# A Machine Learning Approach to Low-Cost Photovoltaic Power Prediction Based on Publicly Available Weather Reports

^{1}

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## Abstract

**:**

## 1. Introduction

_{2}emissions, which represent one of the main reasons for the greenhouse effect in the atmosphere and global warming. A plan to limit global warming is described in the Paris Agreement, which entered into force on 4 November 2016. The first point of this agreement defines that the increase in global average temperature should not exceed 2 °C in comparison to the pre-industrial level [1].

## 2. Data

#### 2.1. Photovoltaic Power Output

#### 2.2. Weather Data

^{2}) were taken from the year 2019.

#### 2.3. Additional Descriptive Feature

#### 2.3.1. PV Power under Clear-Sky Conditions

- Latitude, longitude, altitude, and time zone of PV system location;
- Some meteorological parameters, like air temperature and pressure (if these parameters are not available, pvlib uses default values: T = 12 °C, pressure = none);
- Time period for which the GHI is calculated.

^{2}). For this step, the maximum value of the PV power measurements ${P}_{PV,max}$ (W) was divided by the maximum value of the GHI under clear-sky conditions $GH{I}_{clearsky,max}$ (W/m

^{2}) (see Equation (1)).

#### 2.3.2. Maximum PV Power

#### 2.4. Data Exploration

#### 2.5. Correlation Analysis and Feature Selection

## 3. Methodology

#### 3.1. Machine Learning Algorithm

- LSTM is able to learn long-term dependencies that are typically found in time series. All used input datasets were time series (weather data and measurements of PV power).
- This structure of the ANN can remember relevant information for long periods of time.
- In the case of great time lags, the special structure of the LSTM prevents the error signals from increasing or vanishing.

#### 3.2. Description of Developed Predictive Model

- First layer with five input parameters;
- Two hidden LSTM layers with 64 and 32 neurons;
- Output dense layer;
- The total number of trainable parameters was 30,369.

#### 3.3. Content and Sizes of the Training and Test Sets

#### 3.4. Evaluation of Prediction Accuracy

_{0}is the installed capacity of the PV system.

- The season was taken as one day;
- $m$ in Equation (8) was set to 48, because the time resolution of the data was 30 min;
- ${\mathrm{P}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}}$ in Equation (8) was the measured power of the PV system at time $i$;
- ${\mathrm{P}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s},\mathrm{i}-\mathrm{m}}$ in Equation (8) was the measured power of the PV system at the same time yesterday.

## 4. Results and Discussion

#### 4.1. Choice of the Additional Descriptive Feature

_{P}). Both training datasets contained 90 days of data. The architecture of the predictive model and the procedure of the predictive process also remained the same. The only difference was that the first input dataset contained maximum PV power and the second input dataset contained clear-sky PV power as the additional descriptive feature.

#### 4.2. Prediction with Publicly Available Weather Reports

#### 4.3. Prediction with Fee-Based Solar Irradiance Data

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**PV power output under clear-sky conditions on (

**a**) June 1st and (

**b**) December 1st 2017 estimated for the PV system in Oldenburg with an installed capacity of 1.14 kW

_{P}.

**Figure 2.**Correlation values between descriptive, additional, and target features. Values close to −1 mean a strong negative linear correlation, values close to 1 mean a strong positive linear correlation, and values around 0 mean no linear correlation [19].

**Figure 3.**Monthly correlation values among measured PV power, selected meteorological parameters, and additional features.

**Figure 4.**Internal structure of a single long short-term memory (LSTM) block (following the description of Hua et al. [28]).

**Figure 7.**Distribution of daily MAE values of PV power prediction after training the model without any additional feature and with maximum PV power or clear-sky PV power as additional features (training set 90 days; test set 8 August 2017–31 August 2017).

**Figure 8.**Daily values of MAE, RMSE, MAPE, and mean absolute scaled error (MASE) of PV power prediction for warm and cold seasons, which were made after training with four sizes of the training set containing publicly available weather reports.

**Figure 10.**MASE of PV power predictions with publicly available data and fee-based data. The prediction was made for the Munich PV system (installed capacity of 99.9 kW

_{P}).

**Figure 11.**Normalized distribution of the energy forecast errors of predictions with publicly available weather reports (training set with 90 days) and fee-based data (training set with 14 days). The prediction was made for the Munich PV system (installed capacity of 99.9 kW

_{P}).

**Figure 12.**Measured PV power of the Munich PV system in comparison to the PV power predictions made by the model with publicly available weather reports (training set with 90 days) and fee-based solar irradiance data (training set with 14 days) on 20 and 29 June 2019.

Location | Oldenburg | Munich |
---|---|---|

Installation year | 2010 | 2018 |

Total capacity | 1.14 kW_{P} | 99.9 kW_{P} |

Orientation | 237° | 177.5° |

Inclination | 7° | 10° |

Solar cell type | a-Si | mono-Si |

Nominal cell efficiency at standard test conditions | 6.6% | 17.9% |

Step 1 | |

Collection of PV power measurements of the last five days and plotting them in an overlaid manner. The power values of the PV system were recorded and presented in W. | |

Step 2 | |

Finding a maximum of the PV power for each time point. The maximum values are marked bold in the picture. | |

Step 3 | |

Leaving only the maximum values for each time point and deleting other values. These maximum PV power values had the same unit as PV power measurements (W). |

**Table 3.**Statistical metrics of OpenWeatherMap (OWM) forecast: MAE—mean absolute error; RMSE—root-mean-square error; sMAPE—symmetric mean absolute percentage error.

Investigated Meteorological Parameters from OWM | MAE | RMSE | sMAPE (%) |
---|---|---|---|

Temperature | 0.023 | 0.031 | 2.61 |

Pressure | 0.017 | 0.022 | 1.56 |

Humidity | 0.219 | 0.263 | 15.43 |

Cloudiness | 0.236 | 0.339 | 33.79 |

Wind speed | 0.079 | 0.100 | 20.11 |

Precipitation (rain) | 0.415 | 0.644 | 41.48 |

Precipitation (snow) | 0.023 | 0.150 | 2.31 |

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**MDPI and ACS Style**

Maitanova, N.; Telle, J.-S.; Hanke, B.; Grottke, M.; Schmidt, T.; Maydell, K.v.; Agert, C.
A Machine Learning Approach to Low-Cost Photovoltaic Power Prediction Based on Publicly Available Weather Reports. *Energies* **2020**, *13*, 735.
https://doi.org/10.3390/en13030735

**AMA Style**

Maitanova N, Telle J-S, Hanke B, Grottke M, Schmidt T, Maydell Kv, Agert C.
A Machine Learning Approach to Low-Cost Photovoltaic Power Prediction Based on Publicly Available Weather Reports. *Energies*. 2020; 13(3):735.
https://doi.org/10.3390/en13030735

**Chicago/Turabian Style**

Maitanova, Nailya, Jan-Simon Telle, Benedikt Hanke, Matthias Grottke, Thomas Schmidt, Karsten von Maydell, and Carsten Agert.
2020. "A Machine Learning Approach to Low-Cost Photovoltaic Power Prediction Based on Publicly Available Weather Reports" *Energies* 13, no. 3: 735.
https://doi.org/10.3390/en13030735