# Short-Term Forecasting of the Output Power of a Building-Integrated Photovoltaic System Using a Metaheuristic Approach

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Materials and Methods

#### 3.1. Proposed Hybrid DEPSO Forecasting Method

#### 3.1.1. Overview of the DE Algorithm

#### Theory

#### Initialization

#### Mutation

#### Crossover

#### Selection

#### 3.1.2. Overview of the PSO Algorithm

#### Theory

#### Initialization

#### Movement

#### Evaluation

#### 3.1.3. DEPSO Algorithm

#### 3.2. Implementation of DEPSO in Forecasting

#### 3.3. Data Collection

#### 3.4. Forecast Model

## 4. Experimental Forecasting Results

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**Representation of the fitness function to evaluate particle position and velocity using PSO algorithm.

**Figure 10.**Geographical location of the test location [46].

**Figure 14.**Evolution of the measured solar irradiance and air temperature during the data collection period with an hourly time scale.

**Figure 18.**Comparison of DE-, PSO-, and DEPSO-forecasted values with actual value of PV output power.

Ref. | Year of Publication | Method Used | Location | Error Evaluated | Horizon | Training Data |
---|---|---|---|---|---|---|

[10] | 2011 | RBF | Online | MAPE, MAE, RMSE | 24 h | 1 year |

[11] | 2016 | NWP | California, USA | MAE, MBE, RMSE | 1 h, 3 h | 18 months |

[12] | 2017 | MLR, RT, SVM, NN | New South Wales, Australia | RMSE | 2 h | 3 years |

[15] | 2012 | SVM | China | RMSE, MRE | 15 m | ~1 year |

[16] | 2014 | SVR | Taiwan | MRE, RMSE | 1 h | 1 year |

[18] | 2012 | BPNN, RBFNN, WT + BPNN, WT + RBFNN | Ashland, Oregon | MAPE, MAE, RMSE | 1 h | 30 days |

[29] | 2013 | NWP | Ontario, Canada | RMSE, MBE, MAE | 48 h | 1 year |

[30] | 2017 | PSO-ANN, NWP | Beijing, China | MAPE, RMSE, SDE | 1 h | 1 year |

[33] | 2014 | ANN | Italy | SD, NRMSE, NMAE, NMBE, MSE | 1 h | 1 year |

[34] | 2010 | GA, PSO, DE, ARIMA, NN, AWINN, | Canada | WME, VAR | 1 day | 4 weeks |

[35] | 2012 | ARIMA, kNN, ANN, GA/ANN | Merced, California, USA | MAE, MBE, RMSE | 1 h, 2 h | ~2 years |

C1 | C2 | W | CR | F | K |
---|---|---|---|---|---|

2 | 1.5 | 1.2 | 0.8 | 0.7 | 0.5 |

Parameter | Value |
---|---|

Solar module type | CS6P-250M |

Number of modules | 12 |

Module rated power output | 250 W |

Open circuit voltage (${V}_{oc}$) | 37.5 V |

Short Circuit Current | 8.74 A |

Optimum operating voltage (${V}_{mp}$) | 30.4 V |

Optimum operating current (${I}_{mp}$) | 8.22 A |

**Note:**All parameters are based on the standard testing condition, in which the ambient temperature is 25 °C and the irradiance level is 1000 W/m

^{2}.

Parameter | Value |
---|---|

Number of particles | 100 |

Number of iterations | 1000 |

Number of algorithm run | 20 |

${a}_{3}$ | 4.7 × 10^{−5} |

${a}_{2}$ | 3.1 × 10^{−3} |

${a}_{1}$ | −9.2 × 10^{−3} |

${a}_{0}$ | 9.4 × 10^{−4} |

${b}_{2}$ | −1.4 × 10^{−3} |

${b}_{1}$ | 2.5 × 10^{−3} |

Technique | 1 h | 2 h | 4 h | 1 h | 2 h | 4 h |
---|---|---|---|---|---|---|

RMSE (%) | MRE (%) | |||||

PSO | 14.2 | 15.8 | 21.9 | 9.2 | 11.5 | 13.3 |

DE | 9.4 | 21.2 | 19.8 | 6.3 | 13.7 | 9.7 |

DEPSO | 4.4 | 5.2 | 3.5 | 3.1 | 3.17 | 1.6 |

MAE | MBE | |||||

PSO | 0.05 | 0.26 | 0.25 | −3.67 | −7.45 | −3.82 |

DE | 0.06 | 0.23 | 0.19 | −8.25 | −14.25 | −2.15 |

DEPSO | 0.03 | 0.03 | 0.01 | −1.63 | 5.19 | −1.2 |

WME | VAR | |||||

PSO | 0.19 | 0.65 | 0.66 | 0.03 | 0.222 | 0.18 |

DE | 0.2 | 0.68 | 1.18 | 0.064 | 1.24 | 0.21 |

DEPSO | 0.16 | 0.28 | 0.16 | 0.01 | 0.79 | 0.12 |

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## Share and Cite

**MDPI and ACS Style**

Seyedmahmoudian, M.; Jamei, E.; Thirunavukkarasu, G.S.; Soon, T.K.; Mortimer, M.; Horan, B.; Stojcevski, A.; Mekhilef, S. Short-Term Forecasting of the Output Power of a Building-Integrated Photovoltaic System Using a Metaheuristic Approach. *Energies* **2018**, *11*, 1260.
https://doi.org/10.3390/en11051260

**AMA Style**

Seyedmahmoudian M, Jamei E, Thirunavukkarasu GS, Soon TK, Mortimer M, Horan B, Stojcevski A, Mekhilef S. Short-Term Forecasting of the Output Power of a Building-Integrated Photovoltaic System Using a Metaheuristic Approach. *Energies*. 2018; 11(5):1260.
https://doi.org/10.3390/en11051260

**Chicago/Turabian Style**

Seyedmahmoudian, Mehdi, Elmira Jamei, Gokul Sidarth Thirunavukkarasu, Tey Kok Soon, Michael Mortimer, Ben Horan, Alex Stojcevski, and Saad Mekhilef. 2018. "Short-Term Forecasting of the Output Power of a Building-Integrated Photovoltaic System Using a Metaheuristic Approach" *Energies* 11, no. 5: 1260.
https://doi.org/10.3390/en11051260