aggregated PV production in Germany.We compare its performance to the persistencemodel and to state-of-the-art methods.

1. IntroductionAs of early 2019, 184 out of 197 Parties have ratified theParis Agreement, which was negotiated at the 21st Confer-ence of the Parties (COP21) to reduce the risks and effectsof climate change. These signatures show a world-wideawareness of global warming issues and a commitment onplanning initiatives that mitigate greenhouse gas emissions.Countries are taking actions in order to better integrate re-newable clean energies into their grids.

Solar photovoltaic (PV) production is one of the most popu-lar renewable energy sources. According to the InternationalAgency of Energy (IAE) 1, cumulative solar PV capacity

1Anonymous Institution, Anonymous City, Anonymous Region,Anonymous Country. Correspondence to: Anonymous Author<anon.email@domain.com>.

Preliminary work. Under review by the International Conferenceon Machine Learning (ICML). Do not distribute.

1https://www.iea.org/topics/renewables/solar/

reached almost 398 GW in 2017, representing around 2%of global power output. Furthermore, solar PV is expectedto lead renewable electricity capacity growth, increasing toover 1000 GW by 2023.

Integrating solar PV production into the energy grids re-quires an accurate and reliable forecast of the PV power,in order to guarantee the optimal management of energydemand and supply. Yet, accurate PV power forecastingremains a challenge as the PV output depends on fluctuatingweather conditions, like solar irradiance or other meteoro-logical factors (Li et al., 2016a).

1.1. Related Works

Many studies have tackled the challenge of PV power fore-cast. They rely on statistical time-series methods, phys-ical methods, or ensemble methods which combine dif-ferent models to enhance accuracy (Sobri et al., 2018).Widely used time-series models can be separated into twogroups: linear and non-linear models. Linear time-seriesmodels used in PV forecast include the combination of auto-regressive models (AR) with moving average models (MA)into auto-regressive moving average models (ARMA) (Liet al., 2014; Kardakos et al., 2013). While linear modelsare usually more transparent towards their feature selec-tion, non-linear models often show better prediction accu-racy when enough data are available. Among non-lineartime-series models, Artificial Neural Networks (ANN) havebecome increasingly popular for PV forecast (Ding et al.,2011; Kardakos et al., 2013; Dolara et al., 2015) and amongthem Recurrent Neural Networks (Malvoni et al., 2013)and Long-Short Term Memory Networks (Abdel-Nasser &Mahmoud, 2017; Gensler et al., 2017). We note that ANNmodels can be interpreted as a non-linear version of AR,also called NAR, while Recurrent Neural Networks can beseen as a type of non-linear ARMA, also called NARMA.

The most successful methods among the ones mentionedabove are models adding Numerical Weather Prediction(NWP) like predictions of solar irradiance or temperatureinto the time-series approach. They may also include an-alytical physical models outputs, like atmospheric mod-els and several types of Clear Sky Models (Inman et al.,2013). NWP can be obtained from the European Centre

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PVNet: LRCN for Spatio-Temporal PV Forecast from NWP

for Medium-Range Weather Forecasts (ECMWF) 2 and theNational Oceanic and Atmospheric Administration (NOAA)3. Clear Sky Models, and additional physical models, areprovided by open-source libraries (Holmgren et al., 2018).Time-series models including these additional inputs are re-ferred to as ARMA model with exogenous inputs (ARMAX)for the linear versions (Kardakos et al., 2013) or NAR withexogenous inputs (NARX) (Di Piazza et al., 2016) as well asArtificial Neural Networks with multiples inputs (Malvoniet al., 2013; Dolara et al., 2015; Hossain et al., 2018; Onetoet al., 2018).

Adding NWP and physical model inputs to time-series mod-els show better forecast prediction, yet limited computa-tional resources as well as dataset sizes often prohibit studiesto integrate an exhaustive list of these variables, especiallyin non-linear models. Instead, the impact of the variablesis assessed by independent experiments (Kardakos et al.,2013) of by fitting regression models like multiregressionanalyses (Malvoni et al., 2013) or multivariate adaptive re-gression splines (Li et al., 2016a). Eventually, a subset ofthe variables may be selected for prediction. These variablesselection analyses are conducted at specific locations, at fourPV plants in Greece (Kardakos et al., 2013), one PV plantin Southern Italy (Malvoni et al., 2013) and in Macau (Liet al., 2016b), while the variables impact on the predictionis likely to be location-dependent.

