# Photovoltaic Power Forecasting: Assessment of the Impact of Multiple Sources of Spatio-Temporal Data on Forecast Accuracy

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Framework for Spatio-Temporal Forecasting

#### 2.1. PV Power Data and Weather Forecasts

#### 2.2. Satellite Images

## 3. Proposed Model

#### 3.1. Identifying the Pixels of Interest

#### 3.2. The Forecasting Model

#### 3.3. Comparison of the Models

- The reference model is the autoregressive model AR which is a model exploiting only the temporal dependencies of the production data only from the site of interest :$$\begin{array}{c}\hfill {P}_{t}=f({P}_{t-1},\dots ,{P}_{t-k})\end{array}$$
- The first model we evaluate is the spatio-temporal model which exploits both temporal dependencies in the measurements but also spatial correlation between measurements of different power plants:$$\begin{array}{cc}\hfill ST=& \mathrm{f}(\mathrm{Prodution}\phantom{\rule{4.pt}{0ex}}\mathrm{data}\phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}\mathrm{the}\phantom{\rule{4.pt}{0ex}}\mathrm{site}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{interest},\\ & \mathrm{Production}\phantom{\rule{4.pt}{0ex}}\mathrm{data}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{neighboring}\phantom{\rule{4.pt}{0ex}}\mathrm{sites},\\ & \mathrm{lags}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{all}\phantom{\rule{4.pt}{0ex}}\mathrm{these}\phantom{\rule{4.pt}{0ex}}\mathrm{production}\phantom{\rule{4.pt}{0ex}}\mathrm{data})\end{array}$$
- The second model investigated is an enhancement of the “ST” model with the integration of local meteorological data. This new model is called a spatio-temporal model with conditioning ST(Z) as the parameters are estimated according to the value of the local meteorological variable Z used.
- The last models investigated are the spatio-temporal model which exploits satellite images, NWP forecasts or both.$$\begin{array}{ccc}\hfill ST+SAT& =& ST+\sum \left(\mathrm{Satellites}\phantom{\rule{4.pt}{0ex}}\mathrm{images}\phantom{\rule{4.pt}{0ex}}\mathrm{data}\right)\hfill \\ \hfill ST+NWP& =& ST+\sum \left(\mathrm{NWP}\phantom{\rule{4.pt}{0ex}}\mathrm{data}\right)\hfill \\ \hfill ST\_global& =& ST+SAT+NWP\hfill \end{array}$$

## 4. Evaluation of the Forecasts

#### 4.1. Variable Selection and Reduction of Dimension

#### 4.2. Forecasting Performances

- for 15 min horizon, all the models show similar performances;
- for longer horizons the ST model outperforms the AR model;
- the integration of the local meteorological information reduce the MAE compared to when this info is not used;
- the model resulting from the combination of spatio-temporal and satellite data is the best model;
- the use of satellite data in combination with ST measured data results to more efficient forecasts for the short-term forecasting than the combination of ST and NWPs;
- the level of the observed errors is similar to the lowest observed in the literature.

- ${M}_{0}$ is the reference AR model
- For each power plants ${P}_{i},i=1,\dots ,9$ in Table A1 and for each model ${M}_{i},i=1,\dots ,4$ between the one presented in Section 3.2 (ST, ST(Z), ST+SAT and ST+NWP)
- —
- For each hour $h,h=1,\dots ,6$ of the forecasting horizon, compute on the testing set the RMSE improvement of model ${M}_{i}$ over reference model ${M}_{0}$:$$Improvement({P}_{i},{M}_{i},{M}_{0},h)=100*\frac{RMSE({P}_{i},{M}_{i},h)-RMSE({P}_{i},{M}_{0},h)}{RMSE({P}_{i},{M}_{0},h)}$$

- Each line on Figure 8 represents the average improvement at each horizon over all the 9 power plants of a model ${M}_{i}$ (over ${M}_{0}$).

**Figure 8.**Comparison of the average (over all power plants) forecasting performances of the models. The time step is 15 min.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

TLA | Three letter acronym |

LD | Linear dichroism |

## Appendix A. Detailed Evaluation Results

**Table A1.**Evaluation results for 9 power plants for the horizon of 6 h ahead (in % of Nominal Power).

Power Plant | Criterion | AR | ST | ST(Z) | ST_SAT | ST_NWP |
---|---|---|---|---|---|---|

