# Comparison of Training Approaches for Photovoltaic Forecasts by Means of Machine Learning

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## Abstract

**:**

## 1. Introduction

## 2. Training Database Composition Approaches

- the “training set” (or equally “training database”), which is used to adjust the weights among neurons by performing the forecast on the same samples,
- the “validation set”, which is used as a stopping criteria to avoid over-fitting and under-fitting. It proves the goodness of the trained network on additional samples which have not been previously included in the training set. The purpose of this step is to test the generalization capability of the neural network on a new data-set.

- error back-propagation (EBP)
- gradient descent
- conjugate gradient
- evolutionary algorithms (genetic algorithms, particle swarm optimization, etc.)

#### 2.1. Incremental Training Data-Set

- Method A employs the same chronologically consecutive samples by grouping the 90% of the samples which are closest to the forecast day for the training set and the remaining 10% of the samples for the validation set.
- Method A* employs the same chronologically consecutive samples by grouping the 90% of the samples for the training set and the 10% of the samples which are closest to the forecast day for the validation set.
- Method B employs the samples by randomly grouping them separately, 90% for the training set and 10% for the validation set.

#### 2.2. Complete Training Data-Set

## 3. Evaluation Indexes

## 4. Case Study

- PV technology: Silicon mono crystalline,
- Rated power (Net capacity of the PV module): 245 Wp,
- Azimuth: $-{6}^{\circ}30\prime $ (assuming ${0}^{\circ}$ as south direction and counting clockwise),
- Solar panel tilt angle ($\beta $): ${30}^{\circ}$,

- ${T}_{amb}$ ambient temperature (${}^{\circ}$C),
- $GHI$ global horizontal irradiance (W/m${}^{2}$),
- $GPOA$ global irradiance on the plane of the array (W/m${}^{2}$),
- ${W}_{s}$ wind speed (m/s),
- ${W}_{d}$ wind direction (${}^{\circ}$),
- P pressure (hPa),
- R precipitation (mm),
- ${C}_{c}$ cloud cover (%),
- ${C}_{t}$ cloud type (Low/Medium/High).

- neurons in the input layer: 11,
- neurons in the first hidden layer: 11,
- neurons in the second hidden layer: 5,
- neurons in the output layer: 1,
- training algorithm: Levenberg–Marquardt,
- activation function: sigmoid,
- number of trials in the ensemble forecast: 40.

## 5. Results

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Hourly samples are progressively available in an incremental training database. PV: photovoltaic.

**Figure 5.**Hourly samples belonging to an extended period of time are available in a complete training database.

**Figure 6.**Hourly samples belonging to an extended period of time in a complete training database are randomly mixed.

**Figure 7.**Example of the daily errors trend. $NMAE$: normalized mean absolute error; $nRMSE$: normalized root mean square error; $WMAE$: weighted mean absolute error.

**Figure 9.**Example of a sunny day forecast—1 April 2014—with the relevant evaluation indexes. $EMAE\%$: envelope-weighted mean absolute error.

**Table 1.**Different methods for the composition of the ANN training data-sets which have been analysed. ${}^{\u2020}\phantom{\rule{3.33333pt}{0ex}}$(90%$ts$ 10%$vs$) $ts$ = training set; $vs$ = validation set.

Method | Data-Set | Trials | Samples |
---|---|---|---|

A | Incremental | Dependent | Consecutive (10%$vs$ 90%$ts$) |

A* | Incremental | Dependent | Consecutive (90%$ts$ 10%$vs$) |

B1 | Incremental | Independent | Random ${}^{\u2020}$ |

B2 | Incremental | Dependent | Random ${}^{\u2020}$ |

C1 | Complete | Independent | Random ${}^{\u2020}$ |

C2 | Complete | Dependent | Random ${}^{\u2020}$ |

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**MDPI and ACS Style**

Dolara, A.; Grimaccia, F.; Leva, S.; Mussetta, M.; Ogliari, E.
Comparison of Training Approaches for Photovoltaic Forecasts by Means of Machine Learning. *Appl. Sci.* **2018**, *8*, 228.
https://doi.org/10.3390/app8020228

**AMA Style**

Dolara A, Grimaccia F, Leva S, Mussetta M, Ogliari E.
Comparison of Training Approaches for Photovoltaic Forecasts by Means of Machine Learning. *Applied Sciences*. 2018; 8(2):228.
https://doi.org/10.3390/app8020228

**Chicago/Turabian Style**

Dolara, Alberto, Francesco Grimaccia, Sonia Leva, Marco Mussetta, and Emanuele Ogliari.
2018. "Comparison of Training Approaches for Photovoltaic Forecasts by Means of Machine Learning" *Applied Sciences* 8, no. 2: 228.
https://doi.org/10.3390/app8020228