In this paper, we present a method that takes into accountthe spatial distribution of the input variables, in order tosimultaneously increase the model’s inference capacity - anunderstanding of which inputs variables are important atwhich geographic locations - as well as the model’s predic-tion accuracy. In the above studies, the spatial distributionof the NWP and physical models variables are not takeninto account: models focus for example on solar irradianceor temperature only at the specific location of the targetplant. The time-series and neural network architectures of-ten model the temporal structure of the variables, not theirspatial structure and initiatives to incorporate spatial infor-mation are often restricted to sparse data at neighboringplants for example (Gutierrez-Corea et al., 2016; Agouaet al., 2018). Yet, weather variables and physical modeloutputs on the zone surrounding a target plant are additionaldata, especially valuable while fitting non-linear flexiblemodels, that can be integrated into the input data for higheraccuracy. To the best of our knowledge, there is no modelthat fully integrates both temporal and dense spatial numeri-cal weather predictions and physical models outputs in PVforecasting.

Meanwhile, flexible non-linear predictions models tak-ing into account the spatio-temporal structure of the data,

2https://www.ecmwf.int/en/forecasts/datasets/set-i3https://www.emc.ncep.noaa.gov/GFS/doc.php

like Long-Term Recurrent Convolutional Network (LRCN)(Donahue et al., 2015), 2D LSTM or Convolutional LSTMarchitectures (ConvLSTM) (Shi et al., 2015), have been suc-cessfully applied to a variety of problems. LRCN modelshave been used in activity recognition, image captioningand visual question answering (Donahue et al., 2015). A2D LSTM model has been applied to traffic forecasting(Zhao et al., 2017) while a ConvLSTM has shown promis-ing results on a precipitation forecast that predicts rainfallintensity in a local region on a very short time horizon (Shiet al., 2015) (also known as nowcasting), a weather-relatedprediction problem that shares similarities with PV forecast.

1.2. Contributions and Outline

This paper presents PVNet, a PV forecasting model thatintroduces a LRCN architecture in order to integrates pastPV power 1D time-series with dense spatio-temporal NWPand physical models’ inputs. Our model extends the state-of-the-art 1D time-series models by learning spatial featureswith CNN modules, whose channels encode the NWP andphysical models variables. We focus our analysis on the day-ahead PV forecast, whose accuracy is known to be highlydependent on NWP integration, and which is particularlyinteresting as energy market bids are placed one day in ad-vance. Our experimental results show that our architecturemanages to leverage this additional spatial data for predic-tion accuracy. We train a highly non-linear prediction modelthat reaches a high accuracy on our validation dataset. Fur-thermore, our model provides a location-dependent assess-ment of the impact of the different input variables, throughan occlusion sensitivity analysis that shows a strong infer-ence capability.

In Section 2, we describe the data representation used forthe PV power output and the NWP and physical models vari-ables. We then present our spatio-temporal LRCN modelPVNet, with its CNN and LSTM modules. Section 5 de-scribes our experimental studies and accuracy results, aswell as the results of the occlusion sensitivity analysis thatvalidates our spatio-temporal approach.

2. Data Representation2.1. Photovoltaic Panel

A photovoltaic solar panel, also called photovoltaic module,is a device that absorbs sunlight as a source of energy inorder to generate electricity. We are interested in the poweroutput produced by the module, which is a time series thatdepends on weather conditions, see Figure 2.

There are different ways to model the solar panel produc-tion from external factors, one of which is the equivalentelectrical circuit of a solar cell is composed of a diode, a

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PVNet: LRCN for Spatio-Temporal PV Forecast from NWP

resistor in series and in parallel as shown in see Figure 1 4).

+

V

–

IL

ID ISH

RSH

RS I

Figure 1. Equivalent Circuit of a Solar Cell.

The diode current is given by the Shockley diode equation:

ID = I0(eVj

nVT − 1) (1)

With VT :

VT =kT

q(2)

With k the Boltzmann constant, T the absolute temperatureof the p-n junction, and q the elementary charge.

Thus the output power produced by the module obviouslydepends on solar irradiance, but also on its temperature(Fesharaki et al., 2011).

Ppv = Vpv × Ipv (3)

Ipv = Il−I0(eq(Vpv+IpvRs)/AKT−1)−Vpv + IpvRs

Rsh(4)

Furthermore, recent experimental research suggests that amodule’s temperature is related to numerical weather datasuch as the ambient temperature, the local irradiance andwind speed. (Muzathik, 2014):

Tm(◦C) = 0.94T + 0.02I− 1.5S + 0.35 (5)

where Tm is the module’s temperature, T is the ambienttemperature, I is the solar irradiance and S the wind speed.However, this model essentially comes from an heuristicand there are likely more weather data - and their non-linearrelationships - that could be taken into account to fullycharacterize the module’s temperature and hence, its poweroutput.