P1 | RMSE | 16.67 | 9.68 | 9.68 | 9.31 | 10.53 |

MAE | 15.15 | 12.59 | 12.59 | 10.14 | 14.76 | |

P2 | RMSE | 17.02 | 9.53 | 9.55 | 9.32 | 10.12 |

MAE | 14.73 | 12.56 | 12.56 | 11.23 | 13.48 | |

P3 | RMSE | 16.82 | 9.72 | 9.72 | 9.22 | 10.01 |

MAE | 14.33 | 12.84 | 12.84 | 10.89 | 12.33 | |

P4 | RMSE | 18.21 | 10.02 | 10.02 | 9.88 | 10.35 |

MAE | 16.13 | 12.94 | 12.94 | 12.72 | 13.08 | |

P5 | RMSE | 16.34 | 9.88 | 9.88 | 9.33 | 10.54 |

MAE | 14.92 | 12.33 | 12.33 | 10.14 | 14.83 | |

P6 | RMSE | 17.12 | 9.66 | 9.66 | 9.29 | 10.21 |

MAE | 17.23 | 12.10 | 12.10 | 10.48 | 14.55 | |

P7 | RMSE | 15.88 | 9.55 | 9.55 | 9.22 | 10.12 |

MAE | 14.67 | 12.43 | 12.43 | 10.08 | 13.97 | |

P8 | RMSE | 16.42 | 9.77 | 9.77 | 9.4 | 10.02 |

MAE | 14.87 | 12.65 | 12.65 | 10.42 | 14.88 | |

P9 | RMSE | 17.01 | 9.82 | 9.82 | 9.62 | 10.33 |

MAE | 15.64 | 12.71 | 12.71 | 11.01 | 14.66 |

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**Figure 1.**The 136 PV power plants in the test case d. The figure on the right is a zoom of the one on the left.

**Figure 2.**GHI from satellite data covering the power plants of data set d. The black dots represent the power plants.

**Figure 3.**Distribution of correlation values between production and satellite data according to the distance of the pixels.

**Figure 4.**Area of interest around 3 PV power plants of the dataset d. The time is 1 January 2015 at 12:00 UTC. The black dots represent the power plants.

**Figure 5.**Correlation between on-site measurements and times series resulting from the satellite images for three PV plants. Correlations are calculated for the month of January 2015; the series are at the time step of 15 min. PV plants are represented by black dots.

**Figure 6.**Values of the association coefficient between on-site measurement with time offsets and satellite image estimates for a power plant in the West of the covered region. The PV plant is represented by the black dot, $\tau $ represents the time offset.

Horizons | Initial Number of Variables = 1351 | ||
---|---|---|---|

Number of Pixels Selected | Number of PV Plants Selected | Total Number of Variables Selected (Lags and Pixels Included) | |

15 min | 4 | 28 | 67 |

1 h | 4 | 22 | 64 |

3 h | 7 | 25 | 56 |

Metric | Models | ||||
---|---|---|---|---|---|

MAE (% Pmax) | AR | ST | ST(Z) | ST + SAT | ST + NWP |

15 min | 2.75 | 2.69 | 2.62 | 2.53 | 2.69 |

1 h | 5.69 | 5.33 | 5.23 | 4.82 | 5.59 |

3 h | 11.81 | 10.21 | 10.21 | 8.66 | 11.61 |

6 h | 15.15 | 12.59 | 12.59 | 10.14 | 14.76 |

Metric | Models | ||||
---|---|---|---|---|---|

RMSE (% Pmax) | AR | ST | ST(Z) | ST + SAT | ST + NWP |

15 min | 4.32 | 3.12 | 3.00 | 2.90 | 3.34 |

1 h | 8.34 | 6.72 | 6.5 | 6.30 | 6.90 |

3 h | 10.46 | 8.84 | 8.84 | 8.41 | 9.12 |

6 h | 16.67 | 9.68 | 9.68 | 9.31 | 10.53 |

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**MDPI and ACS Style**

Agoua, X.G.; Girard, R.; Kariniotakis, G.
Photovoltaic Power Forecasting: Assessment of the Impact of Multiple Sources of Spatio-Temporal Data on Forecast Accuracy. *Energies* **2021**, *14*, 1432.
https://doi.org/10.3390/en14051432

**AMA Style**

Agoua XG, Girard R, Kariniotakis G.
Photovoltaic Power Forecasting: Assessment of the Impact of Multiple Sources of Spatio-Temporal Data on Forecast Accuracy. *Energies*. 2021; 14(5):1432.
https://doi.org/10.3390/en14051432

**Chicago/Turabian Style**

Agoua, Xwégnon Ghislain, Robin Girard, and Georges Kariniotakis.
2021. "Photovoltaic Power Forecasting: Assessment of the Impact of Multiple Sources of Spatio-Temporal Data on Forecast Accuracy" *Energies* 14, no. 5: 1432.
https://doi.org/10.3390/en14051432