# Computational Intelligence Techniques Applied to the Day Ahead PV Output Power Forecast: PHANN, SNO and Mixed

^{*}

## Abstract

**:**

## 1. Introduction

- the deterministic five parameters PV model (with NOCT PV cells thermal model) estimated by SNO; and
- the Physical Hybrid Artificial Neural Network (PHANN) method.

## 2. Forecasting Methods

#### 2.1. Persistence

#### 2.2. Physical Hybrid Artificial Neural Network

^{TM}[32] in Matlab, which automatically includes these techniques, overfitting is avoided.

#### 2.3. Physical Model Methodology

^{2}, cell temperature equal to 25 °C and Air Mass equal to 1.5. In this model, the variations of the five parameters with the cell temperature and the irradiation are neglected.

#### 2.4. Mixed Forecasting Method

## 3. Assessment Indicators

- Normalized mean absolute error ($NMA{E}_{\%}$) is mean absolute error divided by the rated power of the PV module C expressed in watt:$$NMA{E}_{\%}=\frac{1}{N\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}C}{\displaystyle \sum _{i=1}^{N}}\left|{P}_{m,h}-{P}_{p,h}\right|\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}100$$
- Envelope-weighted mean absolute error ($EMA{E}_{\%}$) [21] is defined as:$$EMA{E}_{\%}={\displaystyle \frac{{\sum}_{i=1}^{N}\left|{P}_{m,h}-{P}_{p,h}\right|}{{\sum}_{i=1}^{N}\mathrm{max}({P}_{m,h}-{P}_{p,h})}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}100$$
- Root mean square error ($RMSE$) is used as the main error metric because it emphasizes the large errors:$$RMSE=\sqrt{\frac{{({P}_{m,h}-{P}_{p,h})}^{2}}{N}}$$
- It can be also normalized when divided by the maximum output dc power measured in the whole period:$$nRMSE=\frac{1}{\mathrm{max}\left({P}_{m,h}\right)}\sqrt{\frac{{({P}_{m,h}-{P}_{p,h})}^{2}}{N}}$$

## 4. Case Study

- PV technology: Silicon mono crystalline
- Rated power: 285 Wp
- Azimuth: −6°30′ (assuming 0° as South direction and counting clockwise)
- Solar panel tilt angle: 30°

^{2}), normal solar radiation on PV cell (G, W/m

^{2}), wind speed (m/s), wind direction (°), pressure (hPa), precipitation (mm), cloud cover (%) and cloud type (low/medium/high).

^{2}) are also required. As regards the SNO based physical model, only the G solar irradiation and the ambient temperature are used for the forecasting.

## 5. Results and Discussion

#### 5.1. Case (A)—Training Curves

#### 5.2. Case (B)—Daily Errors 2014

#### 5.3. Case (C)—Daily Errors 2017

#### 5.4. Focus on Peculiar Days

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Diagram of the optimization process: interaction between the optimizer and the physical model.

**Figure 11.**Comparison between the SNO-based model, the PHANN and the mixed model on the best and the worst days in terms of power output and $EMAE$ % error trend: (

**a**) Worst performance day; and (

**b**) Best performance day.

**Figure 12.**Comparison between the SNO-based model, the PHANN and the mixed model on a cloudy day and on an intermittent day in terms of power output and $EMAE$ % error trend: (

**a**) cloudy day; and (

**b**) intermittent day.

Electrcal Data | STC ^{1} | NOCT ^{2} | |
---|---|---|---|

Rated Power | ${P}_{MPP}$ (W) | 285 | 208 |

Rated Voltage | ${V}_{MPP}$ (V) | 31.3 | 28.4 |

Rated Current | ${I}_{MPP}$ (A) | 9.10 | 7.33 |

Open-Circuit Voltage | ${V}_{OC}$ (V) | 39.2 | 36.1 |

Short-Circuit Current | ${I}_{SC}$ (A) | 9.73 | 7.87 |

^{1}Electrical values measured under Standard Test Conditions: 1000 W/m

^{2}, cell temperature 25 °C, AM 1.5;

^{2}Electrical values measured under Nominal Operating Conditions of cells: 800 W/m

^{2}, ambient temperature 20 °C, AM 1.5, wind speed 1 m/s, NOCT: 48 °C (nominal operating cell temperature).

Analysis | Year | Methods | Weather Data | |
---|---|---|---|---|

(A) | Training curves | 2014 | SNO, PHANN | Forecasts |

(B) | Daily Errors | 2014 | SNO, PHANN | Forecasts |

(C) | Daily Errors | 2017 | SNO, PHANN, Mixed | Measurements, Forecasts |

Min EMAE % | Corresponding Days of Training | Independent Trials | |
---|---|---|---|

PHANN | 32.4 | 180 | 40 |

SNO | 34.4 | >20 | 40 |

NMAE % | nRMSE % | EMAE % | s % | |
---|---|---|---|---|

PERS | 5.63 | 34.38 | 32.59 | 0 |

PHANN | 3.79 | 21.52 | 25.07 | 37 |

SNO | 6.94 | 32.78 | 35.33 | 5 |

MIXED | 4.48 | 18.16 | 24.67 | 47 |

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**MDPI and ACS Style**

Ogliari, E.; Niccolai, A.; Leva, S.; Zich, R.E. Computational Intelligence Techniques Applied to the Day Ahead PV Output Power Forecast: PHANN, SNO and Mixed. *Energies* **2018**, *11*, 1487.
https://doi.org/10.3390/en11061487

**AMA Style**

Ogliari E, Niccolai A, Leva S, Zich RE. Computational Intelligence Techniques Applied to the Day Ahead PV Output Power Forecast: PHANN, SNO and Mixed. *Energies*. 2018; 11(6):1487.
https://doi.org/10.3390/en11061487

**Chicago/Turabian Style**

Ogliari, Emanuele, Alessandro Niccolai, Sonia Leva, and Riccardo E. Zich. 2018. "Computational Intelligence Techniques Applied to the Day Ahead PV Output Power Forecast: PHANN, SNO and Mixed" *Energies* 11, no. 6: 1487.
https://doi.org/10.3390/en11061487