We just showed that the behavior of a photovoltaic panel isboth non linear because of its semi-conductor nature andalso dependant on the temperature of the panel. Temperaturewhich is itself dependant on external factors like externaltemperature and windspeed which are available and forecastthrough numerical services.

4https://commons.wikimedia.org

Figure 2. Aggregated power over a few days

2.2. Numerical Weather Predictions

We incorporate weather prediction data as well as theirnon-linear relationships in our model. Rather than just in-corporating the irradiance and temperature at the specificlocation of the power plant(s), our model aims to leveragethe full spatial scalar fields of the meteorological parame-ters over the whole area of interest. These forecasts can beobtained from global forecast systems, like the ECMWFHRES model (temporal resolution of 1 hour and spatialresolution of 0.1 degree) 5 or the NOAA GFS 6 (temporalresolution of 3 hours and spatial resolution of 0.5 degrees).Each of these models provide a set of weather-related vari-ables.

Figure 3 shows examples of variables of interest, in this caseover our country of interest Germany.

Figure 3. Temperature (in Kelvin) and Cloud Cover (unitless) mapsover Germany on May 1st, 2016

Figure 4 shows a collection of weather patches that typicallyrepresents input data. Here one patch every three hours.

5https://www.ecmwf.int/en/forecasts/datasets/set-i6https://www.emc.ncep.noaa.gov/GFS/doc.php

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PVNet: LRCN for Spatio-Temporal PV Forecast from NWP

Figure 4. NOAA GFS Irradiance over Germany for 7 days - onepatch every 3 hours - time goes from left to right. Lighter colorvalues are higher irradiance. High level view show alternance ofdays and nights.

In order to predict PV power output in the day-ahead fore-cast, we use the numerical weather predictions of the abovevariables for this time horizon.

XNWP,t(x, y) =

NWP1(x, y)...

NWPK(x, y)

(6)

where t is the time, measured in hours from the currenttime, (x, y) is the longitude-latitude coordinates of a pointin the region of interest, andK is the number meteorologicalfactors of interests.

We chose this set of weather features after investigating theintersection of various available data in the NWP forecastdatasets and the current state of the art for the impact ofthe variables affecting the irradiance (here cloud cover andirradiance) and the performance of the solar panel (hereoutside temperature).

2.3. Incorporation of Standard Models Predictions

We also incorporate predictions of standard forecast modelsinto our feature vector. We consider first the persistencemodel, a simple - yet popular - forecast model. The per-sistence model predicts that future PV output is likely tobe similar as the current value at the same time of the day(Cornaro et al., 2015). We denote with the subscript PSS,the PV output predicted by a persistence model:

XPSS(x, y, t) = Ppv(t− Tp) (7)

where time Tp is measured in hours, and (x, y) the longitude-latitude coordinates. Here we take two specific values ofpersistence. One will be used for comparing the perfor-mance of the algorithm at T24 and the one we use as a

feature of our algorithm is at T48. Indeed when used in thecontext of energy forecast, there is a 24 hours delay, as seenin figure 5.

A clear sky model estimates irradiance under the assumptionthat there are no clouds in the sky (Reno et al.) . This is afunction of the altitude, location, and various atmosphericconditions. The irradiance predicted predicted by the clearsky model is:

XCSM,t(x, y) = CSM(t, x, y, α(t, x, y)) (8)

where t is the time, measured in hours from the current time,(x, y) is the longitude-latitude coordinates of a point in theregion of interest and α is a set of external variables usedfor the Clear Sky Model. In our case we

Specifically, we form a feature at time t, Xt by aggregatingthe weather forecast variables with the predictions of thestandard models:

Xt(x, y) =

XNWP,t(x, y)XPSS,t

XCSM,t(x, y)

∈ RK+2 (9)

where t is the time, measured in hours from the current time,(x, y) is the longitude-latitude coordinates of a point in theregion of interest. thus, our feature vector incorporates bothspatial weather forecasts as well as some predictions fromexisting models.

