# High-Resolution PV Forecasting from Imperfect Data: A Graph-Based Solution

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Graph-Based Data Reconstruction: Filling the Gaps

#### 2.2. Spatio-Temporal Forecast Method

#### 2.2.1. Normalization and De-Trending

#### 2.2.2. Spatio-Temporal Auto-Regressive Forecast Model

#### 2.2.3. Prediction for Short-Term Horizon

## 3. Results

#### 3.1. Evaluation Data and Metrics

#### 3.2. Results of the Graph-Based Algorithm for Data Reconstruction

#### 3.3. Forecasting Results Using Uninterrupted Data

#### 3.4. Forecasting Results Using Incomplete Data

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Block diagram of the proposed approach for robust photovoltaic (PV) production forecasting.

**Figure 2.**Example of a graph constructed using the locations (coordinates) of the monitored PV plants over Switzerland. The edges are selected using the 10 nearest neighboring plants.

**Figure 3.**Example of normalization of the PV production signal at one site over four days: original signal (gold), clear sky profile (black, dashed) and normalized signal (brown).

**Figure 4.**Example of a set of edges obtained by the group LASSO approach for a node in central Switzerland with a past history horizon of three hours.

**Figure 5.**Spatial distribution of the different datasets. (

**a**) Real dataset. (

**b**) Synthetic dataset. Colors indicate the peak production of each plant.

**Figure 6.**Daytime normalized root-mean-square error (NRMSE) for signal reconstruction against expected length of gaps (in hours) per day in the data for both the real and synthetic datasets. “GSR” stands for the graph signal reconstruction technique introduced in this paper.

**Figure 7.**Reconstruction example of a corrupted signal with gaps of expected length of 8 h per day. Visualization for three nodes in a window of six days. The signals are normalized by the peak production.

**Figure 8.**Comparison between spatio-temporal autoregressive (ST-AR), single autoregressive (AR) and persistence models. (

**a**) Forecast NRMSE for the real dataset. (

**b**) Forecast NRMSE for the synthetic dataset. The forecast horizon is six hours in steps of 15 min. Solid lines show the median error while the shaded areas show the inter-quantile distance of the errors.

**Figure 9.**Illustration of the annual PV production for the selected sites. (

**a**) Measured and forecasted production for Bern. (

**b**) Measured and forecasted production for Bätterkinden. The forecasts are done every six hours with a horizon of six hours.

**Figure 10.**Forecast error (NRMSE) comparison between ST-AR and SVR with numerical weather predictions (NWP) for a single site. The forecast horizon is six hours in steps of 15 min.

**Figure 11.**Forecast error comparison between ST-AR with uninterrupted data and ST-AR with data with gaps. (

**a**) Forecast NRMSE for the real dataset. (

**b**) Forecast NRMSE for the synthetic dataset. The forecast horizon is six hours in steps of 15 min. Solid lines show the median error while the shaded areas show the inter-quantile distance of the errors.

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**MDPI and ACS Style**

Carrillo, R.E.; Leblanc, M.; Schubnel, B.; Langou, R.; Topfel, C.; Alet, P.-J.
High-Resolution PV Forecasting from Imperfect Data: A Graph-Based Solution. *Energies* **2020**, *13*, 5763.
https://doi.org/10.3390/en13215763

**AMA Style**

Carrillo RE, Leblanc M, Schubnel B, Langou R, Topfel C, Alet P-J.
High-Resolution PV Forecasting from Imperfect Data: A Graph-Based Solution. *Energies*. 2020; 13(21):5763.
https://doi.org/10.3390/en13215763

**Chicago/Turabian Style**

Carrillo, Rafael E., Martin Leblanc, Baptiste Schubnel, Renaud Langou, Cyril Topfel, and Pierre-Jean Alet.
2020. "High-Resolution PV Forecasting from Imperfect Data: A Graph-Based Solution" *Energies* 13, no. 21: 5763.
https://doi.org/10.3390/en13215763