# Probabilistic Load Forecasting for Building Energy Models

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Simulation Process through a BEM

#### 2.2. Probabilistic Load Forecast

## 3. Description of the Case Study

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural network |

ARIMA | Autoregressive integrated moving average |

ARMA | Autoregressive moving average |

BEM | Building energy model |

BMS | Building management system |

CDF | Cumulative distribution function |

DR | Demand response |

DSM | Demand-side management |

EPW | EnergyPlus weather file |

HVAC | Heating, ventilation, and air conditioning |

Iot | Internet of things |

KDE | Kernel density estimation |

kWh | Kilowatt hour |

LR | Linear regression |

MAE | Mean absolute error |

MAPE | Mean absolute percentage error |

MCM | Monte Carlo method |

ML | Machine learning |

MPC | Model predictive control |

MPIW | Mean prediction interval width |

Probability density function | |

PICP | Prediction interval coverage probability |

PINC | Prediction interval nominal confidence |

PLF | Probabilistic load forecast |

PI | Prediction intervals |

SVM | Support vector machine |

${R}^{2}$ | Coefficient of determination |

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**Figure 1.**Components and steps of the proposed probabilistic load forecasting methodology based on white-box models (building energy model (BEM)).

**Figure 5.**Library building from Gedved School, Denmark. Left: Outdoor image. Middle: Weather station installed on the building’s roof. Right: The building energy model (OpenStudio plugin for SketchUp [64]).

**Figure 6.**Probability histogram of the 6 forecast days and the Gaussian kernel density estimation (red line).

**Figure 8.**Probabilistic heating load forecast results: Hourly uncertainty map of the heating load forecast due to weather forecast data for the first 24 h ahead of the forecast hour (09:00 h).

**Figure 9.**Probabilistic heating load forecast results: Hourly uncertainty map of the heating load forecast due to weather forecast data for 1 to 6 days ahead.

**Figure 10.**Application of the map of the heating load forecast uncertainty due to forecast weather data using the whole period of the study for a random day: 2 January 2020.

**Figure 11.**Results for the validation of the probabilistic load forecasting methodology for the testing period (April 2020). Above: from 1 to 10 April 2020; middle: from 11 to 20 April 2020; and below: from 21 to 30 April 2020.

**Table 1.**Error metrics for the point load forecast. Comparison between forecast and real heating load.

Index | Forecast Day 1 | Forecast Day 2 | Forecast Day 3 | Forecast Day 4 | Forecast Day 5 | Forecast Day 6 |
---|---|---|---|---|---|---|

MAE (kWh) | 9.91 | 10.50 | 11.04 | 11.57 | 12.43 | 13.74 |

MAPE (%) | 38.99 | 41.26 | 43.56 | 47.39 | 51.10 | 55.84 |

${R}^{2}$ (%) | 74.48 | 70.82 | 65.99 | 59.65 | 49.72 | 45.66 |

**Table 2.**Prediction interval coverage probability (PICP) and mean prediction interval width (MPIW) results when using a gradually increasing amount of data for the creation of the uncertainty map. April 2020 is maintained as the testing period.

Months Uncertainty Map | March 2020 | February 2020 March 2020 | January 2020 March 2020 | December 2019 March 2020 | November 2019 March 2020 | October 2019 March 2020 | May 2019 March 2020 | April 2019 March 2020 | March 2019 March 2020 | February 2019 March 2020 | January 2019 March 2020 | December 2018 March 2020 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

N° of months | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

PICP (%) | 91.5 | 89.9 | 84.4 | 82.2 | 83.1 | 84.2 | 83.8 | 84.3 | 84.4 | 84.2 | 84.0 | 83.1 |

MPIW (kWh) | 27.1 | 23.1 | 18.8 | 18.4 | 18.3 | 17.8 | 17.5 | 17.2 | 17.7 | 17.4 | 17.7 | 17.5 |

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**MDPI and ACS Style**

Lucas Segarra, E.; Ramos Ruiz, G.; Fernández Bandera, C. Probabilistic Load Forecasting for Building Energy Models. *Sensors* **2020**, *20*, 6525.
https://doi.org/10.3390/s20226525

**AMA Style**

Lucas Segarra E, Ramos Ruiz G, Fernández Bandera C. Probabilistic Load Forecasting for Building Energy Models. *Sensors*. 2020; 20(22):6525.
https://doi.org/10.3390/s20226525

**Chicago/Turabian Style**

Lucas Segarra, Eva, Germán Ramos Ruiz, and Carlos Fernández Bandera. 2020. "Probabilistic Load Forecasting for Building Energy Models" *Sensors* 20, no. 22: 6525.
https://doi.org/10.3390/s20226525