3. PVNet ModelThe goal of PV power output forecasting is to use numericalweather predictions, to forecast the future PV output in aregion, in our case: at the day ahead forecast at the scale ofa country. We consider t = 0 the time at which we makethe prediction, and thus tforecast = 24h is the forecast time.Precisely, we consider a sliding window of size T , and:

(Xt1 , ..., XtT ) (10)

where Xt is the feature maps at time t, as defined in Equa-tion 6 and tT = tforecast. Our goal is to predict:

Ppv(tT ),

an estimate of the PV production at the fore-cast horizon. Our training set is thus a set of((Xt0+t1 , ..., Xt0+tT ) , Ppv(t0 + tT ))t0 for differentvalues of t0.

Our model presents a long term recurrent convolutional net-work which combines a convolutional network (CNN) anda bi-directional long short term memory (LSTM) (Schuster& Paliwal, 1997) network, as shown in Figure 6. In practice,

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PVNet: LRCN for Spatio-Temporal PV Forecast from NWP

Figure 5. Timeline of day ahead prediction

we use a time window of T = 8 values, spread at 3 hourstime interval, so as to represent a window that is a full dayof data history.

3.1. The CNN Module

The model applies a convolutional neural network to eachT images Xt of shape (width, height) and K + 2 numberof channels. This results into a feature vector of dimension(T, d):

(xt1 , ..., xtT ) = (g(Xt1), ..., g(XtT )) (11)

where each xt is now a feature vector of dimension d. Weuse one single CNN architecture, and a single set of weights,to transform the feature Xt, independently of the time t.Therefore, this feature transformation step can be describedby a single function g.

The aim of the CNN module is to encode the spatial datainto a new feature vector of lower dimension as runningthe LSTM directly on the whole images would be too com-putationally expensive. Rather than hand-crafting spatiallyaggregated features, we let the CNN learn spatial featuresthat are the most relevant for the following LSTM-based PVpower predictions..

3.2. The LSTM Module

Each of the feature tensor is then fed into an LSTM (Hochre-iter & Schmidhuber, 1997) network, to incorporate the time-series information. A LSTM network is a special case ofRecurrent Neural Network (RNN), which introduces a mem-ory cell ct, that serves as an accumulator of state informa-tion. The cell ct can be accessed, written and cleared byself-parameterized controlling gates. If the input gate it

is activated, the information of each new input, that is ourfeature vector xt, is accumulated to the cell. If the forgetgate ft is activated, the previous cell status ct−1 can beforgotten. The output gate ot controls if the cell output ctwill be propagated to the final state ht. The model can besummarized with the following equations:

ft = σg(Wfxt + Ufht−1 + bf )

it = σg(Wixt + Uiht−1 + bi)

ot = σg(Woxt + Uoht−1 + bo)

ct = ft ◦ ct−1 + it ◦ σc(Wcxt + Ucht−1 + bc)

ht = ot ◦ σh(ct)

(12)

One of the limitations of the LSTM is that any hidden layerassociated with a timestep t only has access to past data.Bidirectional RNNs (Schuster & Paliwal, 1997) have shownto be more efficient in natural language processing tasks(Arisoy et al., 2015). The following equations show howthe RNN take into account past and future data:

−→ht = f(

−→Wxt +

−→V−−→ht−1 +

−→b )

←−ht = f(

←−Wxt +

←−V←−−ht−1 +

←−b )

yt = g(Ugt + c) = g(U [−→ht ;←−ht ] + c)

(13)

The intent of the BiLSTM module is to design features, ateach time t that take into account the temporal structure ofthe input signal.

3.3. Full Model

The convolutional network extracts spatial features (in ourcase spatial weather related features) and then forwardsthem to the LSTM. We then have a fully connected layertaking all the LSTM hidden outputs and producing a singlescalar value that is the estimated value of aggregated PVoutput prediction for the whole country.

We highlight that this model differs from the ConvLSTMmodel from (Shi et al., 2015), in the sense that the ConvL-STM model integrates convolutional structures directly inthe LSTM cells.

Both CNN and LSTM modules are trained simultaneously,to minimize the mean squared error loss function:

MSE =1

N

tN−1∑t=t0

(Ppv(t+ tT )− Ppv(t+ tT )

)2, (14)

summed over window’s initial time values t0.

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PVNet: LRCN for Spatio-Temporal PV Forecast from NWP

Input Sequence X - length T

Time

FC

Temp

Cloud

CSM

Presistence

Irradiance

CNN

LSTM

FC

CNN

FC

CNN

FC

CNN

FC

CNN

FC

CNN

LSTM LSTM

FC

One CNN Per Timestep

Figure 6. PVNet Architecture Details

3.4. Implementation Details

We implement PVNet using the Tensorflow (Abadi et al.)framework. Our convolutional networks are built alternat-ing 2D convolution layers, PReLu activations (He et al.),dropout and max pooling.

There is also a 20% dropout after each convolutional layer.We added a fully connected layer between the CNN layersand the LSTM, with a 30% dropout in between.

In this implementation we use the hard sigmoid for the recur-rent activation and the hyperbolic tangent for the activationitself.

4. DatasetWe consider an aggregated production of PV power acrossGermany. We gather past data from 2014 to 2018, sampledat a time resolution of 15 minutes.

We use numerical weather prediction data from the NationalOceanic and Atmospheric Administration, more specificallythe Global Forecasting System (GFS). This data is freely

Table 1. CNN Layers Details

LAYER PARAMETERS ACTIVATION

CONV2D 3X3X64 PRELUCONV2D 3X3X64 PRELUMAXPOOL 2X2 N/ACONV2D 3X3X128 PRELUCONV2D 3X3X128 PRELUMAXPOOL N/ACONV2D 3X3X256 PRELUCONV2D 3X3X256 PRELUMAXPOOL 2X2FLATTEN N/A N/AFC 512 N/A

available, has a spatial resolution of 0.5 degrees of latitudeand longitude and a time resolution of 3 hours. The timeresolution of the PV power is downsampled at 3h, to matchthe time resolution of the NWP. We consider K = 3 mete-orological variables: Downward short wave radiation flux(DSWRF), Cloud Cover (EACC) and Temperature (TMP).We incorporate data from the persistence model and theClear Sky Model.

4.1. Time Alignment

Time alignment is extremely important for the training towork properly. When first looking at the GFS data one has tobe careful about time shifts. The persistence data includedin the model is not the one used to evaluate the performanceof the model. Indeed in a production setting one only hasaccess to the data from the day before. This means that wecan only use persistence data from 48 hours before the pointto estimate, whereas the actual persistence metrics is done24 hours before.

4.2. Training and Validation Split

We split the training and validation dataset as follows: thefirst 3 years are used for training and the last year is usedfor validation. This approach guarantees that our validationscore is not affected by seasonal patterns. Indeed, the dura-tion of the day being very different between the summer andthe winder solstice, performance measures could be affectedwithout this specific care.

5. Experiments and ResultsOur experiments are run on a computer with a singleNVIDIA Titan X GPU. The training time of the networkis 5 hours. We train our model using the Adam optimizer(Kingma & Ba, 2014), with a learning rate of 0.0015 anda batch size of 32. We run our training for a total of 500epochs, as shown in Figure 7.

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PVNet: LRCN for Spatio-Temporal PV Forecast from NWP

Figure 7. PVNet Training and Validation Losses for n=500 epochs.

5.1. Metrics and Results

We use two metrics to evaluate the quality of PVNet: theroot mean squared error (RMSE) and mean absolute er-ror (MAE) of the prediction. We compute these metricsonly when the measured predicted power is higher than 0(PPV (t) > 0). We do not take nights into accounts be-cause these values tend to increase the performance sincethe estimator of the PV night is trivially ˆPPV (t) = 0 Thenormalized RMSE and MAE (nRMSE and nMAE) are nor-malized with the country-wide PV capacity, which is 41.2GW in our case.

Tables 1 and 2 present our results for PVNet comparedto the persistence model and the current state of the artfor day ahead country wide PV prediction (Lorenz et al.,2011). (Lorenz et al., 2011) used data from 2009-2010and a different formulation of the nRMSE. The authors of(Lorenz et al., 2011) indeed normalized the production ona per plant basis while we normalize it at the scale of thewhole country. We re-implement their method in order tocompute the metrics MAE, nMAE, RMSE and nRMSE forthe same times as the ones used in our validation dataset.

We compute the persistence model RMSE by taking thevalue of the country-aggregated prediction 24 hours beforethe current value. We first observe a RMSE improvementof 17.31 percents compared to the persistence model, whichis expected since the persistence model is fairly naive. Wedo also use the persistence data in our model as one of theinputs - even though the timing is quite different. We use 24hours persistence for verification and 48 hours persistenceas the PVNet input layer.

We also observe a 1.38% decrease in accuracy error innRMSE and a 0.74% decrease in accuracy error in nMAE

Table 2. PVNet Experimental Performance

METHOD NRMSE (%) NMAE (%)

PERSISTENCE 22.04 15.28LORENZ ET AL 6.11 4.37PVNET 4.73 3.63

METHOD RMSE (MW) MAE (MW)

PERSISTENCE 8816 6297LORENZ ET AL 2518 1798PVNET 1949 1499

compared to the state of the art in country-wide day aheadaggregation (Lorenz et al., 2011). Non-linear spatio tem-poral features are being captured in much more details inPVNet, allowing a better overall performance.

5.2. Occlusion Sensitivity Analysis

One of the main interests of this model is to build a spatialrepresentation of the impact of various variables (weather,clear sky model and persistence) on the aggregated PV pro-duction. One way to verify if this is the case is to perform asensitivity analysis in order to evaluate the spatial impact ofeach variable.

This type of analysis has been shown to work well in thecase of deep neural networks (Zeiler & Fergus, 2013).

We perform an occlusion sensitivity analysis by setting thevalues of a patch to a fixed value and recording the changesin value of the predicted power prediction. We perform thisanalysis for each channel and aggregated the values in aheatmap form. We then overlay this heatmap with the mapof Germany and we obtain the results as shown in 8. Theresults show that our network sees the biggest impact withirradiance, followed by cloud cover, clear sky, persistenceand finally temperature.

In order to compare the results of the sensitivity analysis webuild a heatmap representing the distribution of PV powergenerated across Germany on May 1st, 2016. We aggregatethe nominal capacity of the plants on a spatial grid of 0.25×0.25 degrees by summing all plant maximum power onthis area. We overlay this heatmap with Germany countryboundaries for more clarity (see figure 9). This clearlyclearly that the south / east of Germany produces morepower per squared meter, which is consistent with the resultsof our occlusion map. Indeed most of the metrics in thesensitivity maps (figure 8) show higher incidence in thesouth west.

This sensitivity analysis also shows which input featureshave the biggest impact on the outputs. Indeed we that in

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PVNet: LRCN for Spatio-Temporal PV Forecast from NWP

order or decreasing importance, the values are irradiance,followed by cloud cover, the clear sky channel and finallyPersistence and Temperature. This analysis also gives us agood insight about PVNet - looking at these two figures wecan conclude that applying PV net and a Sensitivity analysiscan be used to learn an estimate of the surface density of PVpower production for a given area.

Figure 8. Occlusion Sensitivity Analysis for a 2x2 Patch. Black ishighest sensitivity, white/light orange is lowest sensitivity.

6. Conclusion and Future WorkGlobal warming and the current energy crisis are both call-ing for the integration of renewable energies, including solarPV energy, into countries power grids. Yet, such an inte-gration is still limited by our ability in making reliable PVpower forecast. Accurate PV forecast remains challengingbecause of its correlation with highly fluctuating weathervariables.

This paper introduced PVNet, a country-wide PV forecastmodel that fully integrates 1D time-series of past PV powerwith dense spatio-temporal exogenous inputs. Specifically,PVNet leverages a LRCN architecture that tackles spatio-temporal regression problems using numerical weather pre-dictions and physical models as additional inputs. The

Figure 9. Distribution of PV power generated across Germany. Theunit is power in Watts produced per area of 0.25× 0.25 degreesof latitude and longitude.

model enjoys good performances in terms of prediction.Our results show a decrease in nRMSE of 1.38% comparedto the state-of-the-art model for country-aggregated PV out-put prediction.

This LRCN model also demonstrates inference capability.NWP variables and physical models inputs have intricateand location-dependent correlations with PV power output.We showed that the CNN modules of the LRCN model areable to learn the geographic impact of different meteoro-logical factors on the PV power prediction. Our occlusionsensitivity analysis validates our dense spatial approach andalso allows us to better understand the dominant features asa function of location. It provides an interesting visualiza-tion tool for energy providers in order to estimate the effectof several weather variables of their PV power output. Wealso show that combining PVNet and a Sensitivity analysiscan be used to learn an estimate of the surface density of PVpower production for a given area.

Future work will first involve refinements of the currentmodel, introducing for example interpolation of NWP in-puts in order to avoid temporal down-sampling and dataloss. Then, we will build on the LRCN architecture by in-corporating new spatial information, like satellite imageryor fish-eye data imagery. A reliable PV forecast thus relieson models that fully leverage the available geographicaldata. With this work, we aim to open the doors to morespatio-temporal methods in PV output forecasting. The ob-jective of such models is to enable a secure and economicintegration of PV power into smart energy grids of countriesover the world. This leads, in turn, to an increase of theproportion of renewable clean energies in the world’s energyconsumption.

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PVNet: LRCN for Spatio-Temporal PV Forecast from NWP

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